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The Rouse model is one of the simplest coarse-grained descriptions of the dynamics of polymer chains. [ 1 ] It treats a single polymer as an Ideal chain of N point-like beads connected by harmonic springs and neglects both excluded volume and long-range hydrodynamic interactions. Each bead experiences random thermal forces and a Stokes drag, so the chain undergoes overdamped Brownian motion described by Langevin dynamics . Although first proposed for dilute solutions, the model also describes polymer melts whose chain length is below the entanglement threshold. [ 1 ]
A flexible polymer is represented by an ideal freely jointed chain of beads with mean bond length l . Neglecting inertia, the overdamped equation of motion for the position R n ( t ) {\displaystyle \mathbf {R} _{n}(t)} of bead n is
where k is the spring constant, ζ {\displaystyle \zeta } the one-bead friction coefficient and random force f n ( t ) {\displaystyle \mathbf {f} _{n}(t)} a zero-mean Gaussian noise that fulfills the fluctuation–dissipation theorem. [ 2 ] At either chain end the missing neighbor term is omitted.
Solving the coupled stochastic equations yields several characteristic quantities: [ 2 ] [ 3 ]
This subdiffusive behavior with τ 1 / 2 {\displaystyle \tau ^{1/2}} time dependence is characteristic of Rouse dynamics and distinguishes polymer motion from simple Brownian diffusion. [ 4 ] Given that the excluded volume is ignored, the model is strictly valid for melts or θ-solvents where intrachain interactions are screened. In good solvents, where excluded volume effects become significant, more complex models such as the Zimm model are required to accurately describe polymer dynamics. [ 5 ]
A significant extension was published in 1956 by Bruno Zimm : [ 6 ] His model (often referred to simply as the "Zimm model") also takes into account *hydrodynamic interactions* between the beads of the chain.
These interactions are forces mediated by the surrounding solvent molecules: when a bead moves, it drags solvent molecules along, which in turn exert a force on adjacent beads (see figure). Because of this additional coupling, the Zimm model gives a more realistic description of polymers in dilute solution than the Rouse model and agrees with experimental data for certain dilute-solution polymers. [ 6 ]
The Langevin equation of the Rouse model is extended by a tensor (matrix) H n m {\displaystyle \mathrm {H} _{nm}} , which represents the hydrodynamic force between the n {\displaystyle n} -th and m {\displaystyle m} -th segments:
Here the tensor H n m {\displaystyle \mathrm {H} _{nm}} depends on the positions R → 0 , … , R → N − 1 {\displaystyle {\vec {R}}_{0},\dots ,{\vec {R}}_{N-1}} of all segments. Consequently, the equation is nonlinear and cannot be solved analytically. Zimm therefore replaced H n m ( R → 0 , … , R → N − 1 ) {\displaystyle \mathrm {H} _{nm}({\vec {R}}_{0},\dots ,{\vec {R}}_{N-1})} by its equilibrium average ⟨ H n m ⟩ eq {\displaystyle \langle \mathrm {H} _{nm}\rangle _{\text{eq}}} , which can be evaluated. From this approximation the following properties of a Zimm polymer are obtained: | https://en.wikipedia.org/wiki/Rouse_model |
The Rouse number ( P or Z ) is a non-dimensional number in fluid dynamics which is used to define a concentration profile of suspended sediment and which also determines how sediment will be transported in a flowing fluid. It is a ratio between the sediment fall velocity w s {\displaystyle w_{s}} and the upwards velocity on the grain as a product of the von Kármán constant κ {\displaystyle \kappa } and the shear velocity u ∗ {\displaystyle u_{*}} .
Occasionally the factor β is included before the von Kármán constant in the equation, which is a constant which correlates eddy viscosity to eddy diffusivity. This is generally taken to be equal to 1, and therefore is ignored in actual calculation. However, it should not be ignored when considering the full equation.
It is named after the American fluid dynamicist Hunter Rouse . It is a characteristic scale parameter in the Rouse Profile of suspended sediment concentration with depth in a flowing fluid. The concentration of suspended sediment with depth goes as the power of the negative Rouse number. It also is used to determine how the particles will move in the fluid. The required Rouse numbers for transport as bed load , suspended load , and wash load , are given below.
This sedimentology article is a stub . You can help Wikipedia by expanding it .
This fluid dynamics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rouse_number |
Route Mobile (formerly Routesms Solutions Ltd) is an Indian cloud communications platform as a service (CPaaS) company. Started in 2004 and headquartered in Mumbai , the company has presence in more than 15 locations across Asia-Pacific , Middle East , Africa , Europe and North America . [ 2 ]
Route Mobile was started in Mumbai in May 2004 as a cloud communications platform provider for over the top (OTT) and mobile network operators (MNO). [ 3 ] [ 4 ] [ 5 ] It partnered with companies including Idea Cellular , [ 6 ] Lanka Bell , and Arab Financials Services for providing messaging services in India , Sri Lanka , Middle East and North Africa region. [ 7 ]
In May 2017, Route Mobile acquired Call 2 Connect, an ITES provider based out of India. [ 8 ] In the same year, Route Mobile acquired 365squared, a SMS firewall company based out of Malta . [ 9 ] [ 10 ]
In July 2023, it was announced that Belgian telecommunications company Proximus Group would be taking a majority stake in Route Mobile through its daughter holding Opal. [ 11 ] On May 8, 2024, it was announced that this transaction had been completed. [ 12 ] | https://en.wikipedia.org/wiki/Route_Mobile |
Route panorama is a continuous 2D image that includes all the scenes visible from a route, as it first appeared in Zheng and Tsuji's work of panoramic views in 1990. [ 1 ]
Different from a local panorama at a static viewpoint, a digital route panorama is constructed from partial views at consecutive viewpoints along a path. [ 2 ] A general approach to obtain such a complete route panorama is to use a line camera or slit camera mounted on a vehicle moving along the path smoothly. The camera scans temporal scenes in the side direction of the path and connect them to the spatial image. This is realized by a program that processes temporal image data or video data in a computer. The route panorama can extend to a long distance for indexing scenes and navigation on the Internet. The long image can further be transmitted to and be scrolled on computer screens or handheld devices as moving panorama for access of geospatial locations, navigation, georeferencing, [ 3 ] etc.
Mathematically, the route panorama employs a parallel-and-perspective projection [ 4 ] that is a continuous and extreme case of multi-perspective view to pixel lines. It may have the aspect ratio of an object different from what a normal perspective projection generates. In addition, a video camcorder is used to produce the route panorama by taking only one pixel line in the video frame at a time with the auto-exposure function of the camcorder and shaking removal function using the inter-frame matching.
If the depth of scenes from the path has a dominant layer, a route panorama can also be created on that layer by stitching discrete photos consecutively taken along the path [ 5 ] using Photomontage . Under the same circumstance, a dynamic slit selected in the video frame can generate a route panorama with less shape distortion. [ 6 ] [ 7 ] | https://en.wikipedia.org/wiki/Route_panorama |
Route Reconnaissance is the investigation of the operational environment in reconnaissance operations of routes for military use, including methods of reconnoitering and classifying them for other troops. In a k during ll the primary purpose of conducting route reconnaissance is to find and report all enemy forces that can interfere with movement along a route, and to identify the limit of direct-fire range and terrain that dominates the route.
Route reconnaissance includes creation of reconnaissance overlays to identify land and water features, bridge reconnaissance and classification , road reconnaissance and classification , special terrain reconnaissance such as that used during cross-country movement, at the landing areas , on the inland waterways , or when using footpaths and trails , engineer reconnaissance , and use of military route signs (standard signs, sign lighting, bridge signs).
A significant part of route reconnaissance is the ability to identify choke points that prohibit military traffic by using conversion factors and tables to identify non-standard surfaces or inadequate load bearing in structure. To do so, Military Load Classifications are used for standard vehicles of a given armed force .
Route reconnaissance is typically conducted by a foot, horse or vehicle-mounted route reconnaissance patrol , sometimes with aid of aerial reconnaissance aircraft . The patrol would include regular reconnaissance elements and a combat engineering team.
Consequence of little or no route reconnaissance and engineer reconnaissance leads to hurdles in operational mobility and tactical frontal assault , leading to defeat or wipe out as it happened to Pakistan in the Battle of Longewala against India. [ 1 ] | https://en.wikipedia.org/wiki/Route_reconnaissance |
A router [ a ] is a computer and networking device that forwards data packets between computer networks , including internetworks such as the global Internet . [ 2 ] [ 3 ] [ 4 ]
Routers perform the "traffic directing" functions on the Internet. A router is connected to two or more data lines from different IP networks . When a data packet comes in on a line, the router reads the network address information in the packet header to determine the ultimate destination. Then, using information in its routing table or routing policy , it directs the packet to the next network on its journey. Data packets are forwarded from one router to another through an internetwork until it reaches its destination node . [ 5 ]
The most familiar type of IP routers are home and small office routers that forward IP packets between the home computers and the Internet. More sophisticated routers, such as enterprise routers, connect large business or ISP networks to powerful core routers that forward data at high speed along the optical fiber lines of the Internet backbone .
Routers can be built from standard computer parts but are mostly specialized purpose-built computers . Early routers used software -based forwarding, running on a CPU . More sophisticated devices use application-specific integrated circuits (ASICs) to increase performance or add advanced filtering and firewall functionality.
The concepts of a switching node using software and an interface computer were first proposed by Donald Davies in 1966 for the NPL network . [ 6 ] [ 7 ] [ 8 ] The same idea was conceived by Wesley Clark the following year for use in the ARPANET , which were named Interface Message Processors (IMPs). [ 9 ] The first interface computer was implemented at the National Physical Laboratory in the United Kingdom in early 1969, followed later that year by the IMPs at the University of California, Los Angeles , the Stanford Research Institute , the University of California, Santa Barbara , and the University of Utah School of Computing in the United States. [ 10 ] [ 11 ] [ 12 ] [ 13 ] All were built with the Honeywell 516 . These computers had fundamentally the same functionality as a router does today.
The idea for a router (called a gateway at the time) initially came about through an international group of computer networking researchers called the International Network Working Group (INWG). [ 14 ] These gateway devices were different from most previous packet switching schemes in two ways. First, they connected dissimilar kinds of networks, such as serial lines and local area networks . Second, they were connectionless devices, which had no role in assuring that traffic was delivered reliably, leaving that function entirely to the hosts . [ 15 ] This particular idea, the end-to-end principle , was contained in the work of Donald Davies. [ 16 ] [ 17 ]
The concept was explored in practice by various groups, with the intention to produce a working system for internetworking . There were three notable contemporaneous programs. The first was an implementation directed by Louis Pouzin of the CYCLADES network, which was designed and developed during 1972-3. [ 18 ] [ 19 ] [ 20 ] The second was program at Xerox PARC to explore new networking technologies, which produced the PARC Universal Packet system. Some time after early 1974, the first Xerox routers became operational. Due to corporate intellectual property concerns, it received little attention outside Xerox for years. [ 21 ] [ 22 ] The third was a DARPA -initiated program, which began during 1973-4. This drew on the work of the other two programs, [ 23 ] expanded significantly, and went on to create the TCP/IP architecture in use today. [ 24 ] [ 25 ] University College London (UCL) provided a gateway between British research groups and the ARPANET from 1973 until the late 1980s, latterly using SATNET . [ 26 ] [ 27 ] [ 28 ]
The first true IP router was developed by Ginny Travers at BBN , as part of that DARPA-initiated effort, during 1975–1976. [ 29 ] [ 30 ] By the end of 1976, three PDP-11 -based routers were in service in the experimental prototype Internet. [ 31 ] Mike Brecia, Ginny Travers, and Bob Hinden received the IEEE Internet Award for early IP routers in 2008. [ 32 ]
The first multiprotocol routers were independently created by staff researchers at MIT and Stanford in 1981 and both were also based on PDP-11s. Stanford's router program was led by William Yeager and MIT's by Noel Chiappa . [ 33 ] [ 34 ] [ 35 ] [ 36 ] Virtually all networking now uses TCP/IP, but multiprotocol routers are still manufactured. They were important in the early stages of the growth of computer networking when protocols other than TCP/IP were in use. Modern routers that handle both IPv4 and IPv6 are multiprotocol but are simpler devices than ones processing AppleTalk, DECnet, IPX, and Xerox protocols.
From the mid-1970s and in the 1980s, general-purpose minicomputers served as routers. Modern high-speed routers are network processors or highly specialized computers with extra hardware acceleration added to speed both common routing functions, such as packet forwarding, and specialized functions such as IPsec encryption. There is substantial use of Linux and Unix software-based machines, running open source routing code, for research and other applications. The Cisco IOS operating system was independently designed. Major router operating systems, such as Junos and NX-OS , are extensively modified versions of Unix software.
When multiple routers are used in interconnected networks, the routers can exchange information about destination addresses using a routing protocol . Each router builds up a routing table , a list of routes, between two computer systems on the interconnected networks. [ 37 ] [ 38 ]
The software that runs the router is composed of two functional processing units that operate simultaneously, called planes : [ 39 ]
A router may have interfaces for multiple types of physical layer connections, such as copper cables, fiber optic , or wireless transmission. It can also support multiple network layer transmission standards. Each network interface is used to enable data packets to be forwarded from one transmission system to another. Routers may also be used to connect two or more logical groups of computer devices known as subnets , each with a unique network prefix .
Routers may provide connectivity within enterprises, between enterprises and the Internet, or between internet service providers ' (ISPs') networks, they are also responsible for directing data between different networks. [ 40 ] The largest routers (such as the Cisco CRS-1 or Juniper PTX) interconnect the various ISPs, or may be used in large enterprise networks. [ 41 ] Smaller routers usually provide connectivity for typical home and office networks.
All sizes of routers may be found inside enterprises. [ 42 ] The most powerful routers are usually found in ISPs, academic and research facilities. Large businesses may also need more powerful routers to cope with ever-increasing demands of intranet data traffic. A hierarchical internetworking model for interconnecting routers in large networks is in common use. [ 43 ] Some routers can connect to Data service units for T1 connections [ 44 ] [ 45 ] [ 46 ] via serial ports. [ 47 ] [ 48 ]
The hierarchical internetworking model divides enterprise networks into three layers: core, distribution, and access.
Access routers, including small office/home office (SOHO) models, are located at home and customer sites such as branch offices that do not need hierarchical routing of their own. Typically, they are optimized for low cost. Some SOHO routers are capable of running alternative free Linux-based firmware like Tomato , OpenWrt , or DD-WRT . [ 49 ]
Distribution routers aggregate traffic from multiple access routers. Distribution routers are often responsible for enforcing quality of service across a wide area network (WAN), so they may have considerable memory installed, multiple WAN interface connections, and substantial onboard data processing routines. They may also provide connectivity to groups of file servers or other external networks. [ 50 ]
In enterprises, a core router may provide a collapsed backbone interconnecting the distribution tier routers from multiple buildings of a campus, or large enterprise locations. They tend to be optimized for high bandwidth but lack some of the features of edge routers. [ 51 ]
External networks must be carefully considered as part of the overall security strategy of the local network. A router may include a firewall , VPN handling, and other security functions, or they may be handled by separate devices. Routers also commonly perform network address translation which restricts connections initiated from external connections but is not recognized as a security feature by all experts. [ 52 ] Some experts argue that open source routers are more secure and reliable than closed source routers because errors and potentially exploitable vulnerabilities are more likely to be discovered and addressed in an open-source environment. [ 53 ] [ 54 ]
Routers are also often distinguished on the basis of the network in which they operate. A router in a local area network (LAN) of a single organization is called an interior router . A router that is operated in the Internet backbone is described as exterior router . While a router that connects a LAN with the Internet or a wide area network (WAN) is called a border router , or gateway router . [ 55 ]
Routers intended for ISP and major enterprise connectivity usually exchange routing information using the Border Gateway Protocol (BGP). RFC 4098 defines the types of BGP routers according to their functions: [ 56 ]
Wi-Fi routers combine the functions of a router with those of a wireless access point . They are typically devices with a small form factor, operating on the standard electric power supply for residential use. Connected to the Internet as offered by an Internet service provider , they provide Internet access through a wireless network for home or office use.
The main purpose of a router is to connect multiple networks and forward packets destined either for directly attached networks or more remote networks. A router is considered a layer-3 device because its primary forwarding decision is based on the information in the layer-3 IP packet, specifically the destination IP address. When a router receives a packet, it searches its routing table to find the best match between the destination IP address of the packet and one of the addresses in the routing table. Once a match is found, the packet is encapsulated in the layer-2 data link frame for the outgoing interface indicated in the table entry. A router typically does not look into the packet payload, [ 62 ] but only at the layer-3 addresses to make a forwarding decision, plus optionally other information in the header for hints on, for example, quality of service (QoS). For pure IP forwarding, a router is designed to minimize the state information associated with individual packets. [ 63 ] Once a packet is forwarded, the router does not retain any historical information about the packet. [ b ]
The routing table itself can contain information derived from a variety of sources, such as a default or static routes that are configured manually, or dynamic entries from routing protocols where the router learns routes from other routers. A default route is one that is used to route all traffic whose destination does not otherwise appear in the routing table; it is common – even necessary – in small networks, such as a home or small business where the default route simply sends all non-local traffic to the Internet service provider . The default route can be manually configured (as a static route); learned by dynamic routing protocols; or be obtained by DHCP . [ c ] [ 64 ]
A router can run more than one routing protocol at a time, particularly if it serves as an autonomous system border router between parts of a network that run different routing protocols; if it does so, then redistribution may be used (usually selectively) to share information between the different protocols running on the same router. [ 65 ]
Besides deciding to which interface a packet is forwarded, which is handled primarily via the routing table, a router also has to manage congestion when packets arrive at a rate higher than the router can process. Three policies commonly used are tail drop , random early detection (RED), and weighted random early detection (WRED). Tail drop is the simplest and most easily implemented: the router simply drops new incoming packets once buffer space in the router is exhausted. RED probabilistically drops datagrams early when the queue exceeds a pre-configured portion of the buffer, until reaching a pre-determined maximum, when it drops all incoming packets, thus reverting to tail drop. WRED can be configured to drop packets more readily dependent on the type of traffic.
Another function a router performs is traffic classification and deciding which packet should be processed first. This is managed through QoS , which is critical when Voice over IP is deployed, so as not to introduce excessive latency . [ 66 ]
Yet another function a router performs is called policy-based routing where special rules are constructed to override the rules derived from the routing table when a packet forwarding decision is made. [ 67 ]
Some of the functions may be performed through an application-specific integrated circuit (ASIC) to avoid the overhead of scheduling CPU time to process the packets. Others may have to be performed through the CPU as these packets need special attention that cannot be handled by an ASIC. [ 68 ] | https://en.wikipedia.org/wiki/Router_(computing) |
In classical mechanics, Routh's procedure or Routhian mechanics is a hybrid formulation of Lagrangian mechanics and Hamiltonian mechanics developed by Edward John Routh . Correspondingly, the Routhian is the function which replaces both the Lagrangian and Hamiltonian functions. Although Routhian mechanics is equivalent to Lagrangian mechanics and Hamiltonian mechanics, and introduces no new physics, it offers an alternative way to solve mechanical problems.
The Routhian, like the Hamiltonian, can be obtained from a Legendre transform of the Lagrangian, and has a similar mathematical form to the Hamiltonian, but is not exactly the same. The difference between the Lagrangian, Hamiltonian, and Routhian functions are their variables. For a given set of generalized coordinates representing the degrees of freedom in the system, the Lagrangian is a function of the coordinates and velocities, while the Hamiltonian is a function of the coordinates and momenta.
The Routhian differs from these functions in that some coordinates are chosen to have corresponding generalized velocities, the rest to have corresponding generalized momenta. This choice is arbitrary, and can be done to simplify the problem. It also has the consequence that the Routhian equations are exactly the Hamiltonian equations for some coordinates and corresponding momenta, and the Lagrangian equations for the rest of the coordinates and their velocities. In each case the Lagrangian and Hamiltonian functions are replaced by a single function, the Routhian. The full set thus has the advantages of both sets of equations, with the convenience of splitting one set of coordinates to the Hamilton equations, and the rest to the Lagrangian equations.
In the case of Lagrangian mechanics, the generalized coordinates q 1 , q 2 , ... and the corresponding velocities dq 1 / dt , dq 2 / dt , ... , and possibly time [ nb 1 ] t , enter the Lagrangian,
where the overdots denote time derivatives .
In Hamiltonian mechanics, the generalized coordinates q 1 , q 2 , ... and the corresponding generalized momenta p 1 , p 2 , ..., and possibly time, enter the Hamiltonian,
where the second equation is the definition of the generalized momentum p i corresponding to the coordinate q i ( partial derivatives are denoted using ∂ ). The velocities dq i / dt are expressed as functions of their corresponding momenta by inverting their defining relation. In this context, p i is said to be the momentum "canonically conjugate" to q i .
The Routhian is intermediate between L and H ; some coordinates q 1 , q 2 , ..., q n are chosen to have corresponding generalized momenta p 1 , p 2 , ..., p n , the rest of the coordinates ζ 1 , ζ 2 , ..., ζ s to have generalized velocities dζ 1 / dt , dζ 2 / dt , ..., dζ s / dt , and time may appear explicitly; [ 1 ] [ 2 ]
R ( q 1 , … , q n , ζ 1 , … , ζ s , p 1 , … , p n , ζ ˙ 1 , … , ζ ˙ s , t ) = ∑ i = 1 n p i q ˙ i ( p i ) − L ( q 1 , … , q n , ζ 1 , … , ζ s , q ˙ 1 ( p 1 ) , … , q ˙ n ( p n ) , ζ ˙ 1 , … , ζ ˙ s , t ) , {\displaystyle R(q_{1},\ldots ,q_{n},\zeta _{1},\ldots ,\zeta _{s},p_{1},\ldots ,p_{n},{\dot {\zeta }}_{1},\ldots ,{\dot {\zeta }}_{s},t)=\sum _{i=1}^{n}p_{i}{\dot {q}}_{i}(p_{i})-L(q_{1},\ldots ,q_{n},\zeta _{1},\ldots ,\zeta _{s},{\dot {q}}_{1}(p_{1}),\ldots ,{\dot {q}}_{n}(p_{n}),{\dot {\zeta }}_{1},\ldots ,{\dot {\zeta }}_{s},t)\,,}
where again the generalized velocity dq i / dt is to be expressed as a function of generalized momentum p i via its defining relation. The choice of which n coordinates are to have corresponding momenta, out of the n + s coordinates, is arbitrary.
The above is used by Landau and Lifshitz , and Goldstein . Some authors may define the Routhian to be the negative of the above definition. [ 3 ]
Given the length of the general definition, a more compact notation is to use boldface for tuples (or vectors) of the variables, thus q = ( q 1 , q 2 , ..., q n ) , ζ = ( ζ 1 , ζ 2 , ..., ζ s ) , p = ( p 1 , p 2 , ..., p n ) , and d ζ / dt = ( dζ 1 / dt , dζ 2 / dt , ..., dζ s / dt ) , so that
where · is the dot product defined on the tuples, for the specific example appearing here:
For reference, the Euler-Lagrange equations for s degrees of freedom are a set of s coupled second order ordinary differential equations in the coordinates
where j = 1, 2, ..., s , and the Hamiltonian equations for n degrees of freedom are a set of 2 n coupled first order ordinary differential equations in the coordinates and momenta
Below, the Routhian equations of motion are obtained in two ways, in the process other useful derivatives are found that can be used elsewhere.
Consider the case of a system with two degrees of freedom , q and ζ , with generalized velocities dq / dt and dζ / dt , and the Lagrangian is time-dependent. (The generalization to any number of degrees of freedom follows exactly the same procedure as with two). [ 4 ] The Lagrangian of the system will have the form
The differential of L is
Now change variables, from the set ( q , ζ , dq / dt , dζ / dt ) to ( q , ζ , p , dζ / dt ), simply switching the velocity dq / dt to the momentum p . This change of variables in the differentials is the Legendre transformation . The differential of the new function to replace L will be a sum of differentials in dq , dζ , dp , d ( dζ / dt ) , and dt . Using the definition of generalized momentum and Lagrange's equation for the coordinate q :
we have
and to replace pd ( dq / dt ) by ( dq / dt ) dp , recall the product rule for differentials, [ nb 2 ] and substitute
to obtain the differential of a new function in terms of the new set of variables:
Introducing the Routhian
where again the velocity dq / dt is a function of the momentum p , we have
but from the above definition, the differential of the Routhian is
Comparing the coefficients of the differentials dq , dζ , dp , d ( dζ / dt ) , and dt , the results are Hamilton's equations for the coordinate q ,
and Lagrange's equation for the coordinate ζ
which follow from
and taking the total time derivative of the second equation and equating to the first. Notice the Routhian replaces the Hamiltonian and Lagrangian functions in all the equations of motion.
The remaining equation states the partial time derivatives of L and R are negatives
For n + s coordinates as defined above, with Routhian
the equations of motion can be derived by a Legendre transformation of this Routhian as in the previous section, but another way is to simply take the partial derivatives of R with respect to the coordinates q i and ζ j , momenta p i , and velocities dζ j / dt , where i = 1, 2, ..., n , and j = 1, 2, ..., s . The derivatives are
The first two are identically the Hamiltonian equations. Equating the total time derivative of the fourth set of equations with the third (for each value of j ) gives the Lagrangian equations. The fifth is just the same relation between time partial derivatives as before. To summarize [ 5 ]
q ˙ i = ∂ R ∂ p i , p ˙ i = − ∂ R ∂ q i , {\displaystyle {\dot {q}}_{i}={\frac {\partial R}{\partial p_{i}}}\,,\quad {\dot {p}}_{i}=-{\frac {\partial R}{\partial q_{i}}}\,,}
d d t ∂ R ∂ ζ ˙ j = ∂ R ∂ ζ j . {\displaystyle {\frac {d}{dt}}{\frac {\partial R}{\partial {\dot {\zeta }}_{j}}}={\frac {\partial R}{\partial \zeta _{j}}}\,.}
The total number of equations is 2 n + s , there are 2 n Hamiltonian equations plus s Lagrange equations.
Since the Lagrangian has the same units as energy , the units of the Routhian are also energy. In SI units this is the Joule .
Taking the total time derivative of the Lagrangian leads to the general result
If the Lagrangian is independent of time, the partial time derivative of the Lagrangian is zero, ∂ L /∂ t = 0 , so the quantity under the total time derivative in brackets must be a constant, it is the total energy of the system [ 6 ]
(If there are external fields interacting with the constituents of the system, they can vary throughout space but not time). This expression requires the partial derivatives of L with respect to all the velocities dq i / dt and dζ j / dt . Under the same condition of R being time independent, the energy in terms of the Routhian is a little simpler, substituting the definition of R and the partial derivatives of R with respect to the velocities dζ j / dt ,
Notice only the partial derivatives of R with respect to the velocities dζ j / dt are needed. In the case that s = 0 and the Routhian is explicitly time-independent, then E = R , that is, the Routhian equals the energy of the system. The same expression for R in when s = 0 is also the Hamiltonian, so in all E = R = H .
If the Routhian has explicit time dependence, the total energy of the system is not constant. The general result is
which can be derived from the total time derivative of R in the same way as for L .
Often the Routhian approach may offer no advantage, but one notable case where this is useful is when a system has cyclic coordinates (also called "ignorable coordinates"), by definition those coordinates which do not appear in the original Lagrangian. The Lagrangian equations are powerful results, used frequently in theory and practice, since the equations of motion in the coordinates are easy to set up. However, if cyclic coordinates occur there will still be equations to solve for all the coordinates, including the cyclic coordinates despite their absence in the Lagrangian. The Hamiltonian equations are useful theoretical results, but less useful in practice because coordinates and momenta are related together in the solutions - after solving the equations the coordinates and momenta must be eliminated from each other. Nevertheless, the Hamiltonian equations are perfectly suited to cyclic coordinates because the equations in the cyclic coordinates trivially vanish, leaving only the equations in the non cyclic coordinates.
The Routhian approach has the best of both approaches, because cyclic coordinates can be split off to the Hamiltonian equations and eliminated, leaving behind the non cyclic coordinates to be solved from the Lagrangian equations. Overall fewer equations need to be solved compared to the Lagrangian approach.
The Routhian formulation is useful for systems with cyclic coordinates , because by definition those coordinates do not enter L , and hence R . The corresponding partial derivatives of L and R with respect to those coordinates are zero, which equates to the corresponding generalized momenta reducing to constants. To make this concrete, if the q i are all cyclic coordinates, and the ζ j are all non cyclic, then
where the α i are constants. With these constants substituted into the Routhian, R is a function of only the non cyclic coordinates and velocities (and in general time also)
The 2 n Hamiltonian equation in the cyclic coordinates automatically vanishes,
and the s Lagrangian equations are in the non cyclic coordinates
Thus the problem has been reduced to solving the Lagrangian equations in the non cyclic coordinates, with the advantage of the Hamiltonian equations cleanly removing the cyclic coordinates. Using those solutions, the equations for q ˙ i {\displaystyle {\dot {q}}_{i}} can be integrated to compute q i ( t ) {\displaystyle q_{i}(t)} .
If we are interested in how the cyclic coordinates change with time, the equations for the generalized velocities corresponding to the cyclic coordinates can be integrated.
Routh's procedure does not guarantee the equations of motion will be simple, however it will lead to fewer equations.
One general class of mechanical systems with cyclic coordinates are those with central potentials , because potentials of this form only have dependence on radial separations and no dependence on angles.
Consider a particle of mass m under the influence of a central potential V ( r ) in spherical polar coordinates ( r , θ , φ )
Notice φ is cyclic, because it does not appear in the Lagrangian. The momentum conjugate to φ is the constant
in which r and dφ / dt can vary with time, but the angular momentum p φ is constant. The Routhian can be taken to be
We can solve for r and θ using Lagrange's equations, and do not need to solve for φ since it is eliminated by Hamiltonian's equations. The r equation is
and the θ equation is
The Routhian approach has obtained two coupled nonlinear equations. By contrast the Lagrangian approach leads to three nonlinear coupled equations, mixing in the first and second time derivatives of φ in all of them, despite its absence from the Lagrangian.
The r equation is
the θ equation is
the φ equation is
Consider the spherical pendulum , a mass m (known as a "pendulum bob") attached to a rigid rod of length l of negligible mass, subject to a local gravitational field g . The system rotates with angular velocity dφ / dt which is not constant. The angle between the rod and vertical is θ and is not constant.
The Lagrangian is [ nb 3 ]
and φ is the cyclic coordinate for the system with constant momentum
which again is physically the angular momentum of the system about the vertical. The angle θ and angular velocity dφ / dt vary with time, but the angular momentum is constant. The Routhian is
The θ equation is found from the Lagrangian equations
or simplifying by introducing the constants
gives
This equation resembles the simple nonlinear pendulum equation , because it can swing through the vertical axis, with an additional term to account for the rotation about the vertical axis (the constant a is related to the angular momentum p φ ).
Applying the Lagrangian approach there are two nonlinear coupled equations to solve.
The θ equation is
and the φ equation is
The heavy symmetrical top of mass M has Lagrangian [ 7 ] [ 8 ]
where ψ , φ , θ are the Euler angles , θ is the angle between the vertical z -axis and the top's z ′ -axis, ψ is the rotation of the top about its own z ′ -axis, and φ the azimuthal of the top's z ′ -axis around the vertical z -axis. The principal moments of inertia are I 1 about the top's own x ′ axis, I 2 about the top's own y ′ axes, and I 3 about the top's own z ′ -axis. Since the top is symmetric about its z ′ -axis, I 1 = I 2 . Here the simple relation for local gravitational potential energy V = Mgl cos θ is used where g is the acceleration due to gravity, and the centre of mass of the top is a distance l from its tip along its z ′ -axis.
The angles ψ , φ are cyclic. The constant momenta are the angular momenta of the top about its axis and its precession about the vertical, respectively:
From these, eliminating dψ / dt :
we have
and to eliminate dφ / dt , substitute this result into p ψ and solve for dψ / dt to find
The Routhian can be taken to be
and since
we have
The first term is constant, and can be ignored since only the derivatives of R will enter the equations of motion. The simplified Routhian, without loss of information, is thus
The equation of motion for θ is, by direct calculation,
or by introducing the constants
a simpler form of the equation is obtained
Although the equation is highly nonlinear, there is only one equation to solve for, it was obtained directly, and the cyclic coordinates are not involved.
By contrast, the Lagrangian approach leads to three nonlinear coupled equations to solve, despite the absence of the coordinates ψ and φ in the Lagrangian.
The θ equation is
the ψ equation is
and the φ equation is
Consider a classical charged particle of mass m and electric charge q in a static (time-independent) uniform (constant throughout space) magnetic field B . [ 9 ] The Lagrangian for a charged particle in a general electromagnetic field given by the magnetic potential A and electric potential ϕ {\displaystyle \phi } is
It is convenient to use cylindrical coordinates ( r , θ , z ) , so that
In this case of no electric field, the electric potential is zero, ϕ = 0 {\displaystyle \phi =0} , and we can choose the axial gauge for the magnetic potential
and the Lagrangian is
Notice this potential has an effectively cylindrical symmetry (although it also has angular velocity dependence), since the only spatial dependence is on the radial length from an imaginary cylinder axis.
There are two cyclic coordinates, θ and z . The canonical momenta conjugate to θ and z are the constants
so the velocities are
The angular momentum about the z axis is not p θ , but the quantity mr 2 dθ / dt , which is not conserved due to the contribution from the magnetic field. The canonical momentum p θ is the conserved quantity. It is still the case that p z is the linear or translational momentum along the z axis, which is also conserved.
The radial component r and angular velocity dθ / dt can vary with time, but p θ is constant, and since p z is constant it follows dz / dt is constant. The Routhian can take the form
where in the last line, the p z 2 /2 m term is a constant and can be ignored without loss of continuity. The Hamiltonian equations for θ and z automatically vanish and do not need to be solved for. The Lagrangian equation in r
is by direct calculation
which after collecting terms is
and simplifying further by introducing the constants
the differential equation is
To see how z changes with time, integrate the momenta expression for p z above
where c z is an arbitrary constant, the initial value of z to be specified in the initial conditions .
The motion of the particle in this system is helicoidal , with the axial motion uniform (constant) but the radial and angular components varying in a spiral according to the equation of motion derived above. The initial conditions on r , dr / dt , θ , dθ / dt , will determine if the trajectory of the particle has a constant r or varying r . If initially r is nonzero but dr / dt = 0 , while θ and dθ / dt are arbitrary, then the initial velocity of the particle has no radial component, r is constant, so the motion will be in a perfect helix. If r is constant, the angular velocity is also constant according to the conserved p θ .
With the Lagrangian approach, the equation for r would include dθ / dt which has to be eliminated, and there would be equations for θ and z to solve for.
The r equation is
the θ equation is
and the z equation is
The z equation is trivial to integrate, but the r and θ equations are not, in any case the time derivatives are mixed in all the equations and must be eliminated. | https://en.wikipedia.org/wiki/Routhian_mechanics |
In the control system theory , the Routh–Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time-invariant (LTI) dynamical system or control system . A stable system is one whose output signal is bounded; the position, velocity or energy do not increase to infinity as time goes on. The Routh test is an efficient recursive algorithm that English mathematician Edward John Routh proposed in 1876 to determine whether all the roots of the characteristic polynomial of a linear system have negative real parts. [ 1 ] German mathematician Adolf Hurwitz independently proposed in 1895 to arrange the coefficients of the polynomial into a square matrix, called the Hurwitz matrix , and showed that the polynomial is stable if and only if the sequence of determinants of its principal submatrices are all positive. [ 2 ] The two procedures are equivalent, with the Routh test providing a more efficient way to compute the Hurwitz determinants ( Δ i {\displaystyle \Delta _{i}} ) than computing them directly. A polynomial satisfying the Routh–Hurwitz criterion is called a Hurwitz polynomial .
The importance of the criterion is that the roots p of the characteristic equation of a linear system with negative real parts represent solutions e pt of the system that are stable ( bounded ). Thus the criterion provides a way to determine if the equations of motion of a linear system have only stable solutions, without solving the system directly. For discrete systems, the corresponding stability test can be handled by the Schur–Cohn criterion, the Jury test and the Bistritz test . With the advent of computers, the criterion has become less widely used, as an alternative is to solve the polynomial numerically, obtaining approximations to the roots directly.
The Routh test can be derived through the use of the Euclidean algorithm and Sturm's theorem in evaluating Cauchy indices . Hurwitz derived his conditions differently. [ 3 ]
The criterion is related to Routh–Hurwitz theorem . From the statement of that theorem, we have p − q = w ( + ∞ ) − w ( − ∞ ) {\displaystyle p-q=w(+\infty )-w(-\infty )} where:
By the fundamental theorem of algebra , each polynomial of degree n must have n roots in the complex plane (i.e., for an ƒ with no roots on the imaginary line, p + q = n ). Thus, we have the condition that ƒ is a (Hurwitz) stable polynomial if and only if p − q = n (the proof is given below). Using the Routh–Hurwitz theorem, we can replace the condition on p and q by a condition on the generalized Sturm chain, which will give in turn a condition on the coefficients of ƒ .
Let f ( z ) be a complex polynomial. The process is as follows:
Let f ( z ) = a z 2 + b z + c {\displaystyle f(z)=az^{2}+bz+c} (for the sake of simplicity we take real coefficients) where c ≠ 0 {\displaystyle c\neq 0} (to avoid a root in zero so that we can use the Routh–Hurwitz theorem). First, we have to calculate the real polynomials P 0 ( y ) {\displaystyle P_{0}(y)} and P 1 ( y ) {\displaystyle P_{1}(y)} : f ( i y ) = − a y 2 + i b y + c = P 0 ( y ) + i P 1 ( y ) = − a y 2 + c + i ( b y ) . {\displaystyle f(iy)=-ay^{2}+iby+c=P_{0}(y)+iP_{1}(y)=-ay^{2}+c+i(by).} Next, we divide those polynomials to obtain the generalized Sturm chain : P 0 ( y ) = ( − a b y ) P 1 ( y ) + c , ⟹ P 2 ( y ) = − c , P 1 ( y ) = ( − b c y ) P 2 ( y ) , ⟹ P 3 ( y ) = 0 , {\displaystyle {\begin{aligned}P_{0}(y)&=\left({\tfrac {-a}{b}}y\right)P_{1}(y)+c,&&\implies P_{2}(y)=-c,\\[4pt]P_{1}(y)&=\left({\tfrac {-b}{c}}y\right)P_{2}(y),&&\implies P_{3}(y)=0,\end{aligned}}} and the Euclidean division stops.
Notice that we had to suppose b different from zero in the first division. The generalized Sturm chain is in this case ( P 0 ( y ) , P 1 ( y ) , P 2 ( y ) ) = ( c − a y 2 , b y , − c ) . {\displaystyle {\Bigl (}P_{0}(y),P_{1}(y),P_{2}(y){\Bigr )}=(c-ay^{2},by,-c).} Putting y = + ∞ {\displaystyle y=+\infty } , the sign of ( c − a y 2 ) {\displaystyle (c-ay^{2})} is the opposite sign of a and the sign of by is the sign of b . When we put ( y = − ∞ ) {\displaystyle (y=-\infty )} , the sign of the first element of the chain is again the opposite sign of a and the sign of by is the opposite sign of b . Finally, − c has always the opposite sign of c .
Suppose now that f is Hurwitz-stable. This means that w ( + ∞ ) − w ( − ∞ ) = 2 {\displaystyle w(+\infty )-w(-\infty )=2} (the degree of f ). By the properties of the function w , this is the same as w ( + ∞ ) = 2 {\displaystyle w(+\infty )=2} and w ( − ∞ ) = 0 {\displaystyle w(-\infty )=0} . Thus, a , b and c must have the same sign. We have thus found the necessary condition of stability for polynomials of degree 2.
For a second-order polynomial P ( s ) = a 2 s 2 + a 1 s + a 0 = 0 , {\displaystyle P(s)=a_{2}s^{2}+a_{1}s+a_{0}=0,} all coefficients must be positive, where a i > 0 {\displaystyle a_{i}>0} for ( i = 0 , 1 , 2 ) {\displaystyle (i=0,1,2)} .
For a third-order polynomial P ( s ) = a 3 s 3 + a 2 s 2 + a 1 s + a 0 = 0 , {\displaystyle P(s)=a_{3}s^{3}+a_{2}s^{2}+a_{1}s+a_{0}=0,} all coefficients must be positive, where 0 < a i , for i = 0 , 1 , 2 , 3 ; 0 < a 2 a 1 − a 3 a 0 . {\displaystyle {\begin{aligned}0&<a_{i},\quad {\text{for }}i=0,1,2,3;\\0&<a_{2}a_{1}-a_{3}a_{0}.\end{aligned}}}
For a fourth-order polynomial P ( s ) = a 4 s 4 + a 3 s 3 + a 2 s 2 + a 1 s + a 0 = 0 , {\displaystyle P(s)=a_{4}s^{4}+a_{3}s^{3}+a_{2}s^{2}+a_{1}s+a_{0}=0,} all coefficients must be positive, where [ 4 ] 0 < a i , for i = 0 , 1 , 2 , 3 , 4 ; 0 < a 2 a 1 − a 3 a 0 ; 0 < a 3 a 2 a 1 − a 4 a 1 2 − a 3 2 a 0 . {\displaystyle {\begin{aligned}0&<a_{i},\quad {\text{for }}i=0,1,2,3,4;\\0&<a_{2}a_{1}-a_{3}a_{0};\\0&<a_{3}a_{2}a_{1}-a_{4}a_{1}^{2}-a_{3}^{2}a_{0}.\end{aligned}}} (When this is derived you do not know all coefficients should be positive, and you add a 3 a 2 > a 1 {\displaystyle a_{3}a_{2}>a_{1}} .)
In general the Routh stability criterion states a polynomial has all roots in the open left half-plane if and only if all first-column elements of the Routh array have the same sign.
All coefficients being positive (or all negative) is necessary for all roots to be located in the open left half-plane. That is why here a n {\displaystyle a_{n}} is fixed to 1, which is positive. When this is assumed, we can remove a 3 a 2 > a 1 {\displaystyle a_{3}a_{2}>a_{1}} from fourth-order polynomial, and conditions for fifth- and sixth-order can be simplified. For fifth-order we only need to check that Δ 2 > 0 , Δ 4 > 0 {\displaystyle \Delta _{2}>0,\Delta _{4}>0} and for sixth-order we only need to check Δ 3 > 0 , Δ 5 > 0 {\displaystyle \Delta _{3}>0,\Delta _{5}>0} and this is further optimised in Liénard–Chipart criterion . [ 5 ] Indeed, some coefficients being positive is not independent with principal minors being positive, like a 2 > 0 {\displaystyle a_{2}>0} check can be removed for third-order polynomial.
A tabular method can be used to determine the stability when the roots of a higher order characteristic polynomial are difficult to obtain. For an n th-degree polynomial whose all coefficients are the same signs D ( s ) = a n s n + a n − 1 s n − 1 + ⋯ + a 1 s + a 0 {\displaystyle D(s)=a_{n}s^{n}+a_{n-1}s^{n-1}+\cdots +a_{1}s+a_{0}} the table has n + 1 rows and the following structure:
a n a n − 2 a n − 4 … a n − 1 a n − 3 a n − 5 … b 1 b 2 b 3 … c 1 c 2 c 3 … ⋮ ⋮ ⋮ ⋱ {\displaystyle {\begin{matrix}a_{n}&a_{n-2}&a_{n-4}&\dots \\a_{n-1}&a_{n-3}&a_{n-5}&\dots \\b_{1}&b_{2}&b_{3}&\dots \\c_{1}&c_{2}&c_{3}&\dots \\\vdots &\vdots &\vdots &\ddots \end{matrix}}}
where the elements b i {\displaystyle b_{i}} and c i {\displaystyle c_{i}} can be computed as follows: b i = a n − 1 × a n − 2 i − a n × a n − ( 2 i + 1 ) a n − 1 c i = b 1 × a n − ( 2 i + 1 ) − a n − 1 × b i + 1 b 1 {\displaystyle {\begin{aligned}b_{i}&={\frac {a_{n-1}\times a_{n-2i}-a_{n}\times a_{n-(2i+1)}}{a_{n-1}}}\\[4pt]c_{i}&={\frac {b_{1}\times a_{n-(2i+1)}-a_{n-1}\times b_{i+1}}{b_{1}}}\end{aligned}}} When completed, the number of sign changes in the first column will be the number of roots whose real part are non-negative.
0.75 1.5 0 0 − 3 6 0 0 3 0 0 0 6 0 0 0 {\displaystyle {\begin{matrix}0.75&1.5&\ 0\ &\ 0\ \\-3&6&0&0\\3&0&0&0\\6&0&0&0\end{matrix}}}
In the first column, there are two sign changes ( 0.75 → −3 , and −3 → 3 ), thus there are two roots whose real part are non-negative and the system is unstable.
The characteristic equation of an example servo system is given by: [ 6 ]
b 0 s 4 + b 1 s 3 + b 2 s 2 + b 3 s + b 4 = 0 {\displaystyle b_{0}s^{4}+b_{1}s^{3}+b_{2}s^{2}+b_{3}s+b_{4}=0}
For which we have the following table:
b 0 b 2 b 4 0 b 1 b 3 0 0 b 1 b 2 − b 0 b 3 b 1 b 1 b 4 − b 0 × 0 b 1 = b 4 0 0 ( b 1 b 2 − b 0 b 3 ) b 3 − b 1 2 b 4 b 1 b 2 − b 0 b 3 0 0 0 b 4 0 0 0 {\displaystyle {\begin{matrix}b_{0}&b_{2}&\quad b_{4}\quad &\quad 0\quad \\[4pt]b_{1}&b_{3}&0&0\\[4pt]{\frac {b_{1}b_{2}-b_{0}b_{3}}{b_{1}}}&{\frac {b_{1}b_{4}-b_{0}\times 0}{b_{1}}}=b_{4}&0&0\\{\frac {(b_{1}b_{2}-b_{0}b_{3})b_{3}-b_{1}^{2}b_{4}}{b_{1}b_{2}-b_{0}b_{3}}}&0&0&0\\[4pt]b_{4}&0&0&0\end{matrix}}}
for stability, all the elements in the first column of the Routh array must be positive when b 0 > 0. {\displaystyle b_{0}>0.} And the conditions that must be satisfied for stability of the given system as follows: [ 6 ]
0 < b 1 , 0 < b 1 b 2 − b 0 b 3 , 0 < ( b 1 b 2 − b 0 b 3 ) b 3 − b 1 2 b 4 , 0 < b 4 . {\displaystyle {\begin{aligned}0&<b_{1},\\[4pt]0&<b_{1}b_{2}-b_{0}b_{3},\\[4pt]0&<(b_{1}b_{2}-b_{0}b_{3})b_{3}-b_{1}^{2}b_{4},\\[4pt]0&<b_{4}.\end{aligned}}}
We see that if ( b 1 b 2 − b 0 b 3 ) b 3 − b 1 2 b 4 ≥ 0 {\displaystyle (b_{1}b_{2}-b_{0}b_{3})b_{3}-b_{1}^{2}b_{4}\geq 0} then b 1 b 2 − b 0 b 3 > 0 {\displaystyle b_{1}b_{2}-b_{0}b_{3}>0} is satisfied.
Another example is: [ 7 ]
s 4 + 6 s 3 + 11 s 2 + 6 s + 200 = 0 {\displaystyle s^{4}+6s^{3}+11s^{2}+6s+200=0}
We have the following table :
1 11 200 0 1 1 0 0 1 20 0 0 − 19 0 0 0 20 0 0 0 {\displaystyle {\begin{matrix}1&11&200&0\\1&1&0&0\\1&20&0&0\\-19&0&0&0\\20&0&0&0\end{matrix}}}
there are two sign changes. The system is unstable, since it has two right-half-plane poles and two left-half-plane poles. The system cannot have jω poles since a row of zeros did not appear in the Routh table. [ 7 ]
For the case s 4 + s 3 + 3 s 2 + 3 s + 3 = 0 {\displaystyle s^{4}+s^{3}+3s^{2}+3s+3=0} We have the following table with zero appeared in the first column which prevents further calculation steps:
1 3 3 1 3 0 0 3 0 {\displaystyle {\begin{matrix}1&3&3\\1&3&0\\0&3&0\end{matrix}}}
we replace 0 by ε > 0 {\displaystyle \varepsilon >0} and we have the table
1 3 3 1 3 0 ε 3 0 3 − 3 ε 0 0 3 0 0 {\displaystyle {\begin{matrix}1&3&\quad 3\quad \\1&3&0\\\varepsilon &3&0\\3-{\frac {3}{\varepsilon }}&0&0\\3&0&0\end{matrix}}}
When we make ε → + 0 {\displaystyle \varepsilon \rightarrow +0} , there are two sign changes.
The system is unstable, since it has two right-half-plane poles and two left-half-plane poles.
Sometimes the presence of poles on the imaginary axis creates a situation of marginal stability. In that case the coefficients of the "Routh array" in a whole row become zero and thus further solution of the polynomial for finding changes in sign is not possible. Then another approach comes into play. The row of polynomial which is just above the row containing the zeroes is called the "auxiliary polynomial".
s 6 + 2 s 5 + 8 s 4 + 12 s 3 + 20 s 2 + 16 s + 16 = 0 {\displaystyle s^{6}+2s^{5}+8s^{4}+12s^{3}+20s^{2}+16s+16=0} We have the following table:
1 8 20 16 2 12 16 0 2 12 16 0 0 0 0 0 {\displaystyle {\begin{matrix}1&8&20&16\\2&12&16&0\\2&12&16&0\\0&0&0&0\end{matrix}}}
In such a case the auxiliary polynomial is A ( s ) = 2 s 4 + 12 s 2 + 16 {\displaystyle A(s)=2s^{4}+12s^{2}+16\,} which is again equal to zero. The next step is to differentiate the above equation which yields the polynomial B ( s ) = 8 s 3 + 24 s 1 {\displaystyle B(s)=8s^{3}+24s^{1}} . The coefficients of the row containing zero now become
"8" and "24". The process of Routh array is proceeded using these values which yield two points on the imaginary axis. These two points on the imaginary axis are the prime cause of marginal stability. [ 8 ] | https://en.wikipedia.org/wiki/Routh–Hurwitz_stability_criterion |
In hydrology , routing is a technique used to predict the changes in shape of a hydrograph as water moves through a river channel or a reservoir . In flood forecasting , hydrologists may want to know how a short burst of intense rain in an area upstream of a city will change as it reaches the city. Routing can be used to determine whether the pulse of rain reaches the city as a deluge or a trickle.
Routing also can be used to predict the hydrograph shape (and thus lowland flooding potential) subsequent to multiple rainfall events in different sub-catchments of the watershed. Timing and duration of the rainfall events, as well as factors such as antecedent moisture conditions, overall watershed shape, along with subcatchment-area shapes, land slopes (topography/physiography), geology/hydrogeology (i.e. forests and aquifers can serve as giant sponges that absorb rainfall and slowly release it over subsequent weeks and months), and stream-reach lengths all play a role here. The result can be an additive effect (i.e. a large flood if each subcatchment's respective hydrograph peak arrives at the watershed mouth at the same point in time, thereby effectively causing a "stacking" of the hydrograph peaks), or a more distributed-in-time effect (i.e. a lengthy but relatively modest flood, effectively attenuated in time, as the individual subcatchment peaks arrive at the mouth of the main watershed channel in orderly succession). [ 1 ] [ 2 ] [ 3 ]
Other uses of routing include reservoir and channel design, floodplain studies and watershed simulations. [ 4 ]
If the water flow at a particular point, A, in a stream is measured over time with a flow gauge, this information can be used to create a hydrograph . A short period of intense rain, normally called a flood event , can cause a bulge in the graph, as the increased water travels down the river, reaches the flow gauge at A, and passes along it. If another flow gauge at B, downstream of A is set up, one would expect the graph's bulge (or floodwave) to have the same shape. However, the shape of the river and flow resistance within a river (from the river bed , for example) can affect the shape of the floodwave. Oftentimes, the floodwave will be attenuated (have a reduced peak flow).
Routing techniques can be broadly classified as hydraulic (or distributed) routing , hydrologic (or lumped) routing or semi-distributed routing . In general, based on the available field data and goals of the project, one of routing procedures is selected.
Hydraulic routing is based on the solution of partial differential equations of unsteady open-channel flow . The equations used are the Saint-Venant equations or the associated dynamic wave equations. [ 5 ] [ 6 ]
The hydraulic models (e.g. dynamic and diffusion wave models) require the gathering of a lot of data related to river geometry and morphology and consume a lot of computer resources in order to solve the equations numerically. [ 7 ] [ 8 ] [ 9 ]
Hydrologic routing uses the continuity equation for hydrology. In its simplest form, inflow to the river reach is equal to the outflow of the river reach plus the change of storage:
The hydrologic models (e.g. linear and nonlinear Muskingum models) need to estimate hydrologic parameters using recorded data in both upstream and downstream sections of rivers and/or by applying robust optimization techniques to solve the one-dimensional conservation of mass and storage-continuity equation. [ 10 ]
Semi-distributed models such as Muskingum–Cunge family procedures are also available. Simple physical concepts and common river characteristics such as channel geometry, reach length, roughness coefficient, and slope are used to estimate the model parameters without complex and expensive numerical solutions. [ 11 ] [ 12 ] [ 13 ]
Flood routing is a procedure to determine the time and magnitude of flow (i.e., the flow hydrograph) at a point on a watercourse from known or assumed hydrographs at one or more points upstream. The procedure is specifically known as Flood routing , if the flow is a flood . [ 14 ] [ 15 ] After Routing, the peak gets attenuated & a time lag is introduced. In order to determine the change in shape of a hydrograph of a flood as it travels through a natural river or artificial channel, different flood simulation techniques can be used. Traditionally, the hydraulic (e.g. dynamic and diffusion wave models) and hydrologic (e.g. linear and nonlinear Muskingum models) routing procedures that are well known as distributed and lumped ways to hydraulic and hydrologic practitioners, respectively, can be utilized. The hydrologic models need to estimate hydrologic parameters using recorded data in both upstream and downstream sections of rivers and/or by applying robust optimization techniques to solve the one-dimensional conservation of mass and storage-continuity equation. [ 16 ] On the other hand, hydraulic models require the gathering of a lot of data related to river geometry and morphology and consume a lot of computer resources in order to solve the equations numerically. [ 17 ] [ 18 ] [ 19 ] However, semi-distributed models such as Muskingum–Cunge family procedures are also available. Simple physical concepts and common river characteristic consisting of channel geometry, reach length, roughness coefficient, and slope are used to estimate the model parameters without complex and expensive numerical solutions. [ 20 ] [ 21 ] [ 22 ] In general, based on the available field data and goals of a project, one of these approaches is utilized for the simulation of flooding in rivers and channels.
Runoff routing is a procedure to calculate a surface runoff hydrograph from rainfall. Losses are removed from rainfall to determine the rainfall excess which is then converted to a hydrograph and routed through conceptual storages that represent the storage discharge behaviour of overland and channel flow. [ 23 ] [ 24 ] | https://en.wikipedia.org/wiki/Routing_(hydrology) |
A routing diagram or route diagram in the field of management engineering is a type of diagram , that shows a route through an accessible physical space. [ 1 ] Routing diagrams are used in plant layout study , and manufacturing plant design.
A routing diagrams shows a route through a physical space. They are often considered a type of flow diagram, but they differ from flowcharts, that a routing is pictured in a physical layout. There is a similarity with design of Electrical equipment , where routing diagrams also in show "the physical layout of the facility and equipment and how the circuit how the circuit to the various equipment is run." [ 2 ]
A picture with a routing in geographical space is often called a route map. While the road map and transit map (such as the railway map, metro map, bus map, etc.) show all the roads or lines, the route map regularly shows one rad for a particular occasion. Likewise a ground plan or site map show all the space, buildings and/or rooms, the routing map shows one specific route on site.
Routing diagrams are used in plant layout study . The routing diagram can consist of a floor plan with a trace attached, or a 3d cross section of a building with a trace. The routing diagram transforms into a flow diagram when the physical dimensions are taken out of the equation. [ 3 ] | https://en.wikipedia.org/wiki/Routing_diagram |
Network routing in a cellular network deals with the challenges of traditional telephony such as switching and call setup. [ 1 ]
Most cellular network routing issues in different cells can be attributed to the multiple access methods used for transmission. The location of each mobile phone must be known to reuse a given band of frequencies in different cells and forms space-division multiple access (SDMA).
FDMA is one of the multiple access methods used in cellular networks. 50 MHz blocks of communication channel are assigned, which lie in radio frequency range and contain an equal number of uplinks (terminal to base station) and downlinks (base station to terminal). [ 2 ] One or more bidirectional channels are carried by 10-90 band pairs. The digital networks additionally make use of either CDMA or TDMA methods.
A special service called mobility management provides handover and roaming . Terminals (handsets) can move from one place to another during the call and require calls to be handed over from one channel to another. [ 3 ] Soft handover uses the same frequency channel. [ 4 ] The same terminals can operate in the same area covered by different service providers, which is known as roaming . [ 5 ]
This article related to telecommunications is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Routing_in_cellular_networks |
Rovalpituzumab tesirine ( Rova-T ) is an experimental antibody-drug conjugate targeting the protein DLL3 on tumor cells. [ 1 ] [ 2 ] It was originally developed by Stemcentrx and was purchased by AbbVie . [ 3 ] It was tested for use in small-cell lung cancer , but development was terminated after unsuccessful phase III trial . [ 4 ] [ 5 ]
In 2018, an Independent Data Monitoring Committee found that in the TAHOE phase III trial, Rova-T shortened survival of lung cancer patients compared to SOC chemotherapy topotecan, prompting termination of trial enrollment. Another phase III trial (MERU) demonstrated no survival benefit over placebo. [ 6 ] [ 7 ] A phase II trial using the drug as a third-line treatment for relapsed or refractory lung cancer showed objective response rate at just 16%. [ 8 ]
Chemical structure of "tesirine" (drawn in black). It consists of a pyrrolobenzodiazepine type dimer (top), which is the actual anti-cancer agent, a Val – Ala structure that can be cleaved by an enzyme to detach the anti-cancer agent from the antibody, a polyethylene glycol spacer, and a maleimide linker which is attached to a cysteine in the antibody's (rovalpituzumab's) peptide backbone, drawn blue. Each rovalpituzumab molecule has an average of two such attachments. [ 9 ] | https://en.wikipedia.org/wiki/Rovalpituzumab_tesirine |
The Rover T.P.90 is a British made gas turboprop aircraft engine manufactured by the Rover Company . [ 1 ]
The Rover Company first started the development of gas turbine engines for automobiles in 1949. Years later, the company made gas turbines for APU applications.
The T.P.90 Turboprop was used in the 1940s British Auster Autocrat and in the DHC Chipmunk.
The first known application of the T.P.90 Turboprop engine in the United States came in early 1980s. Mr. Bert Wilcut located on Stinson Municipal Airport in San Antonio, Texas, installed the engine into his experimental Palomino (aircraft) . [ 2 ] | https://en.wikipedia.org/wiki/Rover_T.P._90 |
Rovibronic coupling , also known as rotation/vibration-electron coupling , denotes the simultaneous interactions between ro tational, vib rational, and elect ronic degrees of freedom in a molecule. [ 1 ] When a rovibronic transition occurs, the rotational, vibrational, and electronic states change simultaneously, unlike in rovibrational coupling . The coupling can be observed using spectroscopy , and is most easily seen in the Renner–Teller effect in which a linear polyatomic molecule is in a degenerate electronic state and bending vibrations will cause a large rovibronic coupling.
This spectroscopy -related article is a stub . You can help Wikipedia by expanding it .
This chemistry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rovibronic_coupling |
In linear algebra , the column space (also called the range or image ) of a matrix A is the span (set of all possible linear combinations ) of its column vectors . The column space of a matrix is the image or range of the corresponding matrix transformation .
Let F {\displaystyle F} be a field . The column space of an m × n matrix with components from F {\displaystyle F} is a linear subspace of the m -space F m {\displaystyle F^{m}} . The dimension of the column space is called the rank of the matrix and is at most min( m , n ) . [ 1 ] A definition for matrices over a ring R {\displaystyle R} is also possible .
The row space is defined similarly.
The row space and the column space of a matrix A are sometimes denoted as C ( A T ) and C ( A ) respectively. [ 2 ]
This article considers matrices of real numbers . The row and column spaces are subspaces of the real spaces R n {\displaystyle \mathbb {R} ^{n}} and R m {\displaystyle \mathbb {R} ^{m}} respectively. [ 3 ]
Let A be an m -by- n matrix. Then
If the matrix represents a linear transformation , the column space of the matrix equals the image of this linear transformation.
The column space of a matrix A is the set of all linear combinations of the columns in A . If A = [ a 1 ⋯ a n ] , then colsp( A ) = span({ a 1 , ..., a n }) .
Given a matrix A , the action of the matrix A on a vector x returns a linear combination of the columns of A with the coordinates of x as coefficients; that is, the columns of the matrix generate the column space.
Given a matrix J :
the rows are r 1 = [ 2 4 1 3 2 ] {\displaystyle \mathbf {r} _{1}={\begin{bmatrix}2&4&1&3&2\end{bmatrix}}} , r 2 = [ − 1 − 2 1 0 5 ] {\displaystyle \mathbf {r} _{2}={\begin{bmatrix}-1&-2&1&0&5\end{bmatrix}}} , r 3 = [ 1 6 2 2 2 ] {\displaystyle \mathbf {r} _{3}={\begin{bmatrix}1&6&2&2&2\end{bmatrix}}} , r 4 = [ 3 6 2 5 1 ] {\displaystyle \mathbf {r} _{4}={\begin{bmatrix}3&6&2&5&1\end{bmatrix}}} .
Consequently, the row space of J is the subspace of R 5 {\displaystyle \mathbb {R} ^{5}} spanned by { r 1 , r 2 , r 3 , r 4 } .
Since these four row vectors are linearly independent , the row space is 4-dimensional. Moreover, in this case it can be seen that they are all orthogonal to the vector n = [6, −1, 4, −4, 0] ( n is an element of the kernel of J ), so it can be deduced that the row space consists of all vectors in R 5 {\displaystyle \mathbb {R} ^{5}} that are orthogonal to n .
Let K be a field of scalars . Let A be an m × n matrix, with column vectors v 1 , v 2 , ..., v n . A linear combination of these vectors is any vector of the form
where c 1 , c 2 , ..., c n are scalars. The set of all possible linear combinations of v 1 , ..., v n is called the column space of A . That is, the column space of A is the span of the vectors v 1 , ..., v n .
Any linear combination of the column vectors of a matrix A can be written as the product of A with a column vector:
Therefore, the column space of A consists of all possible products A x , for x ∈ K n . This is the same as the image (or range ) of the corresponding matrix transformation .
If A = [ 1 0 0 1 2 0 ] {\displaystyle A={\begin{bmatrix}1&0\\0&1\\2&0\end{bmatrix}}} , then the column vectors are v 1 = [1, 0, 2] T and v 2 = [0, 1, 0] T .
A linear combination of v 1 and v 2 is any vector of the form c 1 [ 1 0 2 ] + c 2 [ 0 1 0 ] = [ c 1 c 2 2 c 1 ] {\displaystyle c_{1}{\begin{bmatrix}1\\0\\2\end{bmatrix}}+c_{2}{\begin{bmatrix}0\\1\\0\end{bmatrix}}={\begin{bmatrix}c_{1}\\c_{2}\\2c_{1}\end{bmatrix}}} The set of all such vectors is the column space of A . In this case, the column space is precisely the set of vectors ( x , y , z ) ∈ R 3 satisfying the equation z = 2 x (using Cartesian coordinates , this set is a plane through the origin in three-dimensional space ).
The columns of A span the column space, but they may not form a basis if the column vectors are not linearly independent . Fortunately, elementary row operations do not affect the dependence relations between the column vectors. This makes it possible to use row reduction to find a basis for the column space.
For example, consider the matrix
The columns of this matrix span the column space, but they may not be linearly independent , in which case some subset of them will form a basis. To find this basis, we reduce A to reduced row echelon form :
At this point, it is clear that the first, second, and fourth columns are linearly independent, while the third column is a linear combination of the first two. (Specifically, v 3 = −2 v 1 + v 2 .) Therefore, the first, second, and fourth columns of the original matrix are a basis for the column space:
Note that the independent columns of the reduced row echelon form are precisely the columns with pivots . This makes it possible to determine which columns are linearly independent by reducing only to echelon form .
The above algorithm can be used in general to find the dependence relations between any set of vectors, and to pick out a basis from any spanning set. Also finding a basis for the column space of A is equivalent to finding a basis for the row space of the transpose matrix A T .
To find the basis in a practical setting (e.g., for large matrices), the singular-value decomposition is typically used.
The dimension of the column space is called the rank of the matrix. The rank is equal to the number of pivots in the reduced row echelon form , and is the maximum number of linearly independent columns that can be chosen from the matrix. For example, the 4 × 4 matrix in the example above has rank three.
Because the column space is the image of the corresponding matrix transformation , the rank of a matrix is the same as the dimension of the image. For example, the transformation R 4 → R 4 {\displaystyle \mathbb {R} ^{4}\to \mathbb {R} ^{4}} described by the matrix above maps all of R 4 {\displaystyle \mathbb {R} ^{4}} to some three-dimensional subspace .
The nullity of a matrix is the dimension of the null space , and is equal to the number of columns in the reduced row echelon form that do not have pivots. [ 7 ] The rank and nullity of a matrix A with n columns are related by the equation:
This is known as the rank–nullity theorem .
The left null space of A is the set of all vectors x such that x T A = 0 T . It is the same as the null space of the transpose of A . The product of the matrix A T and the vector x can be written in terms of the dot product of vectors:
because row vectors of A T are transposes of column vectors v k of A . Thus A T x = 0 if and only if x is orthogonal (perpendicular) to each of the column vectors of A .
It follows that the left null space (the null space of A T ) is the orthogonal complement to the column space of A .
For a matrix A , the column space, row space, null space, and left null space are sometimes referred to as the four fundamental subspaces .
Similarly the column space (sometimes disambiguated as right column space) can be defined for matrices over a ring K as
for any c 1 , ..., c n , with replacement of the vector m -space with " right free module ", which changes the order of scalar multiplication of the vector v k to the scalar c k such that it is written in an unusual order vector – scalar . [ 8 ]
Let K be a field of scalars . Let A be an m × n matrix, with row vectors r 1 , r 2 , ..., r m . A linear combination of these vectors is any vector of the form
where c 1 , c 2 , ..., c m are scalars. The set of all possible linear combinations of r 1 , ..., r m is called the row space of A . That is, the row space of A is the span of the vectors r 1 , ..., r m .
For example, if
then the row vectors are r 1 = [1, 0, 2] and r 2 = [0, 1, 0] . A linear combination of r 1 and r 2 is any vector of the form
The set of all such vectors is the row space of A . In this case, the row space is precisely the set of vectors ( x , y , z ) ∈ K 3 satisfying the equation z = 2 x (using Cartesian coordinates , this set is a plane through the origin in three-dimensional space ).
For a matrix that represents a homogeneous system of linear equations , the row space consists of all linear equations that follow from those in the system.
The column space of A is equal to the row space of A T .
The row space is not affected by elementary row operations . This makes it possible to use row reduction to find a basis for the row space.
For example, consider the matrix
The rows of this matrix span the row space, but they may not be linearly independent , in which case the rows will not be a basis. To find a basis, we reduce A to row echelon form :
r 1 , r 2 , r 3 represents the rows.
Once the matrix is in echelon form, the nonzero rows are a basis for the row space. In this case, the basis is { [1, 3, 2], [2, 7, 4] } . Another possible basis { [1, 0, 2], [0, 1, 0] } comes from a further reduction. [ 9 ]
This algorithm can be used in general to find a basis for the span of a set of vectors. If the matrix is further simplified to reduced row echelon form , then the resulting basis is uniquely determined by the row space.
It is sometimes convenient to find a basis for the row space from among the rows of the original matrix instead (for example, this result is useful in giving an elementary proof that the determinantal rank of a matrix is equal to its rank). Since row operations can affect linear dependence relations of the row vectors, such a basis is instead found indirectly using the fact that the column space of A T is equal to the row space of A . Using the example matrix A above, find A T and reduce it to row echelon form:
The pivots indicate that the first two columns of A T form a basis of the column space of A T . Therefore, the first two rows of A (before any row reductions) also form a basis of the row space of A .
The dimension of the row space is called the rank of the matrix. This is the same as the maximum number of linearly independent rows that can be chosen from the matrix, or equivalently the number of pivots. For example, the 3 × 3 matrix in the example above has rank two. [ 9 ]
The rank of a matrix is also equal to the dimension of the column space . The dimension of the null space is called the nullity of the matrix, and is related to the rank by the following equation:
where n is the number of columns of the matrix A . The equation above is known as the rank–nullity theorem .
The null space of matrix A is the set of all vectors x for which A x = 0 . The product of the matrix A and the vector x can be written in terms of the dot product of vectors:
where r 1 , ..., r m are the row vectors of A . Thus A x = 0 if and only if x is orthogonal (perpendicular) to each of the row vectors of A .
It follows that the null space of A is the orthogonal complement to the row space. For example, if the row space is a plane through the origin in three dimensions, then the null space will be the perpendicular line through the origin. This provides a proof of the rank–nullity theorem (see dimension above).
The row space and null space are two of the four fundamental subspaces associated with a matrix A (the other two being the column space and left null space ).
If V and W are vector spaces , then the kernel of a linear transformation T : V → W is the set of vectors v ∈ V for which T ( v ) = 0 . The kernel of a linear transformation is analogous to the null space of a matrix.
If V is an inner product space , then the orthogonal complement to the kernel can be thought of as a generalization of the row space. This is sometimes called the coimage of T . The transformation T is one-to-one on its coimage, and the coimage maps isomorphically onto the image of T .
When V is not an inner product space, the coimage of T can be defined as the quotient space V / ker( T ) . | https://en.wikipedia.org/wiki/Row_and_column_spaces |
In linear algebra , a column vector with m {\displaystyle m} elements is an m × 1 {\displaystyle m\times 1} matrix [ 1 ] consisting of a single column of m {\displaystyle m} entries, for example, x = [ x 1 x 2 ⋮ x m ] . {\displaystyle {\boldsymbol {x}}={\begin{bmatrix}x_{1}\\x_{2}\\\vdots \\x_{m}\end{bmatrix}}.}
Similarly, a row vector is a 1 × n {\displaystyle 1\times n} matrix for some n {\displaystyle n} , consisting of a single row of n {\displaystyle n} entries, a = [ a 1 a 2 … a n ] . {\displaystyle {\boldsymbol {a}}={\begin{bmatrix}a_{1}&a_{2}&\dots &a_{n}\end{bmatrix}}.} (Throughout this article, boldface is used for both row and column vectors.)
The transpose (indicated by T ) of any row vector is a column vector, and the transpose of any column vector is a row vector: [ x 1 x 2 … x m ] T = [ x 1 x 2 ⋮ x m ] {\displaystyle {\begin{bmatrix}x_{1}\;x_{2}\;\dots \;x_{m}\end{bmatrix}}^{\rm {T}}={\begin{bmatrix}x_{1}\\x_{2}\\\vdots \\x_{m}\end{bmatrix}}} and [ x 1 x 2 ⋮ x m ] T = [ x 1 x 2 … x m ] . {\displaystyle {\begin{bmatrix}x_{1}\\x_{2}\\\vdots \\x_{m}\end{bmatrix}}^{\rm {T}}={\begin{bmatrix}x_{1}\;x_{2}\;\dots \;x_{m}\end{bmatrix}}.}
The set of all row vectors with n entries in a given field (such as the real numbers ) forms an n -dimensional vector space ; similarly, the set of all column vectors with m entries forms an m -dimensional vector space.
The space of row vectors with n entries can be regarded as the dual space of the space of column vectors with n entries, since any linear functional on the space of column vectors can be represented as the left-multiplication of a unique row vector.
To simplify writing column vectors in-line with other text, sometimes they are written as row vectors with the transpose operation applied to them.
x = [ x 1 x 2 … x m ] T {\displaystyle {\boldsymbol {x}}={\begin{bmatrix}x_{1}\;x_{2}\;\dots \;x_{m}\end{bmatrix}}^{\rm {T}}}
or
x = [ x 1 , x 2 , … , x m ] T {\displaystyle {\boldsymbol {x}}={\begin{bmatrix}x_{1},x_{2},\dots ,x_{m}\end{bmatrix}}^{\rm {T}}}
Some authors also use the convention of writing both column vectors and row vectors as rows, but separating row vector elements with commas and column vector elements with semicolons (see alternative notation 2 in the table below). [ citation needed ]
Matrix multiplication involves the action of multiplying each row vector of one matrix by each column vector of another matrix.
The dot product of two column vectors a , b , considered as elements of a coordinate space, is equal to the matrix product of the transpose of a with b ,
a ⋅ b = a ⊺ b = [ a 1 ⋯ a n ] [ b 1 ⋮ b n ] = a 1 b 1 + ⋯ + a n b n , {\displaystyle \mathbf {a} \cdot \mathbf {b} =\mathbf {a} ^{\intercal }\mathbf {b} ={\begin{bmatrix}a_{1}&\cdots &a_{n}\end{bmatrix}}{\begin{bmatrix}b_{1}\\\vdots \\b_{n}\end{bmatrix}}=a_{1}b_{1}+\cdots +a_{n}b_{n}\,,}
By the symmetry of the dot product, the dot product of two column vectors a , b is also equal to the matrix product of the transpose of b with a ,
b ⋅ a = b ⊺ a = [ b 1 ⋯ b n ] [ a 1 ⋮ a n ] = a 1 b 1 + ⋯ + a n b n . {\displaystyle \mathbf {b} \cdot \mathbf {a} =\mathbf {b} ^{\intercal }\mathbf {a} ={\begin{bmatrix}b_{1}&\cdots &b_{n}\end{bmatrix}}{\begin{bmatrix}a_{1}\\\vdots \\a_{n}\end{bmatrix}}=a_{1}b_{1}+\cdots +a_{n}b_{n}\,.}
The matrix product of a column and a row vector gives the outer product of two vectors a , b , an example of the more general tensor product . The matrix product of the column vector representation of a and the row vector representation of b gives the components of their dyadic product,
a ⊗ b = a b ⊺ = [ a 1 a 2 a 3 ] [ b 1 b 2 b 3 ] = [ a 1 b 1 a 1 b 2 a 1 b 3 a 2 b 1 a 2 b 2 a 2 b 3 a 3 b 1 a 3 b 2 a 3 b 3 ] , {\displaystyle \mathbf {a} \otimes \mathbf {b} =\mathbf {a} \mathbf {b} ^{\intercal }={\begin{bmatrix}a_{1}\\a_{2}\\a_{3}\end{bmatrix}}{\begin{bmatrix}b_{1}&b_{2}&b_{3}\end{bmatrix}}={\begin{bmatrix}a_{1}b_{1}&a_{1}b_{2}&a_{1}b_{3}\\a_{2}b_{1}&a_{2}b_{2}&a_{2}b_{3}\\a_{3}b_{1}&a_{3}b_{2}&a_{3}b_{3}\\\end{bmatrix}}\,,}
which is the transpose of the matrix product of the column vector representation of b and the row vector representation of a ,
b ⊗ a = b a ⊺ = [ b 1 b 2 b 3 ] [ a 1 a 2 a 3 ] = [ b 1 a 1 b 1 a 2 b 1 a 3 b 2 a 1 b 2 a 2 b 2 a 3 b 3 a 1 b 3 a 2 b 3 a 3 ] . {\displaystyle \mathbf {b} \otimes \mathbf {a} =\mathbf {b} \mathbf {a} ^{\intercal }={\begin{bmatrix}b_{1}\\b_{2}\\b_{3}\end{bmatrix}}{\begin{bmatrix}a_{1}&a_{2}&a_{3}\end{bmatrix}}={\begin{bmatrix}b_{1}a_{1}&b_{1}a_{2}&b_{1}a_{3}\\b_{2}a_{1}&b_{2}a_{2}&b_{2}a_{3}\\b_{3}a_{1}&b_{3}a_{2}&b_{3}a_{3}\\\end{bmatrix}}\,.}
An n × n matrix M can represent a linear map and act on row and column vectors as the linear map's transformation matrix . For a row vector v , the product v M is another row vector p :
v M = p . {\displaystyle \mathbf {v} M=\mathbf {p} \,.}
Another n × n matrix Q can act on p ,
p Q = t . {\displaystyle \mathbf {p} Q=\mathbf {t} \,.}
Then one can write t = p Q = v MQ , so the matrix product transformation MQ maps v directly to t . Continuing with row vectors, matrix transformations further reconfiguring n -space can be applied to the right of previous outputs.
When a column vector is transformed to another column vector under an n × n matrix action, the operation occurs to the left,
p T = M v T , t T = Q p T , {\displaystyle \mathbf {p} ^{\mathrm {T} }=M\mathbf {v} ^{\mathrm {T} }\,,\quad \mathbf {t} ^{\mathrm {T} }=Q\mathbf {p} ^{\mathrm {T} },}
leading to the algebraic expression QM v T for the composed output from v T input. The matrix transformations mount up to the left in this use of a column vector for input to matrix transformation. | https://en.wikipedia.org/wiki/Row_and_column_vectors |
In linear algebra , two matrices are row equivalent if one can be changed to the other by a sequence of elementary row operations . Alternatively, two m × n matrices are row equivalent if and only if they have the same row space . The concept is most commonly applied to matrices that represent systems of linear equations , in which case two matrices of the same size are row equivalent if and only if the corresponding homogeneous systems have the same set of solutions, or equivalently the matrices have the same null space .
Because elementary row operations are reversible, row equivalence is an equivalence relation . It is commonly denoted by a tilde (~). [ 1 ]
There is a similar notion of column equivalence , defined by elementary column operations; two matrices are column equivalent if and only if their transpose matrices are row equivalent. Two rectangular matrices that can be converted into one another allowing both elementary row and column operations are called simply equivalent .
An elementary row operation is any one of the following moves:
Two matrices A and B are row equivalent if it is possible to transform A into B by a sequence of elementary row operations.
The row space of a matrix is the set of all possible linear combinations of its row vectors. If the rows of the matrix represent a system of linear equations , then the row space consists of all linear equations that can be deduced algebraically from those in the system. Two m × n matrices are row equivalent if and only if they have the same row space.
For example, the matrices
are row equivalent, the row space being all vectors of the form ( a b b ) {\displaystyle {\begin{pmatrix}a&b&b\end{pmatrix}}} . The corresponding systems of homogeneous equations convey the same information:
In particular, both of these systems imply every equation of the form a x + b y + b z = 0. {\displaystyle ax+by+bz=0.\,}
The fact that two matrices are row equivalent if and only if they have the same row space is an important theorem in linear algebra. The proof is based on the following observations:
This line of reasoning also proves that every matrix is row equivalent to a unique matrix with reduced row echelon form. | https://en.wikipedia.org/wiki/Row_equivalence |
23264
20286
ENSG00000100403
ENSMUSG00000022390
Q9UGR2
F8VPP8
NM_017590
NM_001081016
NP_060060
NP_001074485
RoXaN (Rotavirus 'X'-associated non-structural protein) also known as ZC3H7B (zinc finger CCCH-type containing 7B), is a protein that in humans is encoded by the ZC3H7B gene . [ 5 ] RoXaN is a protein that contains tetratricopeptide repeat and leucine-aspartate repeat as well as zinc finger domains. This protein also interacts with the rotavirus non-structural protein NSP3 . [ 5 ]
Rotavirus mRNAs are capped but not polyadenylated , and viral proteins are translated by the cellular translation machinery. This is accomplished through the action of the viral Nonstructural Protein NSP3 which specifically binds the 3' consensus sequence of viral mRNAs and interacts with the eukaryotic translation initiation factor eIF4G I. [ 6 ]
RoXaN (rotavirus X protein associated with NSP3 ) is 110-kDa cellular protein that contains a minimum of three regions predicted to be involved in protein–protein or nucleic acid–protein interactions. A tetratricopeptide repeat region, a protein–protein interaction domain most often found in multiprotein complexes, is present in the amino-terminal region. In the carboxy terminus, at least five zinc finger motifs are observed, further suggesting the capacity of RoXaN to bind other proteins or nucleic acids. Between these two regions exists a paxillin leucine-aspartate repeat (LD) motif which is involved in protein–protein interactions. [ 6 ]
RoXaN is capable of interacting with NSP3 in vivo and during rotavirus infection. Domains of interaction correspond to the dimerization domain of NSP3 (amino acids 163 to 237) and the LD domain of RoXaN (amino acids 244 to 341). The interaction between NSP3 and RoXaN does not impair the interaction between NSP3 and eIF4G I, and a ternary complex made of NSP3, RoXaN, and eIF4G I can be detected in rotavirus-infected cells, implicating RoXaN in translation regulation. [ 6 ]
Expression of RoXaN was found to be correlated with a higher tumor grad in GIST ( gastrointestinal stromal tumors ). [ 7 ]
This article on a gene on human chromosome 22 is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Roxan |
Roy's identity (named after French economist René Roy ) is a major result in microeconomics having applications in consumer choice and the theory of the firm . The lemma relates the ordinary (Marshallian) demand function to the derivatives of the indirect utility function . Specifically, denoting the indirect utility function as v ( p , w ) , {\displaystyle v(p,w),} the Marshallian demand function for good i {\displaystyle i} can be calculated as
where p {\displaystyle p} is the price vector of goods and w {\displaystyle w} is income , [ 1 ] and where the superscript m {\displaystyle {}^{m}} indicates Marshallian demand. The result holds for continuous utility functions representing locally non-satiated and strictly convex preference relations on a convex consumption set , under the additional requirement that the indirect utility function is differentiable in all arguments.
Roy's identity is akin to the result that the price derivatives of the expenditure function give the Hicksian demand functions . The additional step of dividing by the wealth derivative of the indirect utility function in Roy's identity is necessary since the indirect utility function, unlike the expenditure function, has an ordinal interpretation: any strictly increasing transformation of the original utility function represents the same preferences.
Roy's identity reformulates Shephard's lemma in order to get a Marshallian demand function for an individual and a good ( i {\displaystyle i} ) from some indirect utility function.
The first step is to consider the trivial identity obtained by substituting the expenditure function for wealth or income w {\displaystyle w} in the indirect utility function v ( p , w ) {\displaystyle v(p,w)} , at a utility of u {\displaystyle u} :
This says that the indirect utility function evaluated in such a way that minimizes the cost for achieving a certain utility given a set of prices (a vector p {\displaystyle p} ) is equal to that utility when evaluated at those prices.
Taking the derivative of both sides of this equation with respect to the price of a single good p i {\displaystyle p_{i}} (with the utility level held constant) gives:
Rearranging gives the desired result:
with the second-to-last equality following from Shephard's lemma and the last equality from a basic property of Hicksian demand .
For expositional ease, consider the two-goods case. The indirect utility function v ( p 1 , p 2 , w ) {\displaystyle v(p_{1},p_{2},w)} is the value function of the constrained optimization problem characterized by the following Lagrangian: [ 2 ]
By the envelope theorem , the derivatives of the value function v ( p 1 , p 2 , w ) {\displaystyle v(p_{1},p_{2},w)} with respect to the parameters are:
where x 1 m {\displaystyle x_{1}^{m}} is the maximizer (i.e. the Marshallian demand function for good 1). Hence:
This gives a method of deriving the Marshallian demand function of a good for some consumer from the indirect utility function of that consumer. It is also fundamental in deriving the Slutsky equation . | https://en.wikipedia.org/wiki/Roy's_identity |
Roy McWeeny (19 May 1924 – 29 April 2021) was a British academic physicist and chemist.
McWeeny was born in Bradford , Yorkshire in May 1924. His first degree was in physics from the University of Leeds . He then obtained a D.Phil. in mathematical physics and quantum theory under the supervision of Charles Coulson at the Mathematical Institute, University of Oxford .
From 1948 to 1957 he was lecturer in physical chemistry at King's College, University of Durham (King's College is now the University of Newcastle upon Tyne ). From 1957 to 1965 he was at the University of Keele rising to Professor of Theoretical Physics and Theoretical Chemistry . From 1966 to 1982 he was Professor of Theoretical Chemistry at the University of Sheffield . In 1982 he moved to the University of Pisa , Italy where he remained an Emeritus Professor until his death.
In 1996 a celebratory festschrift volume was published in his honour containing original
papers by 132 scientists from 19 countries. [ 1 ] He was awarded the 2006 Spiers Memorial Medal by the Faraday Division of the Royal Society of Chemistry and the Medal Lecture, "Quantum chemistry: The first seventy years", was published in Faraday Discussions . [ 2 ] [ 3 ] He has served on the editorial board of Molecular Physics , Chemical Physics Letters and International Journal of Quantum Chemistry .
He has written many scientific papers and seven books, of which perhaps the best known are Coulson's Valence in 1979, an update of the famous book by Charles Coulson originally written in 1951, and the two editions of Methods of Molecular Quantum Mechanics , (the first edition with B. T. Sutcliffe in 1969 [ 4 ] and the second edition alone in 1989). He wrote several chapters in the three volumes of the Handbook of Molecular Physics and Quantum Chemistry . [ 5 ] In 1963 he wrote Symmetry: an introduction to group theory and its applications . [ 6 ]
From 2002 he edited an open-access series of Basic Books in Science , several of which he authored himself. He was also an elected member of the International Academy of Quantum Molecular Science and the European Academy of Arts, Sciences and the Humanities .
McWeeny died in Pisa , Italy in April 2021 at the age of 96. [ 7 ] | https://en.wikipedia.org/wiki/Roy_McWeeny |
The Royal Academy of Engineering ( RAEng ) is the United Kingdom 's national academy of engineering .
The Academy was founded in June 1976 as the Fellowship of Engineering with support from Prince Philip, Duke of Edinburgh , who became the first senior fellow and remained so until his death. The Fellowship was incorporated and granted a royal charter on 17 May 1983 and became the Royal Academy of Engineering on 16 March 1992. It is governed according to the charter and associated statutes and regulations (as amended from time to time). [ 3 ] [ 4 ] In June 2024 His Majesty the King became Patron of the Academy. [ 1 ]
Conceived in the late 1960s, during the Apollo space program and Harold Wilson 's espousal of " white heat of technology ", the Fellowship of Engineering was born in the year of Concorde 's first commercial flight. [ 5 ]
The Fellowship's first meeting, at Buckingham Palace on 11 June 1976, enrolled 126 of the UK's leading engineers. [ 6 ] The first fellows included Air Commodore Sir Frank Whittle , the jet engine developer, the structural engineer Sir Ove Arup , radar pioneer Sir George G. MacFarlane , the inventor of the bouncing bomb , Sir Barnes Wallis , Francis Thomas Bacon , the inventor of the alkaline fuel cell , and father of the UK computer industry Sir Maurice Wilkes . The Fellowship's first president, Christopher Hinton , had driven the UK's supremacy in nuclear power . [ 7 ]
The Fellowship focused on championing excellence in all fields of engineering. Activities began in earnest in the mid-1970s with the Distinction lecture series, now known as the Hinton lectures. The Fellowship was asked to advise the Department of Industry for the first time, and the Academy became host and presenter of the MacRobert Award . [ 8 ]
In the 1980s, the Fellowship received its own royal charter along with its first government grant-in-aid . At the same time, it also received significant industrial funding, initiated its research programme to build bridges between academia and industry, and opened its doors to international and honorary fellows. [ 9 ]
In 1990, the Academy launched its first major initiative in education, Engineering Education Continuum, which evolved into the BEST Programme [ 10 ] and Shape the Future and Tomorrow's Engineers. [ 11 ]
The Academy's increasing level of influence – in policy, research and education – was recognized when it was granted a royal title and became The Royal Academy of Engineering in 1992. [ 12 ] In 2014 the academy launched its annual Africa Prize. [ 13 ]
The Academy's current logo [ 14 ] is inspired by the Neolithic hand axe , humans' first technological advance, which was taken to be a symbol appropriate to the Academy, supposedly representative of the ever-changing relationship between humanity and technology. [ 15 ]
The Academy's premises, 3–4 Carlton House Terrace , are in a Grade I listed building overlooking St James's Park , designed by architect John Nash and owned by the Crown Estate . The Academy shares the Terrace with two of its sister academies, the British Academy and the Royal Society , as well as other institutes.
The building was renamed Prince Philip House, [ 16 ] after renovation works were completed in 2012.
The Academy is instrumental in two policy alliances set up in 2009 to provide coherent advice on engineering education and policy across the profession: Education for Engineering [ 17 ] and Engineering the Future . [ 18 ]
The Academy is one of four agencies that receive funding from the UK's Department for Business, Innovation and Skills for activities that support government policy on public understanding of science and engineering. [ 19 ]
As part of its programme to communicate the benefits and value of engineering to society, the Academy publishes a quarterly magazine, Ingenia [1] . The Academy says that Ingenia is written for a non-specialist audience and is "aimed at all those with an interest in engineering, whether working in business and industry, government, academia or the financial community". The Academy also makes Ingenia available to A-Level students in 3,000 schools in the UK.
The president of the Royal Academy of Engineering, the elected officer of the Academy, presides over meetings of the council. The president is elected for a single term of not more than five years.
The Fellowship currently includes more than 1,500 engineers from all sectors and disciplines of engineering. The fellows, distinguished by the title Fellow of The Royal Academy of Engineering and the post-nominal designation FREng , lead, guide, and contribute to the Academy's work and provide expertise. [ 20 ]
The Royal Fellows of the Academy are the Duke of Kent and the Princess Royal .
The Academy strives to ensure that the pool of candidates for election to the Fellowship better reflects the diverse make-up of society as a whole. It set up the Proactive Membership Committee [ 21 ] in 2008 to identify and support the nomination of candidates from underrepresented areas, with the aim of boosting the number of women candidates, engineers from industry and small and medium enterprises , those from emerging technologies and ethnically diverse backgrounds. [ 22 ] | https://en.wikipedia.org/wiki/Royal_Academy_of_Engineering |
The Royal Aeronautical Society , also known as the RAeS , is a British multi-disciplinary professional institution dedicated to the global aerospace community. Founded in 1866, it is the oldest aeronautical society in the world. [ 1 ] Members, Fellows, and Companions of the society can use the post-nominal letters MRAeS, FRAeS, or CRAeS, respectively. [ 2 ]
The objectives of The Royal Aeronautical Society include: to support and maintain high professional standards in aerospace disciplines; to provide a unique source of specialist information and a local forum for the exchange of ideas; and to exert influence in the interests of aerospace in the public and industrial arenas, including universities.
The Royal Aeronautical Society is a worldwide society with an international network of 67 branches. Many practitioners of aerospace disciplines use the Society's designatory post-nominals such as FRAeS , CRAeS, MRAeS, AMRAeS, and ARAeS (incorporating the former graduate grade, GradRAeS).
The RAeS headquarters is at 4 Hamilton Place , London, W1J 7BQ. [ 3 ] In addition to offices for its staff the building is used for Society events [ 4 ] and parts of the building are available for private hire. [ 5 ]
Branches deliver membership benefits and disseminate aerospace information. As of September 2013, branches located in the United Kingdom include: Belfast, Birmingham, Boscombe Down , Bristol, Brough , Cambridge, Cardiff, Chester, Christchurch, Coventry, Cranfield , Cranwell , Derby, FAA Yeovilton , Farnborough , Gatwick, Gloucester & Cheltenham, Hatfield, Heathrow, Highland, Isle of Wight, Isle of Man, Loughborough, Manchester, Marham , Medway, Oxford, Preston, Prestwick, Sheffield, Solent, Southend, Stevenage, Swindon, Weybridge, and Yeovil.
The RAeS international branch network includes: Adelaide, Auckland, Blenheim, Brisbane, Brussels, Canberra, Canterbury, Cyprus, Dublin, Hamburg, Hamilton, Hong Kong, Malaysia, Melbourne, Montreal, Munich, Palmerston North, Paris, Perth, Seattle, Singapore, Sydney, Toulouse, and the UAE.
Divisions of the Society have been formed in countries and regions that can sustain a number of Branches. Divisions operate with a large degree of autonomy, being responsible for their own branch network, membership recruitment, subscription levels, conference and lecture programmes.
Specialist Groups covering various facets of the aerospace industry exist under the overall umbrella of the Society, with the aim of serving the interests of both enthusiasts and industry professionals. Their remit is to consider significant developments in their field through conferences and lectures, with the intention of stimulating debate and facilitating action on key industry issues. The Groups also act as focal points for all enquiries to the Society concerning their specialist subject matter.
As of September 2013, the Specialist Group committees are: Aerodynamics, Aerospace Medicine, Air Power, Air Law, Air Transport, Airworthiness & Maintenance, Avionics & Systems, Environment, Flight Operations, Flight Simulation, [ 7 ] Flight Test, General Aviation, Greener by Design, Historical, Human Factors, Human Powered Flight, Propulsion, Rotorcraft, Space, Structures & Materials, UAS, Weapons Systems & Technologies, and Women in Aviation & Aerospace.
In 2009, the Royal Aeronautical Society formed a group of experts to document how to better simulate aircraft upset conditions, and thus improve training programmes. [ 8 ]
The Society was founded in January 1866 with the name "The Aeronautical Society of Great Britain" and is the oldest aeronautical society in the world. [ 9 ] Early or founding members included James Glaisher , Francis Wenham , the Duke of Argyll , and Frederick Brearey . [ 10 ] In the first year, there were 65 members, at the end of the second year, 91 members, and in the third year, 106 members. [ 11 ] Annual reports were produced in the first decades. In 1868 the Society held a major exhibition at London's Crystal Palace with 78 entries. John Stringfellow 's steam engine was shown there. [ 11 ] [ 12 ] [ 13 ] The Society sponsored the first wind tunnel in 1870–71, designed by Wenham and Browning. [ 11 ]
In 1918, the organisation's name was changed to the Royal Aeronautical Society. [ 14 ]
In 1923 its principal journal was renamed from The Aeronautical Journal to The Journal of the Royal Aeronautical Society and in 1927 the Institution of Aeronautical Engineers Journal was merged into it. [ 15 ]
In 1940, the RAeS responded to the wartime need to expand the aircraft industry. The Society established a Technical Department to bring together the best available knowledge and present it in an authoritative and accessible form – a working tool for engineers who might come from other industries and lack the specialised knowledge required for aircraft design. This technical department became known as the Engineering Sciences Data Unit (ESDU) and eventually became a separate entity in the 1980s.
In 1987 the ' Society of Licensed Aircraft Engineers and Technologists ', previously called the 'Society of Licensed Aircraft Engineers' was incorporated into the Royal Aeronautical Society.
The following have served as President of the Royal Aeronautical Society: [ 16 ]
In addition to the award of Fellowship of the Royal Aeronautical Society (FRAeS), the Society awards several other medals and prizes. These include its Gold, Silver, and Bronze medals. The very first gold medal was awarded in 1909 to the Wright Brothers . [ 34 ] Although it is unusual for more than one medal (in each of the three grades) to be awarded annually, since 2004 the Society has also periodically awarded team medals (Gold, Silver, and Bronze) for exceptional or groundbreaking teamwork in aeronautical research and development. Others awarded have included the R. P. Alston Memorial Prize for developments in flight-testing, the Edward Busk prize for applied aerodynamics, the Wakefield Medal for advances in aviation safety, and an Orville Wright Prize. [ 35 ] Honorary Fellowships and Honorary Companionships are awarded as well.
The Sir Robert Hardingham Sword The Sir Robert Hardingham Sword is awarded in recognition of outstanding service to the RAeS by a member of the Society. Nominally an annual award, in practice the award is only made about one year in two.
Notable Gold Medal recipients include:
The annual Henson & Stringfellow Lecture and Dinner is hosted yearly by the Yeovil Branch of the Royal Aeronautical Society, held at Westland Leisure Complex, and is a key social and networking event of the Yeovil lecture season. It is a black tie event attracting over 200 guests drawn from all sectors of the aerospace community.
John Stringfellow created, alongside William Samuel Henson , the first powered flight aircraft , developed in Chard, Somerset , which flew unmanned in 1848, 63 years prior to brothers Wilbur & Orville Wrights' flight. [ 43 ] [ 44 ] [ 45 ] [ 46 ] [ 47 ] [ 48 ]
The Wilbur & Orville Wright Named Lecture was established in 1911 to honour the Wright brothers , the successful and experienced mechanical engineers who completed the first successful controlled powered flight on 17 December 1903. The Wilbur & Orville Wright Lecture is the principal event in the Society’s year, given by distinguished members of the US and UK aerospace communities.
The 99th Lecture was given by Piers Sellers , astronaut, on 9 December 2010 at the Society's Headquarters in London. [ 49 ]
The 100th Lecture was given by Suzanna Darcy-Henneman , Chief Pilot & Director of Training, Boeing Commercial Airplanes , on 8 December 2011. [ 50 ]
The 101st Lecture was given by Tony Parasida, corporate vice president, The Boeing Company , on 20 December 2012. [ 51 ]
The 102nd Lecture was given by Thomas Enders , CEO of EADS , on 12 December 2013. [ 52 ]
The 103rd Lecture was given by Patrick M Dewar, executive vice president, Lockheed Martin International in December 2014. [ 53 ]
The 104th Lecture was given by Nigel Whitehead, Group Managing Director – Programmes and Support, BAE Systems plc in December 2015. [ 54 ]
The 105th Lecture was given by ACM Sir Stephen Hillier, Chief of the Air Staff, Royal Air Force on 6 December 2016. [ 55 ]
The 106th Lecture was given by Martin Rolfe, chief executive officer, NATS on 5 December 2017. [ 56 ]
The 107th Lecture was given by Leanne Caret , Vice President, The Boeing Company and President & CEO, Boeing Defense, Space & Security on 4 December 2018. [ 57 ]
The 108th Lecture was given by David Mackay FRAeS, Chief Pilot, Virgin Galactic on 10 December 2019. [ 58 ]
The Amy Johnson Named Lecture [ 59 ] was inaugurated in 2011 by the Royal Aeronautical Society's Women in Aviation and Aerospace Committee [ 60 ] to celebrate a century of women in flight [ 61 ] and to honour Britain's most famous woman aviator. The Lecture is held on or close to 6 July every year to mark the date in 1929 when Amy Johnson was awarded her pilot’s licence . The Lecture is intended to tackle serious issues of interest to a wide audience, not just women. High-profile women from industry are asked to lecture on a topic that speaks of future challenges of interest to everyone. [ 62 ]
Carolyn McCall , chief executive of EasyJet , delivered the Inaugural Lecture on 6 July 2011 at the Society's Headquarters in London. [ 63 ]
The second Amy Johnson Named Lecture was delivered by Marion C. Blakey , president and chief executive of Aerospace Industries Association (AIA), on 5 July 2012.
The third Lecture was delivered by Gretchen Haskins, former Group Director of the Safety Regulation Group of the UK Civil Aviation Authority (CAA), on 8 July 2013. [ 64 ]
In 2017, Katherine Bennett OBE FRAeS, Senior Vice President Public Affairs, Airbus gave the Amy Johnson Lecture [ 65 ] and in 2018 Air Vice-Marshal Sue Gray , CB, OBE from the Royal Air Force gave the Amy Johnson Lecture in honour of the 100th anniversary of the RAF. [ 66 ]
The Sopwith Lecture was established in 1990 to honour Sir Thomas Sopwith CBE, Hon FRAeS. In the years prior to World War I, Sopwith became England’s premier aviator and established the first authoritative test pilot school in the world. He also founded England’s first major flight school. Between 1912 and 1920 Sopwith’s Company produced over 16,000 aircraft of 60 types.
In 2017 the lecture was delivered by Tony Wood, chief operating officer of Meggitt PLC . [ 67 ]
In 2018 the lecture was delivered by Group Captain Ian Townsend ADC MA RAF, Station Commander, RAF Marham . [ 68 ]
In 2019 the lecture was delivered by Billie Flynn, F-35 Lightning II Test Pilot, Lockheed Martin . [ 69 ]
In 2020 the lecture was delivered online by Dirk Hoke, CEO, Airbus Defence & Space . [ 70 ]
The July 18th.,1975 edition of the society's Journal included the first use of the misattributed term, " Beam Me Up, Scotty ", in a sentence, viz:"...in a sort of, 'Beam me up, Scotty', routine". | https://en.wikipedia.org/wiki/Royal_Aeronautical_Society |
The Royal Astronomical Society ( RAS ) is a learned society and charity that encourages and promotes the study of astronomy , solar-system science , geophysics and closely related branches of science. [ 3 ] Its headquarters are in Burlington House , on Piccadilly in London . [ 4 ] The society has over 4,000 members, known as fellows, most of whom are professional researchers or postgraduate students. [ 3 ] Around a quarter of Fellows live outside the UK. [ 3 ]
The society holds monthly scientific meetings in London, and the annual National Astronomy Meeting at varying locations in the British Isles . The RAS publishes the scientific journals Monthly Notices of the Royal Astronomical Society , Geophysical Journal International and RAS Techniques and Instruments , along with the trade magazine Astronomy & Geophysics . [ 5 ]
The RAS maintains an astronomy research library , engages in public outreach and advises the UK government on astronomy education. The society recognises achievement in astronomy and geophysics by issuing annual awards and prizes, with its highest award being the Gold Medal of the Royal Astronomical Society . The RAS is the UK adhering organisation to the International Astronomical Union and a member of the UK Science Council .
The society was founded in 1820 as the Astronomical Society of London to support astronomical research. At that time, most members were ' gentleman astronomers ' rather than professionals. It became the Royal Astronomical Society in 1831 on receiving a Royal Charter from William IV . [ 6 ]
In 1846 the RAS absorbed the Spitalfields Mathematical Society , which had been founded in 1717 but was suffering from a decline in membership and dwindling finances. The nineteen remaining members of the mathematical society were given free lifetime membership of the RAS; in exchange, their society's extensive library was donated to the RAS. [ 7 ]
Between 1835 and 1916 women were not allowed to become fellows, but Anne Sheepshanks , Lady Margaret Lindsay Huggins, Agnes Clerke , Annie Jump Cannon and Williamina Fleming were made honorary members. In 1886 Isis Pogson was the first woman to attempt election as a fellow of the RAS, being nominated (unsuccessfully) by her father and two other fellows. All fellows had been male up to this time and her nomination was withdrawn when lawyers claimed that under the provisions of the society's royal charter, fellows were only referred to as he and as such had to be men. A Supplemental Charter in 1915 opened up fellowship to women. On 14 January 1916, Mary Adela Blagg , Ella K Church, A Grace Cook , Irene Elizabeth Toye Warner and Fiammetta Wilson were the first five women to be elected to Fellowship. [ 8 ] [ 9 ]
One of the major activities of the RAS is publishing refereed journals. It publishes three primary research journals: Monthly Notices of the Royal Astronomical Society for topics in astronomy; Geophysical Journal International for topics in geophysics (in association with the Deutsche Geophysikalische Gesellschaft ); and RAS Techniques & Instruments for research methods in those disciplines. The society also publishes a trade magazine for members, Astronomy & Geophysics .
The history of journals published by the RAS (with abbreviations used by the Astrophysics Data System [ 10 ] ) is:
Full members of the RAS are styled Fellows, and may use the post-nominal letters FRAS . Fellowship is open to anyone over the age of 18 who is considered acceptable to the society. As a result of the society's foundation in a time before there were many professional astronomers, no formal qualifications are required. However, around three quarters of fellows are professional astronomers or geophysicists . Most of the other fellows are postgraduate students studying for a PhD in those fields, but there are also advanced amateur astronomers , historians of science who specialise in those disciplines, and other related professionals. The society acts as the professional body for astronomers and geophysicists in the UK and fellows may apply for the Science Council's Chartered Scientist status through the society. The fellowship passed 3,000 in 2003.
In 2009 an initiative was launched for those with an interest in astronomy and geophysics but without professional qualifications or specialist knowledge in the subject. Such people may join the Friends of the RAS, which offers popular talks, visits and social events. [ 13 ]
The Society organises an extensive programme of meetings:
The biggest RAS meeting each year is the National Astronomy Meeting , a major conference of professional astronomers. It is held over 4–5 days each spring or early summer, usually at a university campus in the United Kingdom. Hundreds of astronomers attend each year.
More frequent smaller 'highlight' meetings feature lectures about research topics in astronomy and geophysics, often given by winners of the society's awards . They are normally held in Burlington House in London on the afternoon of the second Friday of each month from October to May. The talks are intended to be accessible to a broad audience of astronomers and geophysicists, and are free for anyone to attend (not just members of the society). Formal reports of the meetings are published in The Observatory magazine. [ 14 ]
Specialist discussion meetings are held on the same day as each highlight meeting. These are aimed at professional scientists in a particular research field, and allow several speakers to present new results or reviews of scientific fields. Usually two discussion meetings on different topics (one in astronomy and one in geophysics) take place simultaneously at different locations within Burlington House, prior to the day's highlight meeting. They are free for members of the society, but charge a small entry fee for non-members. [ 14 ]
The RAS holds a regular programme of public lectures aimed at a general, non-specialist, audience. These are mostly held on Tuesdays once a month, with the same talk given twice: once at lunchtime and once in the early evening. The venues have varied, but are usually in Burlington House or another nearby location in central London. The lectures are free, though some popular sessions require booking in advance. [ 15 ]
The society occasionally hosts or sponsors meetings in other parts of the United Kingdom, often in collaboration with other scientific societies and universities.
The Royal Astronomical Society has a more comprehensive collection of books and journals in astronomy and geophysics than the libraries of most universities and research institutions. The library receives some 300 current periodicals in astronomy and geophysics and contains more than 10,000 books from popular level to conference proceedings. Its collection of astronomical rare books is second only to that of the Royal Observatory in Edinburgh in the UK. The RAS library is a major resource not just for the society but also the wider community of astronomers, geophysicists, and historians. [ 16 ]
The society promotes astronomy to members of the general public through its outreach pages for students, teachers, the public and media researchers. The RAS has an advisory role in relation to UK public examinations , such as GCSEs and A Levels .
The RAS sponsors topical groups, many of them in interdisciplinary areas where the group is jointly sponsored by another learned society or professional body:
The first person to hold the title of President of the Royal Astronomical Society was William Herschel , though he never chaired a meeting, and since then the post has been held by many distinguished astronomers. The post has generally had a term of office of two years, but some holders resigned after one year e.g. due to poor health. Francis Baily and George Airy were elected a record four times each. Baily's eight years in the role are a record (Airy served for seven). Since 1876 no one has served for more than two years in total.
The current president is Mike Lockwood, who began his term in May 2024 and will serve for two years. [ 17 ]
The highest award of the Royal Astronomical Society is its Gold Medal , which can be awarded for any purpose but most frequently recognises extraordinary lifetime achievement. [ 18 ] Among the recipients best known to the general public are Albert Einstein in 1926, and Stephen Hawking in 1985.
Other awards are for particular topics in astronomy or geophysics research, which include the Eddington Medal , the Herschel Medal , the Chapman Medal and the Price Medal . Beyond research, there are specific awards for school teaching (Patrick Moore Medal), public outreach (Annie Maunder Medal), instrumentation ( Jackson-Gwilt Medal ) and history of science (Agnes Mary Clerke Medal). Lectureships include the Harold Jeffreys Lectureship in geophysics , the George Darwin Lectureship in astronomy , and the Gerald Whitrow Lectureship in cosmology . [ 19 ] Each year, the society grants a handful of free memberships for life (termed honorary fellowship) to prominent researchers resident outside the UK. [ 20 ]
The society occupies premises at Burlington House , London, where a library and meeting rooms are available to fellows and other interested parties. The society represents the interests of astronomy and geophysics to UK national and regional, and European government and related bodies, and maintains a press office, through which it keeps the media and the public at large informed of developments in these sciences. The society allocates grants to worthy causes in astronomy and geophysics, and assists in the management of the Paneth Trust . [ 21 ] | https://en.wikipedia.org/wiki/Royal_Astronomical_Society |
The Royal Astronomical Society of Canada ( RASC ) is a national, non-profit, charitable organization devoted to the advancement of astronomy and related sciences. At present, there are 30 local branches of the Society, called Centres, in towns and cities across the country from St. John's, Newfoundland , to Victoria, British Columbia , and as far north as Whitehorse, Yukon . There are about 4500 members from coast to coast to coast, and internationally. The membership is composed primarily of amateur astronomers and also includes numerous professional astronomers and astronomy educators. The RASC is the Canadian equivalent of the British Astronomical Association .
The RASC has its original roots in Toronto, Ontario , Canada , where in 1868 a group of friends began meeting as part of the "Toronto Astronomical Club." The club was formally incorporated as "The Astronomical and Physical Society of Toronto" in 1890, and this is considered the founding date of the Society. The club grew over time, and by 1900, surrounding communities were affiliated with the group. On 1903 March 3, the club was renamed to "The Royal Astronomical Society of Canada" after petitioning King Edward VII to use the prefix "Royal" in the group's name. At the time it had 120 members. In the more than a century since its formal incorporation, the RASC has expanded across Canada with Centres in 30 cities, reaching every province of Canada with the exception of Prince Edward Island. [ 1 ]
The RASC mandate is five-fold:
The Society Office in Toronto employs four staff.
Centre Representatives
Past Presidents
Editors
Staff (Non-voting)
Permanent Committees (Chairs)
The RASC conducts business through a Board of Directors with regular meetings, plus two scheduled meetings at the General Assembly, which is traditionally held on a weekend in May (GA). The GA is hosted by one of the Centres, with annual meetings alternating between eastern and western Canada. Meetings follow Robert's Rules of Order and are governed by the By-Laws of the Society.
Each of the Centres of the Society conduct a variety of activities of interest to its members and to the public. At regular meetings, well-known professional and amateur astronomers give lectures on a variety of topics of current interest. In addition, there are study and special-interest groups. Most Centres publish their own newsletters and hold their own group-observing events. Some members take part in regular observations of variable stars, lunar occultations, sunspots, meteors, comets, and other phenomena; others develop special skills such as astroimaging at workshops.
Most Centres have public education programs, including special outreach star nights when the public is given an opportunity to look through a telescope courtesy of a RASC volunteer. [ 3 ] In 2009, the International Year of Astronomy , many Centres were instrumental in organizing events of educational astronomy outreach for their local communities. [ 4 ] The RASC's Light-Pollution Abatement Committee also administers Canada's Dark-sky preserve program, working with provincial and national parks to create management agreements to preserve the darkness of the nighttime sky.
Many Centres have observing equipment, libraries, and observing locations. For example, the Victoria Centre has telescopes and a large library of books and periodicals available to members in good standing. Additionally the Victoria Centre built and operates the "RASC Victoria Centre Observatory (RASC VCO)" which is located at the Dominion Astrophysical Observatory . The Society has recently purchased a robotic telescope.
The RASC publishes a number of books and periodicals, and issues awards to recognize accomplishments in astronomy and outreach activities.
The annual Observer's Handbook (2021: ISBN 978-1-927879-23-8 ) can be found in observatory control rooms and astronomers' reference shelves worldwide. Published in the autumn of the year, the 352-page Handbook contains detailed information on astronomical events in the upcoming year and is an in-depth reference of significant astronomical data such as observing techniques, physical constants, and optical properties of telescopes. The first two editions were published in 1907 and 1908, respectively. For the following two years information from the Observer's Handbook was integrated into the main Journal, but it was decided eventually that the Handbook return to circulation. The 3rd edition of the Observer's Handbook was published in January 1911, with Editor C. A. Chant aiming to publish the 1912 edition in the autumn of that year. [ 5 ] The 110th edition was published in 2017, covering events in 2018. In addition, for the first time, a USA Edition was created for the American audience, in cooperation with the Astronomical League. The publication is currently in its 113th edition published in 2020, covering the events of 2021.
Editor
1958–1970
Editor
2017–
The Journal of the Royal Astronomical Society of Canada (ISSN 0035-872X) (bib. code - JRASC), continuously published since 1907, is a bi-monthly periodical that features articles about Canadian astronomers, activities of the RASC and its Centres, and peer-reviewed research papers.
The Observer's Calendar (2017: ISBN 978-1-927879-07-8 ) features photos of an astronomical subject taken by amateur astronomers using CCD and other camera equipment on amateur instruments. Each photograph is given an informative caption along with comprehensive astronomical data for dates throughout each month.
Explore the Universe Guide; An Introduction to the RASC ETU Certificate Program ( ISBN 978-1-927879-09-2 ) is a book for the casual backyard astronomer who is thinking about getting serious. | https://en.wikipedia.org/wiki/Royal_Astronomical_Society_of_Canada |
The Royal Australian Chemical Institute ( RACI ) is both the qualifying body in Australia for professional chemists and a learned society promoting the science and practice of chemistry in all its branches. [ 1 ] The RACI hosts conferences, seminars and workshops. It is the professional body for chemistry in Australia, with the ability to award the status of Chartered Chemist (CChem) to suitably qualified candidates.
The RACI was formed as the Australian Chemical Institute in Sydney in September 1917. The driving force was David Orme Masson , professor of chemistry at the University of Melbourne . It was incorporated under the Companies Act in New South Wales in 1923. It was given a royal charter in 1932, but it was not until a supplementary royal charter in 1953 that "Royal" was added to the title of the institute. It moved to Melbourne in 1934. It was incorporated in Victoria in 2000. Since 1993, the institute has had its office at 21 Vale Street, North Melbourne , VIC 3051, Australia. [ 2 ]
The RACI is a member of the Federation of Australian Scientific and Technological Societies (FASTS), [ 3 ] and the Federation of Asian Chemical Societies (FACS). [ 4 ]
It has branches in all states and territories in Australia and divisions for the following areas of chemistry:
In 2022, the Green and Sustainable Chemistry (GASC) National Group [ 5 ] was established.
In addition to the divisions having organised conferences, they have co-operated in running occasional national conventions since 1953. [ 2 ]
A member of the Royal Australian Chemical Institute is designated with the honorific postnominal "MRACI". [ 6 ] As the professional body for chemistry in Australia, the institute is empowered to award the status of Chartered Chemist ("CChem") to suitably qualified candidates. Election to Fellow of the institute ("FRACI") is dependent on a position of eminence, services rendered, academic honours, experience and status, creative achievement, responsibility and contribution to chemical science, and recommendation by the RACI Assessment Committee. [ 7 ] The institute also accepts undergraduate and postgraduate student members, associate members, school affiliate members, and industry affiliate members. [ 6 ]
Chemistry in Australia [ 8 ] is a magazine published by the RACI monthly. It contains news, reviews of books and chemical software, as well as reports and stories aimed at a broad chemical audience. It is free to read online, and also available as a hard copy for members. It was established in 1934 as the Journal and Proceedings of the Australian Chemical Institute . [ 2 ]
The Chemical Education Division publishes the Australian Journal of Education in Chemistry ( ISSN 1445-9698 ). [ 9 ] It was formally called Chemeda: The Australian Journal of Chemical Education . It includes articles on chemical education at all levels in schools and universities, including experiments from the Australasian Chemistry Enhanced Laboratory Learning (ACELL) Project.
The RACI grants several annual awards at branch, divisional, and national levels. [ 10 ] A selection of the more prestigious awards is outlined below.
The H. G. Smith Memorial Award is the premier award of the RACI. It is awarded annually to a member who has contributed most to the development of a branch of chemical science, judged by their publication record during the ten years (or equivalent relative to opportunity) preceding the award. The recipient is required to be a current member for a minimum of 3 years. [ 11 ] Notable recipients of the award include: [ 12 ]
The Cornforth Medal is awarded for the most outstanding PhD thesis submitted by a member. [ 13 ] The thesis must be completed under the auspices of an Australian university. [ 14 ] The medal is named after Sir John Cornforth , the only Australian Nobel Prize winner in chemistry.
The Rennie Memorial Medal is awarded to a member with less than 8 years of professional experience since completing their most recent relevant qualification, who has made the most significant contribution to chemical science. [ 15 ]
The Leighton Memorial Medal is awarded to individuals in recognition of eminent services to chemistry in Australia. [ 16 ]
The Ollé Prize for a member of the institute who submits the "best treatise, writing or paper" on any subject relevant to the institute's interests.
The Adrien Albert award recognises the enormous contributions made by Prof. Adrien Albert to medicinal chemistry. It is the premier award of the Medicinal Chemistry and Chemical Biology Division and is given for sustained, outstanding research in the field of medicinal or agricultural chemistry or chemical biology. The research upon which the award is made must be conducted wholly, or largely, within Australia and New Zealand . | https://en.wikipedia.org/wiki/Royal_Australian_Chemical_Institute |
The Royal Australian Naval Bridging Train was a unique unit of the Royal Australian Navy . It was active only during the First World War , where it served in the Gallipoli and the Sinai and Palestine Campaigns . The Train was formed in February 1915 and stood down in May 1917. Throughout its existence, it was composed of Royal Australian Naval Reservists under the command of Lieutenant Commander Leighton Bracegirdle . Normally under the command of the British IX Corps , the Train also supported the I ANZAC Corps and Imperial Camel Corps in the defence of the Suez Canal .
They were the only Australian naval unit serving in a European theatre of war. They were therefore bent on proving, both to the Royal Navy and to the British Army, that they could overcome any difficulties. [ 2 ]
The Train was Australia's most decorated naval unit of the First World War, with more than 20 decorations awarded to its sailors.
By 1915, with the prompt seizure of Germany's Pacific possessions , it was becoming apparent that there would be very little for the Royal Australian Naval Brigade to do beyond securing Australia's ports. It was also becoming obvious that trench warfare was going to be the main feature of the Western Front , and that engineering units were in strong demand. Reports reached Australia that even a Naval contingent would be acceptable, as the 63rd (Royal Naval) Division , consisting of Royal Marines and Naval Reservists, was preparing to join the Western Front.
Naval Board was quick to move of these reports, making this recommendation to the Minister for Defence:
The Naval Board, having consulted the Chief of the General Staff as to most suitable method by which services of RANR officers and men can be made use of in the present war, propose that an offer be made to the Home Government to supply two Bridging Trains, completed to war establishment, the same to be manned by naval ratings drawn mainly from ranks of RANR It is proposed that, while retaining naval ranks and ratings in all other respects, the men comprising these trains should be paid, organised, equipped, and trained under military supervision. [ 3 ]
On 12 February, the Government made the offer to the Imperial Government to provide one Bridging Train, in accordance with "Imperial War Establishments." Within a week, the offer was accepted. [ 4 ]
Command of the Train was given to Lieutenant Commander Bracegirdle , with Lieutenant (later, Commander) Thomas Bond DSO VD RANR as his First Lieutenant . Both officers had been involved in the surrender of German New Guinea , Bond had led the attack on the wireless station, and Bracegirdle had been left in command of the garrison when Commander Beresford was evacuated for medical treatment. [ 5 ] The two officers were appointed on 24 February 1915.
The Train grew to 115 men by 12 March and was encamped on Kings Domain, Melbourne . Bracegirdle and Bond had also discovered that no one left in Australian in either the Army or the Navy had any useful knowledge on the subject of bridging trains, they would have to wait for their pontoons and vehicles to be built – meaning a wait of at least six weeks before they would be able to begin training, and that almost all of their unit would need to be taught to ride, on very few horses.
The Train embarked upon HMAT A39 Port MacQuarie on 3 June with, according to the Train's Medical Officer, Dr E.W. Morris, [ 6 ] 5 officers, 3 warrant officers , 267 Petty Officers and other ranks , 26 reinforcements, 412 horses, 5 6-horse pontoons and tressle waggons, and 8 other vehicles. They were headed to Chatham, England to be trained in the construction of pontoons. Of course, this was the First World War. The Train reached Port Said, Egypt on 17 July 1915, and was issued orders to continue on to England. The next day, the 18th, they received orders to the Dardanelles . Arriving at the Greek isle of Imbros , yet more new orders were received, transferring control of the Train from the British Admiralty , which had been given operational control of the Royal Australian Navy by the Federal Government on 10 August 1914, [ 7 ] to the British Army and attaching it to IX Army Corps under Lt. General Stopford which was to land at Suvla Bay on 7 August.
While at Imbros, the Train received a grand total of five days of instruction on the use of their pontoons, a task which needed six days worth of unloading and reloading the equipment. After this minimal training, they were considered ready to land under enemy fire.
At 5am on 6 August 1915, the Train, embarked upon HMAT A53 Itria, reached its designated anchorage, and the landing was well underway. A party was sent ashore to find the best place to continue the landing, and where to later build the infrastructure to reinforce the Corps. Mid-morning, when Bracegirdle attempted to confer with the IX Corps Chief Engineer, Brigadier-General E.H. Bland CB CMG RE , as ordered, but was unable to be found. This forced the Train to sit idle until late afternoon when they were tasked with putting together a temporary pier at A Landing, which had been left without a party to construct it. It was the second day at Suvla when the Train began to come into its own, constructing two piers and rowing the second into place at A Beach, a trip of approximately 2 miles (3.2 km), for use by the lifeboats evacuating injured soldiers. The Train assembled the 110-metre-long structure in 20 minutes. [ 8 ] The next few days were occupied with constructing further piers as well as landing troops and supplies to assist the landing and shifting their base from their landing point to Kangaroo Beach.
Soon, the Train was put in charge of the landing's water supply, something that had been neglected during the early stage of the campaign. As there was no supply available, water had to be brought by sea, often in petrol tins. This responsibility was given to the Train on 12 August, they were able to source three fire engines and some hoses, which, with the Train's pontoons were used to pump supplies brought from transport ships to tanks on the beach. The fire hoses were kept under guard, and eventually replaced with metal pipe as soldiers would constantly make holes in it to get at the water inside. [ 8 ] This was just some of the work that saw the Train removed from the 11th Division and directly attached to the IX Corps Engineers, becoming responsible for all work afloat or on the beach up to the high-water mark that the Navy might require.
The principal duties allotted to the unit by the Royal Navy were as follows: Water supply, care of landing-piers, discharging of stores from store-ships and transports, lighterage of same to the shore, salving of lighters and steamboats wrecked during gales, assisting in salving of T.B.D. Louis , disembarking of troops with their baggage on all beaches, and of munitions and stores. ... The duties allotted to the unit by the GOC the IX Army Corps were briefly as follows : Control and issue of all engineer and trench stores and materials, care and issue of trench bombs and demolition stores (for some weeks after landing, and until proper ordnance dumps were established), erection of high-explosive magazines, dug-outs, cookhouses, and galleys, assembly of hospital huttings, construction of iron frames for front-line wire entanglements; and the manning and control of the steam-tug Daphne . [ 9 ]
Other jobs that fell to the Train to were to act as wireless operators and draughtsmen for the Army Corps and Lt Commander Bracegirdle was the "Beachmaster" of Kangaroo Beach.
According to the Train's log, 30 September was a special day. It was the second day in a row that the base had not been shelled by Turkish artillery. Of course, they would make up for the oversight on 1 October, but for the sailors it was a welcome reprieve. [ 9 ] While the Train wasn't itself involved in actual fighting, it was constantly shelled and bombed by Turkish forces. It was a common sight at Suvla to see 40 British soldiers under the direction of a RAN Petty Officer, working to bring supplies ashore during rough weather. The soldiers would openly look forward to returning to their trenches where they at least had the ability to shoot back at anyone who attacked them.
The AIF Official War Correspondent, Charles Bean came to Suvla Bay specifically to report on the Train, where he found that:
There they are to-day, in charge of the landing of a great part of the stores of a British army. They are quite cut off from their own force; they scarcely come into the category of the Australian Force, and scarcely into that of the British; they are scarcely army and scarcely navy. Who it is that looks after their special interests, and which is the authority that has the power of recognising any good work that they have done, I do not know. If you want to see the work, you have only to go to Kangaroo Beach, Suvla Bay, and look about you. They have made a harbour. [ 10 ]
The supplies landed and distributed by the Train were many and varied. This is a summary of munitions and stores discharged from the storeship Perdsto during the month of September. [ 11 ]
In November 1915, the British military hero Field Marshal Lord Kitchener toured the Dardanelles as part of his review of the Middle Eastern theatre of operations . After two hours at Anzac Cove, he instructed Lt General Birdwood, the Commander of the Mediterranean Expeditionary Force to begin planning to evacuate the Peninsula. Winter was coming and already too many soldiers were being taken sick and even dying of hypothermia and frostbite, while the Turks had been stubbornly holding their ground. Retreat made sense, aside from just one problem: once the Turks figured out the troops were pulling back, the retreat would very quickly become a bloodbath.
Once the official decision was made by the War Cabinet, preparations were made, carefully disguised to make it seem as though units that could be would be withdrawn to Mudros safely would be, leaving enough troops to defend the ground taken for the winter, while the bulk of the troops would return in spring for a new offensive. Troops and equipment started slipping away from the front and aboard navy vessels from 8 December 1915. [ 12 ]
During the time, the Train's log shows work parties completion construction of roads and buildings on the same day as other parties were disassembling other buildings and stocking supplies for transport, with shifts working around the clock. The sick list came down from 70 men before preparations began to a low of 7 on 12 December. The Chief Engineer of IX Corps, General Bland praised the Train for its work in preparing to depart Suvla, saying that
From the time the 1st R.A.N.B.T. joined the IX Corps all ranks have worked hard, cheerfully, and well. They have rendered most valuable services in connection with the construction and maintenance of landing-piers, beach water-supply, and the landing, charge of, and distribution of engineer material at Suvla, and have most willingly given their help in many other directions. Their work has been continuously heavy, and they have done it well. [ 13 ]
A fine example of endurance, good organisation, and discipline. Their commanders were indefatigable in anticipating requirements, and assisting whenever and where ever required. I bring them to your notice as two specially valuable and well-commanded units, which can be relied upon to do their best under difficult circumstances. [ 14 ]
The Train was the last Australian unit to leave the Gallipoli Peninsula, a party of 50 men under Sub-Lieutenant Charles Hicks was left behind to oversee the evacuation of the British forces. They left at 4.30am, on 28 December – eight days after the evacuation of Anzac Cove . The Train sailed to the Greek isle of Mudros , along with the rest of IX Corps.
On reaching Mudros, Lt Commander Bracegirdle was hospitalised for Malaria and Jaundice, while command of the Train was returned to the 11th Division from IX Corps. The Train was then temporarily transferred, on 26 December 1915, to the Australian and New Zealand Army Corps . Disciplinary matters, though were handled by Admiral Sir Rosslyn Wemyss , the Royal Navy officer commanding the Port of Moudros . By 5 February 1916, the transfer to I ANZAC Corps was official. [ 14 ]
After recuperating at Mudros , the Train set sail under command of Lt. Bond for Lake Timsah on the Suez Canal on 17 January, arriving there on the 21st. Here, at Suez Canal No. 2 Section, the Train was responsible for manning and controlling existing bridges, building new bridges, control of tugboats and lighters and the distribution of stores. On 11 February, the Train split into three sections, with Lt. Bond commanding 57 men at a Serapeum halfway between Lake Tismah and Bitter Lakes, Sub-Lieutenant Charles Hicks with 65 men at the northern approach to Lake Tismah, a place known as Ferry Point. Lt Commander Bracegirdle had joined up with the Train again on 30 January, and was in command at the main camp on Lake Tismah.
Duties at the main camp were light, mainly consisting of experimenting with new iron pontoons, and assisting at the Ismaïlia Canal Works. The two detachments on the other hand were used to operate the small vessels crossing the Canal at all hours of the day and night, and also forming and breaking the pontoon bridges several times each day.
Come March, the Train was in high demand. Admiral Wemyss, now in command of East Indies & Egyptian Squadron , [ 15 ] who wanted to use the Train to operate river transports and work as gun crews supporting the Mesopotamian campaign . General Sir Julian Byng , who had taken command of IX Corps at Suvla Bay when the elderly General Frederick Stopford was relieved for incompetence, wanted to bring the Train south to No. 4 Section, Suez Canal, which included all of the Canal south of Small Bitter Lake. Also in March, Lieutenant Bond was transferred to the Naval Intelligence detachment in Alexandria , with Lt Clarence Read [ 16 ] taking his place as First Lieutenant.
Byng got his way, and the Train arrived in Suez on 4 May. No.4 Section was the largest of the Canal's divisions, and the Train's responsibilities increased when they arrived. As well as manning bridges and small vessels, building brides, they were now building wharves and piers, controlling tugboats and all military traffic crossing the Canal and constructing pumping machinery IX Corps knew what the Train was capable of and made sure that they got the most out of the Train they could. On the other hand, though, the weather conditions were harsher than they had been up at No. 2 Section, and the Ottoman troops were more active in their attempts at sabotage and air raids were common.
The Train's HQ was set up at Kubri West, with a major detachment at Shallufa, and parties also working at Geneffe, Gurka Post, Baluchi Post, El Shatt , the town of Suez , Port Tewfik and the Canal Quarantine Station, on the Gulf of Suez . [ 17 ]
At this time, Allied forces were working to push the Ottoman Troops back from the Canal and deep into the desert. To get their supplies in, it was decided that a railway would be built by the engineers. There was however a slight problem. There was no way to get the locomotives needed onto these rails. The Bridging Train was therefore tasked with building new wharves to unload the locomotives that would be needed for the desert trains, which they did by converting two small vessels into floating pile drivers .
Despite the best efforts of the railway engineers, by the time of the Battle of Magdhaba , the tracks were still 25 miles (40 km) from the town of El Arish, so the Train was called in to manage the landing of supplies on the beach. Unfortunately, the whole bight was mined and the Royal Navy would be unable to sweep it without raising suspicions. The Train's mission was therefore to land on the beach and then construct two piers through the minefield.
Little action was actually seen as the Turks slipped out of El Arish, apparently getting wind of the attack a day before the Train landed. But it was one of the few times that the Train supported other Australian forces in combat, the Imperial Camel Corps and Australian Light Horse under General Sir Harry Chauvel were both involved in the Battle. However, this was the last real action that the Train saw before being disbanded.
By the end of 1916, when Lieutenant Cameron was appointed First Lieutenant, [ 18 ] new members who had not served under fire started to complain that they were being used for simple work that could be done by the Egyptian labourers . Word of this eventually reached the Defence Department who soon wrote to the Commonwealth Naval Board , which said that the men of the train "would be unsuitable for use aboard HMA Ships ; if no longer required as a Bridging Train, the unit should be disbanded, and its members either sent as reinforcements to the Australian Engineers or Artillery, or brought back to Australia." [ 19 ] Next, the Defence Department took the matter to the War Office , where General Archibald Murray , the General Officer Commanding Egypt made his opinion that the Train was engaged in "work of an important military nature". [ 19 ]
Lt Commander Bracegirdle was informed at the start of January 1917 that the Train would be relieved of it duties on the Canal and get back into the War, heading deeper into Palestine. The Train then spent January preparing for their new mission, only to be informed that only part of the unit would be required for the duties in Palestine on 8 February 1917. He was also instructed to find out how his men could be redistributed. 76 indicated they would be willing to transfer to the AIF , 43 to the Royal Navy , while the remainder wished to stay with the Train.
After this, on 18 February, the War Office sent the Defence Department another telegram on the matter, which does not reflect the outcome of Bracegirdle's survey at all:
Recommend that personnel of Australian Naval Bridging Train be transferred to Australian army, with exception of 4 officers and 80 other ratings who will be retained in unit reorganised in two sections – one consisting of skilled engineers and kindred trades, and one of expert pier-builders and shore-workers. Personnel transferred to Australian army would be posted to whichever arm they are best suited. Anyone not accepting transfer to be discharged and returned to Australia
Nonetheless, the Australian Government accepted the War Office 's recommendation. On the same day, Lt Commander Bracegirdle was relieved of command and appointed Officer Commanding Troops aboard the transport SS Willochra , 5 March 1917.
On 20 March, the Train was informed that they were being disbanded and were asked to make a choice as to their next assignment. The results were very clear, the vast majority of members choosing to remain with the Royal Australian Navy.
Despite the results of this poll, 194 officers and ratings embarked on the troopship HMAT A45 Bulla on 26 May 1917 and arrived at Melbourne on 10 July. [ 20 ] They were then returned to their State of origin and discharged by 22 May. [ 21 ]
Bean's Official History states that this came about through a series of miscommunications between the War Office , Department of Defence , Commonwealth Naval Board and the Train itself, and that several months later, in July 1917, it was decided to reform the Train, but its members had dispersed too far to be recalled.
During its existence, the Train had made two amphibious landings ( Gallipoli and El Arish ), and lost 25 sailors killed. Lieutenant Commander Bracegirdle was awarded the Distinguished Service Order and Mentioned in Despatches three times for his command of the Train, while 16 of his men were also Mentioned in Despatches. | https://en.wikipedia.org/wiki/Royal_Australian_Naval_Bridging_Train |
The Royal Corps of Naval Constructors ( RCNC ) is an institution of the British Royal Navy and Admiralty for training in naval architecture , marine, electrical and weapon engineering. It was established by Order in Council in August 1883, on the recommendation of the naval architect Sir William White . Its precursor was the Royal School of Naval Architecture , London .
According to the Royal Navy 's Books of Reference 3 Chapter 46, it is a "civilian corps and an integrated part of the Defence Engineering & Science Group". Members in certain posts who do not hold commissions are eligible to wear a uniform similar to that of the Royal Navy and are accorded the same respect as commissioned officers.
From Tudor times , the ships of the Royal Navy were built in the Royal Dockyards under the supervision of the Master Shipwright and to the design of the Surveyor of the Navy who was always an ex-Master Shipwright. In 1805, seeing the growing application of science in industry, Lord Barham ’s Commission recommended, that a School of Naval Architecture should be formed to produce men suitably trained both to design the ships of the fleet and to manage the work of the Royal Dockyards. This school was created in 1811 at Portsmouth and after an erratic series of changes it settled down at Greenwich in 1873.
The graduates of these schools were Naval Architects who quickly established high professional standards in the field. Their influence, combined with the effects of the Industrial Revolution led to the formation of the Institution (now the Royal Institution) of Naval Architects in 1860.
Although the number of professionally qualified Naval Architects employed in the design, building and repair of warships had risen to 27 by 1875, ships were still being designed and built against the Chief Constructor’s advice and there were inevitable disasters. The main obstacle to progress was the poor career prospects of the professionally qualified Naval Architect with the linked difficulty of getting sufficient recruits. To solve these linked problems William White, then Professional Assistant to the Director of Naval Construction, proposed a co-ordinated training programme and career structure and these ideas were approved in 1882 by a committee under Lord Brassey .
The first head of the Royal Corps of Naval Constructors was Sir Nathaniel Barnaby . Due to illness his resignation in 1885 led to the appointment of Sir William White as his successor.
The professional Naval Architects of the Royal Corps had grown in number to 91 by 1901 and were heavily involved in the build up to the First World War. The rapid and successful design and building of HMS Dreadnought was probably their best known achievement of the time, although the foundations were being laid for future advances in weapons and machinery and also in the field of submarine design.
The Royal Corps had a flirtation with airship design between 1915 and 1922 but this was overshadowed by the conversion of ships to operate aircraft and the design and construction of the first purpose built ship to carry aircraft, HMS Hermes . The success of these ships, together with that of submarines and escorts designed by the Royal Corps, played a large part in establishing British naval supremacy.
The Second World War saw a similar expansion of the shipbuilding effort and the evacuation to Bath of the Director of Naval Construction. Many members of the Royal Corps served in uniform in the ranks up to the level of Constructor Rear-Admiral.
In the post-war period the major features have been the very considerable achievement in designing and maintaining a fleet of nuclear-powered submarines and the changing nature of the Royal Corps itself.
Recognising the increasing impact of a vessel’s equipment on its hull and structure, the Royal Corps combined with the professional Electrical and Mechanical Engineers of the Royal Naval Engineering Service (RNES) in 1977. Further amalgamation with specialist weapons designers was also enacted. In the last decade this more diverse corps has been instrumental in the design and manufacture of the very latest warships such as the Type 45 destroyer , Astute -class submarines and Queen Elizabeth -class aircraft carriers ; all of which contain highly complex engineering systems.
The Royal Corps currently numbers nearly 100 naval architects, marine, electrical and weapon engineers and, in keeping with its original aims, continues to provide professional engineers for the design, building and maintenance of vessels of the Royal Navy.
Six naval constructors gave their lives in the course of duty; Arthur K Stephens, Assistant Constructor 2c, who was lost 31 May 1916 aboard HMS Queen Mary which was sunk at the Battle of Jutland (listed as ‘Admiralty Civilian’). [ 1 ] F. Bailey and A.A.F. Hill were lost in the HMS Thetis disaster of June 1939. H.H.Palmer was lost at sea on the SS Aguila whilst on route to Gibraltar for Dockyard duties in August 1941, Also during World War Two F. Bryant was killed in the bombing of Bath in 1942 and R. King was killed in Mombasa.
Some members of the RCNC are entitled to wear a modified version of the standard RN uniform, the difference being the presence of grey bands between gold stripes worn on the arms and on shoulder boards. Constructors may wear uniform in certain posts in UK establishments (predominantly naval bases) and in several overseas posts. | https://en.wikipedia.org/wiki/Royal_Corps_of_Naval_Constructors |
The Columbia Detachment of the Royal Engineers was a contingent of the Royal Engineers of the British Army that was responsible for the foundation of British Columbia as the Colony of British Columbia (1858–66) . It was commanded by Colonel Richard Clement Moody FICE FRGS RIBA, Kt. (Fr.) .
When news of the Fraser Canyon Gold Rush reached London, Sir Edward Bulwer-Lytton , Secretary of State for the Colonies, requested that War Office recommend an officer who was "a man of good judgement possessing a knowledge of mankind" to lead 150 (which was later increased to 172) Royal Engineers who had been selected for their "superior discipline and intelligence". [ 1 ] The War Office chose Moody: and Lord Lytton, who described Moody as his "distinguished friend", [ 2 ] accepted their nomination, as a consequence of Moody's military record, and of his success as Governor of the Falkland Islands, and of the distinguished geopolitical record of his father Colonel Thomas Moody, Kt. , at the Colonial Office. [ 1 ] Moody's responsibility was to transform the new Colony of British Columbia (1858–66) into the British Empire's 'bulwark in the farthest west' [ 3 ] and to 'found a second England on the shores of the Pacific'. [ 2 ] [ 4 ] Lytton desired to send to the colony 'representatives of the best of British culture, not just a police force': to send men who possessed 'courtesy, high breeding and urbane knowledge of the world', [ 5 ] such as Moody whom the Government considered to be the archetypal 'English gentleman and British Officer'. [ 6 ] Moody's brother, Colonel Hampden Clement Blamire Moody , already had served with the Royal Engineers in British Columbia, from 1840 to 1848, [ 7 ] to such success that he was granted command of the Royal Engineers across the entirety of China . [ 8 ]
Richard Clement Moody and his wife Mary Hawks (of the Hawks industrial dynasty and of the Boyd merchant banking family) and their four children left England for British Columbia in October 1858 and arrived in British Columbia in December 1858, [ 9 ] with the 172 Royal Engineers of the Royal Engineers, Columbia Detachment , and his secretary Robert Burnaby (after whom he subsequently named Burnaby Lake ). [ 9 ] The 'gentlemen' Royal Engineers defined by Moody were his three Captains Robert Mann Parsons , John Marshall Grant , and Henry Reynolds Luard , and his two Lieutenants Lieutenant Arthur Reid Lempriere (of Diélament, Jersey) and Lieutenant Henry Spencer Palmer , in addition to Captain William Driscoll Gosset (who was to be Colonial Treasurer and Commissary Officer). The contingent also included Doctor John Vernon Seddall and The Rev. John Sheepshanks (who was to be Chaplain of the Columbia Detachment). [ 10 ] Moody was sworn in as the first Lieutenant-Governor of British Columbia and appointed Chief Commissioner of Lands and Works for British Columbia. [ 9 ]
Moody had hoped to begin immediately the foundation of a capital city, but, on his arrival at Fort Langley, he learned of an insurrection, at the settlement of Hill's Bar, by a notorious outlaw, Ned McGowan, and some restive gold miners. [ 9 ] Moody repressed the rebellion, which became popularly known as ' Ned McGowan's War ', without loss of life. [ 9 ] Moody described the incident:
The notorious Ned McGowan, of Californian celebrity at the head of a band of Yankee Rowdies defying the law! Every peaceable citizen frightened out of his wits!—Summons & warrants laughed to scorn! A Magistrate seized while on the Bench, & brought to the Rebel's camp, tried, condemned, & heavily fined! A man shot dead shortly before! Such a tale to welcome me at the close of a day of great enjoyment. [ 11 ]
Moody described the response to his success: 'They gave me a Salute, firing off their loaded Revolvers over my head—Pleasant—Balls whistling over one's head! as a compliment! Suppose a hand had dropped by accident! I stood up, & raised my cap & thanked them in the Queen's name for their loyal reception of me'. [ 12 ]
In British Columbia, Moody 'wanted to build a city of beauty in the wilderness' and planned his city as an iconic visual metaphor for British dominance, 'styled and located with the objective of reinforcing the authority of the Crown and of the robe'. [ 13 ] Subsequent to the enactment of the Pre-emption Act of 1860, Moody settled the Lower Mainland . He founded the new capital city, New Westminster , [ 9 ] [ 14 ] at a site of dense forest of Douglas pine [ 14 ] that he selected for its strategic excellence including the quality of its port. [ 13 ] He, in his letter to his friend Arthur Blackwood of the Colonial Office that is dated 1 February 1859, described the majestic beauty of the site: [ 15 ] [ 6 ]
"The entrance to the Frazer is very striking--Extending miles to the right & left are low marsh lands (apparently of very rich qualities) & yet fr the Background of Superb Mountains- Swiss in outline, dark in woods, grandly towering into the clouds there is a sublimity that deeply impresses you. Everything is large and magnificent, worthy of the entrance to the Queen of England's dominions on the Pacific mainland. [...] My imagination converted the silent marshes into Cuyp -like pictures of horses and cattle lazily fattening in rich meadows in a glowing sunset. [...] The water of the deep clear Frazer was of a glassy stillness, not a ripple before us, except when a fish rose to the surface or broods of wild ducks fluttered away" . [ 4 ]
Moody designed the roads and the settlements of New Westminster, [ 14 ] and his Royal Engineers, under Captain John Marshall Grant, [ 14 ] built an extensive road network, including that which became Kingsway , which connected New Westminster to False Creek ; and the North Road between Port Moody and New Westminster; and the Pacific terminus, at Burrard's Inlet, of Port Moody, of the Canadian and Pacific Railway (which subsequently was extended to the mouth of the Inlet and terminates now at Vancouver); [ 14 ] and the Cariboo Road ; and Stanley Park , which was an important strategic area for invaluable the eventuality of an invasion by America. He named Burnaby Lake after his secretary Robert Burnaby, and he named Port Coquitlam's 400-foot 'Mary Hill' after his wife Mary Hawks . Moody designed the first Coat of arms of British Columbia . [ 1 ] [ 16 ] Richard Clement Moody established Port Moody , which was subsequently named after him, at the end of the trail that connected New Westminster with Burrard Inlet, to defend New Westminster from potential attack from the United States. [ 14 ] Moody also established a town at Hastings which was later incorporated into Vancouver. [ 17 ]
The British designated multiple tracts as government reserves. The Pre-emption Act did not specify conditions for the distribution of the land, and, consequently, large areas were bought by speculators. [ 1 ] Moody requisitioned 3,750 acres (sc. 1,517 hectares) for himself, [ 1 ] and, on this land, he subsequently built for himself, and owned, Mayfield, a model farm near New Westminster. [ 17 ] Moody was criticised by journalists for land grabbing , [ 1 ] but his requisitions were ordered by the Colonial Office, [ 9 ] and Moody throughout his tenure in British Columbia received the approbation of the British authorities in London, [ 14 ] and was in British Columbia described as 'the real father of New Westminster'. [ 18 ] However, Lord Lytton, then Secretary of State for the Colonies, 'forgot the practicalities of paying for clearing and developing the site and the town' and the effort of Moody's Engineers was continually impeded by insufficient funds, which, together with the continuous opposition of Sir James Douglas, Governor of Vancouver Island , whom Sir Thomas Frederick Elliot (1808 - 1880) described as 'like any other fraud', [ 19 ] 'made it impossible for [Moody's] design to be fulfilled'. [ 20 ]
Throughout his tenure in British Columbia, Moody feuded with Douglas whose jurisdictions overlapped. Moody's offices of Chief Commissioner and Lieutenant-Governor were of 'higher prestige [and] lesser authority' than that of Douglas, whom the British Government which had selected Moody to 'out manoeuvre the old Hudson's Bay Factor [Governor Douglas]'. [ 21 ] [ 22 ] Moody had been selected by Lord Lytton as the archetypal 'English gentleman and British Officer', and because his family was 'eminently respectable': he was the son of Colonel Thomas Moody, Kt. , who owned land in the islands in which Douglas's father owned less land and from which Douglas's 'a half-breed' mother originated. Governor Douglas's ethnicity was 'an affront to Victorian society', [ 23 ] whereas Mary Moody was a member of the Hawks industrial dynasty and of the Boyd merchant banking family. [ 24 ] Mary Moody wrote, on 4 August 1859, 'it is not pleasant to serve under a Hudson's Bay Factor', and that the 'Governor and Richard can never get on'. [ 25 ] John Robson, who was the editor of the British Columbian , wanted Richard Clement Moody's office to include that of Governor of British Columbia, and to thereby make obsolete Douglas. [ 1 ] In letter to the Colonial Office of 27 December 1858, Richard Clement Moody states that he has 'entirely disarmed [Douglas] of all jealously'. [ 26 ] Douglas repeatedly insulted the Royal Engineers by attempting to assume their command [ 27 ] and refusing to acknowledge their contribution to the nascent colony. [ 28 ]
Margaret A. Ormsby, who was the author of the Dictionary of Canadian Biography entry for Moody (2002), unpopularly censures Moody for the abortive development of the New Westminster. [ 1 ] However, most significant historians commend Moody's contribution and exculpate Moody from responsibility for the abortive development of New Westminster, primarily because of the perpetual insufficiency of funds and of the personally motivated opposition by Douglas whom Sir Thomas Frederick Elliot (1808 - 1880) described as 'like any other fraud'. [ 29 ] Robert Burnaby observed that Douglas proceeded with 'muddling [Moody's] work and doubling his expenditure' [ 21 ] and with employing administrators to 'work a crooked policy against Moody' to 'retard British Columbia and build up... the stronghold of Hudson's Bay interests' and their own 'landed stake'. [ 30 ] Therefore, Robert Edgar Cail, [ 31 ] Don W. Thomson, [ 32 ] Ishiguro, and Scott commended Moody for his contribution, and Scott accused Ormsby of being 'adamant in her dislike of Colonel Moody' despite the majority of evidence, [ 33 ] and almost all other biographies of Moody, including that by the Institution of Civil Engineers, and that by the Royal Engineers, and that by the British Columbia Historical Association, commend Moody's achievements in British Columbia.
The Royal Engineers, Columbia Detachment was disbanded in July 1863. The Moody family (which now consisted of Moody, and his wife, and seven legitimate children) [ 9 ] and the 22 Royal Engineers who wished to return to England, who had 8 wives between them, departed for England. [ 9 ] 130 of the original Columbia Detachment decided to remain in British Columbia. [ 1 ] Scott contends that the dissolution of the Columbia Detachment, and the consequent departure of Moody, 'doomed' the development of the settlement and the realisation of Lord Lytton's dream. [ 34 ] A vast congregation of New Westminster citizens gathered at the dock to bid farewell to Moody as his boat departed for England. Moody wanted to return to British Columbia, but he died before he was able to do so. [ 35 ] Moody left his library behind, in New Westminster, to become the public library of New Westminster. [ 9 ] [ 1 ]
In April 1863, the Councillors of New Westminster decreed that 20 acres should be reserved and named Moody Square after Richard Clement Moody. The area around Moody Square that was completed only in 1889 has also been named Moody Park after Moody. [ 36 ] Numerous developments occurred in and around Moody Park, including Century House, which was opened by Princess Margaret on 23 July 1958. In 1984, on the occasion of the 125th anniversary of New Westminster, a monument of Richard Clement Moody, at the entrance of the park, was unveiled by Mayor Tom Baker. [ 37 ] For Moody's achievements in the Falkland Islands and in British Columbia, British diplomat David Tatham CMG , who served as Governor of the Falkland Islands, described Moody as an 'Empire builder'. [ 9 ] In January 2014, with the support of the Friends of the British Columbia Archives and of the Royal British Columbia Museum Foundation, The Royal British Columbia Museum purchased a photograph album that had belonged to Richard Clement Moody. The album contains over 100 photographs of the early settlement of British Columbia, including some of the earliest known photographs of First Nations peoples. [ 38 ] | https://en.wikipedia.org/wiki/Royal_Engineers,_Columbia_Detachment |
The Royal Institute of Chemistry was a British scientific organisation. Founded in 1877 as the Institute of Chemistry of Great Britain and Ireland ( ICGBI ), its role was to focus on qualifications and the professional status of chemists, and its aim was to ensure that consulting and analytical chemists were properly trained and qualified.
The society received its first Royal Charter on 13 June 1885, and King George VI awarded the society royal patronage with effect from 14 May 1943, [ 1 ] from which date it became the Royal Institute of Chemistry of Great Britain and Ireland ( RICGBI ). This re-designation was formally confirmed by the grant of a Supplemental Charter on 29 March 1944. [ 2 ]
As well as insisting on thorough professional qualifications, it also laid down strict ethical standards. Its main qualifications were Licentiate (LRIC) (professional training following a course of practical study to a standard lower than an honours degree), Graduate (GRIC) (completion of study equivalent to at least second class honours degree), Associate (ARIC) (LRIC plus professional experience), Member (MRIC) (GRIC plus professional experience) and Fellow (FRIC) (more experience and standing than MRIC) of the Royal Institute of Chemistry. Following a supplemental Charter in 1975, Members and Fellows were permitted to use the letters CChem ( Chartered Chemist ). It published Royal Institute of Chemistry Reviews from 1968 to 1971, [ 3 ] when it combined to form Chemical Society Reviews , and the Journal of the Royal Institute of Chemistry .
At the same time, the Chemical Society had concentrated on the science of chemistry, and publishing learned journals. In 1972 these two organisations, together with the Faraday Society and the Society for Analytical Chemistry , started the process of merging, becoming the Royal Society of Chemistry on 15 May 1980. [ 4 ] | https://en.wikipedia.org/wiki/Royal_Institute_of_Chemistry |
The Royal Institution of Naval Architects (also known as RINA) is a professional institution and global governing body for naval architecture and maritime engineering. Members work in industry, academia, and maritime organisations worldwide, participating in the design, construction, repair, and operation of ships, boats, and marine structures in over 90 countries.
The Patron of the Institution was Queen Elizabeth II but is now King Charles III.
The Royal Institution of Naval Architects was founded in Britain in 1860 as The Institution of Naval Architects and was incorporated by Royal Charter in 1910 and 1960 to "advance the art and science of ship design." [ 1 ]
Founding members included John Scott Russell , Edward Reed , Rev. Joseph Woolley , Nathaniel Barnaby , Frederick Kynaston Barnes, and John Penn . [ 2 ]
On 9 April 1919 Blanche Thornycroft , Rachel Mary Parsons and Eily Keary became the first women admitted into the institution. [ 3 ]
The following have been members of the society historically: | https://en.wikipedia.org/wiki/Royal_Institution_of_Naval_Architects |
The Royal Netherlands Chemical Society (In Dutch : Koninklijke Nederlandse Chemische Vereniging , abbreviated: KNCV ) is a learned society and professional association founded in 1903 to represent the interests of chemists and chemical engineers in the Netherlands . Currently the organisation has approximately 7,400 members.
The organisation supports the professional development of its members who are involved in the fields of chemistry , life sciences and process technology . The organisation is actively involved in protecting the interests of its members. Furthermore, its supports the development and spread of knowledge and inspiration in the field of chemistry. It publishes journals, books and databases, as well as hosting conferences, seminars and workshops.
In the years of 1896 and 1897, two Dutch chemists Willem Paulinus Jorissen and Johannes Rutten made plans to found an Association of Dutch Chemists. Rutten (1873-1946) had obtained the degree of technologist at the Polytechnic School in Delft (now Delft University of Technology ) in 1896 and was appointed chemist at the former Central Guanofabrieken (now AkzoNobel ) at Kralingseveer in Rotterdam . Jorissen obtained his PhD degree at the University of Amsterdam on 21 oktober 1896 with Hendrik Willem Bakhuis Roozeboom as supervisor. Rutten and Jorissen became friends and discussed the possibilities of organizing the Dutch chemists. There were already chemical associations in neighboring countries for a long time: the Chemical Society in London was founded in 1841, the Société chimique de France in 1857, the Deutsche Chemische Gesellschaft zu Berlin in 1867 and the American Chemical Society in 1876. Denmark followed in 1879, Sweden in 1883, Finland in 1891 and Norway in 1893, while the Société Chimique de Belge was established in Brussels in 1887.
In order to successfully establish a Dutch chemical association, it was first of all necessary to find out whether a sufficient number of members could be counted on. Following the medical yearbook for the Netherlands published since 1882, the two friends published a chemical yearbook in 1898 that contained an address list of Dutch chemists at home and abroad. The editors consisted of Jorissen, Rutten, the Amsterdam pharmacist and chemist Bernardus Adrianus van Ketel (1862-1928), H.C. Prinsen Geerligs (born 1864), director of the sugar cane testing station in Kagok, Tegal ( Java ), and Dr. Lodewijk Theodorus Reicher (1857-1943), chemical mechanic at the Municipal Health Service in Amsterdam and chief of the associated chemical laboratory. The second volume appeared in 1901; the third in 1902. The editorial board was expanded with Dr. Albert Jacques Joseph van de Velde (1871-1956), director of the city laboratory in Ghent. The title therefore became: Scheikundig Jaarboekje voor Nederland, België en Nederlands Indië ( English : Chemical Yearbook for the Netherlands, Belgium and the Dutch East Indies). In the meantime, the Journal of Applied Chemistry and Hygiene was founded in 1897 of which Jorissen became co-editor. The chemical yearbook and the journal would play a major role in the founding of the Dutch Chemical Association. [ 3 ] [ 4 ]
The society was founded on 15 April 1903 as the "Algemene Nederlandsche Chemische Vereeniging" ( English : General Netherlands Chemical Society), and renamed on 4 July of the same year as "Nederlandsche Chemische Vereeniging" (English: Netherlands Chemical Society). At the jubilee of 1953, the organisation was granted a Royal Charter (with the designation " Koninklijke ") by Queen Juliana of the Netherlands and thereby became the "Koninklijke Nederlandse Chemische Vereniging" ( English : Royal Netherlands Chemical Society).
Membership is open to anyone who works or studies in the chemistry, life sciences or process technology, and endorses the core values for chemists. The board decides on the admission of the members. [ 5 ]
The society does have the following categories of membership:
The society is organised around 17 sections and associations that are based on subject areas, work groups, and local circles across the Netherlands. The sections and associations cover broad areas of chemistry but also contain many special interest groups for more specific areas: [ 8 ]
There are six local circles covering the Netherlands, i.e. that of 's-Hertogenbosch , Utrecht , Zwolle , Groningen , Haarlem , and Rotterdam . | https://en.wikipedia.org/wiki/Royal_Netherlands_Chemical_Society |
The Royal Norwegian Society of Sciences and Letters ( Danish : Det Kongelige Norske Videnskabers Selskab , DKNVS) is a Norwegian learned society based in Trondheim . It was founded in 1760 and is Norway's oldest scientific and scholarly institution. The society's Protector is King Harald V of Norway . Its membership consists of no more than 435 members elected for life among the country's most prominent scholars and scientists.
The society’s Danish name predates both written standards for Norwegian and has remained unchanged after Norway’s independence from Denmark in 1814 and the spelling reforms of the 20th century.
DKNVS was founded in 1760 by the bishop of Nidaros Johan Ernst Gunnerus , headmaster at the Trondheim Cathedral School Gerhard Schøning and Councillor of State Peter Frederik Suhm under the name Det Trondhiemske Selskab (the Trondheim Society). From 1761 it published academic papers in a series titled Skrifter . It was the northernmost learned society in the world, and was established in a time when Norway did not have universities or colleges. [ 1 ] [ 2 ]
It received the royal affirmation of its statutes on 17 July 1767, [ 3 ] and was given its present name at a ceremony on 29 January 1788, king Christian VII of Denmark 's birthday. [ 4 ] In 1771, when Johann Friedrich Struensee took over the de facto rule of Denmark-Norway , Johan Ernst Gunnerus was summoned to Copenhagen , where he was given the mission to establish a university in Norway. Gunnerus did not suggest that the university be established in Trondhjem, but in southern Christianssand (Kristiansand), due to its proximity to Jutland . If this happened, he would have the Society of Sciences and Letters moved to Christianssand, to correspond with the new university. However, the plan was never carried out. Struensee's reign ended in 1772, but he reportedly dismissed the plan before this. [ 1 ] (Kristiansand got its university in 2007. [ 5 ] )
The society was housed in the premises of Trondheim Cathedral School until 1866, when it acquired its own localities. [ 4 ] Since 1903 its main task was to run a museum . In 1926 there was a split in which the museum became a separate entity, receiving the assets of the learned society. Also in 1926, another publication series Det Kongelige Norske Videnskabers Selskab Forhandlinger was inaugurated. [ 4 ] Ownership of the museum was transferred to the University of Trondheim in 1968, [ 6 ] today the Norwegian University of Science and Technology , [ 3 ] but DKNVS re-received some assets in a 1984 reorganization, and now controls these assets through the foundation DKNVSS. [ 6 ]
A history of the Royal Norwegian Society of Sciences and Letters was written in 1960 by Hans Midbøe , and released in two volumes. [ 7 ]
In connection with the 250th anniversary of the Society, Håkon With Andersen, Brita Brenna, Magne Njåstad, and Astrid Wale wrote an updated history. [ 8 ] Also, Arild Stubhaug wrote a shorter history, prepared for a general audience. [ 9 ]
The board of directors consists of seven people, five men and two women. It is led by praeses Steinar Supphellen and vice-praeses Kristian Fossheim . Other board members are Hanna Mustaparta, Britt Dale, Ola Dale, Joar Grimsbu and Asbjørn Moen. The daily administration is led by a secretary-general; Kristian Overskaug. [ 10 ] The board is responsible for awarding the Gunnerus Medal [ 11 ] for academic achievement. [ 12 ] The medal was inaugurated in 1927. [ 3 ]
Before 1815, the sitting King held the title of praeses, while the highest-ranked non-royal member was vice praeses. In the tradition of Gunnerus the bishop, the latter post was filled by clerics until 1820, when Christian Krohg took the seat. From 1815 the King holds the title of "protector". Today King Harald V of Norway is protector of the society. [ 4 ]
Members of the learned society are divided into two divisions, Letters and Sciences. In 2005 there were 470 members, of whom 134 were foreign. [ 3 ] This is a marked increase from 1996, when it had 399 members, of whom 94 were foreign. [ 4 ]
The society awards the following prizes:
The Gunnerus Sustainability Science Award is the society's highest award. It is awarded for outstanding scientific work that promotes sustainable development globally. As of 2017 the prize is awarded by DKNVS in collaboration with the Norwegian University of Science and Technology . [ 13 ]
The award was established in 2012, as a cooperation between DKNVS, Sparebanken Midt-Norge and the foundation Technoport . It is named after the Norwegian scientist and bishop Johan Ernst Gunnerus , and consists of a cash award of 1,000,000 Norwegian kroner .
The first laureate was announced in February 2012, and the prize was handed over the 17 April in Olavshallen in Trondheim , Norway during the conference Technoport 2012 . [ 14 ] [ 15 ]
Laureates are:
This award is funded by I. K. Lykke . The prize is awarded annually to two people under 40 years who are "Norwegian researchers or foreign researchers at the Norwegian research institutions that have demonstrated outstanding talent, originality and effort, and who have achieved excellent results in their fields". [ 17 ] [ 18 ]
Awardees are:
This is a list of the heads of the Royal Norwegian Society of Sciences and Letters: [ 4 ] | https://en.wikipedia.org/wiki/Royal_Norwegian_Society_of_Sciences_and_Letters |
The Royal Swedish Academy of Engineering Sciences ( Swedish : Kungliga Ingenjörsvetenskapsakademien , IVA ), founded on 24 October 1919 by King Gustaf V , is one of the royal academies in Sweden . The academy is an independent organisation, which promotes contact and exchange between business, research, and government, in Sweden and internationally. It is the world's oldest academy of engineering sciences.(OECD Reviews of Innovation Policy: Sweden 2012).
The King is the patron of the academy. [ 1 ] The following people have been presidents of IVA since its foundation in 1919: [ 2 ]
Each year, outstanding scientists and engineers from universities and industries are elected into membership of IVA. Currently, the academy has 1000 Swedish and 300 foreign members. Foreign members are non-resident and non-citizen of Sweden. All new members are nominated by existing members.
The academy focuses on twelve [ 3 ] areas of engineering sciences:
Each focus area is addressed by a committee with a representative chair.
The academy awards several prizes, medals and scholarships: [ 4 ]
This article about an organization based in Sweden is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Royal_Swedish_Academy_of_Engineering_Sciences |
Royana (2006–2010) was Iran's and the Middle East's first successfully cloned sheep. [ 1 ] Royana was a brown male domestic sheep and was cloned in the Royan Research Institute in Isfahan , Iran (The word Royan means embryo in Persian). He was the second cloned sheep in Royan Research Institute, but whereas the first sheep died few hours after birth, Royana lived for a few years.
On September 30, 2006, a group of scientists in Iran cloned Royana from an adult cell in a test tube in a laboratory. After the embryo proved its stability, scientists transferred it to the uterus of a female sheep. After a period of 145 days, Royana was born by caesarean section . Despite critical conditions, he survived and thrived. Royana was born on April 15, 2006, 1:30 am at Isfahan campus of Royan Institute by cesarean section in a healthy condition.
Royana was euthanized after the abdominal pain was traced to his liver. It was also thought that Royana suffered premature death syndrome . Royana died at the age of three.
His birth was a great step in the production of transgenic lambs containing factor IX transgenic, which is helpful in human blood clotting.
This biotechnology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Royana |
The rp-process (rapid proton capture process) consists of consecutive proton captures onto seed nuclei to produce heavier elements. [ 1 ] It is a nucleosynthesis process and, along with the s -process and the r -process , may be responsible for the generation of many of the heavy elements present in the universe. However, it is notably different from the other processes mentioned in that it occurs on the proton-rich side of stability as opposed to on the neutron-rich side of stability.
The end point of the rp-process (the highest-mass element it can create) is not yet well established, but recent research has indicated that in neutron stars it cannot progress beyond tellurium . [ 2 ] The rp-process is inhibited by alpha decay , which puts an upper limit on the end point at 104 Te , the lightest observed alpha-decaying nuclide, [ 3 ] and the proton drip line in light antimony isotopes . At this point, further proton captures result in prompt proton emission or alpha emission, and thus the proton flux is consumed without yielding heavier elements; this end process is known as the tin–antimony–tellurium cycle. [ 4 ]
The process has to occur in very high-temperature environments (above 10 9 kelvin ) so that the protons can overcome the large Coulomb barrier for charged-particle reactions. A hydrogen-rich environment is also a prerequisite due to the large proton flux needed. The seed nuclei needed for this process to occur are thought to be formed during breakout reactions from the hot CNO cycle . Typically proton capture in the rp-process will compete with (α,p) reactions, as most environments with a high flux of hydrogen are also rich in helium. The time scale for the rp-process is set by β + decays at or near the proton drip line , because the weak interaction is notoriously slower than the strong interaction and electromagnetic force at these high temperatures.
Sites suggested for the rp-process are accreting binary systems where one star is a neutron star . In these systems the donor star is accreting material onto its compact partner star. The accreted material is usually rich in hydrogen and helium because of its origin from the surface layers of the donor star. Because such compact stars have high gravitational fields , the material falls with a high velocity towards the compact star, usually colliding with other accreted material en route, forming an accretion disk . In the case of accretion onto a neutron star, as this material slowly builds up on the surface, it will attain a temperature on the order of 10 8 K.
Eventually it is believed that thermonuclear instabilities arise in this hot atmosphere, allowing the temperature to continue to rise until it leads to a runaway thermonuclear explosion of the hydrogen and helium. During the flash, the temperature quickly rises, becoming high enough for the rp-process to occur. While the initial flash of hydrogen and helium lasts only a second, the rp-process typically takes up to 100 seconds. Therefore, the rp-process is observed as the tail of the resulting X-ray burst . | https://en.wikipedia.org/wiki/Rp-process |
The rpoB gene encodes the β subunit of bacterial RNA polymerase and the homologous plastid -encoded RNA polymerase (PEP). It codes for 1342 amino acids in E. coli , making it the second-largest polypeptide in the bacterial cell. [ 1 ] It is targeted by the rifamycin family of antibacterials, such as rifampin . [ 2 ] Mutations in rpoB that confer resistance to rifamycins do so by altering the protein's drug-binding residues, thereby reducing affinity for these antibiotics. [ 3 ] [ 4 ]
Some bacteria contain multiple copies of the 16S rRNA gene, which is commonly used as the molecular marker to study phylogeny . In these cases, the single-copy rpoB gene can be used to study microbial diversity. [ 5 ] [ 6 ]
An inhibitor of transcription in bacteria, tagetitoxin , also inhibits PEP, showing that the complex found in plants is very similar to the homologous enzyme in bacteria. [ 7 ]
In a bacterium without the proper mutation(s) in rpoB rifampicin binds to a site near the fork in the β subunit and prevents the polymerase from transcribing more than two or three base pairs of any RNA sequence and stopping production of proteins within the cell. [ 8 ] [ 9 ] Bacteria with mutations in the proper loci along the rpoB gene are resistant to this effect. [ 8 ] [ 9 ]
Initial studies were done by Jin and Gross to generate rpoB mutations in E. coli that conferred resistance to rifampicin. Three clusters of mutations were identified, cluster I at codons 507-533, cluster II at codons 563-572, and cluster III at codon 687. [ 1 ] [ 10 ] The majority of these mutations are located within an 81 base pair(bp) region in cluster I dubbed the "Rifampicin Resistance Determining Region (RRDR)". [ 9 ] This resistance is typically associated with a mutation wherein a base in the DNA is substituted for another one and the new sequence codes for an amino acid with a large side chain that inhibits the rifampicin molecules from binding to the polymerase. [ 9 ]
There are additional mutations which can occur in the β subunit of the polymerase which are located away from the rifampicin binding site that can also result in mild resistance. [ 8 ] Potentially indicating that the shape of these areas may affect the formation of the rifampicin binding site. [ 8 ]
Nucleic acid probes can detect mutations in rpoB that confer rifampicin resistance. For Mycobacterium tuberculosis , the rifamycin-resistant mutations most commonly encountered involve codons 516, 526, and 531 (numbered, by convention, as in Escherichia coli rpoB ). [ 11 ] [ 12 ] These mutations result in high rifampicin resistance with a relatively low loss of fitness. [ 8 ] For Staphylococcus aureus , the rifamycin-resistant mutation most commonly encountered involves codon 526. [ 13 ]
In addition to imparting resistance to rifampicin, certain rpoB mutations have been identified in 70% of Vancomycin Intermediate S. aureus (VISA) strains. [ 8 ]
The regions of the rpoB gene which are susceptible to mutations are typically well conserved, indicating they are important for life. [ 9 ] This makes it very likely that mutations within these regions have some effect on the overall fitness of the organism. [ 9 ] These physiological changes can include a reduced rate of growth, increased sensitivity to increases or decreases in temperature, and alterations to the properties of RNA chain elongation and transcription termination. [ 8 ] Such changes are not universal across all bacteria, though. A mutation in codon 450 of M. tuberculosis leads to a minor loss of fitness, while the corresponding mutation in S. aureus results in bacteria barely able to survive. [ 8 ]
In Neisseria meningitidis rpoB mutations have been observed to increase expression of enzymes which are involved in metabolizing carbohydrates, as well as enzymes involved in the citric acid cycle and in transcription elongation. [ 8 ] At the same time enzymes involved in ATP production, cell division, and lipid metabolism are all downregulated, or expressed at a lower than normal level. [ 8 ]
In M. tuberculosis mutations in the rpoB gene can significantly upregulate polyketide synthase , potentially indicating increased production of phthiocerol dimycocerosate, a lipid produced by M. tuberculosis and implicated in virulence of the bacteria. [ 8 ] Mutations also impact promoter binding, elongation, termination, and transcription-coupled repair processes in the RNA polymerase itself. [ 8 ] Because of this, rpoB mutations were used to study transcription mechanisms before interest shifted to their ability to impart antibiotic resistance. [ 9 ] Particular mutations can even result in strains of M. tuberculosis which grow better in the presence of rifampicin than they do when the antibiotic is not present. [ 9 ]
In bacteria which are used to produce naturally occurring antibiotics such as erythromycin ( Saccharopolyspora erythraea ) and vancomycin ( Amycolatopsis orientalis ) certain rpoB mutations can increase the production of antibiotic by bacteria with those mutations. [ 9 ] | https://en.wikipedia.org/wiki/RpoB |
Ribulose-1,5-bisphosphate carboxylase/oxygenase , commonly known by the abbreviations RuBisCo , rubisco , [ 1 ] RuBPCase , [ 2 ] or RuBPco , [ 3 ] is an enzyme ( EC 4.1.1.39 ) involved in the light-independent (or "dark") part of photosynthesis , including the carbon fixation by which atmospheric carbon dioxide is converted by plants and other photosynthetic organisms to energy-rich molecules such as glucose . It emerged approximately four billion years ago in primordial metabolism prior to the presence of oxygen on Earth. [ 4 ] It is probably the most abundant enzyme on Earth. In chemical terms, it catalyzes the carboxylation of ribulose-1,5-bisphosphate (also known as RuBP). [ 5 ] [ 6 ] [ 7 ]
RuBisCO is important biologically because it catalyzes the primary chemical reaction by which inorganic carbon enters the biosphere . While many autotrophic bacteria and archaea fix carbon via the reductive acetyl CoA pathway , the 3-hydroxypropionate cycle , or the reverse Krebs cycle , these pathways are relatively small contributors to global carbon fixation compared to that catalyzed by RuBisCO. Phosphoenolpyruvate carboxylase , unlike RuBisCO, only temporarily fixes carbon. Reflecting its importance, RuBisCO is the most abundant protein in leaves , accounting for 50% of soluble leaf protein in C 3 plants (20–30% of total leaf nitrogen) and 30% of soluble leaf protein in C 4 plants (5–9% of total leaf nitrogen). [ 7 ] Given its important role in the biosphere, the genetic engineering of RuBisCO in crops is of continuing interest (see below ).
In plants, algae , cyanobacteria , and phototrophic and chemoautotrophic Pseudomonadota (formerly proteobacteria), the enzyme usually consists of two types of protein subunit, called the large chain ( L , about 55,000 Da ) and the small chain ( S , about 13,000 Da). The large-chain gene ( rbcL ) is encoded by the chloroplast DNA in plants. [ 8 ] There are typically several related small-chain genes in the nucleus of plant cells, and the small chains are imported to the stromal compartment of chloroplasts from the cytosol by crossing the outer chloroplast membrane . [ 6 ] [ 9 ] The enzymatically active substrate ( ribulose 1,5-bisphosphate) binding sites are located in the large chains that form dimers in which amino acids from each large chain contribute to the binding sites. A total of eight large chains (= four dimers) and eight small chains assemble into a larger complex of about 540,000 Da. [ 10 ] In some Pseudomonadota and dinoflagellates , enzymes consisting of only large subunits have been found. [ a ]
Magnesium ions ( Mg 2+ ) are needed for enzymatic activity. Correct positioning of Mg 2+ in the active site of the enzyme involves addition of an "activating" carbon dioxide molecule ( CO 2 ) to a lysine in the active site (forming a carbamate ). [ 12 ] Mg 2+ operates by driving deprotonation of the Lys210 residue, causing the Lys residue to rotate by 120 degrees to the trans conformer, decreasing the distance between the nitrogen of Lys and the carbon of CO 2 . The close proximity allows for the formation of a covalent bond, resulting in the carbamate. [ 13 ] Mg 2+ is first enabled to bind to the active site by the rotation of His335 to an alternate conformation. Mg 2+ is then coordinated by the His residues of the active site (His300, His302, His335), and is partially neutralized by the coordination of three water molecules and their conversion to − OH. [ 13 ] This coordination results in an unstable complex, but produces a favorable environment for the binding of Mg 2+ . Formation of the carbamate is favored by an alkaline pH . The pH and the concentration of magnesium ions in the fluid compartment (in plants, the stroma of the chloroplast ) increases in the light. The role of changing pH and magnesium ion levels in the regulation of RuBisCO enzyme activity is discussed below . Once the carbamate is formed, His335 finalizes the activation by returning to its initial position through thermal fluctuation. [ 13 ]
RuBisCO is one of many enzymes in the Calvin cycle . When Rubisco facilitates the attack of CO 2 at the C2 carbon of RuBP and subsequent bond cleavage between the C3 and C2 carbon, 2 molecules of glycerate-3-phosphate are formed. The conversion involves these steps: enolisation , carboxylation , hydration , C-C bond cleavage, and protonation . [ 14 ] [ 15 ] [ 16 ]
Substrates for RuBisCO are ribulose-1,5-bisphosphate and carbon dioxide (distinct from the "activating" carbon dioxide). RuBisCO also catalyses a reaction of ribulose-1,5-bisphosphate and molecular oxygen (O 2 ) instead of carbon dioxide (CO 2 ). [ 17 ] Discriminating between the substrates CO 2 and O 2 is attributed to the differing interactions of the substrate's quadrupole moments and a high electrostatic field gradient . [ 13 ] This gradient is established by the dimer form of the minimally active RuBisCO, which with its two components provides a combination of oppositely charged domains required for the enzyme's interaction with O 2 and CO 2 . These conditions help explain the low turnover rate found in RuBisCO: In order to increase the strength of the electric field necessary for sufficient interaction with the substrates’ quadrupole moments , the C- and N- terminal segments of the enzyme must be closed off, allowing the active site to be isolated from the solvent and lowering the dielectric constant . [ 18 ] This isolation has a significant entropic cost, and results in the poor turnover rate.
Carbamylation of the ε-amino group of Lys210 is stabilized by coordination with the Mg 2+ . [ 19 ] This reaction involves binding of the carboxylate termini of Asp203 and Glu204 to the Mg 2+ ion. The substrate RuBP binds Mg 2+ displacing two of the three aquo ligands. [ 14 ] [ 20 ] [ 21 ]
Enolisation of RuBP is the conversion of the keto tautomer of RuBP to an enediol(ate). Enolisation is initiated by deprotonation at C3. The enzyme base in this step has been debated, [ 20 ] [ 22 ] but the steric constraints observed in crystal structures have made Lys210 the most likely candidate. [ 14 ] Specifically, the carbamate oxygen on Lys210 that is not coordinated with the Mg ion deprotonates the C3 carbon of RuBP to form a 2,3-enediolate. [ 20 ] [ 21 ]
Carboxylation of the 2,3-enediolate results in the intermediate 3-keto-2-carboxyarabinitol-1,5-bisphosphate and Lys334 is positioned to facilitate the addition of the CO 2 substrate as it replaces the third Mg 2+ -coordinated water molecule and add directly to the enediol. No Michaelis complex is formed in this process. [ 14 ] [ 22 ] Hydration of this ketone results in an additional hydroxy group on C3, forming a gem-diol intermediate. [ 20 ] [ 23 ] Carboxylation and hydration have been proposed as either a single concerted step [ 20 ] or as two sequential steps. [ 23 ] Concerted mechanism is supported by the proximity of the water molecule to C3 of RuBP in multiple crystal structures. Within the spinach structure, other residues are well placed to aid in the hydration step as they are within hydrogen bonding distance of the water molecule. [ 14 ]
The gem-diol intermediate cleaves at the C2-C3 bond to form one molecule of glycerate-3-phosphate and a negatively charged carboxylate. [ 14 ] Stereo specific protonation of C2 of this carbanion results in another molecule of glycerate-3-phosphate. This step is thought to be facilitated by Lys175 or potentially the carbamylated Lys210. [ 14 ]
When carbon dioxide is the substrate, the product of the carboxylase reaction is an unstable six-carbon phosphorylated intermediate known as 3-keto-2-carboxyarabinitol-1,5-bisphosphate, which decays rapidly into two molecules of glycerate-3-phosphate . This product, also known as 3-phosphoglycerate, can be used to produce larger molecules such as glucose .
When molecular oxygen is the substrate, the products of the oxygenase reaction are phosphoglycolate and 3-phosphoglycerate. Phosphoglycolate is recycled through a sequence of reactions called photorespiration , which involves enzymes and cytochromes located in the mitochondria and peroxisomes (this is a case of metabolite repair ). In this process, two molecules of phosphoglycolate are converted to one molecule of carbon dioxide and one molecule of 3-phosphoglycerate, which can reenter the Calvin cycle. Some of the phosphoglycolate entering this pathway can be retained by plants to produce other molecules such as glycine . At ambient levels of carbon dioxide and oxygen, the ratio of the reactions is about 4 to 1, which results in a net carbon dioxide fixation of only 3.5. Thus, the inability of the enzyme to prevent the reaction with oxygen greatly reduces the photosynthetic capacity of many plants. Some plants, many algae, and photosynthetic bacteria have overcome this limitation by devising means to increase the concentration of carbon dioxide around the enzyme, including C 4 carbon fixation , crassulacean acid metabolism , and the use of pyrenoid .
Rubisco side activities can lead to useless or inhibitory by-products. Important inhibitory by-products include xylulose 1,5-bisphosphate and glycero-2,3-pentodiulose 1,5-bisphosphate , both caused by "misfires" halfway in the enolisation-carboxylation reaction. In higher plants, this process causes RuBisCO self-inhibition, which can be triggered by saturating CO 2 and RuBP concentrations and solved by Rubisco activase (see below). [ 24 ]
Some enzymes can carry out thousands of chemical reactions each second. However, RuBisCO is slow, fixing only 3–10 carbon dioxide molecules each second per molecule of enzyme. [ 25 ] The reaction catalyzed by RuBisCO is, thus, the primary rate-limiting factor of the Calvin cycle during the day. Nevertheless, under most conditions, and when light is not otherwise limiting photosynthesis, the speed of RuBisCO responds positively to increasing carbon dioxide concentration.
RuBisCO is usually only active during the day, as ribulose 1,5-bisphosphate is not regenerated in the dark. This is due to the regulation of several other enzymes in the Calvin cycle. In addition, the activity of RuBisCO is coordinated with that of the other enzymes of the Calvin cycle in several other ways:
Upon illumination of the chloroplasts, the pH of the stroma rises from 7.0 to 8.0 because of the proton (hydrogen ion, H + ) gradient created across the thylakoid membrane. The movement of protons into thylakoids is driven by light and is fundamental to ATP synthesis in chloroplasts (Further reading: Photosynthetic reaction centre ; Light-dependent reactions ) . To balance ion potential across the membrane, magnesium ions ( Mg 2+ ) move out of the thylakoids in response, increasing the concentration of magnesium in the stroma of the chloroplasts. RuBisCO has a high optimal pH (can be >9.0, depending on the magnesium ion concentration) and, thus, becomes "activated" by the introduction of carbon dioxide and magnesium to the active sites as described above.
In plants and some algae, another enzyme, RuBisCO activase (Rca, GO:0046863 , P10896 ), is required to allow the rapid formation of the critical carbamate in the active site of RuBisCO. [ 26 ] [ 27 ] This is required because ribulose 1,5-bisphosphate (RuBP) binds more strongly to the active sites of RuBisCO when excess carbamate is present, preventing processes from moving forward. In the light, RuBisCO activase promotes the release of the inhibitory (or — in some views — storage) RuBP from the catalytic sites of RuBisCO. Activase is also required in some plants (e.g., tobacco and many beans) because, in darkness, RuBisCO is inhibited (or protected from hydrolysis) by a competitive inhibitor synthesized by these plants, a substrate analog 2-carboxy-D-arabitinol 1-phosphate (CA1P). [ 28 ] CA1P binds tightly to the active site of carbamylated RuBisCO and inhibits catalytic activity to an even greater extent. CA1P has also been shown to keep RuBisCO in a conformation that is protected from proteolysis . [ 29 ] In the light, RuBisCO activase also promotes the release of CA1P from the catalytic sites. After the CA1P is released from RuBisCO, it is rapidly converted to a non-inhibitory form by a light-activated CA1P-phosphatase . Even without these strong inhibitors, once every several hundred reactions, the normal reactions with carbon dioxide or oxygen are not completed; other inhibitory substrate analogs are still formed in the active site. Once again, RuBisCO activase can promote the release of these analogs from the catalytic sites and maintain the enzyme in a catalytically active form. However, at high temperatures, RuBisCO activase aggregates and can no longer activate RuBisCO. This contributes to the decreased carboxylating capacity observed during heat stress. [ 30 ] [ 31 ]
The removal of the inhibitory RuBP, CA1P, and the other inhibitory substrate analogs by activase requires the consumption of ATP . This reaction is inhibited by the presence of ADP , and, thus, activase activity depends on the ratio of these compounds in the chloroplast stroma. Furthermore, in most plants, the sensitivity of activase to the ratio of ATP/ADP is modified by the stromal reduction/oxidation ( redox ) state through another small regulatory protein, thioredoxin . In this manner, the activity of activase and the activation state of RuBisCO can be modulated in response to light intensity and, thus, the rate of formation of the ribulose 1,5-bisphosphate substrate. [ 32 ]
In cyanobacteria, inorganic phosphate (P i ) also participates in the co-ordinated regulation of photosynthesis: P i binds to the RuBisCO active site and to another site on the large chain where it can influence transitions between activated and less active conformations of the enzyme. In this way, activation of bacterial RuBisCO might be particularly sensitive to P i levels, which might cause it to act in a similar way to how RuBisCO activase functions in higher plants. [ 33 ]
Since carbon dioxide and oxygen compete at the active site of RuBisCO, carbon fixation by RuBisCO can be enhanced by increasing the carbon dioxide level in the compartment containing RuBisCO ( chloroplast stroma ). Several times during the evolution of plants, mechanisms have evolved for increasing the level of carbon dioxide in the stroma (see C 4 carbon fixation ). The use of oxygen as a substrate appears to be a puzzling process, since it seems to throw away captured energy. However, it may be a mechanism for preventing carbohydrate overload during periods of high light flux. This weakness in the enzyme is the cause of photorespiration , such that healthy leaves in bright light may have zero net carbon fixation when the ratio of O 2 to CO 2 available to RuBisCO shifts too far towards oxygen. This phenomenon is primarily temperature-dependent: high temperatures can decrease the concentration of CO 2 dissolved in the moisture of leaf tissues. This phenomenon is also related to water stress : since plant leaves are evaporatively cooled, limited water causes high leaf temperatures. C 4 plants use the enzyme PEP carboxylase initially, which has a higher affinity for CO 2 . The process first makes a 4-carbon intermediate compound, hence the name C 4 plants, which is shuttled into a site of C 3 photosynthesis then decarboxylated, releasing CO 2 to boost the concentration of CO 2 .
Crassulacean acid metabolism (CAM) plants keep their stomata closed during the day, which conserves water but prevents the light-independent reactions (a.k.a. the Calvin Cycle ) from taking place, since these reactions require CO 2 to pass by gas exchange through these openings. Evaporation through the upper side of a leaf is prevented by a layer of wax .
Since RuBisCO is often rate-limiting for photosynthesis in plants, it may be possible to improve photosynthetic efficiency by modifying RuBisCO genes in plants to increase catalytic activity and/or decrease oxygenation rates. [ 34 ] [ 35 ] [ 36 ] [ 37 ] This could improve sequestration of CO 2 and be a strategy to increase crop yields. [ 38 ] Approaches under investigation include transferring RuBisCO genes from one organism into another organism, engineering Rubisco activase from thermophilic cyanobacteria into temperature sensitive plants, increasing the level of expression of RuBisCO subunits, expressing RuBisCO small chains from the chloroplast DNA , and altering RuBisCO genes to increase specificity for carbon dioxide or otherwise increase the rate of carbon fixation. [ 39 ] [ 40 ]
In general, site-directed mutagenesis of RuBisCO has been mostly unsuccessful, [ 38 ] though mutated forms of the protein have been achieved in tobacco plants with subunit C 4 species, [ 41 ] and a RuBisCO with more C 4 -like kinetic characteristics have been attained in rice via nuclear transformation. [ 42 ] Robust and reliable engineering for yield of RuBisCO and other enzymes in the C 3 cycle was shown to be possible, [ 43 ] and it was first achieved in 2019 through a synthetic biology approach. [ 37 ]
One avenue is to introduce RuBisCO variants with naturally high specificity values such as the ones from the red alga Galdieria partita into plants. This may improve the photosynthetic efficiency of crop plants, although possible negative impacts have yet to be studied. [ 44 ] Advances in this area include the replacement of the tobacco enzyme with that of the purple photosynthetic bacterium Rhodospirillum rubrum . [ 45 ] In 2014, two transplastomic tobacco lines with functional RuBisCO from the cyanobacterium Synechococcus elongatus PCC7942 (Se7942) were created by replacing the RuBisCO with the large and small subunit genes of the Se7942 enzyme, in combination with either the corresponding Se7942 assembly chaperone, RbcX, or an internal carboxysomal protein, CcmM35. Both mutants had increased CO 2 fixation rates when measured as carbon molecules per RuBisCO. However, the mutant plants grew more slowly than wild-type. [ 46 ]
A recent theory explores the trade-off between the relative specificity (i.e., ability to favour CO 2 fixation over O 2 incorporation, which leads to the energy-wasteful process of photorespiration ) and the rate at which product is formed. The authors conclude that RuBisCO may actually have evolved to reach a point of 'near-perfection' in many plants (with widely varying substrate availabilities and environmental conditions), reaching a compromise between specificity and reaction rate. [ 47 ] It has been also suggested that the oxygenase reaction of RuBisCO prevents CO 2 depletion near its active sites and provides the maintenance of the chloroplast redox state. [ 48 ]
Since photosynthesis is the single most effective natural regulator of carbon dioxide in the Earth's atmosphere , [ 49 ] a biochemical model of RuBisCO reaction is used as the core module of climate change models. Thus, a correct model of this reaction is essential to the basic understanding of the relations and interactions of environmental models.
There currently are very few effective methods for expressing functional plant Rubisco in bacterial hosts for genetic manipulation studies. This is largely due to Rubisco's requirement of complex cellular machinery for its biogenesis and metabolic maintenance including the nuclear-encoded RbcS subunits, which are typically imported into chloroplasts as unfolded proteins. [ 50 ] [ 51 ] Furthermore, sufficient expression and interaction with Rubisco activase are major challenges as well. [ 39 ] One successful method for expression of Rubisco in E. coli involves the co-expression of multiple chloroplast chaperones, though this has only been shown for Arabidopsis thaliana Rubisco. [ 52 ]
Due to its high abundance in plants (generally 40% of the total protein content), RuBisCO often impedes analysis of important signaling proteins such as transcription factors , kinases , and regulatory proteins found in lower abundance (10-100 molecules per cell) within plants. [ 53 ] For example, using mass spectrometry on plant protein mixtures would result in multiple intense RuBisCO subunit peaks that interfere and hide those of other proteins.
Recently, one efficient method for precipitating out RuBisCO involves the usage of protamine sulfate solution. [ 54 ] Other existing methods for depleting RuBisCO and studying lower abundance proteins include fractionation techniques with calcium and phytate, [ 55 ] gel electrophoresis with polyethylene glycol, [ 56 ] [ 57 ] affinity chromatography , [ 58 ] [ 59 ] and aggregation using DTT , [ 60 ] though these methods are more time-consuming and less efficient when compared to protamine sulfate precipitation. [ 53 ]
The chloroplast gene rbcL , which codes for the large subunit of RuBisCO has been widely used as an appropriate locus for analysis of phylogenetics in plant taxonomy . [ 61 ]
Non-carbon-fixing proteins similar to RuBisCO, termed RuBisCO-like proteins (RLPs), are also found in the wild in organisms as common as Bacillus subtilis . This bacterium has a rbcL-like protein with a 2,3-diketo-5-methylthiopentyl-1-phosphate enolase function, part of the methionine salvage pathway . [ 62 ] Later identifications found functionally divergent examples dispersed all over bacteria and archaea, as well as transitionary enzymes performing both RLP-type enolase and RuBisCO functions. It is now believed that the current RuBisCO evolved from a dimeric RLP ancestor, acquiring its carboxylase function first before further oligomerizing and then recruiting the small subunit to form the familiar modern enzyme. [ 15 ] The small subunit probably first evolved in anaerobic and thermophilic organisms, where it enabled RuBisCO to catalyze its reaction at higher temperatures. [ 63 ] In addition to its effect on stabilizing catalysis, it enabled the evolution of higher specificities for CO 2 over O 2 by modulating the effect that substitutions within RuBisCO have on enzymatic function. Substitutions that do not have an effect without the small subunit suddenly become beneficial when it is bound. Furthermore, the small subunit enabled the accumulation of substitutions that are only tolerated in its presence. Accumulation of such substitutions leads to a strict dependence on the small subunit, which is observed in extant Rubiscos that bind a small subunit.
With the mass convergent evolution of the C 4 -fixation pathway in a diversity of plant lineages, ancestral C 3 -type RuBisCO evolved to have faster turnover of CO 2 in exchange for lower specificity as a result of the greater localization of CO 2 from the mesophyll cells into the bundle sheath cells . [ 64 ] This was achieved through enhancement of conformational flexibility of the “open-closed” transition in the Calvin cycle . Laboratory-based phylogenetic studies have shown that this evolution was constrained by the trade-off between stability and activity brought about by the series of necessary mutations for C 4 RuBisCO. [ 65 ] Moreover, in order to sustain the destabilizing mutations, the evolution to C 4 RuBisCO was preceded by a period in which mutations granted the enzyme increased stability, establishing a buffer to sustain and maintain the mutations required for C 4 RuBisCO. To assist with this buffering process, the newly-evolved enzyme was found to have further developed a series of stabilizing mutations. While RuBisCO has always been accumulating new mutations, most of these mutations that have survived have not had significant effects on protein stability. The destabilizing C 4 mutations on RuBisCO has been sustained by environmental pressures such as low CO 2 concentrations, requiring a sacrifice of stability for new adaptive functions. [ 65 ]
The term "RuBisCO" was coined humorously in 1979, by David Eisenberg at a seminar honouring the retirement of the early, prominent RuBisCO researcher, Sam Wildman , and also alluded to the snack food trade name " Nabisco " in reference to Wildman's attempts to create an edible protein supplement from tobacco leaves. [ 66 ] [ 67 ]
The capitalization of the name has been long debated. It can be capitalized for each letter of the full name ( R ib u lose-1,5 bis phosphate c arboxylase/ o xygenase), but it has also been argued that is should all be in lower case (rubisco), similar to other terms like scuba or laser. [ 1 ] | https://en.wikipedia.org/wiki/RuBisCO |
Ruthenium(II) chloride is an inorganic compound , a metal salt of ruthenium and hydrochloric acid with the formula RuCl 2 . [ 1 ] [ 2 ]
Ruthenium(II) chloride forms brown crystals.
Ruthenium(II) chloride is poorly soluble in cold water, but is soluble in ethanol .
Ruthenium(II) chloride can form complexes with aromatic hydrocarbons . [ 4 ]
The compound can be reduced to elemental ruthenium by hydrogen.
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/RuCl2 |
Ruthenium(III) chloride is the chemical compound with the formula RuCl 3 . "Ruthenium(III) chloride" more commonly refers to the hydrate RuCl 3 · x H 2 O. Both the anhydrous and hydrated species are dark brown or black solids. The hydrate, with a varying proportion of water of crystallization , often approximating to a trihydrate, is a commonly used starting material in ruthenium chemistry.
Anhydrous ruthenium(III) chloride is usually prepared by heating powdered ruthenium metal with chlorine . In the original synthesis, the chlorination was conducted in the presence of carbon monoxide , the product being carried by the gas stream and crystallising upon cooling. [ 1 ] [ 2 ] Two polymorphs of RuCl 3 are known. The black α-form adopts the CrCl 3 -type structure with long Ru-Ru contacts of 346 pm . This polymorph has honeycomb layers of Ru 3+ which are surrounded with an octahedral cage of Cl − anions. The ruthenium cations are magnetic residing in a low-spin J~1/2 ground state with net angular momentum L=1. [ 3 ] [ 4 ] Layers of α-RuCl 3 are stacked on top of each other with weak Van der Waals forces . These can be cleaved to form mono-layers using scotch tape. [ 5 ]
The dark brown metastable β-form crystallizes in a hexagonal cell; this form consists of infinite chains of face-sharing octahedra with Ru-Ru contacts of 283 pm, similar to the structure of zirconium trichloride . The β-form is irreversibly converted to the α-form at 450–600 °C. The β-form is diamagnetic, whereas α-RuCl 3 is paramagnetic at room temperature. [ 6 ]
RuCl 3 vapour decomposes into the elements at high temperatures; the enthalpy change at 750 °C (1020 K), Δ diss H 1020 has been estimated as +240 kJ/mol.
α-RuCl 3 was proposed as a candidate for a Kitaev quantum spin liquid state [ 7 ] when neutron scattering revealed an unusual magnetic spectrum, [ 8 ] [ 9 ] [ 10 ] and thermal transport revealed chiral Majorana Fermions when subject to a magnetic field. [ 11 ]
As the most commonly available ruthenium compound, RuCl 3 · x H 2 O is the precursor to many hundreds of chemical compounds. The noteworthy property of ruthenium complexes, chlorides and otherwise, is the existence of more than one oxidation state, several of which are kinetically inert. All second and third-row transition metals form exclusively low spin complexes, whereas ruthenium is special in the stability of adjacent oxidation states, especially Ru(II), Ru(III) (as in the parent RuCl 3 · x H 2 O) and Ru(IV).
Some of these compounds were utilized in the research related to two Nobel Prizes . Ryōji Noyori was awarded the Nobel Prize in Chemistry in 2001 for the development of practical asymmetric hydrogenation catalysts based on ruthenium. Robert H. Grubbs was awarded the Nobel Prize in Chemistry in 2005 for the development of practical alkene metathesis catalysts based on ruthenium alkylidene derivatives.
RuCl 3 (H 2 O) x reacts with carbon monoxide under mild conditions. [ 18 ] In contrast, iron chlorides do not react with CO. CO reduces the red-brown trichloride to yellowish Ru(II) species. Specifically, exposure of an ethanol solution of RuCl 3 (H 2 O) x to 1 atm of CO gives, depending on the specific conditions, [Ru 2 Cl 4 (CO) 4 ], [Ru 2 Cl 4 (CO) 4 ] 2− , and [RuCl 3 (CO) 3 ] − . Addition of ligands (L) to such solutions gives Ru-Cl-CO-L compounds (L = PR 3 ). Reduction of these carbonylated solutions with Zn affords the orange triangular cluster Ru 3 (CO) 12 . | https://en.wikipedia.org/wiki/RuCl3 |
Ruthenium(IV) oxide is the inorganic compound with the formula Ru O 2 . This black solid is the most common oxide of ruthenium . It is widely used as an electrocatalyst for producing chlorine, chlorine oxides, and O 2 . [ 1 ] Like many dioxides, RuO 2 adopts the rutile structure. [ 2 ] [ 3 ]
It is usually prepared by oxidation of ruthenium trichloride . Nearly stoichiometric single crystals of RuO 2 can be obtained by chemical vapor transport , using O 2 as the transport agent: [ 4 ] [ 5 ]
Films of RuO 2 can be prepared by chemical vapor deposition (CVD) from volatile ruthenium compounds. [ 6 ] RuO 2 can also be prepared through electroplating from a solution of ruthenium trichloride. [ 7 ]
Electrostatically stabilized hydrosols of pristine ruthenium dioxide hydrate have been prepared by exploiting the autocatalytic reduction of ruthenium tetroxide in aqueous solution. The resulting particle populations may be controlled to comprise substantially monodisperse, uniform spheres with diameters in the range 40 nm - 160 nm. [ 8 ]
Ruthenium(IV) oxide is being used as the main component in the catalyst of the Sumitomo- Deacon process which produces chlorine by the oxidation of hydrogen chloride . [ 9 ] [ 10 ]
RuO 2 can be used as catalyst in many other situations. Noteworthy reactions are the Fischer–Tropsch process , Haber–Bosch process , and various manifestations of fuel cells .
RuO 2 is extensively used for the coating of titanium anodes for the electrolytic production of chlorine and for the preparation of resistors or integrated circuits . [ 11 ] [ 12 ] Ruthenium oxide resistors can be used as sensitive thermometers in the temperature range .02 < T < 4 K. It can be also used as active material in supercapacitor because it has very high charge transfer capability. Ruthenium oxide has great capacity to store charge when used in aqueous solutions. [ 13 ] Average capacities of ruthenium(IV) oxide have reached 650 F/g when in sulfuric acid and annealed at temperatures lower than 200 °C. [ 14 ] In attempts to optimise its capacitive properties, prior work has looked at the hydration, crystallinity and particle size of ruthenium oxide. | https://en.wikipedia.org/wiki/RuO2 |
Ruthenium tetroxide is the inorganic compound with the formula RuO 4 . It is a yellow volatile solid that melts near room temperature. [ 3 ] It has the odor of ozone. [ 4 ] Samples are typically black due to impurities. The analogous OsO 4 is more widely used and better known. It is also the anhydride of hyperruthenic acid (H 2 RuO 5 ). One of the few solvents in which RuO 4 forms stable solutions is CCl 4 . [ 5 ]
RuO 4 is prepared by oxidation of ruthenium(III) chloride with NaIO 4 . [ 3 ] The reaction initially produces sodium diperiododihydroxoruthenate(VI), which then decomposes in acid solution to the tetroxide: [ 6 ]
Due to its challenging reactivity, RuO 4 is always generated in situ and used in catalytic quantities, at least in organic reactions. [ 5 ]
RuO 4 forms two crystal structures, one with cubic symmetry and another with monoclinic symmetry, isotypic to OsO 4 . The molecule adopts a tetrahedral geometry, with the Ru–O distances ranging from 169 to 170 pm. [ 8 ]
The main commercial value of RuO 4 is as an intermediate in the production of ruthenium compounds and metal from ores. Like other platinum group metals (PGMs), ruthenium occurs at low concentrations and often mixed with other PGMs. Together with OsO 4 , it is separated from other PGMs by distillation of a chlorine-oxidized extract. Ruthenium is separated from OsO 4 by reducing RuO 4 with hydrochloric acid , a process that exploits the highly positive reduction potential for the [RuO 4 ] 0/- couple. [ 9 ] [ 10 ]
RuO 4 is of specialized value in organic chemistry because it oxidizes virtually any hydrocarbon. [ 11 ] For example, it will oxidize adamantane to 1-adamantanol. Because it is such an aggressive oxidant, reaction conditions must be mild, generally room temperature. Although a strong oxidant, RuO 4 oxidations do not perturb stereocenters that are not oxidized. Illustrative is the oxidation of the following diol to a carboxylic acid :
Oxidation of epoxy alcohols also occurs without degradation of the epoxide ring:
Under milder conditions, oxidative reaction yields aldehydes instead. RuO 4 readily converts secondary alcohols into ketones . Although similar results can be achieved with other cheaper oxidants such as PCC - or DMSO -based oxidants, RuO 4 is ideal when a very vigorous oxidant is needed, but mild conditions must be maintained. It is used in organic synthesis to oxidize internal alkynes to 1,2- diketones , and terminal alkynes along with primary alcohols to carboxylic acids . When used in this fashion, the ruthenium(VIII) oxide is used in catalytic amounts and regenerated by the addition of sodium periodate to ruthenium(III) chloride and a solvent mixture of acetonitrile , water and carbon tetrachloride . RuO 4 readily cleaves double bonds to yield carbonyl products, in a manner similar to ozonolysis . OsO 4 , a more familiar oxidant that is structurally similar to RuO 4 , does not cleave double bonds, instead producing vicinal diol products. However, with short reaction times and carefully controlled conditions, RuO 4 can also be used for dihydroxylation. [ 12 ]
Because RuO 4 degrades the "double bonds" of arenes (especially electron-rich ones) by dihydroxylation and cleavage of the C-C bond in a way few other reagents can, it is useful as a "deprotection" reagent for carboxylic acids that are masked as aryl groups (typically phenyl or p -methoxyphenyl). Because the fragments formed are themselves readily oxidizable by RuO 4 , a substantial fraction of the arene carbon atoms undergo exhaustive oxidation to form carbon dioxide. Consequently, multiple equivalents of the terminal oxidant (often in excess of 10 equivalents per aryl ring) are required to achieve complete conversion to the carboxylic acid, limiting the practicality of the transformation. [ 13 ] [ 14 ] [ 15 ]
Although used as a direct oxidant , due to the relatively high cost of RuO 4 it is also used catalytically with a cooxidant. For an oxidation of cyclic alcohols with RuO 4 as a catalyst and bromate as oxidant under basic conditions, RuO 4 is first activated by hydroxide, turning into the hyperruthenate anion: [ 16 ]
The reaction proceeds via a glycolate complex.
Ruthenium tetroxide is a potential staining agent. It is used to expose latent fingerprints by turning to the brown/black ruthenium dioxide when in contact with fatty oils or fats contained in sebaceous contaminants of the print. [ 17 ]
Because of the very high volatility of ruthenium tetroxide ( RuO 4 ) ruthenium radioactive isotopes with their relative short half-life are considered as the second most hazardous gaseous isotopes after iodine-131 in case of release by a nuclear accident. [ 18 ] [ 4 ] [ 19 ] The two most important radioactive isotopes of ruthenium are 103 Ru and 106 Ru. They have half-lives of 39.6 days and 373.6 days, respectively. [ 4 ] | https://en.wikipedia.org/wiki/RuO4 |
Ruaniaceae is an Actinomycete family with two monotypic genera. [ 1 ]
The currently accepted taxonomy is based on the List of Prokaryotic names with Standing in Nomenclature (LPSN) [ 2 ] and National Center for Biotechnology Information (NCBI) [ 3 ] and the phylogeny is based on 16S rRNA-based LTP release 106 by The All-Species Living Tree Project [ 4 ]
Ruania alba Tang et al . 2010
Ruania albidiflava Gu et al . 2007
This Actinomycetota -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ruaniaceae |
Rubber Chemistry and Technology is a quarterly peer-reviewed scientific journal covering fundamental research and technical developments relating to chemistry, materials science, and engineering of rubber , elastomers , and related materials. It was established in 1928, with Carroll C. Davis as its first editor-in-chief . The current editor-in-chief is Christopher G. Robertson. The journal is published by the ACS Rubber Division .
The journal currently publishes four issues per year containing original research contributions and review articles.
The journal is abstracted indexed in:
According to the Journal Citation Reports , the journal has a 2021 impact factor of 2.081. [ 1 ]
The following persons have been editors-in-chief of the journal: | https://en.wikipedia.org/wiki/Rubber_Chemistry_and_Technology |
Rubber elasticity is the ability of solid rubber to be stretched up to a factor of 10 from its original length, and return to close to its original length upon release. This process can be repeated many times with no apparent degradation to the rubber. [ 1 ]
Rubber, like all materials, consists of molecules . Rubber's elasticity is produced by molecular processes that occur due to its molecular structure . Rubber's molecules are polymers , or large, chain-like molecules. Polymers are produced by a process called polymerization . [ 2 ] This process builds polymers up by sequentially adding short molecular backbone units to the chain through chemical reactions . A rubber polymer follows a random winding path in three dimensions, intermingling with many other rubber polymers.
Natural rubbers, such as polybutadiene and polyisoprene , are extracted from plants as a fluid colloid and then solidified in a process called Vulcanization . During the process, a small amount of a cross-linking molecule, usually sulfur , is added. When heat is applied, sections of rubber's polymer chains chemically bond to the cross-linking molecule. These bonds cause rubber polymers to become cross-linked , or joined to each other by the bonds made with the cross-linking molecules. Because each rubber polymer is very long, each one participates in many crosslinks with many other rubber molecules, forming a continuous network. The resulting molecular structure demonstrates elasticity, making rubber a member of the class of elastic polymers called elastomers . [ 2 ] [ 3 ]
Following its introduction to Europe from America in the late 15th century, natural rubber ( polyisoprene ) was regarded mostly as a curiosity. Its most useful application was its ability to erase pencil marks on paper by rubbing, hence its name. One of its most peculiar properties is a slight (but detectable) increase in temperature that occurs when a sample of rubber is stretched. If it is allowed to quickly retract, an equal amount of cooling is observed. This phenomenon caught the attention of the English physicist John Gough . In 1805 he published some qualitative observations on this characteristic as well as how the required stretching force increased with temperature. [ 4 ]
By the mid-nineteenth century, the theory of thermodynamics was being developed and within this framework, the English mathematician and physicist Lord Kelvin [ 5 ] showed that the change in mechanical energy required to stretch a rubber sample should be proportional to the increase in temperature. This would later be associated with a change in entropy. The connection to thermodynamics was firmly established in 1859 when the English physicist James Joule published the first careful measurements of the temperature increase that occurred as a rubber sample was stretched. [ 6 ] This work confirmed the theoretical predictions of Lord Kelvin.
In 1838 the American inventor Charles Goodyear found that natural rubber's elastic properties could be immensely improved by adding a small amount of sulfur to produce chemical cross-links between adjacent polyisoprene molecules.
Before it is cross-linked, the liquid natural rubber consists of very long polymer molecules, containing thousands of isoprene backbone units, connected head-to-tail (commonly referred to as chains). Every chain follows a random, three-dimensional path through the polymer liquid and is in contact with thousands of other nearby chains. When heated to about 150C, reactive cross-linker molecules, such as sulfur or dicumyl peroxide, can decompose and the subsequent chemical reactions produce a chemical bond between adjacent chains. A crosslink can be visualized as the letter 'X' but with some of its arms pointing out of the plane. The result is a three dimensional molecular network.
All of the polyisoprene molecules are connected together at multiple points by these chemical bonds (network nodes) resulting in a single giant molecule and all information about the original long polymers is lost. A rubber band is a single molecule, as is a latex glove. The sections of polyisoprene between two adjacent cross-links are called network chains and can contain up to several hundred isoprene units. In natural rubber, each cross-link produces a network node with four chains emanating from it. It is the network that gives rise to these elastic properties.
Because of the enormous economic and technological importance of rubber, predicting how a molecular network responds to mechanical strains has been of enduring interest to scientists and engineers. To understand the elastic properties of rubber, theoretically, it is necessary to know both the physical mechanisms that occur at the molecular level and how the random-walk nature of the polymer chain defines the network. The physical mechanisms that occur within short sections of the polymer chains produce the elastic forces and the network morphology determines how these forces combine to produce the macroscopic stress that is observed when a rubber sample is deformed (e.g. subjected to tensile strain ).
There are actually several physical mechanisms that produce the elastic forces within the network chains as a rubber sample is stretched. Two of these arise from entropy changes and one is associated with the distortion of the molecular bond angles along the chain backbone. These three mechanisms are immediately apparent when a moderately thick rubber sample is stretched manually.
Initially, the rubber feels quite stiff (i.e. the force must be increased at a high rate with respect to the strain). At intermediate strains, the required increase in force is much lower to cause the same amount of stretch. Finally, as the sample approaches the breaking point, its stiffness increases markedly. What the observer is noticing are the changes in the modulus of elasticity that are due to the different molecular mechanisms. These regions can be seen in Fig. 1, a typical stress vs. strain measurement for natural rubber. The three mechanisms (labelled Ia, Ib, and II) predominantly correspond to the regions shown on the plot.
The concept of entropy comes to us from the area of mathematical physics called statistical mechanics which is concerned with the study of large thermal systems, e.g. rubber networks at room temperature. Although the detailed behavior of the constituent chains are random and far too complex to study individually, we can obtain very useful information about their "average" behavior from a statistical mechanics analysis of a large sample. There are no other examples of how entropy changes can produce a force in our everyday experience. One may regard the entropic forces in polymer chains as arising from the thermal collisions that their constituent atoms experience with the surrounding material. It is this constant jostling that produces a resisting (elastic) force in the chains as they are forced to become straight.
While stretching a rubber sample is the most common example of elasticity, it also occurs when rubber is compressed. Compression may be thought of as a two dimensional expansion as when a balloon is inflated. The molecular mechanisms that produce the elastic force are the same for all types of strain.
When these elastic force models are combined with the complex morphology of the network, it is not possible to obtain simple analytic formulae to predict the macroscopic stress. It is only via numerical simulations on computers that it is possible to capture the complex interaction between the molecular forces and the network morphology to predict the stress and ultimate failure of a rubber sample as it is strained.
The Molecular Kink Paradigm proceeds from the intuitive notion that molecular chains that make up a natural rubber ( polyisoprene ) network are constrained by surrounding chains to remain within a "tube." Elastic forces produced in a chain, as a result of some applied strain, are propagated along the chain contour within this tube. Fig. 2 shows a representation of a four-carbon isoprene backbone unit with an extra carbon atom at each end to indicate its connections to adjacent units on a chain. It has three single C-C bonds and one double bond. It is principally by rotating about the C-C single bonds that a polyisoprene chain randomly explores its possible conformations.
Sections of chain containing between two and three isoprene units have sufficient flexibility that they may be considered statistically de-correlated from one another. That is, there is no directional correlation along the chain for distances greater than this distance, referred to as a Kuhn length . These non-straight regions evoke the concept of "kinks" and are in fact a manifestation of the random-walk nature of the chain.
Since a kink is composed of several isoprene units, each having three carbon-carbon single bonds, there are many possible conformations available to a kink, each with a distinct energy and end-to-end distance. Over time scales of seconds to minutes, only these relatively short sections of the chain (i.e. kinks) have sufficient volume to move freely amongst their possible rotational conformations. The thermal interactions tend to keep the kinks in a state of constant flux, as they make transitions between all of their possible rotational conformations. Because the kinks are in thermal equilibrium , the probability that a kink resides in any rotational conformation is given by a Boltzmann distribution and we may associate an entropy with its end-to-end distance. The probability distribution for the end-to-end distance of a Kuhn length is approximately Gaussian and is determined by the Boltzmann probability factors for each state (rotational conformation). As a rubber network is stretched, some kinks are forced into a restricted number of more extended conformations having a greater end-to-end distance and it is the resulting decrease in entropy that produces an elastic force along the chain.
There are three distinct molecular mechanisms that produce these forces, two of which arise from changes in entropy that is referred to as the low chain extension regime, Ia [ 8 ] and the moderate chain extension regime, Ib. [ 9 ] The third mechanism occurs at high chain extension, as it is extended beyond its initial equilibrium contour length by the distortion of the chemical bonds along its backbone. In this case, the restoring force is spring-like and is referred to as regime II. [ 10 ] The three force mechanisms are found to roughly correspond to the three regions observed in tensile stress vs. strain experiments, shown in Fig. 1.
The initial morphology of the network, immediately after chemical cross-linking, is governed by two random processes: [ 11 ] [ 12 ] (1) The probability for a cross-link to occur at any isoprene unit and, (2) the random walk nature of the chain conformation. The end-to-end distance probability distribution for a fixed chain length (i.e. fixed number of isoprene units) is described by a random walk. It is the joint probability distribution of the network chain lengths and the end-to-end distances between their cross-link nodes that characterizes the network morphology. Because both the molecular physics mechanisms that produce the elastic forces and the complex morphology of the network must be treated simultaneously, simple analytic elasticity models are not possible; an explicit 3-dimensional numerical model [ 13 ] [ 14 ] [ 15 ] is required to simulate the effects of strain on a representative volume element of a network.
The Molecular Kink Paradigm envisions a representative network chain as a series of vectors that follow the chain contour within its tube. Each vector represents the equilibrium end-to-end distance of a kink. The actual 3-dimensional path of the chain is not pertinent, since all elastic forces are assumed to operate along the chain contour. In addition to the chain's contour length, the only other important parameter is its tortuosity , the ratio of its contour length to its end-to-end distance. As the chain is extended, in response to an applied strain, the induced elastic force is assumed to propagate uniformly along its contour. Consider a network chain whose end points (network nodes) are more or less aligned with the tensile strain axis. As the initial strain is applied to the rubber sample, the network nodes at the ends of the chain begin to move apart and all of the kink vectors along the contour are stretched simultaneously. Physically, the applied strain forces the kinks to stretch beyond their thermal equilibrium end-to-end distances, causing a decrease in their entropy. The increase in free energy associated with this change in entropy, gives rise to a (linear) elastic force that opposes the strain. The force constant for the low strain regime can be estimated by sampling molecular dynamics (MD) trajectories of a kink (i.e. short chains) composed of 2–3 isoprene units, at relevant temperatures (e.g. 300K). [ 8 ] By taking many samples of the coordinates over the course of the simulations, the probability distributions of end-to-end distance for a kink can be obtained. Since these distributions (which turn out to be approximately Gaussian) are directly related to the number of states, they may be associated with the entropy of the kink at any end-to-end distance. By numerically differentiating the probability distribution, the change in entropy, and hence free energy , with respect to the kink end-to-end distance can be found. The force model for this regime is found to be linear and proportional to the temperature divided by the chain tortuosity.
At some point in the low extension regime (i.e. as all of the kinks along the chain are being extended simultaneously) it becomes energetically more favourable to have one kink transition to an extended conformation in order to stretch the chain further. The applied strain can force a single isoprene unit within a kink into an extended conformation, slightly increasing the end-to-end distance of the chain, and the energy required to do this is less than that needed to continue extending all of the kinks simultaneously. Numerous experiments [ 16 ] strongly suggest that stretching a rubber network is accompanied by a decrease in entropy. As shown in Fig. 2, an isoprene unit has three single C-C bonds and there are two or three preferred rotational angles (orientations) about these bonds that have energy minima. Of the 18 allowed [ 9 ] rotational conformations, only 6 have extended end-to-end distances and forcing the isoprene units in a chain to reside in some subset of the extended states must reduce the number of rotational conformations available for thermal motion. It is this reduction in the number of available states that causes the entropy to decrease. As the chain continues to straighten, all of the isoprene units in the chain are eventually forced into extended conformations and the chain is considered to be "taut." A force constant for chain extension can be estimated from the resulting change in free energy associated with this entropy change. [ 9 ] As with regime IA, the force model for this regime is linear and proportional to the temperature divided by the chain tortuosity.
When all of the isoprene units in a network chain have been forced to reside in just a few extended rotational conformations, the chain becomes taut. It may be regarded as sensibly straight, except for the zigzag path that the C-C bonds make along the chain contour. However, further extension is still possible by bond distortions (e.g. bond angle increases), bond stretches, and dihedral angle rotations. These forces are spring-like and are not associated with entropy changes. A taut chain can be extended by only about 40%. At this point the force along the chain is sufficient to mechanically rupture the C-C covalent bond. This tensile force limit has been calculated [ 10 ] via quantum chemistry simulations and it is approximately 7 nN, about a factor of a thousand greater than the entropic chain forces at low strain. The angles between adjacent backbone C-C bonds in an isoprene unit vary between about 115–120 degrees and the forces associated with maintaining these angles are quite large, so within each unit, the chain backbone always follows a zigzag path, even at bond rupture. This mechanism accounts for the steep upturn in the elastic stress, observed at high strains (Fig. 1).
Although the network is completely described by only two parameters (the number of network nodes per unit volume and the statistical de-correlation length of the polymer, the Kuhn length), the way in which the chains are connected is actually quite complicated. There is a wide variation in the lengths of the chains and most of them are not connected to the nearest neighbor network node. Both the chain length and its end-to-end distance are described by probability distributions. The term "morphology" refers to this complexity. If the cross-linking agent is thoroughly mixed, there is an equal probability for any isoprene unit to become a network node. For dicumyl peroxide, the cross linking efficiency in natural rubber is unity, [ 17 ] but this is not the case for sulfur. [ 18 ] The initial morphology of the network is dictated by two random processes: the probability for a cross-link to occur at any isoprene unit and the Markov random walk nature of a chain conformation. [ 11 ] [ 12 ] The probability distribution function for how far one end of a chain end can ‘wander’ from the other is generated by a Markov sequence. [ 19 ] This conditional probability density function relates the chain length n {\displaystyle n} in units of the Kuhn length b {\displaystyle b} to the end-to-end distance r {\displaystyle r} :
The probability that any isoprene unit becomes part of a cross-link node is proportional to the ratio of the concentrations of the cross-linker molecules (e.g., dicumyl-peroxide) to the isoprene units: p x = 2 [cross-link] [isoprene] {\displaystyle p_{x}=2{\frac {\text{[cross-link]}}{\text{[isoprene]}}}} The factor of two comes about because two isoprene units (one from each chain) participate in the cross-link. The probability for finding a chain containing N {\displaystyle N} isoprene units is given by:
where N ≥ 1 {\displaystyle N\geq 1} .
The equation can be understood as simply the probability that an isoprene unit is NOT a cross-link (1− p x ) in N −1 successive units along a chain. Since P ( N ) decreases with N , shorter chains are more probable than longer ones. Note that the number of statistically independent backbone segments is not the same as the number of isoprene units. For natural rubber networks, the Kuhn length contains about 2.2 isoprene units, so N ∼ 2.2 n {\displaystyle N\sim 2.2n} . The product of equations ( 1 ) and ( 3 ) (the joint probability distribution ) relates the network chain length ( N {\displaystyle N} ) and end-to-end distance ( r {\displaystyle r} ) between its terminating cross-link nodes:
The complex morphology of a natural rubber network can be seen in Fig. 3, which shows the probability density vs. end-to-end distance (in units of mean node spacing) for an "average" chain. For the common experimental cross-link density of 4x10 19 cm −3 , an average chain contains about 116 isoprene units (52 Kuhn lengths) and has a contour length of about 50 nm. Fig. 3 shows that a significant fraction of chains span several node spacings, i.e., the chain ends overlap other network chains. Natural rubber, cross-linked with dicumyl peroxide, has tetra-functional cross-links (i.e. each cross-link node has 4 network chains emanating from it). Depending on their initial tortuosity and the orientation of their endpoints with respect to the strain axis, each chain associated with an active cross-link node can have a different elastic force constant as it resists the applied strain. To preserve force equilibrium (zero net force) on each cross-link node, a node may be forced to move in tandem with the chain having the highest force constant for chain extension. It is this complex node motion, arising from the random nature of the network morphology, that makes the study of the mechanical properties of rubber networks so difficult. As the network is strained, paths composed of these more extended chains emerge that span the entire sample, and it is these paths that carry most of the stress at high strains.
To calculate the elastic response of a rubber sample, the three chain force models (regimes Ia, Ib and II) and the network morphology must be combined in a micro-mechanical network model. [ 13 ] [ 14 ] [ 15 ] Using the joint probability distribution in equation ( 4 ) and the force extension models, it is possible to devise numerical algorithms to both construct a faithful representative volume element of a network and to simulate the resulting mechanical stress as it is subjected to strain. An iterative relaxation algorithm is used to maintain approximate force equilibrium at each network node as strain is imposed. When the force constant obtained for kinks having 2 or 3 isoprene units (approximately one Kuhn length) is used in numerical simulations, the predicted stress is found to be consistent with experiments. The results of such a calculation [ 18 ] are shown in Fig. 1 (dashed red line) for sulphur cross-linked natural rubber and compared with experimental data [ 20 ] (solid blue line). These simulations also predict a steep upturn in the stress as network chains become taut and, ultimately, material failure due to bond rupture. In the case of sulphur cross-linked natural rubber, the S-S bonds in the cross-link are much weaker than the C-C bonds on the chain backbone and are the network failure points. The plateau in the simulated stress, starting at a strain of about 7, is the limiting value for the network. Stresses greater than about 7 MPa cannot be supported and the network fails. Near this stress limit, the simulations predict [ 15 ] that less than 10% of the chains are taut, i.e. in the high chain extension regime and less than 0.1% of the chains have ruptured. While the very low rupture fraction may seem surprising, it is not inconsistent with the common experience of stretching a rubber band until it breaks. The elastic response of the rubber after breaking is not noticeably different from the original.
For molecular systems in thermal equilibrium, the addition of energy (e.g. by mechanical work) can cause a change in entropy. This is known from the theories of thermodynamics and statistical mechanics. Specifically, both theories assert that the change in energy must be proportional to the entropy change times the absolute temperature. This rule is only valid so long as the energy is restricted to thermal states of molecules. If a rubber sample is stretched far enough, energy may reside in nonthermal states such as the distortion of chemical bonds and the rule does not apply. At low to moderate strains, theory predicts that the required stretching force is due to a change in entropy in the network chains.
It is therefore expected that the force necessary to stretch a sample to some value of strain should be proportional to the temperature of the sample. Measurements showing how the tensile stress in a stretched rubber sample varies with temperature are shown in Fig. 4. In these experiments, [ 21 ] the strain of a stretched rubber sample was held fixed as the temperature was varied between 10 and 70 degrees Celsius. For each value of fixed strain, it is seen that the tensile stress varied linearly (to within experimental error). These experiments provide the most compelling evidence that entropy changes are the fundamental mechanism for rubber elasticity.
The positive linear behaviour of the stress with temperature sometimes leads to the mistaken notion that rubber has a negative coefficient of thermal expansion (i.e. the length of a sample shrinks when heated). Experiments [ 22 ] have shown conclusively that, like almost all other materials, the coefficient of thermal expansion natural rubber is positive.
When stretching a piece of rubber (e.g. a rubber band) it will deform lengthwise in a uniform manner. When one end of the sample is released, it snaps back to its original length too quickly for the naked eye to resolve the process. An intuitive expectation is that it returns to its original length in the same manner as when it was stretched (i.e. uniformly). Experimental observations by Mrowca et al. [ 23 ] suggest that this expectation is inaccurate. To capture the extremely fast retraction dynamics, they utilized an experimental method devised by Exner and Stefan [ 24 ] in 1874. Their method consisted of a rapidly rotating glass cylinder which, after being coated with lamp black, was placed next to the stretched rubber sample. Styli, attached to the mid-point and free end of the rubber sample, were held in contact with the glass cylinder. Then, as the free end of the rubber snapped back, the styli traced out helical paths in the lamp black coating of the rotating cylinder. By adjusting the rotation speed of the cylinder, they could record the position of the styli in less than one complete rotation. The trajectories were transferred to a graph by rolling the cylinder on a piece of damp blotter paper. The mark left by a stylus appeared as a white line (no lamp black) on the paper.
Their data, plotted as the graph in Fig. 5, shows the position of end and midpoint styli as the sample rapidly retracts to its original length. The sample was initially stretched 9.5 in (~24 cm) beyond its unstrained length and then released. The styli returned to their original positions (i.e. a displacement of 0 in) in a little over 6 Ms. The linear behaviour of the displacement vs. time indicates that, after a brief acceleration, both the end and the midpoint of the sample snapped back at a constant velocity of about 50 m/s or 112 mph. However, the midpoint stylus did not start to move until about 3 Ms after the end was released. Evidently, the retraction process travels as a wave, starting at the free end.
At high extensions some of the energy stored in the stretched network chain is due to a change in its entropy, but most of the energy is stored in bond distortions (regime II, above) which do not involve an entropy change. If one assumes that all of the stored energy is converted to kinetic energy, the retraction velocity may be calculated directly from the familiar conservation equation E = 1 ⁄ 2 mv 2 . Numerical simulations, [ 14 ] based on the molecular kink paradigm, predict velocities consistent with this experiment.
Eugene Guth and Hubert M. James proposed the entropic origins of rubber elasticity in 1941. [ 25 ]
Temperature affects the elasticity of elastomers in an unusual way. When the elastomer is assumed to be in a stretched state, heating causes them to contract. Vice versa, cooling can cause expansion. [ 26 ] This can be observed with an ordinary rubber band. Stretching a rubber band will cause it to release heat, while releasing it after it has been stretched will lead it to absorb heat, causing its surroundings to become cooler. This phenomenon can be explained with the Gibbs free energy . Rearranging Δ G =Δ H − T Δ S , where G is the free energy, H is the enthalpy , and S is the entropy, we obtain T Δ S = Δ H − Δ G . Since stretching is nonspontaneous, as it requires external work, T Δ S must be negative. Since T is always positive (it can never reach absolute zero ), the Δ S must be negative, implying that the rubber in its natural state is more entangled (with more microstates ) than when it is under tension. Thus, when the tension is removed, the reaction is spontaneous, leading Δ G to be negative. Consequently, the cooling effect must result in a positive ΔH, so Δ S will be positive there. [ 27 ] [ 28 ]
The result is that an elastomer behaves somewhat like an ideal monatomic gas , inasmuch as (to good approximation) elastic polymers do not store any potential energy in stretched chemical bonds or elastic work done in stretching molecules, when work is done upon them. Instead, all work done on the rubber is "released" (not stored) and appears immediately in the polymer as thermal energy. In the same way, all work that the elastic does on the surroundings results in the disappearance of thermal energy in order to do the work (the elastic band grows cooler, like an expanding gas). This last phenomenon is the critical clue that the ability of an elastomer to do work depends (as with an ideal gas) only on entropy-change considerations, and not on any stored (i.e. potential) energy within the polymer bonds. Instead, the energy to do work comes entirely from thermal energy, and (as in the case of an expanding ideal gas) only the positive entropy change of the polymer allows its internal thermal energy to be converted efficiently into work.
Invoking the theory of rubber elasticity, a polymer chain in a cross-linked network may be seen as an entropic spring . When the chain is stretched, the entropy is reduced by a large margin because there are fewer conformations available. [ 29 ] As such there is a restoring force which causes the polymer chain to return to its equilibrium or unstretched state, such as a high entropy random coil configuration, once the external force is removed. This is the reason why rubber bands return to their original state. Two common models for rubber elasticity are the freely-jointed chain model and the worm-like chain model.
The freely joined chain, also called an ideal chain, follows the random walk model. Microscopically, the 3D random walk of a polymer chain assumes the overall end-to-end distance is expressed in terms of the x, y and z directions:
R → = R x x ^ + R y y ^ + R z z ^ {\displaystyle {\vec {R}}=R_{x}{\hat {x}}+R_{y}{\hat {y}}+R_{z}{\hat {z}}}
In the model, b {\displaystyle b} is the length of a rigid segment, N {\displaystyle N} is the number of segments of length b {\displaystyle b} , R {\displaystyle R} is the distance between the fixed and free ends, and L c {\displaystyle L_{\text{c}}} is the "contour length" or N b {\displaystyle Nb} . Above the glass transition temperature, the polymer chain oscillates and r {\displaystyle r} changes over time. The probability distribution of the chain is the product of the probability distributions of the individual components, given by the following Gaussian distribution: P ( R → ) = P ( R x ) P ( R y ) P ( R z ) = ( 2 n b 2 π 3 ) − 3 / 2 exp ( − 3 R 2 2 N b 2 ) {\displaystyle P({\vec {R}})=P(R_{x})P(R_{y})P(R_{z})=\left({\frac {2nb^{2}\pi }{3}}\right)^{-{3}/{2}}\exp \left({\frac {-3R^{2}}{2Nb^{2}}}\right)}
Therefore, the ensemble average end-to-end distance is simply the standard integral of the probability distribution over all space. Note that the movement could be backwards or forwards, so the net average ⟨ R ⟩ {\displaystyle \langle R\rangle } will be zero. However, the root mean square can be a useful measure of the distance.
⟨ R ⟩ = 0 ⟨ R 2 ⟩ = ∫ 0 ∞ R 2 4 π R 2 P ( R → ) d R = N b 2 ⟨ R 2 ⟩ 1 2 = N b {\displaystyle {\begin{aligned}\langle R\rangle &=0\\\langle R^{2}\rangle &=\int _{0}^{\infty }R^{2}4\pi R^{2}P({\vec {R}})dR=Nb^{2}\\\langle R^{2}\rangle ^{\frac {1}{2}}&={\sqrt {N}}b\end{aligned}}}
The Flory theory of rubber elasticity suggests that rubber elasticity has primarily entropic origins. By using the following basic equations for Helmholtz free energy and its discussion about entropy, the force generated from the deformation of a rubber chain from its original unstretched conformation can be derived. The Ω {\displaystyle \Omega } is the number of conformations of the polymer chain. Since the deformation does not involve enthalpy change, the change in free energy can simply be calculated as the change in entropy − T Δ S {\displaystyle -T\Delta S} . Note that the force equation resembles the behaviour of a spring and follows Hooke's law : F = k x {\displaystyle F=kx} , where F is the force, k is the spring constant and x is the distance. Usually, the neo-Hookean model can be used on cross-linked polymers to predict their stress-strain relations: Ω = C exp ( − 3 R → 2 2 N b 2 ) {\displaystyle \Omega =C\exp \left({\frac {-3{\vec {R}}^{2}}{2Nb^{2}}}\right)} S = k B ln Ω ≈ − 3 k B R → 2 2 N b 2 {\displaystyle S=k_{\text{B}}\ln \Omega \,\approx {\frac {-3k_{\text{B}}{\vec {R}}^{2}}{2Nb^{2}}}} Δ F ( R → ) ≈ − T Δ S d ( R → 2 ) = C + 3 k B T N b 2 R → 2 {\displaystyle \Delta F({\vec {R}})\approx -T\Delta S_{d}({\vec {R}}^{2})=C+{\frac {3k_{\text{B}}T}{Nb^{2}}}{\vec {R}}^{2}} f = d F ( R → ) d R → = d d R → ( 3 k B T R → 2 2 N b 2 ) = 3 k B T N b 2 R → {\displaystyle f={\frac {dF({\vec {R}})}{d{\vec {R}}}}={\frac {d}{d{\vec {R}}}}\left({\frac {3k_{\text{B}}T{\vec {R}}^{2}}{2Nb^{2}}}\right)={\frac {3k_{\text{B}}T}{Nb^{2}}}{\vec {R}}}
Note that the elastic coefficient 3 k B T / N b {\displaystyle 3k_{\text{B}}T/Nb} is temperature dependent. If rubber temperature increases, the elastic coefficient increases as well. This is the reason why rubber under constant stress shrinks when its temperature increases.
We can further expand the Flory theory into a macroscopic view, where bulk rubber material is discussed. Assume the original dimension of the rubber material is L x {\displaystyle L_{x}} , L y {\displaystyle L_{y}} and L z {\displaystyle L_{z}} , a deformed shape can then be expressed by applying an individual extension ratio λ i {\displaystyle \lambda _{i}} to the length ( λ x L x {\displaystyle \lambda _{x}L_{x}} , λ y L y {\displaystyle \lambda _{y}L_{y}} , λ z L z {\displaystyle \lambda _{z}L_{z}} ). So microscopically, the deformed polymer chain can also be expressed with the extension ratio: λ x R x {\displaystyle \lambda _{x}R_{x}} , λ y R y {\displaystyle \lambda _{y}R_{y}} , λ z R z {\displaystyle \lambda _{z}R_{z}} . The free energy change due to deformation can then be expressed as follows:
Δ F def ( R → ) = − 3 k B T R → 2 2 N b 2 = − 3 k B T ( ( R x 2 − R x 0 2 ) + ( R y 2 − R y 0 2 ) + ( R z 2 − R z 0 2 ) ) 2 N b 2 = − 3 k B T ( ( λ x 2 − 1 ) R x 0 2 + ( λ y 2 − 1 ) R y 0 2 + ( λ z 2 − 1 ) R z 0 2 ) 2 N b 2 {\displaystyle {\begin{aligned}\Delta F_{\text{def}}({\vec {R}})&=-{\frac {3k_{\text{B}}T{\vec {R}}^{2}}{2Nb^{2}}}=-{\frac {3k_{\text{B}}T\left(\left(R_{x}^{2}-R_{x0}^{2}\right)+\left(R_{y}^{2}-R_{y0}^{2}\right)+\left(R_{z}^{2}-R_{z0}^{2}\right)\right)}{2Nb^{2}}}\\&=-{\frac {3k_{\text{B}}T\left(\left(\lambda _{x}^{2}-1\right)R_{x0}^{2}+\left(\lambda _{y}^{2}-1\right)R_{y0}^{2}+\left(\lambda _{z}^{2}-1\right)R_{z0}^{2}\right)}{2Nb^{2}}}\end{aligned}}}
Assume that the rubber is cross-linked and isotropic, the random walk model gives R x {\displaystyle R_{x}} , R y {\displaystyle R_{y}} and R z {\displaystyle R_{z}} are distributed according to a normal distribution. Therefore, they are equal in space, and all of them are 1/3 of the overall end-to-end distance of the chain: ⟨ R x 0 2 ⟩ = ⟨ R y 0 2 ⟩ = ⟨ R z 0 2 ⟩ = ⟨ R 2 ⟩ / 3 {\displaystyle \langle R_{x0}^{2}\rangle =\langle R_{y0}^{2}\rangle =\langle R_{z0}^{2}\rangle =\langle R^{2}\rangle /3} . Plugging in the change of free energy equation above, it is easy to get: Δ F def ( R → ) = − k B T n s ⟨ R 2 ⟩ ( λ x 2 + λ y 2 + λ z 2 − 3 ) 2 N b 2 = − k B T n s ⟨ R 2 ⟩ ( λ x 2 + λ y 2 + λ z 2 − 3 ) 2 R 0 2 {\displaystyle {\begin{aligned}\Delta F_{\text{def}}({\vec {R}})&=-{\frac {k_{\text{B}}Tn_{s}\langle R^{2}\rangle \left(\lambda _{x}^{2}+\lambda _{y}^{2}+\lambda _{z}^{2}-3\right)}{2Nb^{2}}}\\&=-{\frac {k_{\text{B}}Tn_{s}\langle R^{2}\rangle \left(\lambda _{x}^{2}+\lambda _{y}^{2}+\lambda _{z}^{2}-3\right)}{2R_{0}^{2}}}\end{aligned}}}
The free energy change per volume is just: Δ f def = Δ F def ( R → ) V = − k B T v s β ( λ x 2 + λ y 2 + λ z 2 − 3 ) 2 {\displaystyle \Delta f_{\text{def}}={\frac {\Delta F_{\text{def}}({\vec {R}})}{V}}=-{\frac {k_{\text{B}}Tv_{s}\beta \left(\lambda _{x}^{2}+\lambda _{y}^{2}+\lambda _{z}^{2}-3\right)}{2}}} where n s {\displaystyle n_{s}} is the number of strands in network, the subscript "def" means "deformation", v s = n s / V {\displaystyle v_{s}=n_{s}/V} , which is the number density per volume of polymer chains, β = ⟨ R 2 ⟩ / R 0 2 {\displaystyle \beta =\langle R^{2}\rangle /R_{0}^{2}} which is the ratio between the end-to-end distance of the chain and the theoretical distance that obey random walk statistics. If we assume incompressibility, the product of extension ratios is 1, implying no change in the volume: λ x λ y λ z = 1 {\displaystyle \lambda _{x}\lambda _{y}\lambda _{z}=1} .
Case study: Uniaxial deformation:
In a uniaxial deformed rubber, because λ x λ y λ z = 1 {\displaystyle \lambda _{x}\lambda _{y}\lambda _{z}=1} it is assumed that λ x = λ y = λ z − 1 / 2 {\displaystyle \lambda _{x}=\lambda _{y}=\lambda _{z}^{-1/2}} . So the previous free energy per volume equation is: Δ f def = Δ F def ( R → ) V = − k B T v s β ( λ x 2 + λ y 2 + λ z 2 − 3 ) 2 = k B T v s β 2 ( λ z 2 + 2 λ z − 3 ) {\displaystyle \Delta f_{\text{def}}={\frac {\Delta F_{\text{def}}({\vec {R}})}{V}}=-{\frac {k_{\text{B}}Tv_{s}\beta \left(\lambda _{x}^{2}+\lambda _{y}^{2}+\lambda _{z}^{2}-3\right)}{2}}={\frac {k_{\text{B}}Tv_{s}\beta }{2}}\left(\lambda _{z}^{2}+{\frac {2}{\lambda _{z}}}-3\right)}
The engineering stress (by definition) is the first derivative of the energy in terms of the extension ratio, which is equivalent to the concept of strain: σ eng = d ( Δ f def ) λ z = k B T v s β ( λ z − 1 λ z 2 ) {\displaystyle \sigma _{\text{eng}}={\frac {d(\Delta f_{\text{def}})}{\lambda _{z}}}=k_{\text{B}}Tv_{s}\beta \left(\lambda _{z}-{\frac {1}{\lambda _{z}^{2}}}\right)} and the Young's Modulus E {\displaystyle E} is defined as derivative of the stress with respect to strain, which measures the stiffness of the rubber in laboratory experiments.
E = d ( σ eng ) d λ z = k B T v s β ( 1 + 2 λ z 3 ) | λ z = 1 = 3 k B T v s β = 3 ρ β R T M s {\displaystyle E={\frac {d(\sigma _{\text{eng}})}{d\lambda _{z}}}=k_{\text{B}}Tv_{s}\beta \left.\left(1+{\frac {2}{\lambda _{z}^{3}}}\right)\right|_{\lambda _{z}=1}=3k_{\text{B}}Tv_{s}\beta ={\frac {3\rho \beta RT}{M_{s}}}} where v s = ρ N a / M s {\displaystyle v_{s}=\rho N_{a}/M_{s}} , ρ {\displaystyle \rho } is the mass density of the chain, M s {\displaystyle M_{s}} is the number average molecular weight of a network strand between crosslinks. Here, this type of analysis [ 30 ] links the thermodynamic theory of rubber elasticity to experimentally measurable parameters. In addition, it gives insights into the cross-linking condition of the materials.
The worm-like chain model (WLC) takes the energy required to bend a molecule into account. The variables are the same except that L p {\displaystyle L_{\text{p}}} , the persistence length, replaces b {\displaystyle b} . Then, the force follows this equation: F ≈ k B T L p ( 1 4 ( 1 − r L c ) 2 − 1 4 + r L c ) {\displaystyle F\approx {\frac {k_{\text{B}}T}{L_{\text{p}}}}\left({\frac {1}{4\left(1-{\frac {r}{L_{\rm {c}}}}\right)^{2}}}-{\frac {1}{4}}+{\frac {r}{L_{\text{c}}}}\right)}
Therefore, when there is no distance between chain ends ( r =0), the force required to do so is zero, and to fully extend the polymer chain ( r = L c {\displaystyle r=L_{\text{c}}} ), an infinite force is required, which is intuitive. Graphically, the force begins at the origin and initially increases linearly with r {\displaystyle r} . The force then plateaus but eventually increases again and approaches infinity as the chain length approaches L c {\displaystyle L_{\text{c}}} . | https://en.wikipedia.org/wiki/Rubber_elasticity |
Rubber seed oil is oil extracted from the seeds of rubber trees . In the latex manufacturing process, rubber seeds are not historically collected and commercialized. Recent analysis shows that rubber seed oil contained the following fatty acids: [ 1 ] [ citation needed ]
In India and other rubber manufacturing areas rubber seeds are used to feed livestock. In India in the Virudhunagar district a company Index International
{clarify} extracts oil from rubber seeds and uses the rubber seed cake for cattle feed. [ 2 ] [ citation needed ] Although rubber seed is rich in nutrients it also contains cyanogenic glycosides which will release prussic acid in the presence of enzymes or in slightly acidic conditions. [ 3 ] Oil from the rubber seed could also be of commercial value. Hitherto, rubber seed has largely been allowed to waste with very little use for raising root stock seedlings for propagation purposes. [ 4 ] [ 5 ] The useful properties of the rubber seed oil make it similar to well-known linseed and soybean oil . [ 6 ] [ 7 ] Rubber seed oil also could be used for the paint industry as a semidrying oil , [ 8 ] in the manufacture of soap , [ 9 ] for the production of linoleum and alkyd resin ; [ 10 ] in medicine as antimalaria oil; [ 11 ] and in engineering as core binder for factice preparation. The cake left after oil extraction is used in fertilizer preparation and as feed for cattle and poultry.
The potential of rubber wood as a source of timber is recognized in India, Sri Lanka, Indonesia, and Malaysia, with an increasing volume of sawn rubber wood used for furniture manufacturing and a variety of other applications. [ 12 ] [ 13 ] | https://en.wikipedia.org/wiki/Rubber_seed_oil |
Rubber toughening is a process in which rubber nanoparticles are interspersed within a polymer matrix to increase the mechanical robustness, or toughness , of the material. By "toughening" a polymer it is meant that the ability of the polymeric substance to absorb energy and plastically deform without fracture is increased. Considering the significant advantages in mechanical properties that rubber toughening offers, most major thermoplastics are available in rubber-toughened versions; [ 1 ] [ 2 ] [ 3 ] for many engineering applications, material toughness is a deciding factor in final material selection. [ 4 ]
The effects of disperse rubber nanoparticles are complex and differ across amorphous and partly crystalline polymeric systems. [ 5 ] Rubber particles toughen a system by a variety of mechanisms such as when particulates concentrate stress causing cavitation or initiation of dissipating crazes . [ 6 ] However the effects are not one-sided; excess rubber content or debonding between the rubber and polymer can reduce toughness. [ 7 ] It is difficult to state the specific effects of a given particle size or interfacial adhesion parameter due to numerous other confounding variables. [ 6 ]
The presence of a given failure mechanism is determined by many factors: those intrinsic to the continuous polymer phase, [ 6 ] and those that are extrinsic, pertaining to the stress, loading speed, and ambient conditions. [ 8 ] The action of a given mechanism in a toughened polymer can be studied with microscopy. The addition of rubbery domains occurs via processes such as melt blending in a Rheomix mixer and atom-transfer radical-polymerization. [ 4 ] [ 8 ]
Current research focuses on how optimizing the secondary phase composition and dispersion affects mechanical properties of the blend. Questions of interest include those to do with fracture toughness , tensile strength , and glass transition temperature . [ 9 ]
Different theories describe how a dispersed rubber phase toughens a polymeric substance; most employ methods of dissipating energy throughout the matrix. These theories include: microcrack theory, shear-yielding theory, multiple-crazing theory, shear band and crazing interaction theory, and more recently those including the effects of critical ligament thickness, critical plastic area, voiding and cavitation, damage competition and others. [ 5 ]
In 1956, the microcrack theory became the first to explain the toughening effect of a dispersed rubber phase in a polymer. [ 5 ] Two key observations that went into the initial theory and subsequent expansion were as follows: (1) microcracks form voids over which styrene-butadiene copolymer fibrils form to prevent propagation, and (2) energy stored during elongation of toughened epoxies is released upon breaking of rubber particles. The theory concluded that the combined energy to initiate microcracks and the energy to break rubber particles could account for the increased energy absorption of toughened polymers. This theory was limited, only accounting for a small fraction of the observed increase in fracture energy. [ 6 ]
The matrix crazing theory focuses on explaining the toughening effects of crazing. Crazes start at the equator where principal strain is highest, propagate perpendicular to the stress, and end when they meet another particle. Crazes with perpendicular fibrils can eventually become a crack if the fibrils break. The volume expansion associated with small crazes distributed through a large volume compared to the small volume of a few large cracks in untoughened polymer accounts for a large fraction of the increase in fracture energy. [ 6 ]
Interaction between rubber particles and crazes puts elongation pressures onto the particles in the direction of stress. If this force overcomes the surface adhesion between the rubber and polymer, debonding will occur, thereby diminishing the toughening effect associated with crazing. If the particle is harder, it will be less able to deform, and thus debonding occurs under less stress. This is one reason why dispersed rubbers, below their own glass transition temperature, do not toughen plastics effectively. [ 6 ]
Shear yielding theory is one that, like matrix crazing , can account for a large fraction of the increase in energy absorption of a toughened polymer. Evidence of shear yielding in a toughened polymer can be seen where there is " necking , drawing or orientation hardening." [ 6 ] Shear yielding will result if rubber particles act as stress concentrators and initiate volume-expansion through crazing, debonding and cavitation, to halt the formation of cracks. Overlapping stress fields from one particle to its neighbor will contribute to a growing shear-yielding region. The closer the particles are the more overlap and the larger shear-yielding region. [ 5 ] Shear yielding is an energy absorbing process in itself, but furthermore initiation of shear bands also aids in craze arrest. The occurrence of cavitation is important to shear yielding theory because it acts to lower the yield stress. Cavitation precedes shear yielding, however shear yielding accounts for a much larger increase in toughness than does the cavitation itself. [ 6 ]
Cavitation is common in epoxy resins and other craze resistant toughened polymers, and is prerequisite to shearing in Izod impact strength testing . [ 10 ] During the deformation and fracture of a toughened polymer, cavitation of the strained rubber particles occurs in crazing-prone and non-crazing-prone plastics, including, ABS, PVC, nylon, high impact polystyrene, and CTBN toughened epoxies. Engineers use an energy-balance approach to model how particle size and rubber modulus factors influence material toughness. Both particle size and modulus show positive correlation with brittle-tough transition temperatures. They are both shown to affect the cavitation process occurring at the crack tip process zone early in deformation, preceding large-scale crazing and shear yielding. [ 10 ] [ 11 ]
In order to show increased toughness under strain, the volumetric strain must overcome the energy of void formation as modeled by the equation:
U r ( r ) = 2 3 π R 3 K r ( Δ V R − r 3 R 3 ) + 4 π r 3 Γ + 2 π r 3 G r F ( λ γ ) {\displaystyle U_{r}(r)={\frac {2}{3}}\pi R^{3}K_{r}{\Biggl (}\Delta V_{R}-{\frac {r^{3}}{R^{3}}}{\Biggl )}+4\pi r^{3}\Gamma +2\pi r^{3}G_{r}F(\lambda _{\gamma })} [ 10 ]
"where G r {\displaystyle G_{r}} and K r {\displaystyle K_{r}} are the shear modulus and bulk modulus of the rubber, Δ V R {\displaystyle \Delta V_{R}} is the volume strain in the rubber particle, Γ {\displaystyle \Gamma } is the surface energy of the rubber phase, and the function F ( λ γ ) {\displaystyle F(\lambda _{\gamma })} is dependent on the failure strain of the rubber under biaxial stretching conditions." [ 11 ]
The energy-balancing model applies the physical properties of the whole material to describe the microscopic behavior during triaxial stress. The volume stress and particle radius conditions for cavitation can be calculated, giving the theoretical minimum particle radius for cavitation, useful for practical applications in rubber toughening. Typically cavitation will occur when the average stress on the rubber particles is between 10 and 20 megapascal. The volume strain on the particle is relieved and voiding occurs. The energy absorption due to this increase in volume is theoretically negligible. Instead, it is the consequent shear band formation that accounts for increased toughness. Before debonding, as the strain increases, the rubber phases is forced to stretch further strengthening the matrix. Debonding between the matrix and the rubber reduces the toughness, creating the need for strong adhesion between the polymer and rubber phases. [ 10 ] [ 11 ]
The damage competition theory models the relative contributions of shear yielding and craze failure, when both are present. there are two main assumptions: crazing, microcracks, and cavitation dominate in brittle systems, and shearing dominates in the ductile systems. Systems that are in between brittle and ductile will show a combination of these. The damage competition theory defines the brittle-ductile transition as the point at which the opposite mechanism (shear or yield damage) appears in a system dominated by the other mechanism. [ 5 ]
The dominant failure mechanism can usually be observed directly using TEM , SEM and light microscopy . If cavitation or crazing is dominant, tensile dilatometry ( see dilatometer ) can be used to measure the extent of the mechanism by measuring volume strain. However, if multiple dilatational mechanisms are present, it is difficult to measure the separate contributions. Shear yielding is a constant volume process and cannot be measured with tensile dilatometry. [ 6 ] Voiding can be seen with optical microscopy, however one of two methods, using polarized light or low angle light scattering are necessary to observe the connection between cavitation and shear bands. [ 10 ]
In order to gauge the toughening effects of a dispersed secondary phase, it is important to understand the relevant characteristics of the continuous polymer phase. The mechanical failure characteristics of the pure polymeric continuous phase will strongly influence how rubber toughened polymer failure occurs. When a polymer usually fails due to crazing, rubber toughening particles will act as craze initiators. When it fails by shear yielding, the rubber particles will initiate shear bands. It is also possible to having multiple mechanisms come into play if the polymer is prone to failing by multiple stresses equally. Polystyrene and styrene-acrylonitrile are brittle materials that are prone to craze failure while polycarbonate, polyamides, and polyethylene terephthalate (PET) are prone to shear yield failure. [ 6 ]
Amorphous plastics are used below their glass transition temperature ( T g {\displaystyle T_{g}} ). They are brittle and notch sensitive but creep resistant. Molecules are immobile and the plastic responds to rapidly applied stress by fracturing. Partly crystalline thermoplastics are used for application in temperature conditions between T g {\displaystyle T_{g}} and T m {\displaystyle T_{m}} (melting temperature). Partly crystalline thermoplastics are tough and creep-prone because the amorphous regions surrounding the rigid crystals are afforded some mobility. Often they are brittle at room temperature because they have high glass transition temperatures. Polyethylene is tough at room temperature because its T g {\displaystyle T_{g}} is lower than room temperature. Polyamide 66 and polyvinylchloride have secondary transitions below their T g {\displaystyle T_{g}} that allows for some energy absorbing molecule mobility. [ 6 ]
There are some general guidelines to follow when trying to determine a plastic's toughness from its chemical structure. Vinyl polymers like polystyrene and styrene-acrylonitrile tend to fail by crazing. They have low crack initiation and propagation energies. Polymers with aromatic backbones, such as polyethylene terephthalate and polycarbonate, tend to fail by shear yielding with high crack initiation energy but low propagation energy. Other polymers, including poly(methyl methacrylate) and polyacetal(polyoxymethylene), are not as brittle as "brittle polymers" and are also not as ductile as "ductile polymers". [ 6 ]
The following equations relate the entanglement density v e {\displaystyle v_{e}} and a measure of the flexibility of the unperturbed real chain ( C ∞ {\displaystyle C_{\infty }} ) of a given plastic to its fracture mechanics:
V e = ρ a 3 M v C ∞ 2 {\displaystyle V_{e}={\frac {\rho _{a}}{3M_{v}C_{\infty }^{2}}}}
Where ρ a {\displaystyle \rho _{a}} is the mass density of the amorphous polymer, and M v {\displaystyle M_{v}} is the average molecular weight per statistical unit. [ 6 ] Crazing stress ( σ z ) {\displaystyle (\sigma _{z})} is related to the entanglement density by:
σ z ∝ v e 1 / 2 {\displaystyle \sigma _{z}\varpropto v_{e}^{1/2}}
The normalized stress yield is related to C ∞ {\displaystyle C_{\infty }} by
l o g ( σ ¯ y ) ∝ l o g ( C ∞ ) + c {\displaystyle log({\overline {\sigma }}_{y})\varpropto log(C_{\infty })+c}
c {\displaystyle c} is a constant. The ratio of the crazing stress to the normalized stress yield is used to determine whether a polymer fails due to crazing or yield:
σ z σ ¯ y ∝ ( ρ a 3 M v ) 1 / 2 C ∞ − 2 {\displaystyle {\frac {\sigma _{z}}{{\overline {\sigma }}_{y}}}\propto {\biggl (}{\frac {\rho _{a}}{3M_{v}}}{\biggr )}^{1/2}C_{\infty }^{-2}}
When the ratio is higher, the matrix is prone to yielding; when the ratio is lower, the matrix is prone to failure by crazing. [ 6 ] These formulas form the base of crazing theory, shear-yielding theory, and damage competition theory.
In material selection it is important to look at the interaction between the matrix and the secondary phase. For example, crosslinking within the rubber phase promotes high strength fibril formation that toughens the rubber, preventing particle fracture. [ 6 ]
Carboxyl-terminated butadiene-acrylonitrile (CTBN) is often used to toughen epoxies, but using CTBN alone increases the toughness at the cost of stiffness and heat resistance. Amine-terminated butadiene acrylonitrile (ATBN) is also used. [ 12 ] Using ultra-fine full-vulcanized powdered rubber (UFPR) researchers have been able to improve all three, toughness, stiffness, and heat resistance simultaneously, resetting the stage for rubber toughening with particles smaller than previously thought to be effective. [ 13 ]
In applications where high optical transparency is necessary, examples being poly(methyl methacrylate) and polycarbonate it is important to find a secondary phase that does not scatter light. To do so it is important to match refractive indices of both phases. Traditional rubber particles do not offer this quality. Modifying the surface of nanoparticles with polymers of comparable refractive indices is an interest of current research. [ 8 ]
Increasing the rubber concentration in a nanocomposite decreases the modulus and tensile strength. In one study, looking at PA6-EPDM blend, increasing the concentration of rubber up to 30 percent showed a negative linear relationship with the brittle-tough transition temperature, after which the toughness decreased. This suggests that the toughening effect of adding rubber particles is limited to a critical concentration. [ 6 ] This is examined further in a study on PMMA from 1998; using SAXS to analyze crazing density, it was found that crazing density increases and yield stress decreases until the critical point when the relationship flips. [ 14 ]
A material that is expected to fail by crazing is more likely to benefit from larger particles than a shear prone material, which would benefit from a smaller particle. In materials where crazing and yielding are comparable, a bimodal distribution of particle size may be useful for toughening. At fixed rubber concentrations, one can find that an optimal particle size is a function of the entanglement density of the polymer matrix. The neat polymer entanglement densities of PS, SAN, and PMMA are 0.056, 0.093, and 0.127 respectively. As entanglement density increases, the optimum particle size decreases linearly, ranging between 0.1 and 3 micrometers. [ 6 ]
The effect of particle size on toughening is dependent on the type of test performed. This can be explained because for different test conditions, the failure mechanism changes. For impact strength testing on PMMA where failure occurs by shear-yielding, the optimum size of filler PBA-core PMMA-shell particle was shown in one case to be 250 nm. In the three-point bend test, where failure is due to crazing, 2000 nm particles had the most significant toughening effect. [ 15 ]
Temperature has a direct effect on the fracture mechanics . At low temperatures, below the glass transition temperature of the rubber, the dispersed phase behaves like a glass rather than like a rubber that toughens the polymer. As a result, the continuous phase fails by mechanisms characteristic of the pure polymer, as if the rubber was not present. As temperature increases past the glass transition temperature, the rubber phase increases the crack initiation energy. At this point the crack self-propagates due to the stored elastic energy in the material. As temperature rises further past the glass transition of the rubber phase, the impact strength of a rubber-polymer composite still dramatically increases as crack propagation requires additional energy input. [ 6 ]
Epoxy resins are a highly useful class of materials used in engineering applications. Some of these include use for adhesives, fiber-reinforced composites, and electronics coatings. Their rigidity and low crack propagation resistance makes epoxies a candidate of interest for rubber toughening research to fine-tune the toughening processes. [ 16 ] [ 17 ] [ 18 ] [ 19 ] [ 20 ] [ 21 ] [ 22 ]
Some of the factors affecting the toughness of epoxy nanocomposites include the chemical identity of the epoxy curing agent, entanglement density, and interfacial adhesion. Curing epoxy 618 with piperidine , for example, produces tougher epoxies than when boron trifluoride-ethylamine is used. Low entanglement density increases the toughness. Bisphenol A can be added to lower the crosslinking density of epoxy 618, thereby increasing the fracture toughness. Bisphenol A and a rubber filler increase toughness synergistically. [ 23 ]
In textbooks and literature before 2002 it was assumed that there is a lower limit for rubber-toughening particle diameter at 200 nm; it was then discovered that ultra-fine full-vulcanized powdered rubber particles with diameter of 90 nm show significant toughening of rubber epoxies. [ 13 ] This finding underlines how this field is constantly growing and more work can be done to better model the rubber toughening effect.
Acrylonitrile butadiene styrene (ABS) polymer is an application of rubber toughening. The properties of this polymer come mainly from rubber toughening. The polybutadiene rubber domains in the main styrene-acrylonitrile matrix act as a stop to crack propagation.
PMMA ’s high optical transparency, low cost, and compressibility make it a viable option for practical applications in architecture and car manufacturing as a substitute for glass when high transparency is necessary. Incorporating a rubber filler phase increases the toughness. Such fillers need to form strong interfacial bonds with the PMMA matrix. In applications where optical transparency is important, measures must be taken to limit light scattering. [ 8 ]
It is common in toughening PMMA, and in other composites, to synthesize core-shell particles via atom-transfer radical-polymerization that have an outer polymer layer that has properties similar to those of the primary phase that increases the particle’s adhesion to the matrix. Developing PMMA compatible core-shell particles with low glass transition temperature while maintaining optical transparency is of interest to architects and car companies. [ 8 ]
For optimal transparency the disperse rubber phase needs the following:
Cyclic olefin copolymer , an optically transparent plastic with low moisture uptake and solvent resistance among other useful properties, can be toughened effectively with a styrene-butadiene-styrene rubber with the above properties. The Notched-Izod strength more than doubled from 21 J/m to 57 J/m with an optical haze of 5%. [ 24 ]
Polystyrene generally has stiffness , transparency , processibility, and dielectric qualities that make it useful. However, its low impact resistance at low temperatures makes catastrophic fracture failure when cold more likely. [ 25 ] The most widely used version of toughened polystyrene is called high impact polystyrene or HIPS. Being cheap and easy to thermoform (see thermoforming ), it is utilized for many everyday uses. HIPS is made by polymerizing styrene in a polybutadiene rubber solution. After the polymerization reaction begins, the polystyrene and rubber phases separate. When phase separation begins, the two phases compete for volume until phase inversion occurs and the rubber can distribute throughout the matrix. The alternative emulsion polymerization with styrene-butadiene-styrene or styrene-butadiene copolymers allows fine-tuned manipulation of particle size distribution. This method makes use of the core-shell architecture. [ 26 ]
In order to study the fracture microstructure of HIPS in a transmission electron microscope it is necessary to stain one of the phases with a heavy metal, Osmium tetroxide for example. This produces substantially different electron density between phases. Given a constant particle size, it is the cross-linking density that determines the toughness of a HIPS material. This can be measured by exploiting the negative relationship between the cis-polybutadiene content of the rubber and the crosslink density that can be measured with the swelling index. Lower crosslink density leads to increased toughness. [ 26 ]
The generation of vast quantities of waste rubber from car tires has sparked interest in finding uses for this discarded rubber. The rubber can be turned into a fine powder, which can then be used as a toughening agent for polystyrene . However, poor miscibility between the waste rubber and polystyrene weakens the material. This problem requires the use of a compatibilizer (see compatibilization ) in order to reduce interfacial tension and ultimately make rubber toughening of polystyrene effective. A polystyrene / styrene-butadiene copolymer acts to increase the adhesion between the dispersed and continuous phases. [ 25 ] | https://en.wikipedia.org/wiki/Rubber_toughening |
Rubberized asphalt concrete ( RAC ), also known as asphalt rubber or just rubberized asphalt , is noise reducing pavement material that consists of regular asphalt concrete mixed with crumb rubber made from recycled tires . Asphalt rubber is the largest single market for ground rubber in the United States, consuming an estimated 220,000,000 pounds (100,000,000 kg), or approximately 12 million tires annually. [ 1 ]
Use of rubberized asphalt as a pavement material was pioneered by the city of Phoenix, Arizona in the 1960s because of its high durability. [ 2 ] Since then it has garnered interest for its ability to reduce road noise.
In 2003 the Arizona Department of Transportation began a three-year, $34-million Quiet Pavement Pilot Program, in cooperation with the Federal Highway Administration to determine if sound walls can be replaced by rubberized asphalt to reduce noise alongside highways. After about one year it was determined that asphalt rubber overlays resulted in up to 12 decibels of in road noise reduction, with a typical reduction of 7 to 9 decibels. [ 3 ]
Arizona has been the leader in using rubberized asphalt, but California , Florida , Texas , and South Carolina are also using asphalt rubber. Tests are currently underway in other parts of the United States to determine the durability of rubberized asphalt in northern climates, including a 1.3 mile stretch of Interstate 405 in Bellevue and Kirkland , Washington [ 4 ] and a handful of local roads in the city of Colorado Springs , Colorado. In 2012, the State of Georgia issued a specification for the use of rubber-modified asphalt as a replacement for polymer-modified asphalt. In Belgium, tests in the ring of Brussel and in the F1 circuit of Francorchamp (see the film by Jean-Marie Piquint Rubberized Asphalt for Esso Belgium). [ 5 ] [ 6 ]
Two quality control requirements are necessary when using asphalt rubber: (a) crumb rubber tends to separate and settle down in the asphalt cement and therefore asphalt rubber needs to be agitated continuously to keep the rubber particles in suspension and (b) crumb rubber is prone to degradation (devulcanization and depolymerization) and thus lose its elasticity if asphalt rubber is maintained at high temperatures for more than 6–8 hours. This means asphalt rubber must be used within 8 hours after production. [ 7 ]
Porous Elastic Road Surfaces (PERS) or poroelastic road surfaces improve RAC by incorporating voids and channels, making the pavement porous and further reducing traffic noise. [ 8 ] | https://en.wikipedia.org/wiki/Rubberized_asphalt |
Rubble is broken stone , of irregular size, shape [ 1 ] and texture; undressed especially as a filling-in. Rubble naturally found in the soil is known also as ' brash' (compare cornbrash ). [ 2 ] Where present, it becomes more noticeable when the land is ploughed or worked.
" Rubble-work " is a name applied to several types of masonry . [ 1 ] One kind, where the stones are loosely thrown together in a wall between boards and grouted with mortar almost like concrete , is called in Italian "muraglia di getto" and in French "bocage". [ 1 ] In Pakistan, walls made of rubble and concrete, cast in a formwork, are called 'situ', which probably derives from Sanskrit (similar to the Latin 'in situ' meaning 'made on the spot'). [ citation needed ]
Work executed with more or less large stones put together without any attempt at courses is called rubble [ 1 ] walling. Where similar work is laid in courses, it is known as coursed rubble. Dry-stone walling is somewhat similar work done without the use of mortar. It is bound together by the fit of the stones and the regular placement of stones which extend through the thickness of the wall. A rubble wall built with mortar will be stronger if assembled in this way. [ citation needed ]
Rubble walls ( Maltese : ħitan tas-sejjieħ ) are found all over the island of Malta . Similar walls are also frequently found in Sicily and the Arab countries. The various shapes and sizes of the stones used to build these walls look like stones that were found in the area lying on the ground or in the soil. It is most probable that the practice of building these walls around the field was inspired by the Arabs during their rule in Malta, as in Sicily which was also ruled by the Arabs around the same period. Maltese farmers found that the methods of building these walls was very efficient especially when resources were limited. Rubble walls are used to serve as borders between farms. A great advantage that rubble walls offered is that when heavy rain falls, their structure would allow excessive water to pass through and therefore, excess water will not ruin the products. Soil erosion is minimised as the wall structure allows the water to pass through but it traps the soil and prevents it from being carried away from the field. One can see many rubble walls on the side of the hills and in valleys where the land slopes down and consequently the soil is in greater danger of being carried away. [ citation needed ]
In the British Islands, many mediaeval and post-mediaeval buildings are built of small natural stones, called rubble.
As examples see the descriptions in two official list entries, provided by Historic England : | https://en.wikipedia.org/wiki/Rubble |
In astronomy , a rubble pile is a celestial body that consists of numerous pieces of debris that have coalesced under the influence of gravity . Rubble piles have low density because there are large cavities between the various chunks that make them up.
The asteroids Bennu and Ryugu have a measured bulk density which suggests that their internal structure is a rubble pile. [ 1 ] [ 2 ] Many comets and most smaller minor planets (<10 km in diameter) are thought to be composed of coalesced rubble. [ 3 ] [ 4 ]
Most smaller asteroids are thought to be rubble piles. [ 3 ]
Rubble piles form when an asteroid or moon (which may originally be monolithic) is smashed to pieces by an impact, and the shattered pieces subsequently fall back together, primarily due to self-gravitation. This coalescing usually takes from several hours to weeks. [ 5 ]
When a rubble-pile asteroid passes a much more massive object, tidal forces change its shape. [ 6 ]
Scientists first suspected that asteroids are often rubble piles when asteroid densities were first determined. Many of the calculated densities were significantly less than those of meteorites, which in some cases had been determined to be pieces of asteroids.
Many asteroids with low densities are thought to be rubble piles, for example 253 Mathilde . The mass of Mathilde, as determined by the NEAR Shoemaker mission, is far too low for the volume observed, considering the surface is rock. Even ice with a thin crust of rock would not provide a suitable density. Also, the large impact craters on Mathilde would have shattered a rigid body. However, the first unambiguous rubble pile to be photographed is 25143 Itokawa , which has no obvious impact craters and is thus almost certainly a coalescence of shattered fragments.
The asteroid 433 Eros , the primary destination of NEAR Shoemaker , was determined to be riven with cracks but otherwise solid. Other asteroids, possibly including Itokawa, have been found to be contact binaries , two major bodies touching, with or without rubble filling the boundary.
Large interior voids are possible because of the very low gravity of most asteroids. Despite a fine regolith on the outside (at least to the resolution that has been seen with spacecraft), the asteroid's gravity is so weak that friction between fragments dominates and prevents small pieces from falling inwards and filling the voids.
All the largest asteroids ( 1 Ceres , 2 Pallas , 4 Vesta , 10 Hygiea , 704 Interamnia ) are solid objects without any macroscopic internal porosity. This may be because they have been large enough to withstand all impacts, and have never been shattered. Alternatively, Ceres and some few other of the largest asteroids may be massive enough that, even if they were shattered but not dispersed, their gravity would collapse most voids upon recoalescing. Vesta, at least, has withstood intact one major impact since its formation and shows signs of internal structure from differentiation in the resultant crater that assures that it is not a rubble pile. This serves as evidence for size as a protection from shattering into rubble.
Observational evidence suggest that the cometary nucleus may not be a well-consolidated single body, but may instead be a loosely bound agglomeration of smaller fragments, weakly bonded and subject to occasional or even frequent disruptive events, although the larger cometary fragments are expected to be primordial condensations rather than collisionally derived debris as in the asteroid case. [ 7 ] [ 8 ] [ 9 ] [ 10 ] [ 11 ] However, in situ observations by the Rosetta mission indicate that it may be more complex than that. [ 12 ] [ clarification needed ]
The moon Phobos , the larger of the two natural satellites of the planet Mars , is also thought to be a rubble pile bound together by a thin regolith crust about 100 m (330 ft) thick. [ 13 ] [ 14 ] A rubble-pile morphology may point towards an in situ origin of the Martian moons. Based on this, it has been proposed that Phobos and Deimos may originate from a single destroyed moon. Alternatively, Phobos may have undergone repeated 'recycling,' having been torn apart into a ring before reaccreting and migrating outwards. [ 15 ] | https://en.wikipedia.org/wiki/Rubble_pile |
The rubble trench foundation , an ancient construction approach popularized by architect Frank Lloyd Wright , is a type of foundation that uses loose stone or rubble to minimize the use of concrete and improve drainage. [ 1 ] It is considered more environmentally friendly than other types of foundation because cement manufacturing requires the use of enormous amounts of energy. However, some soil environments are not suitable for this kind of foundation, particularly expansive or poor load-bearing (< ~100 kN/m² or 1 ton/sf) soils. [ 2 ] A rubble trench foundation with a concrete grade beam is not recommended for earthquake prone areas. [ 3 ]
A foundation must bear the structural loads imposed upon it and allow proper drainage of ground water to prevent expansion or weakening of soils and frost heaving. While the far more common concrete foundation requires separate measures to ensure good soil drainage, the rubble trench foundation serves both foundation functions at once.
To construct a rubble trench foundation a narrow trench is dug down below the frost line . The bottom of the trench would ideally be gently sloped to an outlet. Drainage tile , graded 1cm/m or 1":8' to daylight, is then placed at the bottom of the trench in a bed of washed stone protected by filter fabric. The trench is then filled with either screened stone (typically 1-1/2") or recycled rubble. A steel-reinforced concrete grade beam may be poured at the surface to provide ground clearance for the structure.
If an insulated slab is to be poured inside the grade beam, then the outer surface of the grade beam and the rubble trench should be insulated with rigid XPS foam board, which must be protected above grade from mechanical and UV degradation.
The rubble-trench foundation is a relatively simple, inexpensive, and environment-friendly alternative to a conventional foundation, but may require an engineer's approval if building officials are not familiar with it. Frank Lloyd Wright used them successfully for more than 50 years in the first half of the 20th century, and there is a revival of this style of foundation with the increased interest in green building. [ citation needed ] | https://en.wikipedia.org/wiki/Rubble_trench_foundation |
Rubblization is a construction and engineering technique that involves saving time and transportation costs by reducing existing concrete into rubble at its current location rather than hauling it to another location. Rubblization has two primary applications: creating a base for new roadways and decommissioning nuclear power plants.
In road construction, a worn-out Portland cement concrete can be rubblized and then overlaid with a new surface, usually asphalt concrete . Specialized equipment breaks up the old roadway into small pieces to make a base for new pavement. This saves the expense of transporting the old pavement to a disposal site, and purchasing/transporting new base materials for the replacement paving. [ 1 ] The result is a smoother pavement surface than would be obtained if a layer of asphalt were to be applied to the unbroken concrete surface. [ 2 ] The technique has been used on roads since the late 1990s, and is also being used for concrete airport runways. [ 3 ]
The rubblizing process provides many benefits versus other methods of road rehabilitation, such as crack and seat or removal and replacement of a concrete surface including: rubblizing a concrete surface is 52% less expensive than remove and replacing concrete; rubblizing reduces road reconstruction time, from days of lane closures to hours, providing large savings to contractors and reduced impact on travelling public; and rubblization is an environmentally friendly "green" process., [ 4 ] [ 5 ]
Rubblization is used in decommissioning of nuclear power plants . As with other decommissioning techniques, all equipment from buildings is removed and the surfaces are decontaminated. The difference with rubblization is that above-grade structures, including the concrete containment building, are demolished into rubble and buried in the structure's foundation below ground. The site surface is then covered, regraded, and landscaped for unrestricted use. This saves the expense of removing and transporting the building pieces to a different site. [ 6 ] | https://en.wikipedia.org/wiki/Rubblization |
A Rube Goldberg machine , named after American cartoonist Rube Goldberg , is a chain reaction –type machine or contraption intentionally designed to perform a simple task in a comically overcomplicated way. Usually, these machines consist of a series of simple unrelated devices; the action of each triggers the initiation of the next, eventually resulting in achieving a stated goal.
The design of such a "machine" is often presented on paper and would be impossible to implement in actuality. More recently, such machines have been fully constructed for entertainment (for example, a breakfast scene in Pee-wee's Big Adventure ) and in Rube Goldberg competitions .
The expression is named after the American cartoonist Rube Goldberg , whose cartoons often depicted devices that performed simple tasks in indirect convoluted ways. The cartoon above is Goldberg's Professor Butts and the Self-Operating Napkin , which was later reprinted in a few book collections, including the postcard book Rube Goldberg's Inventions! and the hardcover Rube Goldberg: Inventions , both compiled by Maynard Frank Wolfe from the Rube Goldberg Archives. [ 1 ]
The term "Rube Goldberg" was being used in print to describe elaborate contraptions by 1928, [ 2 ] and appeared in the Random House Dictionary of the English Language in 1966 meaning "having a fantastically complicated improvised appearance", or "deviously complex and impractical". [ 3 ] Because Rube Goldberg machines are contraptions derived from tinkering with the tools close at hand, parallels have been drawn with evolutionary processes. [ 4 ]
Many of Goldberg's ideas were utilized in films and TV shows for the comedic effect of creating such rigamarole for such a simple task, such as the front gate mechanism in The Goonies and the breakfast machine shown in Pee-wee's Big Adventure . In Ernest Goes to Jail , Ernest P. Worrell uses his invention simply to turn his TV on. Other films such as Chitty Chitty Bang Bang , the end credits of Waiting... , Diving into the Money Pit , and Back to the Future have featured Rube Goldberg–style devices as well.
Wallace from Wallace and Gromit creates and uses many such machines for numerous, oft trivial tasks and productivity enhancements (e.g. getting dressed). The inspiration for these contraptions, however, is the British cartoonist W. Heath Robinson .
The Incredible Machine is a series of video games in which players create a series of Rube Goldberg devices. The board game Mouse Trap has been referred to as an early practical example of such a contraption.
In early 1987, Purdue University in Indiana started the annual National Rube Goldberg Machine Contest , organized by the Phi chapter of Theta Tau , a national engineering fraternity. In 2009, the Epsilon chapter of Theta Tau established a similar annual contest at the University of California, Berkeley .
Since around 1997, the kinetic artist Arthur Ganson has been the emcee of the annual "Friday After Thanksgiving" (FAT) competition sponsored by the MIT Museum in Cambridge, Massachusetts. Teams of contestants construct elaborate Rube Goldberg style chain-reaction machines on tables arranged around a large gymnasium. Each apparatus is linked by a string to its predecessor and successor machine. The initial string is ceremonially pulled, and the ensuing events are videotaped in closeup, and simultaneously projected on large screens for viewing by the live audience. After the entire cascade of events has finished, prizes are then awarded in various categories and age levels. Videos from several previous years' contests are viewable on the MIT Museum website. [ 5 ]
The Chain Reaction Contraption Contest [ 6 ] is an annual event hosted at the Carnegie Science Center in Pittsburgh, Pennsylvania in which high school teams each build a Rube Goldberg machine to complete some simple task (which changes from year to year) in 20 steps or more (with some additional constraints on size, timing, safety, etc.).
On the TV show Food Network Challenge , competitors in 2011 were once required to create a Rube Goldberg machine out of sugar. [ 7 ]
An event called 'Mission Possible' [ 8 ] in the Science Olympiad involves students building a Rube Goldberg-like device to perform a certain series of tasks.
The Rube Goldberg company holds an annual Rube Goldberg machine contest. [ 9 ] | https://en.wikipedia.org/wiki/Rube_Goldberg_machine |
Rubedo is a Latin word meaning "redness" that was adopted by alchemists to define the fourth and final major stage in their magnum opus . [ 1 ] Both gold and the philosopher's stone were associated with the color red, as rubedo signaled alchemical success, and the end of the great work. [ 2 ] Rubedo is also known by the Greek word iosis .
The three alchemical stages preceding rubedo were nigredo (blackness), which represented putrefaction and spiritual death; albedo (whiteness), which represented purification; and citrinitas (yellowness), the solar dawn or awakening. [ 3 ] Some sources describe the alchemical process as three-phased with citrinitas serving as mere extension and takes place between albedo and rubedo. [ 4 ] The rubedo stage entails the attempt of the alchemist to integrate the psychospiritual outcomes of the process into a coherent sense of self before its re-entry to the world. [ 5 ] The stage can take some time or years to complete due to the required synthesis and substantiation of insights and experiences. [ 5 ]
The symbols used in alchemical writing and art to represent this red stage can include blood , a phoenix , a rose , a crowned king, or a figure wearing red clothes. Countless sources mention a reddening process; the seventeenth dictum of the 12th century Turba Philosophorum is one example:
O Turba of Philosophers and disciples, now hast thou spoken about making into white, but it yet remains to treat concerning the reddening! Know, all ye seekers after this Art, that unless ye whiten, ye cannot make red, because the two natures are nothing other than red and white. Whiten, therefore, the red, and redden the white! [ 6 ]
In the framework of psychological development (especially with followers of Jungian psychology ), these four alchemical steps are viewed as analogous to the process of attaining individuation or the process that allows an individual to attain the integration of opposites, their transcendence, and, finally, emergence out of an undifferentiated unconscious. [ 7 ] In an archetypal schema, rubedo represents the Self archetype , and is the culmination of the four stages, the merging of ego and Self. [ 8 ] It is also described as a stage that gives birth to a new personality. [ 9 ] Represented by the color of blood in alchemy, the stage indicates a process that cannot be reversed since it involves the struggle of the self towards its manifestation. [ 10 ]
The Self manifests itself in "wholeness," a point in which a person discovers their true nature. Another interpretation phrased it as "reunification" which entail the reunion of body, soul, and spirit, leading to a diminished inner conflict. [ 11 ]
This psychology -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rubedo |
Rubella , also known as German measles or three-day measles , [ 6 ] is an infection caused by the rubella virus . [ 3 ] This disease is often mild, with half of people not realizing that they are infected. [ 1 ] [ 7 ] A rash may start around two weeks after exposure and last for three days. [ 1 ] It usually starts on the face and spreads to the rest of the body. [ 1 ] The rash is sometimes itchy and is not as bright as that of measles . [ 1 ] Swollen lymph nodes are common and may last a few weeks. [ 1 ] A fever, sore throat, and fatigue may also occur. [ 1 ] [ 2 ] Joint pain is common in adults. [ 1 ] Complications may include bleeding problems, testicular swelling , encephalitis, and inflammation of nerves . [ 1 ] Infection during early pregnancy may result in a miscarriage or a child born with congenital rubella syndrome (CRS). [ 3 ] Symptoms of CRS manifest as problems with the eyes such as cataracts , deafness , as well as affecting the heart and brain. [ 3 ] Problems are rare after the 20th week of pregnancy. [ 3 ]
Rubella is usually spread from one person to the next through the air via coughs of people who are infected. [ 3 ] [ 4 ] People are infectious during the week before and after the appearance of the rash. [ 1 ] Babies with CRS may spread the virus for more than a year. [ 1 ] Only humans are infected. [ 3 ] Insects do not spread the disease. [ 1 ] Once recovered, people are immune to future infections. [ 3 ] Testing is available that can verify immunity. [ 3 ] Diagnosis is confirmed by finding the virus in the blood, throat, or urine. [ 1 ] Testing the blood for antibodies may also be useful. [ 1 ]
Rubella is preventable with the rubella vaccine , with a single dose being more than 95% effective. [ 3 ] Often it is given in combination with the measles vaccine and mumps vaccine , known as the MMR vaccine . [ 1 ] When some, but less than 80%, of a population is vaccinated, more women may reach childbearing age without developing immunity by infection or vaccination, thus possibly raising CRS rates. [ 3 ] Once infected there is no specific treatment. [ 2 ]
Rubella is a common infection in many areas of the world. [ 2 ] Each year about 100,000 cases of congenital rubella syndrome occur. [ 3 ] Rates of disease have decreased in many areas as a result of vaccination. [ 2 ] [ 7 ] There are ongoing efforts to eliminate the disease globally. [ 3 ] In April 2015, the World Health Organization declared the Americas free of rubella transmission. [ 8 ] [ 9 ] The name "rubella" is from Latin and means little red . [ 1 ] It was first described as a separate disease by German physicians in 1814, resulting in the name "German measles". [ 1 ]
Rubella has symptoms similar to those of flu. However, the primary symptom of rubella virus infection is the appearance of a rash (exanthem) on the face which spreads to the trunk and limbs and usually fades after three days, which is why it is often referred to as three-day measles. The facial rash usually clears as it spreads to other parts of the body. Other symptoms include low-grade fever, swollen glands (sub-occipital and posterior cervical lymphadenopathy ), joint pains , headache , and conjunctivitis . [ 11 ]
The swollen glands or lymph nodes can persist for up to a week and the fever rarely rises above 38 °C (100.4 °F). The rash of rubella is typically pink or light red. The rash causes itching and often lasts for about three days. The rash disappears after a few days with no staining or peeling of the skin. When the rash clears up, the skin might shed in very small flakes where the rash covered it. Forchheimer spots occur in 20% of cases and are characterized by small, red papules on the area of the soft palate . [ 12 ]
Rubella can affect anyone of any age. Adult females are particularly prone to arthritis and joint pains. [ 13 ]
In children, rubella normally causes symptoms that last two days and include:
In older children and adults, additional symptoms may be present, including [ citation needed ]
Severe complications of rubella include:
Coryza in rubella may convert to pneumonia , either direct viral pneumonia or secondary bacterial pneumonia , and bronchitis (either viral bronchitis or secondary bacterial bronchitis). [ 16 ]
Rubella can cause congenital rubella syndrome in the newborn, this being the most severe sequela of rubella. The syndrome (CRS) follows intrauterine infection by the rubella virus and comprises cardiac, cerebral, ophthalmic, and auditory defects. [ 17 ] It may also cause prematurity, low birth weight, neonatal thrombocytopenia, anemia, and hepatitis. The risk of major defects in organogenesis is highest for infection in the first trimester . CRS is the main reason a vaccine for rubella was developed. [ 18 ]
80–90% of mothers who contract rubella within the critical first trimester have either a miscarriage or a stillborn baby. [ 11 ] If the fetus survives the infection, it can be born with severe heart disorders ( patent ductus arteriosus being the most common), blindness, deafness, or other life-threatening organ disorders. The skin manifestations are called "blueberry muffin lesions". [ 18 ] For these reasons, rubella is included in the TORCH complex of perinatal infections. [ 19 ] [ 20 ]
About 100,000 cases of this condition occur each year. [ 3 ]
The disease is caused by the rubella virus, in the genus Rubivirus from the family Matonaviridae, [ 21 ] that is enveloped and has a single-stranded RNA genome. [ 22 ] The virus is transmitted by the respiratory route and replicates in the nasopharynx and lymph nodes . The virus is found in the blood 5 to 7 days after infection and spreads throughout the body. The virus has teratogenic properties and is capable of crossing the placenta and infecting the fetus where it stops cells from developing or destroys them. [ 11 ] During this incubation period, the patient is contagious typically for about one week before he/she develops a rash and for about one week thereafter. [ 1 ]
Increased susceptibility to infection might be inherited as there is some indication that HLA-A1 or factors surrounding A1 on extended haplotypes are involved in virus infection or non-resolution of the disease. [ 23 ] [ 24 ]
Rubella virus specific IgM antibodies are present in people recently infected by rubella virus, but these antibodies can persist for over a year, and a positive test result needs to be interpreted with caution. [ 25 ] The presence of these antibodies along with, or a short time after, the characteristic rash confirms the diagnosis. [ 26 ]
Rubella infections are prevented by active immunization programs using live attenuated virus vaccines . Two live attenuated virus vaccines, RA 27/3 and Cendehill strains, were effective in the prevention of adult disease. However, their use in prepubertal females did not produce a significant fall in the overall incidence rate of CRS in the UK. Reductions were only achieved by immunisation of all children. [ 27 ]
The vaccine is now usually given as part of the MMR vaccine . The WHO recommends the first dose be given at 12 to 18 months of age with a second dose at 36 months. Pregnant women are usually tested for immunity to rubella early on. Women found to be susceptible are not vaccinated until after the baby is born because the vaccine contains live virus. [ 28 ]
The immunisation program has been quite successful. Cuba declared the disease eliminated in the 1990s, and in 2004 the Centers for Disease Control and Prevention announced that both the congenital and acquired forms of rubella had been eliminated from the United States . [ 29 ] [ 30 ] The World Health Organization declared Australia rubella free in October 2018. [ 31 ]
Screening for rubella susceptibility by history of vaccination or by serology is recommended in the United States for all women of childbearing age at their first preconception counseling visit to reduce incidence of congenital rubella syndrome (CRS). [ 32 ] It is recommended that all susceptible non-pregnant women of childbearing age should be offered rubella vaccination. [ 32 ] Due to concerns about possible teratogenicity, use of MMR vaccine is not recommended during pregnancy. [ 32 ] Instead, susceptible pregnant women should be vaccinated as soon as possible in the postpartum period . [ 32 ]
In susceptible people passive immunization , in the form of polyclonal immunoglobulins , appears effective up to the fifth day post-exposure. [ 33 ]
There is no specific treatment for rubella; however, management is a matter of responding to symptoms to diminish discomfort. Treatment of newborn babies is focused on management of the complications. Congenital heart defects and cataracts can be corrected by direct surgery. [ 13 ] [ 34 ]
Management for ocular congenital rubella syndrome (CRS) is similar to that for age-related macular degeneration , including counseling, regular monitoring, and the provision of low vision devices, if required. [ 35 ]
Rubella infection of children and adults is usually mild, self-limiting, and often asymptomatic. The prognosis in children born with CRS is poor. [ 36 ]
Rubella occurs worldwide. The virus tends to peak during the spring in countries with temperate climates. Before the vaccine against rubella was introduced in 1969, widespread outbreaks usually occurred every 6–9 years in the United States and 3–5 years in Europe , mostly affecting children in the 5–9 year old age group. [ 37 ] Since the introduction of vaccine, occurrences have become rare in those countries with high uptake rates. [ citation needed ]
Vaccination has interrupted the transmission of rubella in the Americas : no endemic case has been observed since February 2009. [ 38 ] Vaccination is still strongly recommended as the virus could be reintroduced from other continents should vaccination rates in the Americas drop. [ 39 ] During the epidemic in the US between 1962 and 1965 , rubella virus infections during pregnancy were estimated to have caused 30,000 stillbirths and 20,000 children to be born impaired or disabled as a result of CRS. [ 40 ] [ 41 ] Universal immunisation producing a high level of herd immunity is important in the control of epidemics of rubella. [ 42 ]
In the UK , there remains a large population of men susceptible to rubella who have not been vaccinated. Outbreaks of rubella occurred amongst many young men in the UK in 1993 and in 1996 the infection was transmitted to pregnant women, many of whom were immigrants and were susceptible. Outbreaks still arise, usually in developing countries where the vaccine is not as accessible. [ 43 ] The complications encountered in pregnancy from rubella infection (miscarriage, fetal death, congenital rubella syndrome) are more common in Africa and Southeast Asia at a rate of 121 per 100,000 live births compared to 2 per 100,000 live births in the Americas and Europe. [ 44 ]
In Japan , 15,000 cases of rubella and 43 cases of congenital rubella syndrome were reported to the National Epidemiological Surveillance of Infectious Diseases between October 15, 2012, and March 2, 2014, during the 2012–13 rubella outbreak in Japan. They mainly occurred in men aged 31–51 and young adults aged 24–34. [ 45 ]
Rubella was first described in the mid-eighteenth century. German physician and chemist, Friedrich Hoffmann , made the first clinical description of rubella in 1740, [ 46 ] which was confirmed by de Bergen in 1752 and Orlow in 1758. [ 47 ]
In 1814, George de Maton first suggested that it be considered a disease distinct from both measles and scarlet fever . All these physicians were German, and the disease was known as Rötheln (contemporary German Röteln ). ( Rötlich means "reddish" or "pink" in German.) The fact that three Germans described it led to the common name of "German measles." [ 48 ] Henry Veale, an English Royal Artillery surgeon, described an outbreak in India. He coined the name "rubella" (from the Latin word, meaning "little red") in 1866. [ 46 ] [ 49 ] [ 50 ] [ 51 ]
It was formally recognised as an individual entity in 1881, at the International Congress of Medicine in London . [ 52 ] In 1914, Alfred Fabian Hess theorised that rubella was caused by a virus, based on work with monkeys. [ 53 ] In 1938, Hiro and Tosaka confirmed this by passing the disease to children using filtered nasal washings from acute cases. [ 50 ]
In 1940, there was a widespread epidemic of rubella in Australia . Subsequently, ophthalmologist Norman McAllister Gregg found 78 cases of congenital cataracts in infants and 68 of them were born to mothers who had caught rubella in early pregnancy. [ 49 ] [ 50 ] Gregg published an account, Congenital Cataract Following German Measles in the Mother , in 1941. He described a variety of problems now known as congenital rubella syndrome (CRS) and noticed that the earlier the mother was infected, the worse the damage was. Since no vaccine was yet available, some popular magazines promoted the idea of "German measles parties" for infected children to spread the disease to other children (especially girls) to immunize them for life and protect them from later catching the disease when pregnant. [ 54 ] The virus was isolated in tissue culture in 1962 by two separate groups led by physicians Paul Douglas Parkman and Thomas Huckle Weller . [ 49 ] [ 51 ]
There was a pandemic of rubella between 1962 and 1965, starting in Europe and spreading to the United States. [ 51 ] In the years 1964–65, the United States had an estimated 12.5 million rubella cases ( 1964–1965 rubella epidemic ). This led to 11,000 miscarriages or therapeutic abortions and 20,000 cases of congenital rubella syndrome. Of these, 2,100 died as neonates, 12,000 were deaf, 3,580 were blind, and 1,800 were intellectually disabled. In New York alone, CRS affected 1% of all births. [ 55 ] [ 56 ]
In 1967, the molecular structure of rubella was observed under electron microscopy using antigen-antibody complexes by Jennifer M. Best, June Almeida , J E Banatvala and A P Waterson. [ 57 ] [ 58 ]
In 1969, a live attenuated virus vaccine was licensed. [ 50 ] In the early 1970s, a triple vaccine containing attenuated measles, mumps and rubella (MMR) viruses was introduced. [ 51 ] By 2006, confirmed cases in the Americas had dropped below 3000 a year. However, a 2007 outbreak in Argentina , Brazil , and Chile pushed the cases to 13,000 that year. [ 8 ]
On January 22, 2014, the World Health Organization (WHO) and the Pan American Health Organization declared and certified Colombia free of rubella and became the first Latin American country to eliminate the disease within its borders. [ 59 ] [ 60 ] On April 29, 2015, the Americas became the first WHO region to officially eradicate the disease. The last non-imported cases occurred in 2009 in Argentina and Brazil. The Pan American Health Organization director remarked, "The fight against rubella has taken more than 15 years, but it has paid off with what I believe will be one of the most important pan-American public health achievements of the 21st Century." [ 61 ] The declaration was made after 165 million health records and genetically confirming that all recent cases were caused by known imported strains of the virus. Rubella is still common in some regions of the world and Susan E. Reef, team lead for rubella at the CDC's global immunization division, who joined in the announcement, said there was no chance it would be eradicated worldwide before 2020. [ 8 ] Rubella is the third disease to be eliminated from the Western Hemisphere with vaccination after smallpox and polio . [ 8 ] [ 9 ]
From "rubrum" the Latin for "red", rubella means "reddish and small". "German" measles derives from "germanus" which means "similar" in this context. [ 62 ]
The name rubella is sometimes confused with rubeola , an alternative name for measles in English-speaking countries; the diseases are unrelated. [ 63 ] [ 64 ] In some other European languages, like Spanish , rubella and rubeola are synonyms, and rubeola is not an alternative name for measles. Thus, in Spanish, rubeola refers to rubella and sarampión refers to measles. [ 65 ] [ 66 ] | https://en.wikipedia.org/wiki/Rubella |
In psychological theories of motivation , the Rubicon model , more completely the Rubicon model of action phases , makes a distinction between motivational and volitional processes. The Rubicon model "defines clear boundaries between motivational and action phases." The first boundary "separates the motivational process of the predecisional phase from the volitional processes of postdecisional phase." [ 3 ] Another boundary is that between initiation and conclusion of an action. [ 3 ] A self-regulatory feedback model incorporating these interfaces was proposed later by others, as illustrated in the figure. [ 1 ]
The name "Rubicon model" derives from the tale of Caesar's crossing the Rubicon River , a point of no return, thereby revealing his intentions. According to the Rubicon model, every action includes such a point of no return at which the individual moves from goal setting to goal striving. [ 4 ] [ 5 ]
The Rubicon model addresses four questions, as identified by Achtziger and Gollwitzer : [ 3 ]
The study of these issues is undertaken by both the fields of cognitive neuroscience and social psychology . A possible connection between these approaches is brain imaging work attempting to relate volition to neuroanatomy . [ 6 ]
Human action coordinates such aspects of human behavior as perception, thought, emotion, and skills to classify goals as attainable or unattainable and then to engage or disengage in trying to attain these goals. According to Heckhausen & Heckhausen, [ 7 ] "Research based on the Rubicon model of action phases has provided a wealth of empirical evidence for mental and behavioral resources being orchestrated in this manner." Engagement and disengagement with goals affects personal distress over the unachievable. "By having new goals available, and reengaging in those new goals, a person can reduce distress....while continuing to derive a sense of purpose in life by finding other pursuits of value." [ 8 ]
This psychology -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rubicon_model |
Rubidium acetate is a rubidium salt that is the result of reacting rubidium metal, rubidium carbonate , or rubidium hydroxide with acetic acid . It is soluble in water like other acetates . [ 2 ]
Rubidium acetate is used as a catalyst for the polymerization of silanol terminated siloxane oligomers . [ 5 ]
This inorganic compound –related article is a stub . You can help Wikipedia by expanding it .
This catalysis article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rubidium_acetate |
Rubidium azide is an inorganic compound with the formula Rb N 3 . It is the rubidium salt of the hydrazoic acid HN 3 . Like most azides , it is explosive. [ 4 ]
Rubidium azide can be created by the reaction between rubidium sulfate and barium azide which results in formation of easily separated insoluble barium sulfate : [ 3 ]
In at least one study, rubidium azide was produced by the reaction between butyl nitrite , hydrazine monohydrate , and rubidium hydroxide in the presence of ethanol :
This formula is typically used to synthesize potassium azide from caustic potash . [ 5 ]
Rubidium azide has been investigated for possible use in alkali vapor cells, which are components of atomic clocks , atomic magnetometers and atomic gyroscopes . Azides are desirable starting materials because they decompose into rubidium metal and nitrogen gas when exposed to UV light . According to one publication:
Among the different techniques used to fill microfabricated alkali vapor cell [sic] , UV decomposition of rubidium azide ( RbN 3 ) into metallic Rb and nitrogen in Al 2 O 3 coated cells is a very promising approach for low-cost wafer-level fabrication. [ 6 ]
At room temperature, rubidium azide has the same structure as potassium hydrogen fluoride ; a distorted caesium chloride structure. At 315 °C and 1 atm , rubidium azide will transition to the normal caesium chloride structure. The II/I transition temperature of rubidium azide is within 2 °C of its melting point. [ 4 ]
Rubidium azide has a high pressure structure transition, which occurs at about 4.8 kilobars of pressure at 0 °C. The transition boundary of the II/III transition can be defined by the relationship P = 4.82 + 0.0240 t {\displaystyle P=4.82+0.0240\,t} , where P {\displaystyle P} is the pressure in kilobars and t {\displaystyle t} is the temperature in degrees Celsius . [ 4 ]
As with all azides, it will decompose and release nitrogen gas when heated or severely shocked :
Discharge rubidium azide in nitrogen gas will produce rubidium nitride . [ 7 ]
At 4.1 kilobars of pressure and about 460 °C, rubidium azide will explosively decompose. [ 4 ] Under normal circumstances, it explodes at 395 °C. [ 2 ] It also decomposes upon exposure to ultraviolet light . [ 6 ]
Rubidium azide is very sensitive to mechanical shock , with an impact sensitivity comparable to that of TNT . [ 8 ]
Like all azides, rubidium azide is toxic. | https://en.wikipedia.org/wiki/Rubidium_azide |
Rubika ( Persian : پیامرسان روبیکا ) is an Iranian social media platform, instant messaging (IM), VoIP and video-on-demand service developed by Tusca holding, MCI , and MTN Irancell . It is one of the most widely used social media platforms in Iran , with more than 50 million users, and the largest social media app based in Western Asia . [ 2 ] [ 3 ] [ 4 ] It is available on Android , iOS and the web. Registration requires a mobile telephone number. [ 3 ] [ 5 ] [ 6 ] [ 7 ]
Rubika was launched as part of efforts to provide a communication and social media platform developed by Iran . Over time, it has grown to be a widely recognized platform with a large user base with the support of major organizations like MCI and MTN Irancell . Rubika's success is reflected in its prominence as one of the most used social media apps in Iran, with an increasing focus on expanding to international markets. [ 8 ] [ 9 ] [ 10 ] [ 11 ] It was removed by Google Play in 2022 along with many other Iranian platforms. [ 12 ] [ 13 ] [ 14 ] [ 15 ] It is surveilled in part through MCI Digital platform monitoring center. [ 16 ]
The platform includes AI -driven tools and video calling with end-to-end encryption . For businesses, Rubika offers tools for advertising and customer engagement, including business pages and shopping channels. The platform includes entertainment options such as live broadcasts, TV , and video streaming, alongside a photo-sharing feature. Additionally, Rubika integrates financial services , including a built-in payment system, digital wallet and access to health insurance. Features also include dark mode and location services. [ 9 ] [ 10 ] [ 17 ]
Rubika is part of the Message Exchange Bus (MXB) system, which allows seamless communication between various Iranian messaging platforms, including Bale , Soroush , and Eitaa . MXB enables users send messages and files and ext. between these apps without needing a separate account for each one. This system has been made by Iran for the first time and is instrumental in creating a unified messaging ecosystem in Iran . [ 18 ] [ 19 ] [ 20 ] [ 21 ]
Rubika integrates traditional social media functions with messaging features , offering an all-in-one solution for users. Businesses leverage the platform for direct engagement, advertising, and e-commerce, while individuals enjoy community interactions, photo sharing, and livestreams. [ 22 ] [ 23 ] [ 24 ]
The platform includes a robust video on demand feature, providing access to movies, series, and live TV channels. Users can enjoy personalized recommendations based on viewing habits. [ 25 ] [ 26 ] | https://en.wikipedia.org/wiki/Rubika |
A Rubinstein bargaining model refers to a class of bargaining games that feature alternating offers through an infinite time horizon. The original proof is due to Ariel Rubinstein in a 1982 paper. [ 1 ] For a long time, the solution to this type of game was a mystery; thus, Rubinstein's solution is one of the most influential findings in game theory .
A standard Rubinstein bargaining model has the following elements:
Consider the typical Rubinstein bargaining game in which two players decide how to divide a pie of size 1. An offer by a player takes the form x = ( x 1 , x 2 ) with x 1 + x 2 = 1 and x 1 , x 2 ⩾ 0 {\displaystyle x_{1},x_{2}\geqslant 0} . Assume the players discount at the geometric rate of d , which can be interpreted as cost of delay or "pie spoiling". That is, 1 step later, the pie is worth d times what it was, for some d with 0<d<1.
Any x can be a Nash equilibrium outcome of this game, resulting from the following strategy profile: Player 1 always proposes x = ( x 1 , x 2 ) and only accepts offers x ' where x 1 ' ≥ x 1 . Player 2 always proposes x = ( x 1 , x 2 ) and only accepts offers x ' where x 2 ' ≥ x 2 .
In the above Nash equilibrium, player 2's threat to reject any offer less than x 2 is not credible. In the subgame where player 1 did offer x 2 ' where x 2 > x 2 ' > d x 2 , clearly player 2's best response is to accept.
To derive a sufficient condition for subgame perfect equilibrium , let x = ( x 1 , x 2 ) and y = ( y 1 , y 2 ) be two divisions of the pie with the following property:
i.e.
Consider the strategy profile where player 1 offers x and accepts no less than y 1 , and player 2 offers y and accepts no less than x 2 . Player 2 is now indifferent between accepting and rejecting, therefore the threat to reject lesser offers is now credible. Same applies to a subgame in which it is player 1's turn to decide whether to accept or reject. In this subgame perfect equilibrium, player 1 gets 1/(1+ d ) while player 2 gets d /(1+ d ). This subgame perfect equilibrium is essentially unique.
When the discount factor is different for the two players, d 1 {\displaystyle d_{1}} for the first one and d 2 {\displaystyle d_{2}} for the second, let us denote the value for the first player as v ( d 1 , d 2 ) {\displaystyle v(d_{1},d_{2})} .
Then a reasoning similar to the above gives
1 − v ( d 1 , d 2 ) = d 2 × v ( d 2 , d 1 ) {\displaystyle 1-v(d_{1},d_{2})=d_{2}\times v(d_{2},d_{1})} 1 − v ( d 2 , d 1 ) = d 1 × v ( d 1 , d 2 ) {\displaystyle 1-v(d_{2},d_{1})=d_{1}\times v(d_{1},d_{2})}
yielding v ( d 1 , d 2 ) = 1 − d 2 1 − d 1 d 2 {\displaystyle v(d_{1},d_{2})={\frac {1-d_{2}}{1-d_{1}d_{2}}}} . This expression reduces to the original one for d 1 = d 2 = d {\displaystyle d_{1}=d_{2}=d} .
Rubinstein bargaining has become pervasive in the literature because it has many desirable qualities: | https://en.wikipedia.org/wiki/Rubinstein_bargaining_model |
The Rubottom oxidation is a useful, high-yielding chemical reaction between silyl enol ethers and peroxyacids to give the corresponding α-hydroxy carbonyl product. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] The mechanism of the reaction was proposed in its original disclosure by A.G. Brook [ 6 ] [ 7 ] with further evidence later supplied by George M. Rubottom. [ 8 ] After a Prilezhaev-type oxidation of the silyl enol ether with the peroxyacid to form the siloxy oxirane intermediate, acid-catalyzed ring-opening yields an oxocarbenium ion. [ 1 ] [ 4 ] This intermediate then participates in a 1,4-silyl migration ( Brook rearrangement ) to give an α-siloxy carbonyl derivative that can be readily converted to the α-hydroxy carbonyl compound in the presence of acid, base, or a fluoride source. [ 1 ] [ 9 ] [ 10 ]
In 1974, three independent groups reported on the reaction now known as the Rubottom oxidation: [ 1 ] A.G Brook, [ 6 ] A. Hassner, [ 11 ] and G.M. Rubottom. [ 12 ] Considerable precedent for the reaction already existed. [ 3 ] For instance, it was known as early as the 1930s that highly enolizable β-dicarbonyl compounds would react with peroxyacids, although it was not until the 1950s and 60s α-hydroxy β-dicarbonyl compounds were in fact the product. [ 13 ] [ 14 ]
Considerable work by A.G Brook, during the 1950s on the mechanisms of organosilicon migrations, which are now known as Brook Rearrangements . [ 15 ] [ 16 ] In 1974, C.H. Heathcock described the ozonolysis of silyl enol ethers to give a carboxylic acid product via oxidative cleavage where silyl migrations were observed as side reactions and exclusively in the case of a bicyclic system. [ 17 ]
The original implementations of the Rubottom oxidation featured the peroxyacid meta-chloroperoxybenzoic acid (mCPBA) as the oxidant in dichloromethane (DCM), in the case of Hassner and Brook, and hexanes for Rubottom. [ 6 ] [ 11 ] [ 12 ] While the reaction has been tweaked and modified since 1974, mCPBA is still commonly used as the oxidant with slightly more variation in the solvent choice. [ 1 ] [ 4 ] DCM remains the most common solvent followed by various hydrocarbon solvents including pentane and toluene. [ 1 ] [ 4 ] Notably, the reaction proceeds at relatively low temperatures and heating beyond room temperature is not necessary. [ 1 ] [ 4 ] Low temperatures allow the standard Rubottom oxidation conditions to be amenable with a variety of sensitive functionalities making it ideal for complex molecule synthesis (See synthetic examples below). Silyl enol ether substrates can be prepared regioselectively from ketones or aldehydes by employing thermodynamic or kinetic control to the enolization prior to trapping with the desired organosilicon source (usually a chloride or triflate e.g. TBSCl or TBSOTf). [ 18 ] As illustrated by the synthetic examples below, silyl enol ethers can be isolated prior to exposure to the reaction conditions, or the crude material can be immediately subjected to oxidation without isolation. Both acyclic and cyclic silyl enol ether derivatives can be prepared in this way and subsequently be used as substrates in the Rubottom oxidation. [ 1 ] Below are some representative Rubottom oxidation products synthesized in the seminal papers. [ 6 ] [ 11 ] [ 12 ]
In 1978, Rubottom showed that siloxy 1,3 dienes, derived from acyclic or cyclic enones could also serve as substrates for the Rubottom oxidation to forge α-hydroxy enones after treatment with triethyl ammonium fluoride. [ 1 ] [ 19 ] These substrates give a single regioisomer under the reaction conditions due to the electron-rich nature of the silyl enol pi-bond (See synthesis of Periplanone B below). [ 1 ]
The Rubottom oxidation has remained largely unchanged since its initial disclosure, but one of the major drawbacks of standard conditions is the acidic environment, which can lead to unwanted side reactions and degradation. A simple sodium bicarbonate buffer system is commonly employed to alleviate this issue, which is especially problematic in bicyclic and other complex molecule syntheses (see synthetic examples). [ 1 ] [ 20 ] The introduction of chiral oxidants has also allowed for the synthesis of enantiopure α-hydroxy carbonyl derivatives from their corresponding silyl enol ethers. [ 1 ] The first example of an enantioselective Rubottom oxidation was published by F.A. Davis [ 21 ] in 1987 and showcased the Davis chiral oxaziridine methodology ( Davis oxidation ) to give good yields but modest enantiomeric excesses . In 1992, K.B. Sharpless showed that the asymmetric dihydroxylation conditions developed in his group could be harnessed to give either (R)- or (S)- α-hydroxy ketones from the corresponding silyl enol ethers depending on which Chinchona alkaloid-derived chiral ligands were employed. [ 22 ] The groups of Y. Shi [ 23 ] and W. Adam [ 24 ] published another enantioselective variant of the Rubottom oxidation in 1998 using the Shi chiral ketone in the presence of oxone in a buffered system to furnish α-hydroxy ketones in high yield and high enantiomeric excess . The Adam group also published another paper in 1998 utilizing manganese(III)-(Salen)complexes in the presence of NaOCl (bleach) as the oxidant and 4-phenylpyridine N-oxide as an additive in a phosphate buffered system. [ 25 ] This methodology also gave high yields and enentioselectivities for silyl enol ethers as well as silyl ketene acetals derived from esters.
Along with chiral oxidants, variants of mCPBA have been examined. [ 1 ] Stankovic and Espenson published a variation of the Rubottom oxidation where methyltrioxorhenium is used as a catalytic oxidant in the presence of stoichiometric hydrogen peroxide . [ 1 ] [ 26 ] This methodology gives acyclic and cyclic α-hydroxy ketones in high yield with a cheap, commercially available oxidant. An inherent problem with mCPBA is its inability to oxidize silyl ketene acetals. In order to synthesize α-hydroxy esters, different oxidants are needed such as NaOCl (see above), lead(IV) acetate, or a hypofluorous acid-acetonitrile (HOF-ACN) complex. [ 1 ] [ 27 ] The Rubottom group found that lead(IV) acetate in DCM or benzene gave good yields of acyclic and cyclic α-hydroxy esters after treatment of the crude reaction mixture with triethylammonium fluoride. [ 27 ] Later, the highly electrophilic HOF-ACN complex was used by S. Rozen to oxidize a variety of electron rich silyl enol ethers, silyl ketene acetals, and bis(silyl acetals), derived from carboxylic acids, in good yields at or below room temperature. [ 1 ] [ 28 ]
The following examples represent only a small portion of syntheses that highlight the use of the Rubottom oxidation to install an important α-hydroxy functionality. Some of the major features of the following syntheses include the use of buffered conditions to protect sensitive substrates and the diastereoselective installation of the α-hydroxy group due to substrate controlled facial bias. For more examples see refs [ 1 ] [ 3 ] [ 4 ]
The Rubottom oxidation was used in the synthesis of periplanone B , a sex pheromone excreted by the female American cockroach . [ 29 ] [ 30 ] The synthesis employed an anionic oxy-Cope rearrangement coupled to a Rubottom oxidation. After heating in the presence of potassium hydride (KH) and 18-crown-6 (18-C-6) to effect the anionic oxy-Cope, the enolate intermediate was trapped with trimethylsilyl chloride (TMSCl). The silyl enol ether intermediate could then be treated with mCPBA under Rubottom oxidation conditions to give the desired α-hydroxy carbonyl compound that could then be carried on to (±)-periplanone B and its diastereomers to prove its structure.
Brevisamide, a proposed biosynthetic precursor for a polyether marine toxin, was synthesized by Ghosh and Li, one step of which is a Rubottom oxidation of the cyclic silyl enol ether under buffered conditions. [ 31 ] Chiral chromium catalyst B was developed the Jacobsen group and confers high levels of enantio- and diastereoselectivity. [ 32 ] The stereocenters conveniently set in the Diels-Alder reaction direct the oxidation to the less hindered face, giving a single diastereomer, which could then be carried on in 14 more steps to Brevisamide.
Wang and coworkers developed a robust, kilogram-scale synthesis of the potent derivative 2S-hydroxymutilin from pleuromutilin, an antibiotic produced by various species of basidiomycetes . [ 33 ] Basic hydrolysis to remove the hydroxyl ester moiety of pleuromutilin yielded mutilin. Subsequent treatment with lithium hexamethyldisilazide (LiHMDS) and TMSCl gave the TMS-protected silyl enol ether, which was immediately subjected to an acetic acid - (HOAc) pyridine - (Py) buffered Rubottom oxidation before acidic hydrolysis to afford 2S-hydroxymutilin. This highly optimized sequence features two important aspects. First, the authors originally generated the silyl enol ether using triethylamine, which gave a mixture of the desired kinetic product, (shown below) the undesired thermodynamic product, and hydrolysis back to mutilin. The authors blamed the formation of the acidic triethylammonium (pKa = 10.6) byproduct for the undesired side products and remedied this by using the LiHMDS to exclusively form the desired kinetic product with no acid-catalyzed side reactions due to the significantly lower acidity of the protonated product (pKa = 26). [ 34 ] Second, while oxidation occurred from the desired convex face of the silyl enol ether, the authors saw a significant number of overoxidation products that they attributed to the stability of the oxocarbenium ion intermediate under sodium bicarbonate buffered conditions. They hypothesized that the increased lifetime of the intermediate species would allow for over oxidation to occur. After a significant amount of optimization, it was found that an HOAc/Py buffer trapped the oxocarbenium intermediate and prevented overoxidation to exclusively give 2S-hydroxymutilin after hydrolysis of the silyl protecting groups.
Ovalicin, fumagillin, and their derivatives exhibit strong anti- angiogenesis properties and have seen numerous total syntheses since their isolation. [ 35 ] Corey and Dittami reported the first total synthesis of racemic ovalicin in 1985 [ 36 ] followed by two asymmetric syntheses reported in 1994 by Samadi [ 37 ] [ 38 ] and Corey [ 39 ] which featured a chiral pool strategy from L- quebrachitol and an asymmetric dihydroxylation, respectively. In 2010, Yadav and coworkers reported a route that intercepted the Samadi route from the chiral pool starting material D- ribose . [ 40 ] A standard Rubottom oxidation gives a single stereoisomer due to substrate control and represents the key stereogenic step in the route to the Samadi ketone. Once synthesized, the Samadi ketone could be elaborated to (−)-ovalicin through known steps.
Velutinol A [ 41 ] was first synthesized by Isaka and coworkers. [ 42 ] The authors show that the high regioselectivity of this reaction is directed by the hydroxyl group syn to the ring-fusion proton. Reactions where the stereochemistry of the hydroxyl group is inverted saw lower regioselectivity, and removal of the hydroxyl group gave the exclusive formation of the other regioisomer. It is likely that the close proximity of the hydroxyl group in the syn isomer acidifies the ring-fusion proton through hydrogen-bonding interactions, thus facilitating regioselective deprotonation by triethylamine. The silyl enol ether was then treated with excess mCPBA to facilitate a “double” Rubottom oxidation to give the exo product with both hydroxyl groups on the outside of the fused ring system. This dihydroxy product was then transformed into Velutinol A in three additional steps.
The Clive group utilized the Rubottom oxidation in the synthesis of an advanced intermediate for their degradation studies of the cholesterol -lowering fungal metabolite mevinolin . [ 2 ] [ 43 ] This interesting sequence features the addition of excess n-butyllithium (BuLi) in the presence of lithium diisopropylamide (LDA) for full conversion of the bicyclic ketone derivative to the corresponding silyl enol ether. Without BuLi the authors report a maximum yield of only 72%. Subsequent buffered Rubottom oxidation conditions with sodium bicarbonate in ethyl acetate afforded the α-hydroxy ketone as a single diastereomer.
The Falk group synthesized various derivatives of phosphatidyl-D-myo-inositol to aid in the study of the various phosphatidylinositol 3-kinase (PI3K) cell signaling pathways. [ 2 ] [ 44 ] Their route to the collection of substrate analogs exploits a substrate-controlled stereoselective Rubottom oxidation using dimethyl dioxirane (DMDO) as the oxidant and catalytic camphorsulfonic acid (CSA) to aid in hydrolysis. For protecting groups see ref [ 10 ]
While the Rubottom oxidation generally gives good yields and is highly scalable (see 2S-hydroxymutilin synthesis), there are still some problems with the reaction. As mentioned above, the acidic reaction conditions are not tolerated by many complex substrates, but this can be abrogated with the use of buffer systems. [ 1 ] Poor atom economy is also a major issue with the reaction because it requires stoichiometric oxidant, which generates large amounts of waste. [ 3 ] Peroxides can also be dangerous to work with. mCPBA is known to detonate from shock or sparks. [ 45 ]
Although silyl enol ethers of aldehydes and ketones are the traditional substrates for the Rubottom oxidation, as mentioned above, silyl ketene acetals and bis (silyl acetals) can be oxidized to their α-hydroxy ester or carboxylic acid derivatives using lead(IV) acetate or hypofluorous acid - acetonitrile (HOF–ACN). [ 27 ] However, these α-hydroxylations do not proceed via silyl enol ether intermediates and are therefore not technically Rubottom oxidations. Various oxidants can be used to oxidize many of these carbonyl derivatives after they are converted to their respective enolate or related anion. Some common oxidants are peroxy acids, molecular oxygen, and hypervalent iodine reagents. [ 5 ] | https://en.wikipedia.org/wiki/Rubottom_oxidation |
Rubrocurcumin is a red-colored dye that is formed by the reaction of curcumin and boric acid . [ 1 ]
The reaction of curcumin with borates in presence of oxalic acid produces rubrocurcumin. [ 2 ]
Rubrocurcumin produces a red-colored solution.
Rubrocurcumin is a neutral molecule, while rosocyanine is ionic. In rubrocurcumin, one molecule of curcumin is replaced with oxalate compared to rosocyanine.
Complexes with boron such as rubrocurcumin are called 1,3,2-dioxaborines. [ 2 ] | https://en.wikipedia.org/wiki/Rubrocurcumin |
RubyForge was a collaborative software development management system dedicated to projects related to the Ruby programming language . It was started in 2003 by Ruby Central in an effort to help the Ruby community by providing a home for open source Ruby projects.
In February 2014 it hosted 9,603 projects and had 103,899 registered users.
On 10 Nov 2013, Evan Phoenix announced, without explanation, that RubyForge would be shutting down and unavailable as of May 15 2014. [ 1 ]
This article about a computing website is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/RubyForge |
The ruby fluorescence pressure scale is an optical method to measure pressure within a sample chamber of a diamond anvil cell apparatus. [ 1 ] Since it is an optical method, which fully make use of the transparency of diamond anvils and only requires an access to a small scale laser generator, it has become the most prevalent pressure gauge method in high pressure sciences.
Ruby is chromium -doped corundum (Al 2 O 3 ). The Cr 3+ in corundum's lattice forms an octahedra with surrounding oxygen ions. The octahedral crystal field together with spin-orbital interaction results in different energy levels. Once 3d electrons in Cr 3+ are energized by lasers, the excited electrons would go to 4 T 2 and 2 T 2 levels. Later they return to 2 E levels and the R 1 , R 2 lines come from luminescence from 2 E levels to 4 A 2 ground level. [ 2 ] The energy difference of 2 E levels are 29 cm −1 , corresponding to the splitting of R 1 , R 2 lines at 1.39 nm . [ 2 ]
Ruby fluorescence spectra has two strong sharp lines, R 1 and R 2. R 1 refers to the stronger intensity and lower energy (longer wavelength) excitation and is used to gauge pressure.
Pressure is calculated as: P ( M b a r ) = a b [ ( λ λ 0 ) b − 1 ] {\displaystyle P(Mbar)={\frac {a}{b}}[\left({\frac {\lambda }{\lambda _{0}}}\right)^{b}-1]} , where λ 0 is the R 1 wavelength measured at 1atm, a and b are constants. (e.g. a = 19.04, b = 5 [ 3 ] )
Since first demonstrated by Forman and colleagues in 1972, [ 4 ] [ 5 ] many scientists have contributed to the establishment of accurate ruby pressure scale in various experimental conditions.
A likely incomplete summary of is given below: | https://en.wikipedia.org/wiki/Ruby_pressure_scale |
A rudder angle indicator is a device used to indicate the present position of the rudder blade, usually fitted near the Ship's wheel on the bridge and in the engine control room. [ 1 ]
This article related to water transport is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rudder_angle_indicator |
Rudder ratio refers to a value that is monitored by the computerized flight control systems in modern aircraft . The ratio relates the aircraft airspeed to the rudder deflection setting that is in effect at the time. As an aircraft accelerates, the deflection of the rudder needs to be reduced proportionately within the range of the rudder pedal depression by the pilot. [ 1 ] This automatic reduction process is needed because if the rudder is fully deflected when the aircraft is in high-speed flight, it will cause the plane to sharply and violently yaw , or swing from side to side, leading to loss of control and rudder, tail and other damages, even causing the aircraft to crash.
This aviation -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rudder_ratio |
A ruderal species is a plant species that is first to colonize disturbed lands. The disturbance may be natural – for example, wildfires or avalanches – or the consequences of human activities, such as construction ( of roads , of buildings , mining , etc.) or agriculture (abandoned fields, irrigation , etc.).
The term ruderal originates from the Latin word rudus , meaning " rubble ".
Ruderal species typically dominate the disturbed area for a few years, gradually losing the competition to other native species. However, in extreme disturbance circumstances, such as when the natural topsoil is covered with a foreign substance, a single-species ruderal community may become permanently established. In addition, some ruderal invasive species may have such a competitive advantage over the native species that they, too, may permanently prevent a disturbed area from returning to its original state despite natural topsoil.
Features contributing to a species' success as ruderal are:
Ecologists have proposed various scales for quantifying ruderality, which can be defined as the "ability to thrive where there is disturbance through partial or total destruction of plant biomass" (Grime, Hodgson & Hunt, 1988). [ 1 ] [ 2 ] The ruderality scale of Grime presents values that are readily available, and it takes into account disturbance factors as well as other indicators such as the annual or perennial character of the plants. | https://en.wikipedia.org/wiki/Ruderal_species |
Rudin's conjecture is a mathematical conjecture in additive combinatorics and elementary number theory about an upper bound for the number of squares in finite arithmetic progressions . The conjecture, which has applications in the theory of trigonometric series , was first stated by Walter Rudin in his 1960 paper Trigonometric series with gaps . [ 1 ] [ 2 ] [ 3 ]
For positive integers N , q , a {\displaystyle N,q,a} define the expression Q ( N ; q , a ) {\displaystyle Q(N;q,a)} to be the number of perfect squares in the arithmetic progression q n + a {\displaystyle qn+a} , for n = 0 , 1 , … , N − 1 {\displaystyle n=0,1,\ldots ,N-1} , and define Q ( N ) {\displaystyle Q(N)} to be the maximum of the set { Q ( N ; q , a ) : q , a ≥ 1} . The conjecture asserts (in big O notation ) that Q ( N ) = O ( N ) {\displaystyle Q(N)=O({\sqrt {N}})} and in its stronger form that, if N > 6 {\displaystyle N>6} , Q ( N ) = Q ( N ; 24 , 1 ) {\displaystyle Q(N)=Q(N;24,1)} . [ 3 ]
This combinatorics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rudin's_conjecture |
Rudolf Carnap ( / ˈ k ɑːr n æ p / ; [ 20 ] German: [ˈkaʁnaːp] ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism .
Carnap's father rose from being a poor ribbon-weaver to be the owner of a ribbon-making factory. His mother came from an academic family; her father was an educational reformer and her oldest brother was the archaeologist Wilhelm Dörpfeld . As a ten-year-old, Carnap accompanied Wilhelm Dörpfeld on an expedition to Greece. [ 21 ] Carnap was raised in a profoundly religious Protestant family, but later became an atheist. [ 22 ] [ 23 ]
He began his formal education at the Barmen Gymnasium and the Carolo-Alexandrinum [ de ] Gymnasium in Jena . [ 24 ] From 1910 to 1914, he attended the University of Jena , intending to write a thesis in physics . He also intently studied Immanuel Kant 's Critique of Pure Reason during a course taught by Bruno Bauch , and was one of the very few students to attend Gottlob Frege 's courses in mathematical logic .
During his university years, he became enthralled with the German Youth Movement . [ 1 ]
While Carnap held moral and political opposition to World War I , he felt obligated to serve in the German army. After three years of service, he was given permission to study physics at the University of Berlin , 1917–18, where Albert Einstein was a newly appointed professor. Carnap then attended the University of Jena , where he wrote a thesis defining an axiomatic theory of space and time . The physics department said it was too philosophical, and Bruno Bauch of the philosophy department said it was pure physics. Carnap then wrote another thesis in 1921, under Bauch's supervision, [ 2 ] on the theory of space in a more orthodox Kantian style, published as Der Raum ( Space ) in a supplemental issue of Kant-Studien (1922).
Frege's course exposed him to Bertrand Russell 's work on logic and philosophy, which gave a sense of direction to his studies. He accepted the effort to surpass traditional philosophy with logical innovations that inform the sciences. He wrote a letter to Russell, who responded by copying by hand long passages from his Principia Mathematica for Carnap's benefit, as neither Carnap nor his university could afford a copy of this epochal work. In 1924 and 1925, he attended seminars led by Edmund Husserl , [ 25 ] the founder of phenomenology , and continued to write on physics from a logical positivist perspective.
Carnap discovered a kindred spirit when he met Hans Reichenbach at a 1923 conference. Reichenbach introduced Carnap to Moritz Schlick , a professor at the University of Vienna who offered Carnap a position in his department, which Carnap accepted in 1926. Carnap thereupon joined an informal group of Viennese intellectuals that came to be known as the Vienna Circle , directed largely by Schlick and including Hans Hahn , Friedrich Waismann , Otto Neurath , and Herbert Feigl , with occasional visits by Hahn's student Kurt Gödel . When Wittgenstein visited Vienna, Carnap would meet with him. He (with Hahn and Neurath) wrote the 1929 manifesto of the Circle, and (with Hans Reichenbach ) initiated the philosophy journal Erkenntnis .
In February 1930, Alfred Tarski lectured in Vienna, and during November 1930, Carnap visited Warsaw. On these occasions, he learned much about Tarski's model-theoretic method of semantics . Rose Rand , another philosopher in the Vienna Circle, noted, "Carnap's conception of semantics starts from the basis given in Tarski's work, but a distinction is made between logical and non-logical constants, and between logical and factual truth... At the same time, he worked with the concepts of intension and extension , and took these two concepts as a basis of a new method of semantics." [ 26 ]
In 1931, Carnap was appointed Professor at the German University of Prague . In 1933, W. V. Quine met Carnap in Prague and discussed the latter's work at some length. Thus began the lifelong mutual respect these two men shared, one that survived Quine's eventual forceful disagreements with a number of Carnap's philosophical conclusions.
Carnap, whose socialist and pacifist beliefs put him at risk in Nazi Germany , emigrated to the United States in 1935 and became a naturalized citizen in 1941. Meanwhile, back in Vienna, Schlick was murdered in 1936. From 1936 to 1952, Carnap was a professor of philosophy at the University of Chicago . During the late 1930s, Carnap offered an assistant position in philosophy to Carl Gustav Hempel , who accepted and became one of his most significant intellectual collaborators. Thanks partly to Quine's help, Carnap spent the years 1939–41 at Harvard University , where he was reunited with Tarski. [ 27 ] Carnap (1963) later expressed some irritation about his time at Chicago, where he and Charles W. Morris were the only members of the department committed to the primacy of science and logic. (Their Chicago colleagues included Richard McKeon , Charles Hartshorne , and Manley Thompson.) Carnap's years at Chicago were nonetheless very productive ones. He wrote books on semantics (Carnap 1942, 1943, 1956), modal logic , and on the philosophical foundations of probability and inductive logic (Carnap 1950, 1952).
After a stint at the Institute for Advanced Study in Princeton (1952–1954), he joined the UCLA Department of Philosophy in 1954, Hans Reichenbach having died the previous year. He had earlier refused an offer of a similar job at the University of California, Berkeley , because accepting that position required that he sign a loyalty oath , a practice to which he was opposed on principle. While at UCLA, he wrote on scientific knowledge, the analytic–synthetic distinction , and the verification principle . His writings on thermodynamics and on the foundations of probability and inductive logic were published posthumously as Carnap (1971, 1977, 1980).
Carnap taught himself Esperanto when he was 14 years of age. He later attended the World Congress of Esperanto in Dresden in 1908. [ 28 ] He also attended the 1924 Congress in Vienna, where he met his fellow Esperantist Otto Neurath for the first time. [ 29 ]
In the USA, Carnap was somewhat politically involved. Carnap was a signatory of an open appeal distributed by the National Committee to Secure Justice in the Rosenberg Case to appeal for clemency in the case. [ 30 ] He was listed as a 'sponsor' for the "National Conference to Appeal the Walter-McCarran Law and Defend Its Victims" organised by the American Committee for the Protection of the Foreign Born , [ 31 ] and also for the "Scientific and Cultural Conference for World Peace" organised by the National Council of Arts, Sciences and Professions . [ 32 ]
Carnap had four children by his first marriage to Elizabeth Schöndube, which ended in divorce in 1929. He married his second wife, Elizabeth Ina Stöger, in 1933. [ 21 ] Ina committed suicide in 1964.
Below is an examination of the main topics in the evolution of the philosophy of Rudolf Carnap. It is not exhaustive, but it outlines Carnap's main works and contributions to modern epistemology and philosophy of logic .
From 1919 to 1921, Carnap worked on a doctoral thesis called Der Raum: Ein Beitrag zur Wissenschaftslehre ( Space: A Contribution to the Theory of Science , 1922). In this dissertation on the philosophical foundations of geometry , Carnap tried to provide a logical basis for a theory of space and time in physics . Considering that Carnap was interested in pure mathematics , natural sciences and philosophy, his dissertation can be seen as an attempt to build a bridge between the different disciplines that are geometry, physics, and philosophy. For Carnap thought that in many instances those disciplines use the same concepts, but with totally different meanings. The main objective of Carnap's dissertation was to show that the inconsistencies between theories concerning space only existed because philosophers, as well as mathematicians and scientists, were talking about different things while using the same "space" word. Hence, Carnap characteristically argued that there had to be three separate notions of space. "Formal" space is space in the sense of mathematics: it is an abstract system of relations. "Intuitive" space is made of certain contents of intuition independent of single experiences. "Physical" space is made of actual spatial facts given in experience. The upshot is that those three kinds of "space" imply three different kinds of knowledge and thus three different kinds of investigations. It is interesting to note that it is in this dissertation that the main themes of Carnap's philosophy appear, most importantly, the idea that many philosophical contradictions appear because of a misuse of language, and a stress on the importance of distinguishing formal and material modes of speech.
From 1922 to 1925, Carnap worked on a book which became one of his major works, namely Der logische Aufbau der Welt (translated as The Logical Structure of the World , 1967), which was accepted in 1926 as his habilitation thesis at the University of Vienna and published as a book in 1928. [ 33 ] That achievement has become a landmark in modern epistemology and can be read as a forceful statement of the philosophical thesis of logical positivism. Indeed, the Aufbau suggests that epistemology, based on modern symbolic logic , is concerned with the logical analysis of scientific propositions, while science itself, based on experience, is the only source of knowledge of the external world, i.e. the world outside the realm of human perception. According to Carnap, philosophical propositions are statements about the language of science; they aren't true or false, but merely consist of definitions and conventions about the use of certain concepts. In contrast, scientific propositions are factual statements about the external reality. They are meaningful because they are based on the perceptions of the senses. In other words, the truth or falsity of those propositions can be verified by testing their content with further observations.
In the Aufbau , Carnap wants to display the logical and conceptual structure with which all scientific (factual) statements can be organized. Carnap gives the label " constitution theory " to this epistemic-logical project. It is a constructive undertaking that systematizes scientific knowledge according to the notions of symbolic logic. Accordingly, the purpose of this constitutional system is to identify and discern different classes of scientific concepts and to specify the logical relations that link them. In the Aufbau, concepts are taken to denote objects, relations, properties, classes and states. Carnap argues that all concepts must be ranked over a hierarchy. In that hierarchy, all concepts are organized according to a fundamental arrangement where concepts can be reduced and converted to other basic ones. Carnap explains that a concept can be reduced to another when all sentences containing the first concept can be transformed into sentences containing the other. In other words, every scientific sentence should be translatable into another sentence such that the original terms have the same reference as the translated terms. Most significantly, Carnap argues that the basis of this system is psychological. Its content is the "immediately given", which is made of basic elements, namely perceptual experiences. These basic elements consist of conscious psychological states of a single human subject. In the end, Carnap argues that his constitutional project demonstrates the possibility of defining and uniting all scientific concepts in a single conceptual system on the basis of a few fundamental concepts.
From 1928 to 1934, Carnap published papers ( Scheinprobleme in der Philosophie , 1928; translated as Pseudoproblems in Philosophy , 1967) in which he appears overtly skeptical of the aims and methods of metaphysics , i.e. the traditional philosophy that finds its roots in mythical and religious thought. Indeed, he discusses how, in many cases, metaphysics is made of meaningless discussions of pseudo-problems. For Carnap, a pseudo-problem is a philosophical question that, on the surface, handles concepts that refer to our world while, in fact, these concepts do not actually denote real and attested objects. In other words, these pseudo-problems concern statements that do not, in any way, have empirical implications. They do not refer to states of affairs and the things they denote cannot be perceived. Consequently, one of Carnap's main aim has been to redefine the purpose and method of philosophy. According to him, philosophy should not aim at producing any knowledge transcending the knowledge of science. In contrast, by analyzing the language and propositions of science, philosophers should define the logical foundations of scientific knowledge. Using symbolic logic , they should explicate the concepts, methods, and justificatory processes that exist in science.
Carnap believed that the difficulty with traditional philosophy lay in the use of concepts that are not useful for science. For Carnap, the scientific legitimacy of these concepts was doubtful because the sentences containing them do not express facts. Indeed, a logical analysis of those sentences proves that they do not convey the meaning of states of affairs. In other words, these sentences are meaningless. Carnap explains that to be meaningful, a sentence should be factual. It can be so, for one thing, by being based on experience, i.e., by being formulated with words relating to direct observations. For another, a sentence is factual if one can clearly state what the observations are that could confirm or disconfirm that sentence. After all, Carnap presupposes a specific criterion of meaning, namely the Wittgensteinian principle of verifiability. Indeed, he requires, as a precondition of meaningfulness, that all sentences be verifiable, which implies that a sentence is meaningful only if there is a way to verify if it is true or false. To verify a sentence, one needs to expound the empirical conditions and circumstances that would establish the truth of the sentence. As a result, it is clear for Carnap that metaphysical sentences are meaningless. They include concepts like "god", "soul", and "the absolute" that transcend experience and cannot be traced back or connected to direct observations. Because those sentences cannot be verified in any way, Carnap suggests that science, as well as philosophy, should neither consider nor contain them.
At that point in his career, Carnap attempted to develop a full theory of the logical structure of scientific language. This theory, exposed in Logische Syntax der Sprache (1934; translated as The Logical Syntax of Language , 1937) gives the foundations to his idea that scientific language has a specific formal structure and that its signs are governed by the rules of deductive logic. Moreover, the theory of logical syntax expounds a method with which one can talk about a language: it is a formal meta-theory about the pure forms of language. In the end, because Carnap argues that philosophy aims at the logical analysis of the language of science and thus is the logic of science, the theory of the logical syntax can be considered as a definite language and a conceptual framework for philosophy.
The logical syntax of language is a formal theory. It is not concerned with the contextualized meaning or the truth-value of sentences. In contrast, it considers the general structure of a given language and explores the different structural relations that connect the elements of that language. Hence, by explaining the different operations that allow specific transformations within the language, the theory is a systematic exposition of the rules that operate within that language. In fact, the basic function of these rules is to provide the principles to safeguard coherence, to avoid contradictions, and to deduce justified conclusions. Carnap sees language as a calculus. This calculus is a systematic arrangement of symbols and relations. The symbols of the language are organized according to the class that they belong to—and it is through their combination that we can form sentences. The relations are different conditions under which a sentence can be said to follow, or to be the consequence, of another sentence. The definitions included in the calculus state the conditions under which a sentence can be considered of a certain type and how those sentences can be transformed. We can see the logical syntax as a method of formal transformation, i.e., a method for calculating and reasoning with symbols.
Finally, Carnap introduces his well-known "principle of tolerance." This principle suggests that there is no moral in logic. When it comes to using a language, there is no good or bad, fundamentally true or false. In this perspective, the philosopher's task is not to bring authoritative interdicts prohibiting the use of certain concepts. In contrast, philosophers should seek general agreements over the relevance of certain logical devices. According to Carnap, those agreements are possible only through the detailed presentation of the meaning and use of the expressions of a language. In other words, Carnap believes that every logical language is correct only if this language is supported by exact definitions and not by philosophical presumptions. Carnap embraces a formal conventionalism. That implies that formal languages are constructed and that everyone is free to choose the language they find more suited to their purpose. There should not be any controversy over which language is the correct language; what matters is agreeing over which language best suits a particular purpose. Carnap explains that the choice of a language should be guided according to the security it provides against logical inconsistency. Furthermore, practical elements like simplicity and fruitfulness in certain tasks influence the choice of a language. Clearly enough, the principle of tolerance was a sophisticated device introduced by Carnap to dismiss any form of dogmatism in philosophy.
After having considered problems in semantics, i.e. the theory of the concepts of meaning and truth ( Foundations of Logic and Mathematics , 1939; Introduction to Semantics , 1942; Formalization of Logic , 1943), Carnap turned his attention to the subject of probability and inductive logic . His views on that subject are, for the most part exposed in Logical foundations of probability (1950) where Carnap aims to give a sound logical interpretation of probability. Carnap thought that, according to certain conditions, the concept of probability had to be interpreted as a purely logical concept. In this view, probability is a basic concept anchored in all inductive inferences, whereby the conclusion of every inference that holds without deductive necessity is said to be more or less likely to be the case. In fact, Carnap claims that the problem of induction is a matter of finding a precise explanation of the logical relation that holds between a hypothesis and the evidence that supports it. An inductive logic is thus based on the idea that probability is a logical relation between two types of statements: the hypothesis (conclusion) and the premises (evidence). Accordingly, a theory of induction should explain how, by pure logical analysis, we can ascertain that certain evidence establishes a degree of confirmation strong enough to confirm a given hypothesis.
Carnap was convinced that there was a logical as well as an empirical dimension in science. He believed that one had to isolate the experiential elements from the logical elements of a given body of knowledge. Hence, the empirical concept of frequency used in statistics to describe the general features of certain phenomena can be distinguished from the analytical concepts of probability logic that merely describe logical relations between sentences. For Carnap, the statistical and the logical concepts must be investigated separately. Having insisted on this distinction, Carnap defines two concepts of probability. The first one is logical and deals with the degree to which a given hypothesis is confirmed by a piece of evidence. It is the degree of confirmation . The second is empirical and relates to the long-run rate of one observable feature of nature relative to another. It is the relative frequency. Statements belonging to the second concept are about reality and describe states of affairs. They are empirical and, therefore, must be based on experimental procedures and the observation of relevant facts. On the contrary, statements belonging to the first concept do not say anything about facts. Their meaning can be grasped solely with an analysis of the signs they contain. They are analytical sentences, i.e. true by virtue of their logical meaning. Even though these sentences could refer to states of affairs, their meaning is given by the symbols and relations they contain. In other words, the probability of a conclusion is given by the logical relation it has to the evidence. The evaluation of the degree of confirmation of a hypothesis is thus a problem of meaning analysis.
Clearly, the probability of a statement about relative frequency can be unknown because it depends on the observation of certain phenomena, and one may not possess the information needed to establish the value of that probability. Consequently, the value of that statement can be confirmed only if it is corroborated by facts. In contrast, the probability of a statement about the degree of confirmation could be unknown, in the sense that one may miss the correct logical method to evaluate its exact value. But, such a statement can always receive a certain logical value, given the fact that this value only depends on the meaning of its symbols.
The Rudolf Carnap Papers contain thousands of letters, notes and drafts, and diaries. The majority of his papers were purchased from his daughter, Hanna Carnap-Thost in 1974, by the University of Pittsburgh, with subsequent further accessions. Documents that contain financial, medical, and personal information are restricted. [ 34 ] These were written over his entire life and career. Carnap used the mail regularly to discuss philosophical problems with hundreds of others. The most notable were: Herbert Feigl, Carl Gustav Hempel, Felix Kaufmann, Otto Neurath, and Moritz Schlick. Photographs are also part of the collection and were taken throughout his life. Family pictures and photographs of his peers and colleagues are also stored in the collection. Some of the correspondence is considered notable and consist of his student notes, his seminars with Frege (describing the Begriffsschrift and the logic in mathematics). Carnap's notes from Russell's seminar in Chicago, and notes he took from discussions with Tarski, Heisenberg, Quine, Hempel, Gödel, and Jeffrey are also part of the University of Pittsburgh Library System's Archives and Special Collections. Digitized contents include:
Much material is written in an older German shorthand, the Stolze-Schrey system. He employed this writing system extensively beginning in his student days. [ 34 ] Some of the content has been digitized and is available through the finding aid . The University of California also maintains a collection of Rudolf Carnap Papers. Microfilm copies of his papers are maintained by the Philosophical Archives at the University of Konstanz in Germany. [ 36 ]
*For a more complete listing see Carnap’s Works in "Linked bibliography ". [ 44 ] | https://en.wikipedia.org/wiki/Rudolf_Carnap |
Rudolf Christian Böttger (28 April 1806 – 29 April 1881) was a German inorganic chemist. He conducted most of his research at the University of Frankfurt am Main . He is credited with discovery of nitrocellulose in 1846, independently to Schönbein , and with the synthesis of the first organocopper compound copper(I) acetylide Cu 2 C 2 in 1859. [ 1 ]
Böttger was born in Aschersleben , Principality of Halberstadt in 1806. After attending the primary school there he joined the school of the Franksche Stiftung in Halle an der Saale at the age of eleven. In 1824, Böttger started to study theology, but in parallel also attended the science lectures at the University Halle. The lectures of Johann Salomo Christoph Schweigger had a strong influence on him. Böttger left the university in 1828 and worked as cleric and teacher at different locations. The contact with Schweigger never faded and in 1831 Böttger decided to leave the theology career. He was offered a job at the voluntary association for chemistry in Frankfurt in 1835. His first major work in Frankfurt was the improvement of the electrotyping method for the production of printing plates, he created the first practical nickel electroplating solution (1840). [ 2 ] Böttger received his PhD from the University of Jena in 1837 and was appointed as full professor in Frankfurt in 1842. Böttger married Christiane Harpke in 1841, and they had eight children. He and Christian Friedrich Schönbein , a German-Swiss chemist, discovered nitrocellulose independently in 1846. Both scientists collaborated to earn money with the invention, but they were not successful. The development of the safety match in 1848 and the synthesis of the first organocopper compound, the explosive copper(I) acetylide Cu 2 C 2 in 1859 [ 3 ] were examples for his chemistry research. Böttger stayed at the University of Frankfurt am Main for the rest of his life, although he was offered positions at other universities. He died of a liver illness in 1881. [ 1 ] | https://en.wikipedia.org/wiki/Rudolf_Christian_Böttger |
Rudolf Hoppe (29 October 1922 – 24 November 2014), a German chemist, discovered the first covalent noble gas compounds .
Hoppe studied chemistry at the Christian-Albrechts- University of Kiel and was awarded his doctorate at the Westfälische Wilhelms- University of Münster in 1954 under the supervision of Wilhelm Klemm . He also got his habilitation degree in Münster and gained a professorship for inorganic chemistry in 1958. In 1965, Hoppe accepted an offer for the chair of inorganic and analytic chemistry at the Justus Liebig University Giessen , which he kept until his retirement in 1991.
Hoppe became famous through his synthesis of the stable noble gas compound XeF 2 ( xenon difluoride ), reported in November 1962. His work followed the previous synthesis of by xenon hexafluoroplatinate by Neil Bartlett , in an experiment run on March 23, 1962 and reported in June of that year. [ 1 ] Until then, everyone had assumed that compounds of such kind would not exist, the reason being, first, unsuccessful experiments attempting to synthesize such noble gas compounds and, second, the concept of the "closed octet of electrons", according to which noble gases would not participate in chemical reactions.
Through the properties of the interhalogen compounds it had become obvious that noble gas fluorides were the only accessible ones. Since 1949/50, a research group in Münster had carried out in-depth discussions on the possibility of the formation and the properties of xenon fluorides. This research group was convinced, already in 1951, that XeF 4 and XeF 2 should be thermodynamically stable against the decomposition into the elements.
For a long time it was planned to occasionally perform synthetic experiments targeted at the xenon fluorides. Technical and conceptional difficulties, however, interfered in Münster. On the one hand, xenon was not accessible in sufficient purity; on the other hand, the researchers believed that only pressure syntheses would be successful, for which steel bottles with compressed F 2 were needed. Since 1961, those F 2 -pressure cylinders had been promised by American friends but the transfer could not take place until 1963 because the valves of non-standard U.S. pressure cylinders were not allowed in Germany and vice versa.
Nevertheless, Hoppe’s research group was able to generate XeF 2 in the form of transparent crystals in early 1962. To do so, they let electric sparks impact on xenon-fluorine mixtures. Neil Bartlett tried a similar experiment for the first time in the USA on August 2, 1962. After a few days, he gained xenon tetrafluoride , XeF 4 .
In Gießen, Hoppe continued his extensive research in the field of solid state chemistry with a focus on the synthesis and characterization of oxo- and fluorometalates of the alkali metals. During his research he published over 650 articles in international and national peer-review journals. In addition, he had been the scientific editor for the German Journal of Inorganic and General Chemistry (Zeitschrift für Anorganische und Allgemeine Chemie).
As a professor, Prof. Hoppe taught many young students the fundamentals of chemistry and other more specific topics. In addition, 114 doctoral candidates earned their Ph.D. with Hoppe as their supervisor.
Hoppe was a great pet lover and was known to be a supporter of zoological gardens. He died at the age of 92 on 24 November 2014. [ 2 ]
Furthermore, Hoppe has been a member of several scientific societies and academies as well as of the German National Academy of Sciences Leopoldina in Halle and of the Bavarian Academy of Sciences and Austrian Academy of Sciences . | https://en.wikipedia.org/wiki/Rudolf_Hoppe |
Rudolf Karl Lüneburg (30 March 1903, Volkersheim ( Bockenem ) - 19 August 1949, Great Falls, Montana ), after his emigration at first Lueneburg , later Luneburg , sometimes misspelled Luneb e rg or Lune n b e rg ) was a professor of mathematics and optics at the Dartmouth College Eye Institute. He was born in Germany , received his doctorate at Göttingen , and emigrated to the United States in 1935.
His work included an analysis of the geometry of visual space as expected from physiology and the assumption that the angle of vergence provides a constant measure of distance. From these premises he concluded that near field visual space is hyperbolic .
This article about a German mathematician is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rudolf_Luneburg |
Rudolph Arthur Marcus (born July 21, 1923) is a Canadian-born American chemist who received the 1992 Nobel Prize in Chemistry [ 3 ] "for his contributions to the theory of electron transfer reactions in chemical systems". [ 4 ] Marcus theory , named after him, provides a thermodynamic and kinetic framework for describing one electron outer-sphere electron transfer . [ 5 ] [ 6 ] [ 7 ] He is a professor at Caltech , Nanyang Technological University , Singapore and a member of the International Academy of Quantum Molecular Science .
Marcus was born in Montreal , Quebec , the son of Esther (born Cohen) and Myer Marcus. His father was born in New York and his mother was born in England . His family background is from Ukmergė ( Lithuania ). [ 8 ] He is Jewish [ 9 ] and grew up mostly in a Jewish neighborhood in Montreal but also spent some of his childhood in Detroit , United States. [ 10 ] [ 8 ] His interest in the sciences began at a young age. He excelled at mathematics at Baron Byng High School . He then studied at McGill University under Carl A. Winkler , [ 11 ] who had studied under Cyril Hinshelwood at the University of Oxford . At McGill, Marcus took more math courses than an average chemistry student, which would later aid him in creating his theory on electron transfer. [ 12 ]
Marcus earned a B.Sc. in 1943 and a Ph.D. in 1946, both from McGill University. [ 13 ] [ 14 ] In 1958, he became a naturalized citizen of the United States.
After graduating, in 1946, he took postdoctoral positions first at the National Research Council (Canada) , [ 15 ] followed by the University of North Carolina . He received his first faculty appointment at the Polytechnic Institute of Brooklyn . In 1952, at the University of North Carolina , he developed Rice–Ramsperger–Kassel–Marcus (RRKM) theory by combining the former RRK theory with the transition state theory . In 1964, he taught at the University of Illinois . [ 16 ] His approach to solving a problem is to "go full tilt." [ 17 ] Marcus moved to the California Institute of Technology in 1978. [ 18 ]
Electron transfer is one of the simplest forms of a chemical reaction. It consists of one outer-sphere electron transfer between substances of the same atomic structure likewise to Marcus’s studies between divalent and trivalent iron ions. Electron transfer may be one of the most basic forms of chemical reaction but without it life cannot exist. Electron transfer is used in all respiratory functions as well as photosynthesis . In the process of oxidizing food molecules, two hydrogen ions, two electrons, and half an oxygen molecule react to make an exothermic reaction as well as a water molecule:
Because electron transfer is such a broad, common, and essential reaction within nature, Marcus's theory has become vital within the field of chemistry and biochemistry .
A type of chemical reaction linked to his many studies of electron transfer would be the transfer of an electron between metal ions in different states of oxidation. An example of this type of chemical reaction would be one between a divalent and a trivalent iron ion in an aqueous solution. In Marcus's time chemists were astonished at the slow rate in which this specific reaction took place. This attracted many chemists in the 1950s and is also what began Marcus's interests in electron transfer. Marcus made many studies based on the principles that were found within this chemical reaction, and through his studies was able to elaborate his electron transfer theory. His approach gave way to new experimental programs that contributed to all branches within chemistry and biochemistry. [ 19 ]
As of his 100th birthday, he is still active doing research. [ 20 ]
Marcus was awarded honorary degrees from the University of Chicago in 1983, the University of Gothenburg in 1986, the Polytechnic Institute of Brooklyn in 1987, McGill University in 1988, Queen's University in 1993, the University of New Brunswick in 1993, the University of Oxford in 1995, the University of North Carolina at Chapel Hill in 1996, the Yokohama National University in 1996, the University of Illinois at Urbana–Champaign in 1997, the Technion – Israel Institute of Technology in 1998, the Technical University of Valencia in 1999, Northwestern University in 2000, the University of Waterloo in 2002, the Nanyang Technological University in 2010, the Tumkur University in 2012, the University of Hyderabad in 2012, and the University of Calgary in 2013. In addition, he was awarded an honorary doctorate from the University of Santiago, Chile in 2018.
Among the awards he received before the Nobel Prize in Chemistry in 1992, [ 3 ] Marcus received the Irving Langmuir Prize in Chemical Physics in 1978, the Robinson Award of the Faraday Division of the Royal Society of Chemistry in 1982, Columbia University 's Chandler Award in 1983, the Wolf Prize in Chemistry in 1984-1985, the Centenary Prize , the Willard Gibbs Award and the Peter Debye Award in 1988, the National Medal of Science in 1989, Ohio State 's William Lloyd Evans Award in 1990, the Theodore William Richards Award (NESACS) in 1990, the Pauling Medal , the Remsen Award and the Edgar Fahs Smith Lecturer in 1991, the Golden Plate Award of the American Academy of Achievement [ 21 ] and the Hirschfelder Prize in Theoretical Chemistry in 1993.
He also received a professorial fellowship at University College, Oxford , from 1975 to 1976.
He was elected to the National Academy of Sciences in 1970, the American Academy of Arts and Sciences in 1973, the American Philosophical Society in 1990, received honorary membership in the Royal Society of Chemistry in 1991, and in the Royal Society of Canada in 1993. [ 22 ] He was elected a Foreign Member of the Royal Society (ForMemRS) in 1987 . [ 1 ]
In 2019, he was awarded with the Fray International Sustainability award at SIPS 2019 by FLOGEN Star Outreach. [ 23 ] | https://en.wikipedia.org/wiki/Rudolph_A._Marcus |
Sir Rudolph Albert Peters MC MID FRS [ 1 ] H FRSE FRCP LLD (13 April 1889 – 29 January 1982) was a British biochemist. He led the research team at Oxford who developed British Anti-Lewisite (BAL), an antidote for the chemical warfare agent lewisite . His efforts investigating the mechanism of arsenic war gases were deemed crucial in maintaining battlefield effectiveness. [ 2 ]
He was born in Kensington in London the son of Dr Albert E. D. R. Peters (1863–1945), a physician, and his wife, Agnes Malvina Watts (1867–1950). [ 3 ]
He was educated at Wellington College, Berkshire , then studied medicine at King's College London and Gonville and Caius College, Cambridge . [ 4 ]
In the First World War he served in the Royal Army Medical Corps as Medical Officer to the 60th Rifles. From 1917 he was attached to the chemical warfare section at Porton Down . After the war he returned to Cambridge University lecturing in biochemistry. In 1923 he was created professor of biochemistry at Oxford University .
After the Second World War , he researched pyruvate metabolism, focussing particularly on the toxicity of fluoroacetate . The fact that fluoroacetate in itself is far less toxic than its metabolite fluorocitrate led him to coin the term " lethal synthesis " which was the title of his Croonian Lecture of 1951. [ 2 ] [ 5 ]
Peters retired from academia in 1954 to establish, at age 65, a new department of biochemistry at the Agricultural Research Council Animal Physiology Unit at Babraham ; he retired five years later. [ 6 ]
He was elected FRS in 1935. In 1940, he received the Cameron Prize for Therapeutics of the University of Edinburgh . He was knighted by Queen Elizabeth II in 1952 and elected an Honorary Fellow of the Royal Society of Edinburgh in 1957.
He died in Cambridge on 29 January 1982, and was cremated there on 4 February.
Some of Sir Rudolph's papers are held at the Bodleian Library . [ 7 ]
Peters married Frances Williamina Vérel at the Queen's Park Free Church, Glasgow, on 7 November 1917. [ 8 ] Frances was the daughter of Francis William Vérel, a photographic chemist, and had been at school in Westgate-on-Sea with Peters's sister, Gwendoline. [ 9 ] They had two sons: Rudolph V (1918–2013), [ 10 ] and Francis Raymond (1922–2023). [ 11 ] [ 12 ] | https://en.wikipedia.org/wiki/Rudolph_Peters |
Ruff degradation is a reaction used to shorten the open chain forms of monosaccharides. [ 1 ] It is functionally the reverse reaction of Kiliani-Fischer synthesis .
In 1898, Otto Ruff published his work on the transformation of D- Glucose to D- Arabinose later called the Ruff degradation. In this reaction, D-Glucose is converted to D-Arabinose. In this reaction, the terminal aldehyde group is converted to a carboxylic acid group, using selective oxidation of the aldehyde using Bromine water and then converted to gluconate ion. Next, Fe(OAc) 3 with 30% of H 2 O 2 is added.
Thus COO- ion will form CO 2 and a stereo selective compound will form. And below -CH2OH will convert to -CHO group through the reduction of iron from its +3 state to +2 state, thus forming D-Arabinose.
This reaction was an important tool used by Emil Fischer to show that D-Glucose and D-Mannose each formed the same product upon Ruff degradation (D-Arabinose) indicating them to have opposite configurations at C-2 (epimers). Further Ruff degradation on D-Arabinose gave D- Glyceraldehyde , which established the stereochemistry of the chiral center on C-5.
This chemical reaction article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ruff_degradation |
In mathematics , Ruffini's rule is a method for computation of the Euclidean division of a polynomial by a binomial of the form x – r . It was described by Paolo Ruffini in 1809. [ 1 ] The rule is a special case of synthetic division in which the divisor is a linear factor.
The rule establishes a method for dividing the polynomial:
by the binomial:
to obtain the quotient polynomial:
The algorithm is in fact the long division of P ( x ) by Q ( x ).
To divide P ( x ) by Q ( x ):
The b values are the coefficients of the result ( R ( x )) polynomial, the degree of which is one less than that of P ( x ). The final value obtained, s , is the remainder. The polynomial remainder theorem asserts that the remainder is equal to P ( r ), the value of the polynomial at r .
Here is an example of polynomial division as described above.
Let:
P ( x ) will be divided by Q ( x ) using Ruffini's rule. The main problem is that Q ( x ) is not a binomial of the form x − r , but rather x + r . Q ( x ) must be rewritten as
Now the algorithm is applied:
So, if original number = divisor × quotient + remainder , then
Ruffini's rule can be used when one needs the quotient of a polynomial P by a binomial of the form x − r . {\displaystyle x-r.} (When one needs only the remainder, the polynomial remainder theorem provides a simpler method.)
A typical example, where one needs the quotient, is the factorization of a polynomial p ( x ) {\displaystyle p(x)} for which one knows a root r :
The remainder of the Euclidean division of p ( x ) {\displaystyle p(x)} by r is 0 , and, if the quotient is q ( x ) , {\displaystyle q(x),} the Euclidean division is written as
This gives a (possibly partial) factorization of p ( x ) , {\displaystyle p(x),} which can be computed with Ruffini's rule. Then, p ( x ) {\displaystyle p(x)} can be further factored by factoring q ( x ) . {\displaystyle q(x).}
The fundamental theorem of algebra states that every polynomial of positive degree has at least one complex root. The above process shows the fundamental theorem of algebra implies that every polynomial p ( x ) = a n x n + a n −1 x n −1 + ⋯ + a 1 x + a 0 can be factored as
where r 1 , … , r n {\displaystyle r_{1},\ldots ,r_{n}} are complex numbers.
The method was invented by Paolo Ruffini , who took part in a competition organized by the Italian Scientific Society (of Forty). The challenge was to devise a method to find the roots of any polynomial. Five submissions were received. In 1804 Ruffini's was awarded first place and his method was published. He later published refinements of his work in 1807 and again in 1813. | https://en.wikipedia.org/wiki/Ruffini's_rule |
In anatomy , rugae ( sg. : ruga ) are a series of ridges produced by folding of the wall of an organ . [ 1 ]
In general, rugae are a biological feature found in many organisms, serving purposes such as increasing surface area, flexibility, or structural support.
Most commonly rugae refers to the gastric rugae of the internal surface of the stomach .
For terrestrial gastropods , the rugae often appear as fine, transverse folds or wrinkles on the mantle, back, or sides of the body. They are particularly visible when the animal extends its body or contracts, and may also be interrupted or intersected by other grooves or structures (such as dorsal grooves or keels) .
A purpose of the gastric rugae is to allow for expansion of the stomach after the consumption of foods and liquids. This expansion increases the volume of the stomach to hold larger amounts of food. The folds also result in greater surface area, allowing the stomach to absorb nutrients more quickly.
Rugae can appear in the following locations in humans:
With few exceptions (e.g. the scrotum), rugae are only evident when an organ or tissue is deflated or relaxed. For example, rugae are evident within the stomach when it is deflated. However, when the stomach distends, the rugae unfold to allow for the increase in volume. On the other hand, plicae remain folded regardless of distension as is evident within the plicae of the small intestine walls. | https://en.wikipedia.org/wiki/Rugae |
The Rugg/Feldman benchmarks are a series of seven short BASIC programming language programs that are used to test the performance of BASIC implementations on various microcomputers . They were published by Tom Rugg and Phil Feldman in the June 1977 issue of the US computer magazine, Kilobaud .
The article reported that Integer BASIC , an interpreter program written by Steve Wozniak for the Apple II computer, was much faster than the other programs tested. This sparked widespread comments about the tests, including a lengthy letter from Bill Gates . A follow-up article in the October 1977 issue addressed these concerns in depth and added many new machines and BASICs to the set of results.
John Coll added an eighth test using transcendental functions in an article in the February 1978 issue of the British magazine Personal Computer World (PCW). This expanded set became known as the PCW Benchmarks , and was particularly popular as a test for UK-designed machines like the Grundy NewBrain and BBC Micro .
The benchmark was widely used through the late 1970s, and appears as a standard in many computer magazines and journals. In the 1980s it was not as widely used in the US as the Creative Computing Benchmark or Byte Sieve , but remained in common use in the UK.
The benchmark suite was introduced to test claims that were being made by vendors that their BASIC was much faster than others running on the same machines. The authors were unable to find a set of standardized benchmarks and decided to write their own. [ 1 ] The tests deliberately ignored string and floating point performance, as many BASICs of the era, especially those descended from Tiny BASIC , lacked these features. Strings were further hindered by major differences in syntax between different versions. [ 2 ] [ a ]
The two ran the benchmarks on every machine they could find, typically at friends' houses. All of the major 8-bit CPUs were tested, including the Intel 8080 , Zilog Z80 , Motorola 6800 and MOS 6502 . For comparison, they also ran it on a CDC Cyber 174 supercomputer , which is so fast that they had to add code to time the run using the system's clock as they could not operate a stopwatch quickly enough. They used this machine for two reasons; one was simply to see how fast such a machine ran, and the other was to ensure no one micro would end up at the top of the list and then claim they had been proven to be the fastest. [ 3 ]
The article makes a special note of the BASIC that shipped with IMSAI computers, as it basically didn't work. The machine was very new at the time and the BASIC was described by the company as "preliminary". During this period, different IMSAI machines were delivered with different versions of BASIC. Each version had different features, but none of them were able to run even the majority of the programs. [ 4 ]
The Apple II , using the original Integer BASIC , finished well in front of all the other machines. As the tests did not make use of any floating point features, this result was not surprising given the much simpler internal representation of numbers. [ b ] The next fastest, albeit significantly slower, was Zapple BASIC on a Zilog Z80 add-in card in an Altair 8800 . The rest of the list contained a number of very closely spaced entries, dominated by what would later be known as Microsoft BASIC . Across the entire suite of 8080 and Z80 machines and versions of BASICs, the spread was only 20%. In contrast, the 6800-based machines were isolated entirely at the bottom of the list, 30 to 40% slower than the 8080 and Z80 entries. [ 4 ]
As the article went to press, the editors of Kilobaud visited several local computer stores to test the programs on newer machines. This process added the production version of IMSAI BASIC, North Star BASIC and the 11 kB BASIC on the Poly-88 . IMSAI's results were at the bottom of the pack, while North Star and Poly were in the middle. [ 5 ]
Rugg and Feldman revisited the suite in the October 1977 issue. The new article opened by noting they had been deluged with mail about the original article. Among them was a letter from Bill Gates , who they introduce as the author of "Altair BASIC (8080 and 6800 versions), OSI BASIC and PET BASIC". The last entry refers to a member of the " 1977 trinity " of machines, the Commodore PET , which was made available in prototype form for inclusion in the article. [ 6 ]
Gates complained that the original test series "let an integer BASIC be compared against... more powerful BASIC... using floating point." He suggested that the test include a DEFINT A-Z at the start, which would make newer versions of Altair BASIC use integer math as well. Instead, Rugg and Feldman took another approach and eliminated all integer-only BASICs from the new test results. [ 6 ] This did not eliminate the Apple II, which by this time had introduced the MS-derived Applesoft BASIC on cassette. [ 7 ]
Gates also noted that the results for the 6800 machine were not indicative of this processor. The machine they used, the Altair 680, runs the CPU at half its rated speed. He suggested a more typical 6800-based machine would be slightly faster than the 8080. However, the 6800 once again put in a poor showing even on newer machines running at higher speeds. [ 6 ]
Gates also suggested that the Cyber 173's time was likely due to it being a compiler rather than an interpreter . The authors point out this was not the case for the TRW BASIC they used in the original test, and then use this as a segue to compare the differences between compilers and interpreters. [ 6 ]
Gates concluded his letter by noting that a number of the results were identical in spite of being on different machines. He suggests this is because the BASICs in question contained "signatures" from Altair BASIC and are thus "illegitimate software". He did not specify which ones he claimed were stolen, and the authors responded by saying that if "Bill can stop people from selling them through legal means, we'll stop listing them." [ 8 ]
Rugg and Feldman conclude the article by mentioning some of the other concerns that were raised after the original article. One common issue was the lack of more advanced mathematical functions, which they acknowledge, but suggest this is something best left to the reader. The other was the lack of string manipulation, but they note that the syntax of string handling differed considerably between platforms and thus could not be made in a single version. [ 8 ] [ c ]
In this series of tests, the list was topped by the OSI Challenger , a 6502-based machine that had been "souped up" to 2 MHz, double that of typical 1 MHz 6502 machines of the era like the Apple II and PET. When running at its normal 1 MHz speed, the Challenger was just beaten by Zapple BASIC on Z80 machines running at 4 MHz. PET BASIC was next, only slightly behind the Challenger. [ 9 ] They conclude that the 6502 is the highest performing of the CPUs, agreeing with comments Gates had made in his letter. The 6800 once again ends up in last place. [ 10 ]
As part of a longer article discussing new entries into the computer market, including the TRS-80 , John Coll used the Rugg/Feldman tests to benchmark a variety of machines available to him in the UK in October 1977. He added an eighth test to exercise the math routines, and provided the resulting run times both on their own as well as the additional time compared to Test 7, in keeping with the earlier concept of each test modifying the last. [ 11 ] The results were published in the first issue of Personal Computer World in February 1978, [ 12 ] with a short follow-up in their November 1978 issue. [ 13 ]
As one of the earliest sets of BASIC benchmarks, the F/R tests were seen primarily in the late 1970s and early 1980s. It was a standard among reviews in Kilobaud , used to compare the many new varieties of BASIC that continued to appear for early microcomputers. [ 14 ] Compute! used it for their 1979 review of the Challenger 1P , [ 15 ] and 68 Journal used it to demonstrate the extremely high performance of BASIC09 . [ 16 ] InfoWorld used it for their 1981 review of a new BASIC for the TRS-80, [ 17 ] and the TRS-80 Color Computer as a whole. [ 18 ]
After that point the Byte Sieve began to become popular and the number of articles referring to the F-R benchmark become less common, but it could be found even such rarefied sources as the HP Journal. [ 19 ]
The PCW versions remained very popular in the UK, and can be found in many reviews of UK-centric machines like the Grundy NewBrain , various Sinclair Research machines, [ 20 ] and the BBC Micro . [ 21 ]
The programs were designed to allow a user to type in the first test, run it, and then modify it in-place to run the subsequent tests. This meant the user did not have to type in seven different programs, but simply modify a single one. [ 3 ] The first seven listings are the originals from the 1977 article, [ 1 ] the eighth is the PCW addition. [ 22 ]
FOR-NEXT loops are one of the most fundamental constructs in the BASIC language, and if the performance of these loops is slow it is highly likely that any program running in that BASIC will be slow as well. A famous example of this is Atari BASIC , which had several problems that greatly slowed the performance of FOR-NEXT loops compared to contemporary examples, and BASIC programs on the Atari were generally very slow as a result. [ 23 ]
This test ultimately performs the same operations as test 1, but in this case, it uses an explicit test and jump rather than using the built-in FOR-NEXT construct. Generally, this program runs much slower than 1 because most BASICs parse the parameters in the FOR, including the line number, only once when it is first encountered. Using the IF, as in test 1, causes it to parse the values every time through the loop. Moreover, most BASICs do not simply store the parsed line number of the top of the loop, but the memory address, whereas a THEN requires the interpreter to scan through the program for the corresponding line number, in this case 500 . Although this test does not show it due to its small size, this search takes increasingly long times as the program length grows. Some versions of BASIC optimized GOTO using explicit labels, [ 24 ] or pushing the GOTO targets on a stack to make them perform like NEXT. [ 25 ] Turbo-Basic XL did both, and ran much faster than any similar BASIC as a result. [ 24 ]
Test 3 is an expansion of test 2, this time adding some basic mathematics and variable access. By comparing the time to run tests 2 and 3, one can get an idea of the performance of the language's math library. [ 1 ]
The same as test 3 except that the variable K is replaced by numeric constants. This requires the interpreter to convert the values from their textual representation into their internal storage format, which takes time (unless this is performed once and for all, before execution, as in some more advanced BASICs). Some idea of the performance of this conversion functionality can be determined by comparing this time to benchmark 3. [ 1 ]
Test 5 introduces a subroutine call. Long programs in early versions of BASIC would make extensive use of subroutines and thus the efficiency of the calling mechanism was important. Depending on the way the system worked, the return might cache the location of the calling line in a fashion similar to NEXT, and thus run very quickly. Others might store the line number of the calling line, and thus require the code to scan the program listings to RETURN. [ 1 ]
Test 6 defines a small array at the start and adds another FOR-NEXT loop inside the main loop. This has little effect on the code, but is used to set a baseline for test 7. [ 1 ]
This assigns a value to each of the array elements every time through the loop. Comparing the time needed to run 7 to 6 indicates the efficiency of array access. [ 1 ]
Test 8 was added by PCW, [ 11 ] performing several transcendental functions in order to test their performance. This code does not include the code from test 7, which breaks the original pattern of each test adding to the last. Instead, the associated article listed both the time to run 8 and 7 and 8 combined. [ 12 ]
This list is not meant to be exhaustive, but instead a quick overview of the results seen on some popular systems of the early microcomputer and home computer era. The first table includes a selection of machines from the original tests in June 1977, with exceptions as noted. [ 1 ] Test time is in seconds. | https://en.wikipedia.org/wiki/Rugg/Feldman_benchmarks |
Rugosity , f r , is a measure of small-scale variations of amplitude in the height of a surface,
where A r is the real (true, actual) surface area and A g is the macroscopic geometric surface area . [ 1 ]
Rugosity calculations are commonly used in materials science to characterize surfaces, amongst others, in marine science to characterize seafloor habitats. A common technique to measure seafloor rugosity is Risk's chain-and-tape method [ 2 ] but with the advent of underwater photography less invasive quantitative methods have been developed. Some examples include measuring small-scale seafloor bottom roughness from microtopographic laser scanning (Du Preez and Tunnicliffe 2012), [ 3 ] and deriving multi-scale measures of rugosity, slope and aspect from benthic stereo image reconstructions (Friedman et al. 2012). [ 4 ]
Despite the popularity of using rugosity for two- and three-dimensional surface analyses, methodological inconsistency has been problematic. Building off recent advances, the new arc-chord ratio (ACR) rugosity index is capable of measuring the rugosity of two-dimensional profiles and three-dimensional surfaces using a single method (Du Preez 2015). [ 5 ] The ACR rugosity index is defined as the contoured (real) surface area divided by the area of the surface orthogonally projected onto a plane of best fit (POBF), where the POBF is a function ( linear interpolation ) of the boundary data only. Using a POBF, instead of an arbitrary horizontal geometric plane, results in an important advantage of the ACR rugosity index: unlike most rugosity indices ACR rugosity is not confounded by slope.
Ecology : As a measure of complexity , rugosity is presumed to be an indicator of the amount of available habitat available for colonization by benthic organisms (those attached to the seafloor), and shelter and foraging area for mobile organisms.
Geology : For marine geologists and geomorphologists, rugosity is a useful characteristic in distinguishing different types of seafloors in remote sensing applications (e.g., sonar and laser altimetry, based from ships, planes or satellites).
Oceanography : Among oceanographers, rugosity is recognized to influence small-scale hydrodynamics by converting organized laminar or oscillatory flow into energy-dissipating turbulence.
Coral biology : High rugosity is often an indication of the presence of coral, which creates a complex surface as it grows. A rugose seafloor's tendency to generate turbulence is understood to promote the growth of coral and coralline algae by delivering nutrient-rich water after the organisms have depleted the nutrients from the envelope of water immediately surrounding their tissues. | https://en.wikipedia.org/wiki/Rugosity |
Rui Luís Reis (born 19 April 1967) is a Portuguese scientist known for his research in tissue engineering , regenerative medicine , biomaterials, biomimetics , stem cells , and biodegradable polymers .
Reis is a professor of at the University of Minho in Braga and Guimarães. He is the Founding Director of the 3B's Research Group, part of the Research Institute on Biomaterials, Biodegradables and Biomimetics (I3Bs) of UMinho (www.i3bs.uminho.pt), a group that specializes in the areas of Regenerative Medicine, Tissue Engineering, Stem Cells and Biomaterials. He is also the Director of the ICVS/3B's Associate Laboratory of UMinho. He is the CEO of the European Institute of Excellence on Tissue Engineering and Regenerative Medicine. Rui L. Reis was, from 2013 to 2017, the Vice-Rector (vice-president) for research and innovation of UMinho. From 2007 to 2021 Reis was the editor-in-chief of the Journal of Tissue Engineering and Regenerative Medicine . [ 1 ] From 2016 to 2018, he was president of the Tissue Engineering and Regenerative Medicine International Society (TERMIS).
Reis is in the board of several scientific societies, companies and associations. From 2017 to 2019, he was the President of TECMINHO - the technology transfer office of the University of Minho.
Reis is the CEO of the European Institute of Excellence on Tissue Engineering and Regenerative Medicine in Avepark, Guimarães.
He co-founded different start up companies originating from the research and activities of 3B's research group, such as Stemmatters and HydruStent/HydruMedical.
Reis is the current president of the I3B's research institute, and one of the most cited Portuguese researchers in science. [ 2 ] [ 3 ]
Reis was born and has always lived in Porto , being one of three children of a chemical engineering professor and a domestic. Reis spent a small part of his childhood in Metangula , Mozambique , a small town near Lake Niassa , while his father was engaged in military service during the Portuguese Colonial War . [ 4 ] He is married with Olga Paiva and has one son, Bernardo Reis (born in 2001). He is a strong supporter of FC Porto .
Reis graduated in Metallurgical Engineering , University of Porto, Portugal, in 1990. He then completed a master's degree at the University of Porto, Portugal, in 1994. Reis did his PhD on Polymer Engineering – Biomaterials, Regenerative Medicine & Tissue Engineering, in the University of Minho, Portugal and Brunel University London , in 1999. He also completed a Doctor of Science (D.Sc.) degree on Biomedical Engineering - Biomaterials & Tissue Engineering, by University of Minho, Portugal, in 2007.
Reis has also received two Honoris Causa degrees: A first in Medicine from University of Granada , Spain, in 2010 and a second in Engineering from University Polytechnica of Bucharest, Romania, in 2018.
Reis is a researcher who has been involved in the field of biomaterials since 1990. He has worked with several universities and companies abroad.
Some of Reis' research has been on liver and neurological tissues regeneration, new strategies for antimicrobial materials, innovative high-throughput approaches for studying cell/materials interactions, as well as on TE approaches for developing different 3D disease models, including different cancer models, and therapies for treatment of diabetes and Alzheimers. [ 5 ]
Reis has also been responsible for several cooperation programs with universities and companies worldwide. He has coordinated four major EU research projects, including the STREP "HIPPOCRATES". [ 6 ]
Under HORIZON 2020, Reis was the coordinator of the ERA Chairs FoReCast grant for 3B's-UMinho. [ 7 ] He has coordinated two TWINNING projects Gene2Skin and Chem2Nature, and is currently coordinating another TWINNING project. Until 2021, he was the coordinator of the 15 MEuros EC funded TEAMING proposal, "The Discoveries Centre for Regenerative and Precision Medicine" with UCL - University College London, UPorto, UAveiro, ULisboa, and UNova Lisboa. [ 8 ] He is also the PI of a major project of the Portuguese roadmap for strategic infrastructures, TERM Research Hub. | https://en.wikipedia.org/wiki/Rui_L._Reis |
Ruin value ( German : Ruinenwert ) is the concept that a building be designed in such a way that if it eventually collapsed, it would leave behind aesthetically pleasing ruins that would last far longer without any maintenance at all. The idea was pioneered by German architect Albert Speer while planning for the 1936 Summer Olympics and published as "The Theory of Ruin Value" ( Die Ruinenwerttheorie ), although he was not its original inventor. [ 1 ] [ 2 ] The intention did not stretch only to the eventual collapse of the buildings, but rather assumed such buildings were inherently better designed and more imposing during their period of use.
The idea was supported by Adolf Hitler , who planned for such ruins to be a symbol of the greatness of the Third Reich , just as Ancient Greek and Roman ruins were symbolic of those civilisations.
In his memoirs, Albert Speer claimed to have invented the idea, which he referred to as the theory of Ruin Value ( Gr. Ruinenwerttheorie ). It was supposedly an extension of Gottfried Semper 's views about using "natural" materials and the avoidance of iron girders. In reality it was a much older concept, even becoming a Europe-wide Romantic fascination at one point. [ when? ] [ 3 ] Predecessors include a "new ruined castle" built by the Landgraf of Hesse-Kassel in the 18th century, and the designs for the Bank of England built in the 19th century produced by Sir John Soane . [ 3 ] When he presented the bank's governors with three oil sketches of the planned building one of them depicted it when it would be new, another when it would be weathered, and a third what its ruins would look like a thousand years onward. [ 3 ]
Speer's memoirs reveal Hitler's thoughts about Nazi state architecture in relation to Roman imperial architecture:
Hitler liked to say that the purpose of his building was to transmit his time and its spirit to posterity. Ultimately, all that remained to remind men of the great epochs of history was their monumental architecture, he remarked. What then remained of the emperors of the Roman Empire? What would still give evidence of them today, if not their buildings […] So, today the buildings of the Roman Empire could enable Mussolini to refer to the heroic spirit of Rome when he wanted to inspire his people with the idea of a modern imperium. Our buildings must also speak to the conscience of future generations of Germans. With this argument Hitler also underscored the value of a durable kind of construction.
Hitler accordingly approved Speer's recommendation that, in order to provide a "bridge to tradition" to future generations, modern "anonymous" materials such as steel girders and ferroconcrete should be avoided in the construction of monumental party buildings wherever possible, since such materials would not produce aesthetically acceptable ruins. Thus, the most politically significant buildings of the Reich were intended, to some extent, even after falling into ruins after thousands of years, to resemble their Roman models.
Speer expressed his views on the matter in the Four Year Plan of 1937 in his contribution Stone Not Iron in which he published a photograph of the Parthenon with the subscript: "The stone buildings of antiquity demonstrate in their condition today the permanence of natural building materials." Later, after saying modern buildings rarely last more than fifty years, he continues: "The ages-old stone buildings of the Egyptians and the Romans still stand today as powerful architectural proofs of the past of great nations, buildings which are often ruins only because man's lust for destruction has made them such." Hitler approved Speer's "Law of Ruin Value" ( Gr. Ruinengesetz ) after Speer had shown him a sketch of the Haupttribüne as an ivy-covered ruin. The drawing pleased Hitler but scandalised his entourage. [ 4 ]
However, due to the onset of the Second World War , Nazi German architecture made extensive use of concrete.
A more modern example of intended ruins were the planned warning signs for the proposed nuclear waste repository at Yucca Mountain (see Human Interference Task Force ), which were intended to endure for 10,000 years, and yet still convey an enduring (if negative) impression on future generations: "Keep out. Don't dig here." [ 5 ]
Architect Charles Jencks mentions "Ruins in the Garden", a section of the Neue Staatsgalerie , as a postmodern subversion of ruin value. [ 6 ] | https://en.wikipedia.org/wiki/Ruin_value |
Rule-based modeling is a modeling approach that uses a set of rules that indirectly specifies a mathematical model. The rule-set can either be translated into a model such as Markov chains or differential equations, or be treated using tools that directly work on the rule-set in place of a translated model, as the latter is typically much bigger. Rule-based modeling is especially effective in cases where the rule-set is significantly simpler than the model it implies, meaning that the model is a repeated manifestation of a limited number of patterns. An important domain where this is often the case is biochemical models of living organisms. Groups of mutually corresponding substances are subject to mutually corresponding interactions.
BioNetGen [ 1 ] is a suite of software tools used to generate mathematical models consisting of ordinary differential equations without generating the equations directly. For example below is an example rule in the BioNetGen format:
A ( a , a ) + B ( b ) − > A ( a ! 1 ) . B ( b ! 1 ) {\displaystyle A(a,a)+B(b)->A(a!1).B(b!1)}
Where:
With the above line of code, BioNetGen will automatically create an ODE for each model species with the correct mass balance. Additionally, an additional species will be created because the rule above implies that two B molecules can bind to a single A molecule since there are two binding sites. Therefore, the following species will be generated:
4. A(a!1,a!2).B(b!1).B(b!2): Molecule A with both binding sites occupied by two different B molecules.
Early efforts to use rule-based modeling in simulation of biochemical systems include the stochastic simulation systems StochSim [ 2 ]
A widely used tool for rule-based modeling of biochemical networks is BioNetGen [ 3 ] It is released under the GNU GPL , version 3. BioNetGen includes a language to describe chemical substances, including the states they can assume and the bindings they can undergo. These rules can be used to create a reaction network model or to perform computer simulations directly on the rule set. The biochemical modeling framework Virtual Cell includes a BioNetGen interpreter.
A close alternative is the Kappa language. [ 4 ] Another alternative is BioChemical Space language. [ 5 ]
This molecular or cell biology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rule-based_modeling |
A rule complex is a set consisting of rules and/or other rule complexes. This is a generalization of a set of rules, and provides a tool to investigate and describe how rules can function as values, norms , judgmental or prescriptive rules, and meta-rules. Also possible is to examine objects consisting of rules such as roles, routines , algorithms , models of reality, social relationships, and institutions. In game theory , rules and rule complexes can be used to define the behavior and interactions of the players (although in generalized game theory , the rules are not necessarily static. Rule complexes are especially associated with sociologist Tom R. Burns and Anna Gomolinska and the Uppsala Theory Circle .
In this setting, a rule is type of knowledge (in the sense of epistemic logic (see Fagin, 2003)) formalized as a set of premises or conditions, a set of justifications, and a set of conclusions (this may be written as a triple, a rule r := ( X , Y , α ) {\displaystyle r:=(X,Y,\alpha )} ). Elements of X should hold, and of Y may hold. If Y , the justifications, do not hold, then the rule cannot be applied. If X , the premises, obtain and the justifications are not known to not apply, then the rule is applied, and α {\displaystyle \alpha } is concluded. If X and Y are empty, then the rule is axiomatic (a "fact" or unconditional directive). Thus, rules can be seen as the basic objects of knowledge.
Formally, a rule complex is the class which contains all finite sets of rules, is closed under set-theoretical union and power set , and preserves inclusion:
This means that for rule complexes C 1 {\displaystyle C_{1}} and C 2 {\displaystyle C_{2}} , C 1 ∩ C 2 , C 1 − C 2 {\displaystyle C_{1}\cap C_{2},C_{1}-C_{2}} are also rule complexes. A complex B {\displaystyle B} is a subcomplex of the complex A {\displaystyle A} if B = A {\displaystyle B=A} or B {\displaystyle B} may be obtained from A {\displaystyle A} by deleting some rules from A {\displaystyle A} and/or redundant parentheses (Burns, 2005).
socially embedded games: A granular computing perspective. In S. K. Pal, L. Polkowski and A. Skowron (eds). "Rough-Neural Computing: Techniques for Computing with Words", Springer, Berlin Heidelberg, pages 411–434. | https://en.wikipedia.org/wiki/Rule_complex |
In finance , the rule of 72 , the rule of 70 [ 1 ] and the rule of 69.3 are methods for estimating an investment 's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (usually years) to obtain the approximate number of periods required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and when only a basic calculator is available. [ 2 ]
These rules apply to exponential growth and are therefore used for compound interest as opposed to simple interest calculations. They can also be used for decay to obtain a halving time. The choice of number is mostly a matter of preference: 69 is more accurate for continuous compounding, while 72 works well in common interest situations and is more easily divisible.
There are a number of variations to the rules that improve accuracy. For periodic compounding, the exact doubling time for an interest rate of r percent per period is
where t is the number of periods required. The formula above can be used for more than calculating the doubling time. If one wants to know the tripling time, for example, replace the constant 2 in the numerator with 3. As another example, if one wants to know the number of periods it takes for the initial value to rise by 50%, replace the constant 2 with 1.5.
To estimate the number of periods required to double an original investment, divide the most convenient "rule-quantity" by the expected growth rate, expressed as a percentage.
Similarly, to determine the time it takes for the value of money to halve at a given rate, divide the rule quantity by that rate.
The value 72 is a convenient choice of numerator, since it has many small divisors : 1, 2, 3, 4, 6, 8, 9, and 12. It provides a good approximation for annual compounding, and for compounding at typical rates (from 6% to 10%); the approximations are less accurate at higher interest rates.
For continuous compounding, 69 gives accurate results for any rate, since ln (2) is about 69.3%; see derivation below. Since daily compounding is close enough to continuous compounding, for most purposes 69, 69.3 or 70 are better than 72 for daily compounding. For lower annual rates than those above, 69.3 would also be more accurate than 72. [ 3 ] For higher annual rates, 78 is more accurate.
Note: The most accurate value on each row is in bold.
An early reference to the rule is in the Summa de arithmetica (Venice, 1494. Fol. 181, n. 44) of Luca Pacioli (1445–1514). He presents the rule in a discussion regarding the estimation of the doubling time of an investment, but does not derive or explain the rule, and it is thus assumed that the rule predates Pacioli by some time.
A voler sapere ogni quantità a tanto per 100 l'anno, in quanti anni sarà tornata doppia tra utile e capitale, tieni per regola 72 , a mente, il quale sempre partirai per l'interesse, e quello che ne viene, in tanti anni sarà raddoppiato. Esempio: Quando l'interesse è a 6 per 100 l'anno, dico che si parta 72 per 6; ne vien 12, e in 12 anni sarà raddoppiato il capitale. (emphasis added).
Roughly translated:
In wanting to know of any capital, at a given yearly percentage, in how many years it will double adding the interest to the capital, keep as a rule [the number] 72 in mind, which you will always divide by the interest, and what results, in that many years it will be doubled. Example: When the interest is 6 percent per year, I say that one divides 72 by 6; 12 results, and in 12 years the capital will be doubled.
For periodic compounding , future value is given by:
where P V {\displaystyle PV} is the present value , t {\displaystyle t} is the number of time periods, and r {\displaystyle r} stands for the interest rate per time period.
The future value is double the present value when:
which is the following condition:
This equation is easily solved for t {\displaystyle t} :
A simple rearrangement shows
If r / 100 {\displaystyle r/100} is small, then ln ( 1 + r / 100 ) {\displaystyle \ln(1+r/100)} approximately equals r / 100 {\displaystyle r/100} (this is the first term in the Taylor series ). That is, the latter factor grows slowly when r {\displaystyle r} is close to zero.
Call this latter factor ( r / 100 ) / ln ( 1 + r / 100 ) = f ( r ) {\displaystyle (r/100)/\ln(1+r/100)=f(r)} . The function f ( r ) {\displaystyle f(r)} is shown to be accurate in the approximation of t {\displaystyle t} for a small, positive interest rate when r = 8 {\displaystyle r=8} (see derivation below). f ( 8 ) ≈ 1.03949 {\displaystyle f(8)\approx 1.03949} , and we therefore approximate time t {\displaystyle t} as:
This approximation increases in accuracy as the compounding of interest becomes continuous (see derivation below).
In order to derive a more precise adjustment, it is noted that ln ( 1 + r / 100 ) {\displaystyle \ln(1+r/100)} is more closely approximated by r / 100 − 1 2 ( r / 100 ) 2 {\displaystyle r/100-{\tfrac {1}{2}}(r/100)^{2}} (using the second term in the Taylor series ). 0.693 / ( r / 100 − 1 2 ( r / 100 ) 2 ) {\displaystyle 0.693/\left(r/100-{\tfrac {1}{2}}(r/100)^{2}\right)} can then be further simplified by Taylor approximations: [ 4 ]
Replacing the r {\displaystyle r} in r / 200 {\displaystyle r/200} with 7.79 gives 72 in the numerator. This shows that the rule of 72 is most accurate for periodically compounded interests around 8 %. Similarly, replacing the r {\displaystyle r} in r / 200 {\displaystyle r/200} with 2.02 gives 70 in the numerator, showing the rule of 70 is most accurate for periodically compounded interests around 2 %.
As a sophisticated but elegant mathematical method to achieve a more accurate fit, the function t ( r ) = ln ( 2 ) / ln ( 1 + r / 100 ) {\displaystyle t(r)=\ln(2)/\ln(1+r/100)} is developed in a Laurent series at the point r = 0 {\displaystyle r=0} . [ 5 ] With the first two terms one obtains:
In the case of theoretical continuous compounding , the derivation is simpler and yields to a more accurate rule: | https://en.wikipedia.org/wiki/Rule_of_72 |
In matrix theory , the rule of Sarrus is a mnemonic device for computing the determinant of a 3 × 3 {\displaystyle 3\times 3} matrix named after the French mathematician Pierre Frédéric Sarrus . [ 1 ]
Consider a 3 × 3 {\displaystyle 3\times 3} matrix
then its determinant can be computed by the following scheme.
Write out the first two columns of the matrix to the right of the third column, giving five columns in a row. Then add the products of the diagonals going from top to bottom (solid) and subtract the products of the diagonals going from bottom to top (dashed). This yields [ 1 ] [ 2 ]
A similar scheme based on diagonals works for 2 × 2 {\displaystyle 2\times 2} matrices: [ 1 ]
Both are special cases of the Leibniz formula , which however does not yield similar memorization schemes for larger matrices. Sarrus' rule can also be derived using the Laplace expansion of a 3 × 3 {\displaystyle 3\times 3} matrix. [ 1 ]
Another way of thinking of Sarrus' rule is to imagine that the matrix is wrapped around a cylinder, such that the right and left edges are joined. | https://en.wikipedia.org/wiki/Rule_of_Sarrus |
The rule of marteloio is a medieval technique of navigational computation that uses compass direction, distance and a simple trigonometric table known as the toleta de marteloio . The rule told mariners how to plot the traverse between two different navigation courses by means of resolving triangles with the help of the Toleta and basic arithmetic .
Those uncomfortable with manipulating numbers could resort to the visual tondo e quadro (circle-and-square) and achieve their answer with dividers . The rule of marteloio was commonly used by Mediterranean navigators during the 14th and 15th centuries, before the development of astronomical navigation .
The etymology comes from the Venetian language . In his 1436 atlas, Venetian captain and cartographer Andrea Bianco introduced a table of numbers which he called the toleta de marteloio ("table of marteloio"), and the method of using it as the raxon de marteloio ("reason of marteloio").
The meaning of marteloio itself is uncertain. The most widely accepted hypothesis, first forwarded by A.E. Nordenskiöld , is that marteloio relates to " hammer " ("martelo" in Venetian), referring to the small hammer that was used to hit the on-board ship's bell to mark the passage of time. [ 1 ] It has been suggested that the - oio suffix implies that marteloio meant not quite the hammer itself nor the hammerer, but rather "the hammering", intending to indicate "the hammering, the din, the racket" from the change of the watch every four hours. As there were many hands on deck during a change of the watch, it would be an opportune moment for the ship's pilot to order a change in bearing (if necessary). [ 2 ]
Alternative hypotheses (not nearly as accepted) are that "marteloio" is a corruption of mari logio (meaning "rule of the sea"), [ 3 ] or from mare tela (meaning "sea network"), [ 4 ] or that it derives from the Greek homartologium ( όμαρτόλογίον , meaning "companion piece"), [ 5 ] or from the Greek imeralogium ( ήμερόλογίον , meaning "daily calculation") [ 6 ] or that it might be from the northern French matelot , which in turn comes from Breton martolod (meaning "sailors"). [ 7 ]
The "rule of marteloio" was used in European navigation in the Middle Ages , most notably in the Mediterranean Sea between the 14th and 16th centuries, although it may have older roots. It was an integral part of navigation by "compass and chart", before the advent of geographical coordinates and the development of celestial navigation in Europe. [ 8 ]
Medieval navigation relied on two parameters, direction and distance. On board ship, direction was determined by the mariner's compass (which emerged around 1300). [ 9 ] Distance was measured by dead reckoning , ( i.e. , distance = speed × time), where time was measured by a half- hour-glass , and speed readings were taken with by some form of a chip log (the archaic method, used in the 14th and 15th centuries, involved heaving a piece of wood or flotsam overboard; the crew engaged in a rhythmic chant to mark the time it took for the chip to float past the length of the ship). [ 10 ]
Plotting a course required knowing the compass direction and distance between point A and point B. Knowledge of where ports lay relative to each other was acquired by navigators by long experience at sea. This information was sometimes collected and written down in a pilot's handbook, known as a portolano ("port book", in Italian, equivalent to the Greek periplus , the Portuguese roteiro and the English rutter ). These handbooks were used to construct a class of nautical maps known as portolan charts . Portolan charts began being produced in Genoa in the late 13th century, and soon spread to Venice and Majorca . Portolan charts were not gridded by longitude and latitude lines, but rather by a web of compass rhumb lines , giving mariners an idea of only the distance and direction between places.
By a handbook or a portolan chart, a navigator could see immediately that, for example, Pisa lay 85 miles southeast ("Scirocco" in the traditional compass rose nomenclature) of Genoa , and so a ship that set out from Genoa to Pisa would simply maintain that bearing for that distance. However, most sailing courses were not nearly that neat. A mariner wishing to sail from Majorca to Naples could tell the latter was due east ("Levante") by some 600 miles – but the island of Sardinia lies in the way, therefore the ship's bearing must be changed along the route. This is easier said than done, as geographical coordinates did not exist during this era. The only way to determine the exact position of the ship at sea would be to calculate via past bearing and distance travelled. [ 11 ]
Islands were a predictable obstacle – circumventing Sardinia would be simply a matter of sailing southeast for a set distance then changing the bearing to northeast ("Greco") for the remainder. More problematic is if the ship were blown off its intended route by fitful winds, or had to engage in tacking , changing bearing repeatedly. How does it return to its intended course? This is where the rule of marteloio came in.
The rule of marteloio addressed the problem of changing bearing at sea. More specifically, it helped a navigator plot the traverse from one navigational course to another. [ 12 ] For example, suppose a ship was to sail from Corsica to Genoa , a course bearing straight north ("Tramontana") for some 130 miles. But the winds are not cooperative, and the ship was forced to sail northwest ("Maestro") for some 70 miles. How does it return to its original route? Re-setting its bearing to northeast ("Greco") seems sensible enough, but how long should it sail on that bearing? How would a navigator know when the ship had reached its old route and should turn north again? How to avoid overshooting or undershooting the old course?
This is a mathematical problem of solving a triangle . If a navigator knows how long the ship has sailed on the erroneous course, he can calculate its current distance from its intended course, and estimate how long it must sail back on a new bearing until it recovers its old course. In the Corsica-to-Genoa example, there is an implied triangle ACD , with one side given ( AC = 70 miles on actual NW course), a 45° angle at A (angle of difference between actual course NW and intended course N) and another angle of 90° at C (angle of difference between actual course NW and return course NE). The challenge to the navigator is to find how long one must sail on the NE return course (the length of side CD , what is called the ritorno ) and how far one has advanced on the intended course by the time one straightens out (the length of the hypotenuse AD , or what is called the total avanzo ).
This is elementary trigonometry , solving for two sides given one side (70) and two angles (45° and 90°). This is quickly done by applying the law of sines :
yielding up the solutions ritorno = 70 miles and total avanzo = 98.99 miles. This means that if the ship bears NE from its current position ( C ), it will reach its original intended course after 70 miles of sailing on the NE bearing. By the time it reaches its junction point ( D ), it will have covered 98.99 miles of its original intended course. There it can straighten its bearing N and sail the remaining 30 miles or so to Genoa.
Unfortunately, Medieval sailors with the rudimentary educational levels of the 14th and 15th centuries, were not likely to know the Law of Sines or manipulate it with ease. [ 13 ] As a result, Medieval navigators needed simpler and more accessible method of calculation.
The scholar-cleric Ramon Llull of Majorca , was the first writer to refer to a rule to solve the traverse problem of navigation. In his Arbor Scientiae (1295), in the section of questions on geometry, Llul writes:
How do mariners measure miles at sea ( miliaria in mari )? Mariners consider the four general winds, that is to say the eastern, western, northern and southern, and also another four winds that lie between them, grec (NE), exaloch (SE), lebeg (SW) and maestre (NW). And they look carefully at the center of the circle in which the winds (rhumbs) meet at angles; they consider when a ship travels by the East wind ( levant ) 100 miles from the center, how many miles it would make on the southeast ( exaloch ) wind; and for 200 miles, they double the number by multiplying and then they know how many miles there are from the end of each 100 miles in an easterly direction to the corresponding point in a southeasterly direction. And for this they have this instrument [a mathematical table?] and a chart, rutter, needle and the pole star." [ 14 ]
What Llull seems to be trying to explain is that a ship actually sailing E, but intending to sail SE, it can figure out how much of its intended southeastward distance it has already made good – what Italians called the " avanzar ", but Lull seems to call the " miliaria in mari ". Llull does not explain exactly how, but refers only to an "instrument", presumably some sort of trigonometric table. Lull is implying that mariners can calculate the miliaria on the intended course by multiplying the distance actually sailed on the erroneous course by the cosine of the angle between the two routes. [ 15 ]
where θ is the angle of difference between the two routes.
Using Lull's example, a ship that intended to sail southeast ("Exaloch" is Catalan for "Scirocco") but was instead forced to sail east ("Levant"), then the angle of difference is θ = 45°. After 100 miles on the erroneous route, the miliaria on the intended route is 100 × cos 45° = 70.71. Doubling the sailing on the erroneous route to 200 miles will double the miliaria on the intended route to 141.42 miles (= 200 cos 45°).
(Diagramatically, Lull's miliaria in mari is measured by constructing a right-angled triangle by running a cord from the distance sailed on the actual course to the intended course, meeting the latter at a 90° angle).
Llull is a little more explicit in his Ars magna generalis et ultima (written c. 1305). [ 16 ] Reversing his example, with a ship actually sailing Southeast but intending to sail East, Llull notes that for every four miles on the southeast bearing, it "gains three miles" (2.83 actually) on the intended eastward route. Thus, Lull notes, the ship "loses 25 miles" (29 actually) of its intended course for every 100 miles it sails on the current course.
Notice that in his passages, Ramon Lull is not recommending the rule, but reporting it, insinuating that this rule was already known and used by contemporary sailors in practice. [ 17 ] This is perhaps unsurprising – although trigonometry was only in its infancy in Christian Europe, sine and cosine tables were already known in Arab mathematics . [ 18 ] The Kingdom of Majorca , under Muslim rule until the 1230s, remained a multicultural center in Lull's time, with flourishing Jewish communities , many of whom dabbled in mathematics and astronomy, and whose seafarers had extensive contact across the Mediterranean Sea. [ 19 ] That Majorcan navigators had some sort of trigonometric table at hand is not improbable. Nonetheless, the exact content and layout of this table implied by Ramon Llull in 1295 is uncertain.
We get our first glimpse of a mariner's trigonometric table more than a century after Llull. In the first folio of his 1436 portolan atlas , the Venetian captain Andrea Bianco explains the raxon de marteloio , how to calculate the traverse and recover the course. He lays out a simple trigonometric table he calls the toleta de marteloio and recommends that mariners commit the table to memory. [ 20 ]
The toleta de marteloio is set out as follows: [ 21 ]
The numbers in the Toleta can be approximated by the modern formulas: [ 22 ]
where q = number of quarter winds (angle of difference expressed in number of quarter winds). The numbers work with quarter-winds set at 11.25° intervals, or 11°15', the usual definition of a quarter wind.
The Toleta is a simple table with several columns of numbers. In the first column is the angle of difference between the actual and intended courses, expressed by number of quarter-winds . Once that difference is determined, the second column gives the Alargar (the "Widening", the current distance the ship is from the intended course) while the third column tells the Avanzar (the "Advance", how much of the distance on the intended course has already been covered by sailing on the current bearing – this is equivalent of Ramon Llull's miliaria di mari ). The Alargar and Avanzar numbers are shown on the Bianco's table for 100 miles of sailing on the current course.
Example : suppose a ship intended to sail bearing east ("Levante") from point A to point B. But suppose that winds forced it to sail on a southeast-by-east course (SEbE, "Quarto di Scirocco verso Levante"). Southeast-by-east is three quarter winds (or 33.75°) away from east (on a 32-point compass , in order of quarter-winds away from east, 1 quarter is east-by-south, 2 quarters is East-southeast, 3 quarters is southeast-by-east). That means that the navigator should consult the third row, q = 3, on the toleta.
Suppose the ship sailed 100 miles on the SE-by-E bearing. To check his distance from the intended eastward course, the mariner will read the corresponding entry on the alargar column and immediately see he is 55 miles away from the intended course. The avanzar column informs him that having sailed 100 miles on the current SEbE course, he has covered 83 miles of the intended E course.
The next step is to determine how to return to the intended course. Continuing the example, to get back to the intended Eastward course, our mariner has to re-orient the ship's bearing in a northeasterly direction. But there are various northeasterly angles – NbE, NNE, NE, ENE, etc. The mariner has a choose the bearing – if he returns by a sharp angle (e.g. North by east), he will return to the intended course faster than at a more gentle gradient (e.g. East by north). Whichever angle he chooses, he must deduce exactly how long he must sail on that bearing in order to reach his old course. If he sails too long, he risks overshooting it.
Calculating the return course is what the last three columns of the toleta are for. In the fourth column, the return angles are expressed as quarters from the intended course bearing ( not the current course bearing). In our example, the mariner intended to go east, but has been sailing southeast-by-east for 100 miles. Given the winds, he decides it is best to return to the original course by re-orienting the ship east-northeast (ENE, "Greco-Levante"). ENE is two quarter-winds above the intended bearing, East, so now he looks at second row ("quarters = 2") on the fourth column of the table.
The fifth column is the ritorno , the distance he must travel on the chosen return angle to recover the original course. Given he has chosen to return by ENE bearing (q = 2), then he must read the second row of the ritorno column, which shows the number 26. This represents the required number of miles he must travel on ENE bearing for every 10 miles he deviated. Remember, his alargar (distance from intended course) was 55 miles. So in order to return to his intended course he must travel 5.5 × 26 = 143 miles on ENE. In other words, he needs to hold his ENE bearing for 143 miles; once that distance is traveled, he should straighten his ship east, and he will be exactly back on the intended course.
The sixth and final column ( avanzo di ritorno ) gives the length on the intended course he has made good by his return travel. This is also expressed in terms per 10 miles alargar. His alargar was 55, and his angle of return was ENE (thus q = 2), that means his avanzo di ritorno is 5.5 × 24 = 132. In other words, if everything goes right, and our mariner holds his ENE bearing for 143 miles ( ritorno ), then during that return, he will have covered an additional 132 miles on his intended eastward course ( avanzo di ritorno ).
Finally, to calculate the total distance made good (total avanzo) on the eastward bearing by his whole adventure, he must add the avanzar during the deviation (83 miles) plus the avanzo di ritorno (132 miles). Thus on the whole, he has covered 83 + 132 = 215 miles on the intended course. Measuring that distance on the map from the starting point ( A ), the mariner can figure out his exact current position.
This is the simplest use of the toleta de marteloio. It is, at root, a trigonometric table. However, it does not tackle the traverse problem in one go, like the Law of Sines, but rather splits the problem into two right-angled triangles which it proceeds to solve successively. Modern trigonometry would dispense with the step of calculating the alargar, and calculate the ritorno directly – but for that, one needs to be armed with a full sine table . The toleta is a rather simple table, easy to consult and perform calculations with, and sufficiently compact to be memorized by navigators (as Bianco recommends).
The toleta de marteloio is expressed for nice round numbers, 100 and 10. But, in practice, a ship would not usually sail 100 miles before trying to return, but some other distance, say 65 miles. To calculate this is a simple problem of solving ratios . For example, if the ship had sailed 65 miles on southeast-by-east, then calculating the alargar from the intended Eastward course is simply a matter of solving the following for x :
where 55 is the alargar for 100 miles (as given in the second column of the table at q = 3). This is easily done by the simple " Rule of Three ", a method of cross-multiplication, using three numbers to solve for the fourth by successive multiplication and division:
So, sailing for 65 miles on SE by E implies alargar = x = 35.75 miles. The avanzar, etc. can be figured out analogously.
While the "rule of three" was already known in the 14th century, skill in executing multiplication and division could be elusive for Medieval sailors drawn from what was a largely illiterate society. Nonetheless, it was not inaccessible. As Andrea Bianco urged, navigators should "know how to multiply well and divide well" ("saver ben moltiplichar e ben partir") [ 23 ] It is here where we see the important interface of commerce and navigation. The mathematics of commerce – Arabic numerals , multiplication, division, fractions , the tools needed to calculate purchases and sales of goods and other commercial transactions – was essentially the same as the mathematics of navigation. [ 24 ] And this kind of mathematics was taught at the abacus schools which were set up in the 13th century in the commercial centers of northern Italy to train the sons of merchants, the very same class where Italian navigators were drawn from. As historian E.G.R. Taylor notes, "sailors were the first professional group to use mathematics in their everyday work" [ 25 ]
For those troubled by the high art of manipulating numbers, there was an alternative. This was the visual device known as the "circle and square" ( tondo e quadro ), also supplied by Andrea Bianco in his 1436 atlas. [ 26 ]
The circle was a 32-wind compass rose (or gathering of rhumb-lines). The circle was inscribed with an 8 × 8 square grid.
The compass rose in the center can be overlooked – indeed, the circle itself can be ignored, as it seems to have no other purpose than the construction of the rays that run across the grid. [ 27 ] The rose of interest is in the upper left corner of the square grid. From that corner, emanate a series of compass rhumb lines . In his original 1436 tondo e quadro , Bianco has sixteen emanating rays – that is, Bianco includes half-quarter winds, or eighth-winds ( otava ), so that the emanating rays are at intervals of 5.625 degrees. Other constructions of the circle-and-square, e.g. the Cornaro Atlas , use only eight rays emanating at quarter-wind distances (11.25 degrees). Visually, these rays replicate the bottom right quarter of a 32-wind compass rose : East (0q), E by S (1q), ESE (2q), SE by E (3q), SE (4q), SE by S (5q), SSE (6q), S by E (7q) and South (8q).
Above the grid is a distance bar scale , notched with sub-units. There are two sets of numbers on the scale, one for measuring each grid square by 20 miles, another for measuring each grid square by 100 miles (see diagram). [ 28 ] The top bar is the 20m-per-square scale, with every black dot denoting one mile. The bottom bar is the 100m-per-square scale, where the length of a unit square is divided into two equal 50m sub-squares, and a set of dots and red lines break it down further into lengths of 10 miles. So depending on which scale one chooses, the length of the side of the entire grid (eight squares) could be measured up to 160 miles (using the 20 m-per-square scale) or up to 800 miles (using the 100m-per-square scale).
The cherub with the dividers suggests how a navigator is supposed to use the grid to calculate alargar and avanzar by visual measurement rather than manipulating numbers.
Example : suppose the ship has travelled 120 miles at two quarter-winds below the intended course (e.g. traveled at ESE, when the intended course is East). Using the dividers and the 20m scale, the navigator can measure out 120 miles with his dividers. Then setting one end at the top left corner ( A ), he lays out the dividers along the ESE ray (= two quarter-winds below the East ray, or horizontal top of the grid) and marks the spot (point B on the diagram). Then using a straightedge ruler draws a line up to the East ray, and marks the corresponding spot C .
It is easy to see immediately that a right-angled triangle ABC has been created. The length BC is the alargar (distance from intended course), which can be measured as 46 miles (this can be visually seen as two grid squares plus a bit, that is 20m + 20m and a little bit which can be assessed as 6m by using the dividers and the 20m bar scale). The length AC is the avanzar (distance made good), which is 111 miles – visually, five grid squares and a bit, or (20 × 5) + 11, measured by dividers and scale again.
This is how the "circle and square" dispenses manipulating numbers by multiplication and division or the rule of three. The navigator can assess the avanzar and alargar visually, by measurement alone.
This method can be used for any intended bearing and deviation, as the only purpose is to solve the triangle by dividers and scale. e.g. using our first Corsica-to-Genoa example, where intended bearing was North but the ship actually sailed Northwest, the navigator would set the dividers at length 70 miles and lay it along the fourth quarter wind (= SE ray in the tondo e quadro , as NW is four quarter winds away from North). He would calculate the alargar and avanzar in exactly the same way – draw a line to the horizontal top of the grid, measure the squares, etc.
The tondo e quadro device is very similar to the Arab sine quadrant ( Rubul mujayyab ), with the corner rays replicating the role of the adjustable plumb line . [ 29 ]
While the toleta de marteloio (and its visual counterpart, the tondo e quadro ) are designed for the explicit task of recovering an intended course, they can be used in more ways, for many classes of navigational problems, e.g. plotting out a course with multiple-bearing changes, etc. [ 30 ]
One of the interesting applications of the rule of marteloio is for triangulation , e.g. determining the distance of the ship from shore landmark. (This was the final exercise attempted in the notebook of the Venetian navigator Michael of Rhodes , which we replicate here.) [ 31 ]
Example : Suppose a ship sailing NW ("Maestro") spots a landmark due West ("Ponente") one evening, but distance unknown. Suppose the ship continues sailing on the NW route overnight, and the next morning, 40 miles later, it notices that landmark is now west-southwest (WSW, "Ponente-Libeccio") of its current position. Finding the distance of the landmark from the ship is just an application of the rule of marteloio.
To solve the problem, start from the evening position ( A on the map) and treat the distance between the ship and the landmark (length AB ) as the intended course, and the actual route of the ship (NW) as a deviation. To figure out the distance of the landmark from the ship's position in the morning ( C ) is a matter of treating the distance BC as the calculated ritorno. Since we need to know the alargar to calculate the ritorno, this is a two-step procedure.
First, notice that NW is four quarter-winds above W, so looking up on the toleta , in the q = 4 row, the alargar is 71 miles for every 100 miles on the NW course. But the ship only sailed 40 miles overnight, so we have to solve the ratio 71/100 = x /40, which by the rule of three means x = alargar = 28.4 miles. In other words, by the overnight sailing NW by 40 miles from A to C, the ship is now 28.4 miles away from its "intended" Westward course.
Now for the ritorno. The landmark, as noted, is WSW of the ship's morning position ( C ). So to "return" to the landmark, the ship must change its bearing from its current NW bearing to a WSW bearing – that is, 6 quarter-winds below NW. However, the toleta specifies quarter winds in terms of "intended" direction (in this case, West), and WSW is two quarter winds below West, so we need to look at the q = 2 row. This means the ritorno is 26 miles for every 10 miles alargar. Since the alargar is 28.4, that means the ritorno is 26 × 2.84 = 73.84. And there we have it. The landmark is 73.84 miles away from the ship's morning position.
(To complete the story, we might wish to find out the distance that landmark was the evening before (i.e. from point A to landmark B). That is simply a matter of adding the avanzar and the avanzo in ritorno. Quick calculations show the avanzar (@ q = 4, for 40 miles) is 28.4 miles (= 71 × 40/100) and the avanzo di ritorno (@ q = 2 for 28.4 miles alargar), is 2.84 × 24 = 68.16. So total avanzo = 28.4 + 68.16 = 96.56 miles. That was the distance between the landmark and the ship the evening before.)
The rule of marteloio can also be used with the avanzar as a target, e.g. suppose a ship sets out with the intention of finding the Tordesillas Line , the meridian legally set in a 1494 treaty at 370 leagues west of Cape Verde . The ship need not set out from Cape Verde and set sail constantly at West bearing to find it. Rather, it can sail out at a more convenient bearing (e.g. SW), and treat West as an "intended" course. So using the marteloio rule, it can sail on until the avanzar on the "intended" West course reaches 370 leagues.
Indeed, it need not even set out from Cape Verde, but can set out from another place, say, Seville , and use the known distance and bearing of Cape Verde (viz. Seville) and the rule of marteloio to calculate when it has finally reached the Tordesillas meridian. This takes a couple of steps. Suppose Cape Verde ( B on map) is 400 leagues Southwest of Seville ( A on map), but the ship intends to go straight West from Seville to reach the Tordesillas meridian in the open sea. How long does it need to sail?
The way to solve this by the rule of marteloio is to pose the problem in reverse: treat West as intended bearing and SW as the actual course. SW is four quarter-winds below W, so looking up the toleta for q = 4, the avanzar is 71 for every 100 miles sailed. So if a ship sailed 400 leagues on the "actual" SW course to Cape Verde, it would achieve an avanzar of 284 leagues (= 71 × 4) on the "intended" Westward course. Of course, the ship is not actually sailing SW to Cape Verde, but sailing W into the open sea. In other words, when the ship sets sail West from Seville, it knows it needs to sail 284 leagues on the West bearing before it reaches the implied Cape Verde meridian (point C on map), and should only start counting the 370 leagues to the Tordesillas line thereafter. In other words, it needs to sail a total of 284 + 370 = 654 leagues West of Seville to reach the Tordesillas line (point D on map).
While this particular example shows the flexibility of the rule of marteloio, it also shows one of its principal drawbacks: the result completely ignores the curvature of the Earth , i.e. the fact that the longitude meridian lines converge on the North Pole , and thus narrow at higher latitudes. Contrary to what the marteloio suggests, 370 leagues West of Cape Verde is not on the same longitude meridian as 654 leagues West of Seville. Because Seville is well north of Cape Verde, the meridians are clustered closer together at Seville's latitude than at Cape Verde's latitude. A ship sailing west of Seville will, in fact, reach the real Tordesillas meridian (point T on map) well before 654 leagues are sailed (point D ).
The rule of marteloio has sailors plot routes by drawing plane triangles on a chart, as if the world's surface were flat. While this might be practical enough for sailing confined to the compact latitudes of the Mediterranean Sea , it is quite misleading on a grander scale.
In the late 15th and 16th centuries, the improvement of nautical astronomy and the introduction of latitude parallels allowed navigators to determine their position at sea by celestial readings, rather than relying on estimation of distance sailed. [ 32 ] The successor of the rule of marteloio was the "Regiment of the Leagues" ( regimento das léguas ), that was used by Portuguese navigators sailing in the Atlantic Ocean. Or, to use the term introduced by William Bourne (1571), the "Rule to Raise or Lay a Degree", also known as the "Table of Leagues" or the "Rule for Raising the Pole". [ 33 ] It was first written down in the Portuguese navigation manual Regimento do astrolabio e do quadrante (published in Lisbon c. 1509, but written c. 1480) [ 34 ] It was popularized by Martín Cortés de Albacar in his 1551 Breve compendio la esfera y del arte de navegar .
The "Regiment of the Leagues" is not very different from the rule of marteloio. The Regiment of the Leagues always considers the west-east bearing as the "intended course" and measures set deviations from it. More specifically, the league table considers a fixed value of alargar – set at 1 latitude degree (or, in the measurements of the time, 17.5 (Portuguese) leagues , or equivalently 70 (Italian) miles ). [ 35 ] It then gives for every different quarter wind of sailing direction (always designated as quarters away from the north-south axis, rather than away from the intended course), the relevar and the afastar . The relevar is the number of leagues on the actual course that a ship must sail in order to cover the pre-set 1 degree of latitude (17.5 leagues of alargar from the starting parallel). The afastar is merely the corresponding avanzar on the west-east bearing.
Example : Suppose a ship sets out on an East-southeast (ESE) bearing. That is six quarter-winds above South (remember: unlike the marteloio, the Regiment of the Leagues always measures quarter-winds away from the north–south meridian). Looking at any regiment of the leagues table (e.g. Martín Cortés de Albacar , 1551), [ 36 ] for q = 6, the table gives the relevar as 45 11 ⁄ 15 leagues and the afastar as 42 1 ⁄ 4 leagues. This means that a ship sailing on the ESE bearing will have to sail 45.73 leagues to cover one degree of latitude (17.5 leagues of alargar from the east bearing, to use the marteloio language), and the corresponding afastar ( avanzar in marteloio terms) will be 42.25 leagues.
If, instead, the ship had set out on a SE bearing, that is four quarter-winds above South, the corresponding values of the Regiment of the Leagues table at q = 4 are relevar = 24 3 ⁄ 4 and the afastar = 17 1 ⁄ 2 .
Notice that the SE bearing reaches the 1 degree alargar faster (i.e. smaller relevar ) than that the ESE bearing, and will have less afastar (closer to the N–S meridian).
Mathematically,
where θ = 11.25 × number of quarters-winds away from the north-south axis.
Despite the difference in terminology, notably the use of latitude degrees, the rule of marteloio and the Regiment of the Leagues are very similar – they are both about solving triangles on a plane chart. The advantage of the regiment over the marteloio is the introduction of latitude parallels in the table, so that the position can be checked by astronomical observation (via quadrant , astrolabe , etc.), and not have to rely wholly on sailor estimations of distance and direction.
With the regiment, geographical coordinates can also be used to guide navigation. For instance, the search for the Todesillas line (meridian 370 leagues west of Cape Verde) is much simplified by reference to a precise latitude. For instance, suppose two ships depart from Cape Verde (17° N), one on a West by North bearing (WbN, that is one quarter above West, or q = 7 from North axis), the other by a west-northwest bearing (WNW, two quarters above west, or q = 6 from the North axis). Using the Regiment of the Leagues, it is possible to calculate the precise latitudes when they will cross the Tordesillas meridian – simply divide 370 leagues west by the implied afastar at the different bearings. The WbN ship will reach the meridian when it achieves latitude 21° 21' N, while the WNW ship will reach it when it achieves latitude 29° N. [ 37 ] So rather than counting leagues with hourglass and speed readings, the ships can just maintain bearing, and take periodic astronomical observations to assess their latitude.
The toleta de marteloio is ancestral to the modern " traverse table " used in more modern navigation. [ 38 ] In the modern nomenclature, the traverse is the "crooked path made by a ship when she sails in several successive directions" and resolving the traverse is "the method of finding a single course and distance which would bring a ship to the same place as two or more courses and distances". [ 39 ] In marteloio language, when "resolving the traverse", the known information given is the "actual course" and the "ritorno", while the unknowns are the "intended bearing" and "total avanzo".
Traverse tables use three values for each of the crooked course segments – the Distance (Dist.), Difference of Latitude (D.Lat., movement along N–S axis) and the Departure (Dep., movement along E–W axis), the latter two calculated by the formulas:
where θ is the angular difference of the course from the N–S axis if the values of θ are less than 45°; if, however, the angle exceeds 45°, then θ is expressed as the angle of difference from the E–W axis, and the formulas are flipped, i.e. the Difference of Latitude formula becomes the Departure, and the Departure formula is the Difference of Latitude). Or, even more simply, calculate θ as the angle of difference from the nearest principal wind (N, S, E, W), run the formulas and then place the larger number in the appropriate column (D.Lat. or Dep.).
For each course segment, the navigator inserts the relevant trio (Dist., D.Lat., Dep.) and can calculate the implied bearing from the beginning to the endpoint and the distance made good on that bearing. He then combines, by addition and subtraction, all the differences of latitude and departure, to get the overall difference of latitude and departure, and converts that back to overall bearing and distance made good. [ 40 ]
Ramon Llull 's suggestive 1295 remarks aside, the earliest known reference to marteloio is dated 1390, in the inventory of the estate of the mother of a certain Oberto Foglieto of Genoa, where an entry reads unum martelogium....item carta una pro navegando . [ 41 ] The first clear appearance and explanation is the 1436 atlas of Venetian captain Andrea Bianco . Other early manuscripts have since been found relating the rule of marteloio, include: [ 42 ] | https://en.wikipedia.org/wiki/Rule_of_marteloio |
In materials science , a general rule of mixtures is a weighted mean used to predict various properties of a composite material . [ 1 ] [ 2 ] [ 3 ] It provides a theoretical upper- and lower-bound on properties such as the elastic modulus , [ 1 ] ultimate tensile strength , thermal conductivity , and electrical conductivity . [ 3 ] In general there are two models, the rule of mixtures for axial loading (Voigt model), [ 2 ] [ 4 ] and the inverse rule of mixtures for transverse loading (Reuss model). [ 2 ] [ 5 ]
For some material property E {\displaystyle E} , the rule of mixtures states that the overall property in the direction parallel to the fibers could be as high as
The inverse rule of mixtures states that in the direction perpendicular to the fibers, the elastic modulus of a composite could be as low as
where
If the property under study is the elastic modulus, these properties are known as the upper-bound modulus , corresponding to loading parallel to the fibers; and the lower-bound modulus , corresponding to transverse loading. [ 2 ]
Consider a composite material under uniaxial tension σ ∞ {\displaystyle \sigma _{\infty }} . If the material is to stay intact, the strain of the fibers, ϵ f {\displaystyle \epsilon _{f}} must equal the strain of the matrix, ϵ m {\displaystyle \epsilon _{m}} . Hooke's law for uniaxial tension hence gives
where σ f {\displaystyle \sigma _{f}} , E f {\displaystyle E_{f}} , σ m {\displaystyle \sigma _{m}} , E m {\displaystyle E_{m}} are the stress and elastic modulus of the fibers and the matrix, respectively. Noting stress to be a force per unit area, a force balance gives that
where f {\displaystyle f} is the volume fraction of the fibers in the composite (and 1 − f {\displaystyle 1-f} is the volume fraction of the matrix).
If it is assumed that the composite material behaves as a linear-elastic material, i.e., abiding Hooke's law σ ∞ = E ∥ ϵ c {\displaystyle \sigma _{\infty }=E_{\parallel }\epsilon _{c}} for some elastic modulus of the composite parallel to the fibres E ∥ {\displaystyle E_{\parallel }} and some strain of the composite ϵ c {\displaystyle \epsilon _{c}} , then equations 1 and 2 can be combined to give
Finally, since ϵ c = ϵ f = ϵ m {\displaystyle \epsilon _{c}=\epsilon _{f}=\epsilon _{m}} , the overall elastic modulus of the composite can be expressed as [ 6 ]
Assuming the Poisson's ratio of the two materials is the same, this represents the upper bound of the composite's elastic modulus. [ 7 ]
Now let the composite material be loaded perpendicular to the fibers, assuming that σ ∞ = σ f = σ m {\displaystyle \sigma _{\infty }=\sigma _{f}=\sigma _{m}} . The overall strain in the composite is distributed between the materials such that
The overall modulus in the material is then given by
since σ f = E f ϵ f {\displaystyle \sigma _{f}=E_{f}\epsilon _{f}} , σ m = E m ϵ m {\displaystyle \sigma _{m}=E_{m}\epsilon _{m}} . [ 6 ]
Similar derivations give the rules of mixtures for
A generalized equation for any loading condition between isostrain and isostress can be written as: [ 8 ]
where k is a value between 1 and −1.
For a composite containing a mixture of n different materials, each with a material property E i {\displaystyle E_{i}} and volume fraction V i {\displaystyle V_{i}} , where
then the rule of mixtures can be shown to give:
and the inverse rule of mixtures can be shown to give:
Finally, generalizing to some combination of the rule of mixtures and inverse rule of mixtures for an n -component system gives:
When considering the empirical correlation of some physical properties and the chemical composition of compounds, other relationships, rules, or laws, also closely resembles the rule of mixtures: | https://en.wikipedia.org/wiki/Rule_of_mixtures |
The rule of mutual exclusion in molecular spectroscopy relates the observation of molecular vibrations to molecular symmetry . It states that no normal modes can be both Infrared and Raman active in a molecule that possesses a center of symmetry . This is a powerful application of group theory to vibrational spectroscopy , and allows one to easily detect the presence of this symmetry element by comparison of the IR and Raman spectra generated by the same molecule. [ 1 ]
The rule arises because, in a centrosymmetric point group , a normal mode of vibration must have the same character (i.e. transform similarly, according to the same irreducible representation ) under inversion as the property which generates it. IR active modes are generated by one of the components of the dipole moment vector. Vectors transform as spatial coordinates, and are thus of ungerade (u) symmetry, i.e. their character under inversion is -1. Thus, IR active modes must have character -1 under inversion.
Raman active modes, meanwhile, are generated by the polarizability tensor. Since tensor components transform as bilinear products of two spatial coordinates, they are invariant under inversion and are thus of gerade (g) symmetry, i.e. their character under inversion is +1. Thus, in the character table there is no irreducible representation that spans both IR and Raman active modes, and so there is no overlap between the two spectra. [ 2 ]
This does not mean that a vibrational mode which is not Raman active must be IR active: in fact, it is still possible that a mode of a particular symmetry is neither Raman nor IR active. Such spectroscopically "silent" or "inactive" modes exist in molecules such as ethylene (C 2 H 4 ), benzene (C 6 H 6 ) and the tetrachloroplatinate ion (PtCl 4 2− ). [ 3 ]
This spectroscopy -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rule_of_mutual_exclusion |
In combinatorics , the rule of product or multiplication principle is a basic counting principle (a.k.a. the fundamental principle of counting ). Stated simply, it is the intuitive idea that if there are a ways of doing something and b ways of doing another thing, then there are a · b ways of performing both actions. [ 1 ] [ 2 ]
In this example, the rule says: multiply 3 by 2, getting 6.
The sets { A , B , C } and { X , Y } in this example are disjoint sets , but that is not necessary. The number of ways to choose a member of { A , B , C }, and then to do so again, in effect choosing an ordered pair each of whose components are in { A , B , C }, is 3 × 3 = 9.
As another example, when you decide to order pizza, you must first choose the type of crust: thin or deep dish (2 choices). Next, you choose one topping: cheese, pepperoni, or sausage (3 choices).
Using the rule of product, you know that there are 2 × 3 = 6 possible combinations of ordering a pizza.
In set theory , this multiplication principle is often taken to be the definition of the product of cardinal numbers . [ 1 ] We have
where × {\displaystyle \times } is the Cartesian product operator. These sets need not be finite, nor is it necessary to have only finitely many factors in the product.
An extension of the rule of product considers there are n different types of objects, say sweets, to be associated with k objects, say people. How many different ways can the people receive their sweets?
Each person may receive any of the n sweets available, and there are k people, so there are n ⋯ ⋅ n ⏞ k = n k {\displaystyle \overbrace {n\cdots \cdot n} ^{k}=n^{k}} ways to do this.
The rule of sum is another basic counting principle . Stated simply, it is the idea that if we have a ways of doing something and b ways of doing another thing and we can not do both at the same time, then there are a + b ways to choose one of the actions. [ 3 ] | https://en.wikipedia.org/wiki/Rule_of_product |
In probability theory , the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of treating the sunrise problem . [ 1 ] The formula is still used, particularly to estimate underlying probabilities when there are few observations or events that have not been observed to occur at all in (finite) sample data.
If we repeat an experiment that we know can result in a success or failure, n times independently, and get s successes, and n − s failures, then what is the probability that the next repetition will succeed?
More abstractly: If X 1 , ..., X n +1 are conditionally independent random variables that each can assume the value 0 or 1, then, if we know nothing more about them,
Since we have the prior knowledge that we are looking at an experiment for which both success and failure are possible, our estimate is as if we had observed one success and one failure for sure before we even started the experiments. In a sense we made n + 2 observations (known as pseudocounts ) with s + 1 successes. Although this may seem the simplest and most reasonable assumption, which also happens to be true, it still requires a proof. Indeed, assuming a pseudocount of one per possibility is one way to generalise the binary result, but has unexpected consequences — see Generalization to any number of possibilities , below.
Nevertheless, if we had not known from the start that both success and failure are possible, then we would have had to assign
But see Mathematical details , below, for an analysis of its validity. In particular it is not valid when s = 0 {\displaystyle s=0} , or s = n {\displaystyle s=n} .
If the number of observations increases, P {\displaystyle P} and P ′ {\displaystyle P'} get more and more similar, which is intuitively clear: the more data we have, the less importance should be assigned to our prior information.
Laplace used the rule of succession to calculate the probability that the Sun will rise tomorrow, given that it has risen every day for the past 5000 years. One obtains a very large factor of approximately 5000 × 365.25, which gives odds of about 1,826,200 to 1 in favour of the Sun rising tomorrow.
However, as the mathematical details below show, the basic assumption for using the rule of succession would be that we have no prior knowledge about the question whether the Sun will or will not rise tomorrow, except that it can do either. This is not the case for sunrises.
Laplace knew this well, and he wrote to conclude the sunrise example: "But this number is far greater for him who, seeing in the totality of phenomena the principle regulating the days and seasons, realizes that nothing at the present moment can arrest the course of it." [ 2 ] Yet Laplace was ridiculed for this calculation; his opponents [ who? ] gave no heed to that sentence, or failed to understand its importance. [ 2 ]
In the 1940s, Rudolf Carnap investigated a probability-based theory of inductive reasoning , and developed measures of degree of confirmation, which he considered as alternatives to Laplace's rule of succession. [ 3 ] [ 4 ] See also New riddle of induction#Carnap .
The rule of succession can be interpreted in an intuitive manner by considering points randomly distributed on a circle rather than counting the number "success"/"failures" in an experiment. [ 5 ] To mimic the behavior of the proportion p on the circle, we will color the circle in two colors and the fraction of the circle colored in the "success" color will be equal to p . To express the uncertainty about the value of p , we need to select a fraction of the circle.
A fraction is chosen by selecting two uniformly random points on the circle. The first point Z corresponds to the zero in the [0, 1] interval and the second point P corresponds to p within [0, 1]. In terms of the circle the fraction of the circle from Z to P moving clockwise will be equal to p . The n trials can be interpreted as n points uniformly distributed on the circle; any point in the "success" fraction is a success and a failure otherwise. This provides an exact mapping from success/failure experiments with probability of success p to uniformly random points on the circle. In the figure the success fraction is colored blue to differentiate it from the rest of the circle and the points P and Z are highlighted in red.
Given this circle, the estimate of p is the fraction colored blue. Let us divide the circle into n+2 arcs corresponding to the n+2 points such that the portion from a point on the circle to the next point (moving clockwise) is one arc associated with the first point. Thus, Z defines the first blue arc while P defines the first non-blue/failure arc. Since the next point is a uniformly random point, if it falls in any of the blue arcs then the trial succeeds while if it falls in any of the other arcs, then it fails. So the probability of success p is b t {\displaystyle {\frac {b}{t}}} where b is the number of blue arcs and t is the total number of arcs. Note that there is one more blue arc (that of Z ) than success point and two more arcs (those of P and Z ) than n points. Substituting the values with number of successes gives the rule of succession.
Note: The actual probability needs to use the length of blue arcs divided by the length of all arcs. However, when k points are uniformly randomly distributed on a circle, the distance from a point to the next point is 1/k. So on average each arc is of the same length and ratio of lengths becomes ratio of counts.
The proportion p is assigned a uniform distribution to describe the uncertainty about its true value. (This proportion is not random, but uncertain. We assign a probability distribution to p to express our uncertainty, not to attribute randomness to p . But this amounts, mathematically, to the same thing as treating p as if it were random).
Let X i be 1 if we observe a "success" on the i th trial , otherwise 0, with probability p of success on each trial. Thus each X is 0 or 1; each X has a Bernoulli distribution . Suppose these X s are conditionally independent given p .
We can use Bayes' theorem to find the conditional probability distribution of p given the data X i , i = 1, ..., n. For the " prior " (i.e., marginal) probability measure of p we assigned a uniform distribution over the open interval (0,1)
For the likelihood of a given p under our observations, we use the likelihood function
where s = x 1 + ... + x n is the number of "successes" and n is the number of trials (we are using capital X to denote a random variable and lower-case x as the data actually observed). Putting it all together, we can calculate the posterior:
To get the normalizing constant , we find
(see beta function for more on integrals of this form).
The posterior probability density function is therefore
This is a beta distribution with expected value
Since p tells us the probability of success in any experiment, and each experiment is conditionally independent , the conditional probability for success in the next experiment is just p . As p is being treated as if it is a random variable , the law of total probability tells us that the expected probability of success in the next experiment is just the expected value of p . Since p is conditional on the observed data X i for i = 1, ..., n , we have
The same calculation can be performed with the (improper) prior that expresses total ignorance of p , including ignorance with regard to the question whether the experiment can succeed, or can fail. This improper prior is 1/( p (1 − p )) for 0 ≤ p ≤ 1 and 0 otherwise. [ 6 ] If the calculation above is repeated with this prior, we get
Thus, with the prior specifying total ignorance, the probability of success is governed by the observed frequency of success. However, the posterior distribution that led to this result is the Beta( s , n − s ) distribution, which is not proper when s = n or s = 0 (i.e. the normalisation constant is infinite when s = 0 or s = n ). This means that we cannot use this form of the posterior distribution to calculate the probability of the next observation succeeding when s = 0 or s = n . This puts the information contained in the rule of succession in greater light: it can be thought of as expressing the prior assumption that if sampling was continued indefinitely, we would eventually observe at least one success, and at least one failure in the sample. The prior expressing total ignorance does not assume this knowledge.
To evaluate the "complete ignorance" case when s = 0 or s = n can be dealt with, we first go back to the hypergeometric distribution , denoted by H y p ( s | N , n , S ) {\displaystyle \mathrm {Hyp} (s|N,n,S)} . This is the approach taken in Jaynes (2003). The binomial B i n ( r | n , p ) {\displaystyle \mathrm {Bin} (r|n,p)} can be derived as a limiting form, where N , S → ∞ {\displaystyle N,S\rightarrow \infty } in such a way that their ratio p = S N {\displaystyle p={S \over N}} remains fixed. One can think of S {\displaystyle S} as the number of successes in the total population, of size N {\displaystyle N} .
The equivalent prior to 1 p ( 1 − p ) {\displaystyle {1 \over p(1-p)}} is 1 S ( N − S ) {\displaystyle {1 \over S(N-S)}} , with a domain of 1 ≤ S ≤ N − 1 {\displaystyle 1\leq S\leq N-1} . Working conditional to N {\displaystyle N} means that estimating p {\displaystyle p} is equivalent to estimating S {\displaystyle S} , and then dividing this estimate by N {\displaystyle N} . The posterior for S {\displaystyle S} can be given as:
And it can be seen that, if s = n or s = 0, then one of the factorials in the numerator cancels exactly with one in the denominator. Taking the s = 0 case, we have:
Adding in the normalising constant, which is always finite (because there are no singularities in the range of the posterior, and there are a finite number of terms) gives:
So the posterior expectation for p = S N {\displaystyle p={S \over N}} is:
An approximate analytical expression for large N is given by first making the approximation to the product term:
and then replacing the summation in the numerator with an integral
The same procedure is followed for the denominator, but the process is a bit more tricky, as the integral is harder to evaluate
where ln is the natural logarithm plugging in these approximations into the expectation gives
where the base 10 logarithm has been used in the final answer for ease of calculation. For instance if the population is of size 10 k then probability of success on the next sample is given by:
So for example, if the population be on the order of tens of billions, so that k = 10, and we observe n = 10 results without success, then the expected proportion in the population is approximately 0.43%. If the population is smaller, so that n = 10, k = 5 (tens of thousands), the expected proportion rises to approximately 0.86%, and so on. Similarly, if the number of observations is smaller, so that n = 5, k = 10, the proportion rise to approximately 0.86% again.
This probability has no positive lower bound, and can be made arbitrarily small for larger and larger choices of N , or k . This means that the probability depends on the size of the population from which one is sampling. In passing to the limit of infinite N (for the simpler analytic properties) we are "throwing away" a piece of very important information. Note that this ignorance relationship only holds as long as only no successes are observed. It is correspondingly revised back to the observed frequency rule p = s n {\displaystyle p={s \over n}} as soon as one success is observed. The corresponding results are found for the s=n case by switching labels, and then subtracting the probability from 1.
This section gives a heuristic derivation similar to that in Probability Theory: The Logic of Science . [ 7 ]
The rule of succession has many different intuitive interpretations, and depending on which intuition one uses, the generalisation may be different. Thus, the way to proceed from here is very carefully, and to re-derive the results from first principles, rather than to introduce an intuitively sensible generalisation. The full derivation can be found in Jaynes' book, but it does admit an easier to understand alternative derivation, once the solution is known. Another point to emphasise is that the prior state of knowledge described by the rule of succession is given as an enumeration of the possibilities, with the additional information that it is possible to observe each category. This can be equivalently stated as observing each category once prior to gathering the data. To denote that this is the knowledge used, an I m is put as part of the conditions in the probability assignments.
The rule of succession comes from setting a binomial likelihood, and a uniform prior distribution. Thus a straightforward generalisation is just the multivariate extensions of these two distributions: 1) Setting a uniform prior over the initial m categories, and 2) using the multinomial distribution as the likelihood function (which is the multivariate generalisation of the binomial distribution). It can be shown that the uniform distribution is a special case of the Dirichlet distribution with all of its parameters equal to 1 (just as the uniform is Beta(1,1) in the binary case). The Dirichlet distribution is the conjugate prior for the multinomial distribution, which means that the posterior distribution is also a Dirichlet distribution with different parameters. Let p i denote the probability that category i will be observed, and let n i denote the number of times category i ( i = 1, ..., m ) actually was observed. Then the joint posterior distribution of the probabilities p 1 , ..., p m is given by:
To get the generalised rule of succession, note that the probability of observing category i on the next observation, conditional on the p i is just p i , we simply require its expectation. Letting A i denote the event that the next observation is in category i ( i = 1, ..., m ), and let n = n 1 + ... + n m be the total number of observations made. The result, using the properties of the Dirichlet distribution is:
This solution reduces to the probability that would be assigned using the principle of indifference before any observations made (i.e. n = 0), consistent with the original rule of succession. It also contains the rule of succession as a special case, when m = 2, as a generalisation should.
Because the propositions or events A i are mutually exclusive, it is possible to collapse the m categories into 2. Simply add up the A i probabilities that correspond to "success" to get the probability of success. Supposing that this aggregates c categories as "success" and m-c categories as "failure". Let s denote the sum of the relevant n i values that have been termed "success". The probability of "success" at the next trial is then:
which is different from the original rule of succession. But note that the original rule of succession is based on I 2 , whereas the generalisation is based on I m . This means that the information contained in I m is different from that contained in I 2 . This indicates that mere knowledge of more than two outcomes we know are possible is relevant information when collapsing these categories down to just two. This illustrates the subtlety in describing the prior information, and why it is important to specify which prior information one is using.
A good model is essential (i.e., a good compromise between accuracy and practicality). To paraphrase Laplace on the sunrise problem : Although we have a huge number of samples of the sun rising, there are far better models of the sun than assuming it has a certain probability of rising each day, e.g., simply having a half-life.
Given a good model, it is best to make as many observations as practicable, depending on the expected reliability of prior knowledge, cost of observations, time and resources available, and accuracy required.
One of the most difficult aspects of the rule of succession is not the mathematical formulas, but answering the question: When does the rule of succession apply? In the generalisation section, it was noted very explicitly by adding the prior information I m into the calculations. Thus, when all that is known about a phenomenon is that there are m known possible outcomes prior to observing any data, only then does the rule of succession apply. If the rule of succession is applied in problems where this does not accurately describe the prior state of knowledge, then it may give counter-intuitive results. This is not because the rule of succession is defective, but that it is effectively answering a different question, based on different prior information.
In principle (see Cromwell's rule ), no possibility should have its probability (or its pseudocount) set to zero, since nothing in the physical world should be assumed strictly impossible (though it may be)—even if contrary to all observations and current theories. Indeed, Bayes rule takes absolutely no account of an observation previously believed to have zero probability—it is still declared impossible. However, only considering a fixed set of the possibilities is an acceptable route, one just needs to remember that the results are conditional on (or restricted to) the set being considered, and not some "universal" set. In fact Larry Bretthorst shows that including the possibility of "something else" into the hypothesis space makes no difference to the relative probabilities of the other hypothesis—it simply renormalises them to add up to a value less than 1. [ 8 ] Until "something else" is specified, the likelihood function conditional on this "something else" is indeterminate, for how is one to determine P r ( data | something else , I ) {\displaystyle Pr({\text{data}}|{\text{something else}},I)} ? Thus no updating of the prior probability for "something else" can occur until it is more accurately defined.
However, it is sometimes debatable whether prior knowledge should affect the relative probabilities, or also the total weight of the prior knowledge compared to actual observations. This does not have a clear cut answer, for it depends on what prior knowledge one is considering. In fact, an alternative prior state of knowledge could be of the form "I have specified m potential categories, but I am sure that only one of them is possible prior to observing the data. However, I do not know which particular category this is." A mathematical way to describe this prior is the Dirichlet distribution with all parameters equal to m −1 , which then gives a pseudocount of 1 to the denominator instead of m , and adds a pseudocount of m −1 to each category. This gives a slightly different probability in the binary case of s + 0.5 n + 1 {\displaystyle {\frac {s+0.5}{n+1}}} .
Prior probabilities are only worth spending significant effort estimating when likely to have significant effect. They may be important when there are few observations — especially when so few that there have been few, if any, observations of some possibilities – such as a rare animal, in a given region. Also important when there are many observations, where it is believed that the expectation should be heavily weighted towards the prior estimates, in spite of many observations to the contrary, such as for a roulette wheel in a well-respected casino. In the latter case, at least some of the pseudocounts may need to be very large. They are not always small, and thereby soon outweighed by actual observations, as is often assumed. However, although a last resort, for everyday purposes, prior knowledge is usually vital. So most decisions must be subjective to some extent (dependent upon the analyst and analysis used). | https://en.wikipedia.org/wiki/Rule_of_succession |
The rule of thirds is a rule of thumb for composing visual art such as designs , films , paintings , and photographs . [ 3 ] The guideline proposes that an image should be imagined as divided into nine equal parts by two equally spaced horizontal lines and two equally spaced vertical lines, and that important compositional elements should be placed along these lines or their intersections. [ 4 ] Aligning a subject with these points creates more tension, energy and interest in the composition than simply centering the subject.
The rule of thirds is applied by aligning a subject with the guide lines and their intersection points, placing the horizon on the top or bottom line, or allowing linear features in the image to flow from section to section. The main reason for observing the rule of thirds is to discourage placement of the subject at the center, or prevent a horizon from appearing to divide the picture in half. Michael Ryan and Melissa Lenos, authors of the book An Introduction to Film Analysis: Technique and Meaning in Narrative Film , state that the use of rule of thirds is "favored by cinematographers in their effort to design balanced and unified images" (page 40). [ 5 ]
When filming or photographing people, it is common to line the body up to a vertical line and the person's eyes to a horizontal line. If filming a moving subject, the same pattern is often followed, with the majority of the extra room being in front of the person (the way they are moving). [ 6 ] Likewise, when photographing a still subject who is not directly facing the camera, the majority of the extra room should be in front of the subject with the vertical line running through their perceived center of mass.
The expression "rule of thirds" was first written down [ 7 ] by John Thomas Smith in 1797. In his book Remarks on Rural Scenery, Smith quotes a 1783 work by Sir Joshua Reynolds , in which Reynolds discusses, in unquantified terms, the balance of dark and light in a painting. [ 8 ] John Thomas Smith then continues with an expansion on the idea, naming it the "Rule of thirds":
Two distinct, equal lights, should never appear in the same picture : One should be principal, and the rest subordinate, both in dimension and degree: Unequal parts and gradations lead the attention easily from part to part, while parts of equal appearance hold it awkwardly suspended, as if unable to determine which of those parts is to be considered as the subordinate. "And to give the utmost force and solidity to your work, some part of the picture should be as light, and some as dark as possible: These two extremes are then to be harmonized and reconciled to each other." (Reynolds' Annot. on Du Fresnoy .)
Analogous to this "Rule of thirds", (if I may be allowed so to call it) I have presumed to think that, in connecting or in breaking the various lines of a picture, it would likewise be a good rule to do it, in general, by a similar scheme of proportion; for example, in a design of landscape, to determine the sky at about two-thirds ; or else at about one-third, so that the material objects might occupy the other two : Again, two thirds of one element, (as of water) to one third of another element (as of land); and then both together to make but one third of the picture, of which the two other thirds should go for the sky and aerial perspectives. This rule would likewise apply in breaking a length of wall, or any other too great continuation of line that it may be found necessary to break by crossing or hiding it with some other object : In short, in applying this invention, generally speaking, or to any other case, whether of light, shade, form, or color, I have found the ratio of about two thirds to one third, or of one to two, a much better and more harmonizing proportion, than the precise formal half , the too-far-extending four-fifths —and, in short, than any other proportion whatever. I should think myself honored by the opinion of any gentleman on this point; but until I shall by better informed, shall conclude this general proportion of two and one to be the most pictoresque medium in all cases of breaking or otherwise qualifying straight lines and masses and groupes [sic] , as Hogarth's line is agreed to be the most beautiful, (or, in other words, the most pictoresque) medium of curves . [ 9 ]
Writing in 1845, in his book Chromatics , George Field notes that Sir Joshua Reynolds gives the ratio 2:1 as a rule for the proportion of warm to cold colors in a painting, and attributes to Smith the expansion of that rule to all proportions in painting:
Sir Joshua has given it as a rule, that the proportion of warm to cold colour in a picture should be as two to one, although he has frequently deviated therefrom; and Smith, in his "Remarks on Rural Scenery," would extend a like rule to all the proportions of painting, begging for it the term of the "rule of thirds," according to which, a landscape, having one third of land, should have two thirds of water, and these together, forming about one-third of the picture, the remaining two-thirds to be for air and sky; and he applies the same rule to the crossing and breaking of lines and objects, &c. [ 10 ]
Even at this early date, there was skepticism over the universality of such a rule, at least in regards to color, for Field continues:
This rule, however, does not supply a general law, but universalises a particular, the invariable observance of which would produce a uniform and monotonous practice. But, however occasionally useful, it is neither accurate nor universal, the true mean of nature requiring compensation, which, in the case of warmth and coolness, is in about equal proportions, while, in regard to advancing and retiring colours, the true balance of effect is, approximately, three of the latter to one of the former; nevertheless, the proportions in both cases are to be governed by the predominance of light or shade, and the required effect of a picture, in which, and other species of antagonism, the scale of equivalents affords a guide.
Smith's discussion of this "rule" is independent of the history and use of the term in composition and photography. | https://en.wikipedia.org/wiki/Rule_of_thirds |
In scuba diving , the rule of thirds is a rule of thumb used by divers to plan dives so they have enough breathing gas remaining in their diving cylinder at the end of the dive to be able to complete the dive safely. [ 1 ] [ 2 ] This rule generally only applies to diving in overhead environments, such as caves, wrecks, and ice diving, where a direct ascent to the surface is impossible and the divers must return the way they came.
For divers following the rule, one third of the gas supply is planned for the outward journey, one third is for the return journey and one third is a safety reserve. [ 1 ] However, when diving with a buddy with a higher breathing rate or a different volume of gas, it may be necessary to set one third of the buddy's gas supply as the remaining 'third'. This means that the turn point to exit is earlier, or that the diver with the lower breathing rate carries a larger volume of gas than they alone require.
Reserves are needed at the end of dives in case the diver has gone deeper or longer than planned and must remain underwater to do decompression stops before being able to ascend safely to the surface. A diver without gas cannot do the stops and risks decompression sickness . In an overhead environment , where it is not possible to ascend directly to the surface, the reserve allows the diver to donate gas to an out-of-gas buddy, providing enough gas to let both divers exit the enclosure and ascend to the surface.
By the rule of thirds system the gas in stage cylinders is managed in the same way as the primary supply, whether the primary is carried as back gas or sidemounted. A third of the gas in the stage cylinder is used before the drop, leaving two thirds in the cylinder, the minimum amount for two divers to exit on one cylinder. The cylinder may be carried a few minutes beyond the point at which the first third was used, but is not breathed for this extra distance, to conserve the gas for the return, as this allows it to be reached a bit earlier if one diver loses all gas at the end of the next stage when gas supply is at critical pressure. If all goes to plan, the divers will surface with stages and primary cylinders each containing about one third of the original content. [ 3 ]
With the rule of thirds, the duration of the dive is limited by the point at which the gas reaches 1/3 the starting quantity, by not exceeding the planned decompression obligation, and by returning along the same route in similar conditions. Where a more specific or varied dive profile is planned, the "rock bottom" gas planning procedure is more versatile but more complex to calculate. Other rules of thumb for scuba gas planning exist and may be used where appropriate. | https://en.wikipedia.org/wiki/Rule_of_thirds_(diving) |
In English , the phrase rule of thumb refers to an approximate method for doing something, based on practical experience rather than theory. [ 1 ] [ 2 ] [ 3 ] This usage of the phrase can be traced back to the 17th century and has been associated with various trades where quantities were measured by comparison to the width or length of a thumb .
An erroneous folk etymology began circulating in the 1970s falsely connecting the origins of the phrase "rule of thumb" to legal doctrine on domestic abuse . The error appeared in a number of law journals, and the United States Commission on Civil Rights published a report on domestic abuse titled "Under the Rule of Thumb" in 1982. Some efforts were made to discourage the phrase, which was seen as taboo owing to this false origin. During the 1990s, several authors correctly identified the spurious folk etymology ; [ 4 ] however, the connection to domestic violence was still being cited in some legal sources into the early 2000s.
The exact origin of the phrase is uncertain. [ 5 ] Its earliest (1685) appearance in print comes from a posthumously published collection of sermons by Scottish preacher James Durham : "Many profest Christians are like to foolish builders, who build by guess, and by rule of thumb (as we use to speak), and not by Square and Rule ." [ 1 ] [ 6 ]
The phrase is also found in Sir William Hope's The Compleat Fencing Master (1692): "What he doth, he doth by rule of Thumb, and not by Art ." [ 7 ] James Kelly's The Complete Collection of Scottish Proverbs , 1721, includes: "No Rule so good as Rule of Thumb, if it hit", [ 8 ] [ 9 ] meaning a practical approximation. [ 7 ]
Historically, the width of the thumb, or "thumb's breadth", was used as the equivalent of an inch in the cloth trade; similar expressions existed in Latin and French as well. [ 6 ] [ 8 ] The thumb has also been used in brewing beer, to gauge the heat of the brewing vat. [ 2 ] Ebenezer Cobham Brewer writes that rule of thumb means a "rough measurement". He says that "Ladies often measure yard lengths by their thumb. Indeed, the expression 'sixteen nails make a yard' seems to point to the thumb-nail as a standard" and that "Countrymen always measure by their thumb." [ 10 ] According to Phrasefinder , "The phrase joins the whole nine yards as one that probably derives from some form of measurement but which is unlikely ever to be definitively pinned down." [ 5 ]
A modern folk etymology holds that the phrase is derived from the maximum width of a stick allowed for wife-beating under English common law, but no such law has ever existed. This belief may have originated in a rumored statement by 18th-century judge Sir Francis Buller that a man may beat his wife with a stick no wider than his thumb. Despite there being no record that Buller ever said this, the rumor produced numerous jokes and satirical cartoons at his expense, with Buller being ridiculed as "Judge Thumb".
English jurist Sir William Blackstone wrote in his Commentaries on the Laws of England of an "old law" that once allowed "moderate" beatings by husbands, but he did not mention thumbs or any specific implements. Wife-beating has been officially outlawed for centuries in England and the United States, but continued in practice; several 19th-century American court rulings referred to an "ancient doctrine" that the judges believed had allowed husbands to physically punish their wives using implements no thicker than their thumbs. However, this belief was not connected with the phrase rule of thumb until the 1970s. [ 11 ] : 43–44
In the 1970s, through a misunderstanding of a figure of speech, a common misconception arose that the phrase rule of thumb was related to legally condoned wife beating. [ 12 ] [ 13 ] [ 14 ]
A modern folk etymology [ 15 ] relates the phrase to domestic violence via an alleged rule under English common law which permitted wife-beating provided that the implement used was a rod or stick no thicker than a man's thumb. [ 7 ] Wife-beating has been officially outlawed in England and the United States for centuries, but enforcement of the law was inconsistent, and wife-beating did continue. However, a rule of thumb permitting wife-beating was never codified in law. [ 3 ] [ 16 ] [ 11 ]
English jurist William Blackstone wrote in the late 1700s in his Commentaries on the Laws of England that, by an "old law", a husband had formerly been justified in using "moderate correction" against his wife but was barred from inflicting serious violence; Blackstone did not mention either thumbs or sticks. [ 3 ] [ 8 ] According to Blackstone, this custom was in doubt by the late 1600s, and a woman was allowed "security of the peace" against an abusive husband. [ 8 ] [ a ] Twentieth-century legal scholar William L. Prosser wrote that there was "probably no truth to the legend" that a husband was allowed to beat his wife "with a stick no thicker than his thumb". [ 6 ] [ 16 ]
The association between the thumb and implements of domestic violence can be traced to 1782, when English judge Sir Francis Buller was ridiculed for purportedly stating that a husband could beat his wife, provided that he used a stick no wider than his thumb. [ b ] There is no record of Buller making such a statement, but the rumor generated much satirical press, with Buller being mocked as "Judge Thumb" in published jokes and cartoons. [ 3 ] [ 8 ] [ 17 ]
In the following century, several court rulings in the United States referred to a supposed common-law doctrine which the judges believed had once allowed wife-beating with an implement smaller than a thumb. [ 6 ] [ 11 ] : 41–42 None of these courts referred to such a doctrine as a rule of thumb or endorsed such a rule, but all permitted some degree of wife-beating so long as it did not result in serious injury. [ 3 ]
An 1824 court ruling in Mississippi stated that a man was entitled to enforce "domestic discipline" by striking his wife with a whip or stick no wider than the judge's thumb. In a later case in North Carolina ( State v. Rhodes , 1868), the defendant was found to have struck his wife "with a switch about the size of this fingers"; the judge found the man not guilty due to the switch being smaller than a thumb. [ 11 ] : 41 The judgment was upheld by the state supreme court, although the later judge stated:
Nor is it true that a husband has a right to whip his wife. And if he had, it is not easily seen how the thumb is the standard of size for the instrument which he may use, as some of the old authorities have said [...] The standard is the effect produced , and not the manner of producing it, or the instrument used. [ 8 ] [ 11 ] : 41–42
In 1873, also in North Carolina, the judge in State v. Oliver ruled, "We assume that the old doctrine that a husband had the right to whip his wife, provided that he used a switch no larger than his thumb, is not the law in North Carolina". [ 16 ] [ 11 ] : 42 These latter two cases were cited by the legal scholar Beirne Stedman when he wrote in a 1917 law review article that an "old common law rule" had permitted a husband to use "moderate personal chastisement on his wife" so long as he used "a switch no larger than his thumb". [ 8 ] [ 16 ]
By the late 19th century, most American states had outlawed wife-beating; some had severe penalties such as forty lashes or imprisonment for offenders. [ 11 ] : 40 Although it was commonly believed in parts of the United States that a man was legally permitted to beat his wife with a stick no wider than his thumb, that belief did not have any connection with the phrase rule of thumb until a misunderstanding arose in the 1970s. [ 11 ] : 43–44
In the 20th century, public concern with the problem of domestic violence declined at first, and then re-emerged along with the resurgent feminist movement in the 1970s. [ 3 ] The first recorded link between wife-beating and the phrase rule of thumb appeared in 1976, in a report on domestic violence by women's-rights advocate Del Martin :
For instance, the common-law doctrine had been modified to allow the husband 'the right to whip his wife, provided that he used a switch no bigger than his thumb'—a rule of thumb, so to speak. [ 6 ]
While Martin appears to have meant the phrase rule of thumb only as a figure of speech , some feminist writers treated it as a literal reference to an earlier law. [ 6 ] [ 11 ] : 43 The following year, a book on battered women stated:
One of the reasons nineteenth century British wives were dealt with so harshly by their husbands and by their legal system was the 'rule of thumb'. Included in the British Common Law was a section regulating wifebeating [...] The new law stipulated that the reasonable instrument be only 'a rod not thicker than his thumb.' In other words, wifebeating was legal. [ 18 ]
Despite this erroneous reading of the common law (which is a set of judicial principles rather than a written law with individual sections) the spurious legal doctrine of the "rule of thumb" was soon mentioned in a number of law journals. [ 3 ] [ 8 ] The myth was repeated in a 1982 report by the United States Commission on Civil Rights on domestic abuse titled "Under the Rule of Thumb", as well as a later United States Senate report on the Violence Against Women Act . [ 3 ]
In the late 20th century, some efforts were made to discourage the phrase rule of thumb , [ 8 ] which was seen as taboo owing to this false origin. [ 3 ] Patricia T. O'Conner , former editor of the New York Times Book Review , described it as "one of the most persistent myths of political correctness". [ 6 ] During the 1990s, several authors wrote about the false etymology of rule of thumb , including English professor Henry Ansgar Kelly and conservative social critic Christina Hoff Sommers , [ 3 ] who described its origin in a misunderstanding of Blackstone's commentary. [ 16 ] Nonetheless, the myth persisted in some legal sources into the early 2000s. [ 3 ]
The dictionary definition of rule of thumb at Wiktionary | https://en.wikipedia.org/wiki/Rule_of_thumb |
The rule of twelfths is an approximation to a sine curve . It can be used as a rule of thumb for estimating a changing quantity where both the quantity and the steps are easily divisible by 12. Typical uses are predicting the height of the tide or the change in day length over the seasons.
The rule states that over the first period the quantity increases by 1/12. Then in the second period by 2/12, in the third by 3/12, in the fourth by 3/12, fifth by 2/12 and at the end of the sixth period reaches its maximum with an increase of 1/12. The steps are 1:2:3:3:2:1 giving a total change of 12/12. Over the next six intervals the quantity reduces in a similar manner by 1, 2, 3, 3, 2, 1 twelfths.
In many parts of the world the tides approximate to a semi-diurnal sine curve, that is there are two high- and two low- tides per day. As an estimate then each period equates to 1 hour, with the tide rising by 1, 2, 3, 3, 2, finally 1 twelfths of its total range in each hour, from low tide to high tide in about 6 hours, then the tide is decreasing by the same pattern in the next 6 hours, back to low tide. In places where there is only one high and one low water per day, the rule can be used by assuming the steps are 2 hours. If the tidal curve does not approximate to a sine wave then the rule cannot be used. [ 1 ] [ 2 ] This is important when navigating a boat or a ship in shallow water, and when launching and retrieving boats on slipways on a tidal shore. [ 3 ]
The rule is also useful for estimating the monthly change in sunrise and sunset and thus day length. [ 4 ]
If a tide table gives the information that tomorrow's low water would be at noon and that the water level at this time would be two metres above chart datum , and that at the following high tide the water level would be 14 metres, then the height of water at 3:00 p.m. can be calculated as follows:
This represents only the increase - the total depth of the water (relative to chart datum) will include the 2 m depth at low tide: 6 m + 2 m = 8 metres.
The calculation can be simplified by adding twelfths together and reducing the fraction beforehand:
If midwinter sunrise and set are at 09:00 and 15:00, and midsummer at 06:00 and 18:00, the daylight duration will shift by 0:30, 1:00, 1:30, 1:30, 1:00 and 0:30 over the six months from one solstice to the other. Likewise the day length changes by 0:30, 1:00, 1:30, 1:30, 1:00 and 0:30 each month. More equatorial latitudes change by less, but still in the same proportions; more polar by more.
The rule is a rough approximation only and should be applied with great caution when used for navigational purposes. Officially produced tide tables should be used in preference whenever possible.
The rule assumes that all tides behave in a regular manner, this is not true of some geographical locations, such as Poole Harbour [ 5 ] or the Solent [ 6 ] where there are "double" high waters or Weymouth Bay [ 5 ] where there is a double low water.
The rule assumes that the period between high and low tides is six hours but this is an underestimate and can vary anyway.
The rule relies on the approximation of tan 60° or √3 (~1.732) with 5/3 (~1.667) yielding 3.77% error. The next best rational approximation , 7/4 (1.75) yields 1.04% error. The steps are 1:3:4:4:3:1 giving a total change of 16/16: [ 7 ]
The following best approximations are 19/11 (0.276% error) with steps 3:8:11:11:8:3, and 26/15 (0.074% error) with steps 4:11:15:15:11:4. [ 7 ] | https://en.wikipedia.org/wiki/Rule_of_twelfths |
A ruler , sometimes called a rule , scale or a line gauge or metre/meter stick, is an instrument used to make length measurements , whereby a length is read from a series of markings called "rules" along an edge of the device. [ 1 ] Usually, the instrument is rigid and the edge itself is a straightedge ("ruled straightedge"), which additionally allows one to draw straighter lines.
Rulers have long been made from different materials and in multiple sizes. Historically, they were mainly wood but plastics have also been used. They can be created with length markings instead of being scribed . Metal is also used for more durable rulers for use in the workshop; sometimes a metal edge is embedded into a wooden desk ruler to preserve the edge when used for straight-line cutting. 12 in or 30 cm in length, although some can go up to 100cm, it is useful for a ruler to be kept on a desk to help in drawing. Shorter rulers are convenient for keeping in a pocket. [ 2 ] Longer rulers, e.g., 46 cm (18 in), are necessary in some cases. Rigid wooden or plastic yardsticks , 1 yard long, and meter sticks , 1 meter long, are also used. Classically, long measuring rods were used for larger projects, now superseded by the tape measure , the surveyor's wheel or laser rangefinders .
In geometry, straight lines between points may be drawn using a straightedge (ruler without any markings on it). Furthermore, it is also used to draw accurate graphs and tables.
A ruler and compass construction is a construction that uses a ruler and a compass. It is possible to bisect an angle into two equal parts with a ruler and compass. It can be proven, though, that it is impossible to divide an angle into three equal parts using only a compass and straightedge — the problem of angle trisection . However, if two marks be allowed on the ruler, the problem becomes solvable.
In the history of measurement many distance units have been used which were based on human body parts such as the cubit , hand and foot and these units varied in length by era and location. [ 3 ] In the late 18th century the metric system came into use and has been adopted to varying degrees in almost all countries in the world.
The oldest preserved measuring rod is a copper-alloy bar that dates from c. 2650 BC and was found by the German Assyriologist Eckhard Unger while excavating at the Sumerian city of Nippur (present-day Iraq).
Rulers made of ivory were in use by the Indus Valley civilization period prior to 1500 BC. [ 4 ] Excavations at Lothal (2400 BC) have yielded one such ruler calibrated to about 1.6 millimetres ( 1 ⁄ 16 in). [ 4 ] Ian Whitelaw holds that the Mohenjo-Daro ruler is divided into units corresponding to 33.5 millimetres (1.32 in) and these are marked out in decimal subdivisions with amazing accuracy, to within 0.13 millimetres (0.005 in). Ancient bricks found throughout the region have dimensions that correspond to these units. [ 5 ]
Anton Ullrich invented the folding ruler in 1851. Frank Hunt later made the flexible ruler in 1902. [ 6 ]
The equivalent of a ruler for drawing or reproducing a smooth curve, where it takes the form of a rigid template, is known as a French curve . A flexible device that can be bent to the desired shape is known as a flat spline , or (in its more modern incarnation) a flexible curve . Historically, a flexible lead rule used by masons that could be bent to the curves of a molding was known as a lesbian rule . [ 7 ]
Ludwig Wittgenstein famously used rulers as an example in his discussion of language games in the Philosophical Investigations (1953). He pointed out that the standard meter bar in Paris was the criterion against which all other rulers were determined to be one meter long. However, there was no analytical way to demonstrate that the standard meter bar itself was one meter long. It could only be asserted as one meter as part of a language game. | https://en.wikipedia.org/wiki/Ruler |
In number theory , the ruler function of an integer n {\displaystyle n} can be either of two closely related functions. One of these functions counts the number of times n {\displaystyle n} can be evenly divided by two, which for the numbers 1, 2, 3, ... is
Alternatively, the ruler function can be defined as the same numbers plus one, which for the numbers 1, 2, 3, ... produces the sequence
As well as being related by adding one, these two sequences are related in a different way: the second one can be formed from the first one by removing all the zeros, and the first one can be formed from the second one by adding zeros at the start and between every pair of numbers. For either definition of the ruler function, the rising and falling patterns of the values of this function resemble the lengths of marks on rulers with traditional units such as inches . These functions should be distinguished from Thomae's function , a function on real numbers which behaves similarly to the ruler function when restricted to the dyadic rational numbers .
In advanced mathematics, the 0-based ruler function is the 2-adic valuation of the number, [ 1 ] and the lexicographically earliest infinite square-free word over the natural numbers. [ 2 ] It also gives the position of the bit that changes at each step of the Gray code . [ 3 ]
In the Tower of Hanoi puzzle, with the disks of the puzzle numbered in order by their size, the 1-based ruler function gives the number of the disk to move at each step in an optimal solution to the puzzle. [ 4 ] A simulation of the puzzle, in conjunction with other methods for generating its optimal sequence of moves, can be used in an algorithm for generating the sequence of values of the ruler function in constant time per value. [ 3 ]
This number theory -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ruler_function |
In mathematical logic , the rules of passage govern how quantifiers distribute over the basic logical connectives of first-order logic . The rules of passage govern the "passage" (translation) from any formula of first-order logic to the equivalent formula in prenex normal form , and vice versa.
See Quine (1982: 119, chpt. 23). Let Q and Q' denote ∀ and ∃ or vice versa. β denotes a closed formula in which x does not appear. The rules of passage then include the following sentences, whose main connective is the biconditional :
The following conditional sentences can also be taken as rules of passage:
"Rules of passage" first appeared in French, in the writings of Jacques Herbrand . Quine employed the English translation of the phrase in each edition of his Methods of Logic , starting in 1950.
This logic -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Rules_of_passage |
A dividing engine is a device employed to mark graduations on measuring instruments.
There has always been a need for accurate measuring instruments. Whether it is a linear device such as a ruler or vernier or a circular device such as a protractor , astrolabe , sextant , theodolite , or setting circles for astronomical telescopes , the desire for ever greater precision has always existed. For every improvement in the measuring instruments, such as better alidades or the introduction of telescopic sights, the need for more exact graduations immediately followed.
In early instruments, graduations were typically etched or scribed lines in wood , ivory or brass . Instrument makers devised various devices to perform such tasks. Early Islamic instrument makers must have had techniques for the fine division of their instruments, as this accuracy is reflected in the accuracy of the readings they made. This skill and knowledge seems to have been lost, given that small quadrants and astrolabes in the 15th and 16th centuries did not show fine graduations and were relatively roughly made. [ 1 ]
In the 16th century, European instrument makers were hampered by the materials available. Brass was in hammered sheets with rough surfaces and iron graving tools were poor quality. There were not enough makers to have created a long tradition of practice and few were trained by masters . [ 1 ]
Transversals set a standard in the early 14th century. Tycho Brahe used transversals on his instruments and made the method better known. Transversals based on straight lines do not provide correct subdivisions on an arc, so other methods, such as those based on the use of circular arcs as developed by Philippe de La Hire , were also used.
Another system was created in the 16th century by Pedro Nunes and was called nonius after him. It consisted of tracing a certain number of concentric circles on an instrument and dividing each successive one with one fewer divisions than the adjacent outer circle. Thus the outermost quadrant would have 90° in 90 equal divisions, the next inner would have 89 divisions, the next 88 and so on. When an angle was measured, the circle and the division on which the alidade fell was noted. A table was then consulted to provide the exact measure. However, this system was difficult to construct and used by few. Tycho Brahe was one exception.
Some improvements to Nunes' system were developed by Christopher Clavius and Jacob Curtius . Curtius' work led directly to that of Pierre Vernier , published in 1631. Vernier refined this process and gave us the vernier scale . However, though these various techniques improved the reading of graduations, they did not contribute directly to the accuracy of their construction. Further improvements came slowly, and a new development was required: the dividing engine.
Prior work on the development of gear cutting machines had prepared the way. Such devices were required to cut a circular plate with uniform gear teeth . Clockmakers were familiar with these methods and they were important in developing dividing engines. George Graham devised a process of using geometric methods to divide the limb of an instrument. He developed a sophisticated beam compass to aid marking of the graduations. John Bird and Jeremiah Sisson followed on with these techniques. These beam compass techniques were used into the 19th century, as the dividing engines that followed did not scale up to the largest instruments being constructed.
The first true circular dividing engine was probably constructed by Henry Hindley , a clockmaker, around 1739. This was reported to the Royal Society by John Smeaton in 1785. [ 2 ] It was based directly on a gear cutting machine for clockworks. It used a toothed index plate and a worm gear to advance the mechanism. Duc de Chaulnes created two dividing engines between 1765 and 1768 for dividing circular arcs and linear scales. He desired to improve on the graduation of instruments by removing the skill of the maker from the technique where possible. While beam compass use was critically dependent on the skill of the user, his machine produced more regular divisions by virtue of its design. His machines were also inspired by the prior work of the clockmakers.
Jesse Ramsden followed duc de Chaulnes by five years in the production of his dividing engine. As with the prior inventions, Ramsden's used a tangent screw mechanism to advance the machine from one position to another. However, he had developed a screw-cutting lathe that was particularly advanced and produced a superior product. [ 3 ] [ 4 ] This engine was developed with funding from the Board of Longitude [ 1 ] on condition that it be described in detail (along with the related screw-cutting lathe ) and not be protected by patent. This allowed others to freely copy the device and improve on it. In fact, the Board required that he teach others to construct their own copies and make his dividing engine available to graduate instruments made by others. [ 1 ]
Edward Troughton was the first to build a copy of the Ramsden design. He enhanced the design and produced his own version. This permitted an improvement in the accuracy of the dividing engine.
Samuel Rhee developed his own endless screw cutting machine and was able to sell machines to others. His screws were considered the finest available at the time. [ 1 ]
In France, Étienne Lenoir created a dividing engine of greater accuracy than the English version. Mégnié, Richer, Fortin and Jecker had also built dividing engines of considerable quality. [ 1 ]
By the beginning of the 19th century, it was possible to make instruments such as the sextant that remained fully serviceable and of sufficient accuracy to be in use for a half century or more. [ 5 ]
The dividing engine was unique among developments in the manufacture of scientific instruments, as it was immediately accepted by all makers. There was no uncertainty in the value of this development. [ 5 ]
Bryan Donkin designed and built a screw cutting and dividing engine lathe in 1826, which set new standards of precision for the creation of accurate leadscrews, a necessary precursor to the development of precision machining in the Industrial Revolution. [ 6 ] | https://en.wikipedia.org/wiki/Ruling_engine |
The Rulkov map is a two-dimensional iterated map used to model a biological neuron . It was proposed by Nikolai F. Rulkov in 2001. [ 1 ] The use of this map to study neural networks has computational advantages because the map is easier to iterate than a continuous dynamical system . This saves memory and simplifies the computation of large neural networks.
The Rulkov map, with n {\displaystyle n} as discrete time, can be represented by the following dynamical equations:
where x {\displaystyle x} represents the membrane potential of the neuron. The variable y {\displaystyle y} in the model is a slow variable due to a very small value of μ {\displaystyle \mu } ( 0 < μ << 1 ) {\displaystyle (0<\mu <<1)} . Unlike variable x {\displaystyle x} , variable y {\displaystyle y} does not have explicit biological meaning, though some analogy to gating variables can be drawn. [ 2 ] The parameter σ {\displaystyle \sigma } can be thought of as an external dc current given to the neuron and α {\displaystyle \alpha } is a nonlinearity parameter of the map. Different combinations of parameters σ {\displaystyle \sigma } and α {\displaystyle \alpha } give rise to different dynamical states of the neuron like resting, tonic spiking and chaotic bursts . The chaotic bursting is enabled above α > 4 {\displaystyle \alpha >4}
The dynamics of the Rulkov map can be analyzed by analyzing the dynamics of its one dimensional fast submap. Since the variable y {\displaystyle y} evolves very slowly, for moderate amount of time it can be treated as a parameter with constant value in the x {\displaystyle x} variable's evolution equation (which we now call as one dimensional fast submap because as compared to y {\displaystyle y} , x {\displaystyle x} is a fast variable). Depending on the value of y {\displaystyle y} , this submap can have either one or three fixed points. One of these fixed points is stable, another is unstable and third may change the stability. [ 3 ] As y {\displaystyle y} increases, two of these fixed points (stable one and unstable one) merge and disappear by saddle-node bifurcation .
Coupling of two neurons has been investigated by Irina Bashkirtseva and Alexander Pisarchik who explored transitions between stationary, periodic, quasiperiodic, and chaotic regimes. [ 4 ] They also addresses the additional consequences of random disturbances on this system, leading to noise-induced transitions between periodic and chaotic stochastic oscillations. [ 5 ]
Adaptations of the Rulkov map have found applications in labor and industrial economics, particularly in the realm of corporate dynamics. [ 6 ] The proposed framework leverages synchronization and chaos regularization to account for dynamic transitions among multiple equilibria, incorporate skewness and idiosyncratic elements, and unveil the influence of effort on corporate profitability. The results are substantiated through empirical validation with real-world data. [ 6 ] Orlando and Bufalo introduced a deterministic model based on the Rulkov map, [ 7 ] effectively modeling volatility fluctuations in corporate yields and spreads, even during distressed periods like COVID-19. Comparing it to the ARIMA-EGARCH model, designed for handling various volatility aspects, both models yield comparable results. Nevertheless, the deterministic nature of the Rulkov map model may provide enhanced explanatory capabilities. [ 8 ]
Other applications of the Rulkov map include memristors, [ 9 ] [ 10 ] financial markets, [ 11 ] [ 12 ] biological systems, [ 13 ] etc. | https://en.wikipedia.org/wiki/Rulkov_map |
Ruma Falk ( Hebrew : רומה פלק , née Oren-Aharonovich, [ 1 ] 1932–2020) was an Israeli psychologist and philosopher of mathematics known for her work on probability theory and human understanding of probability and statistics. [ 2 ]
Falk was born in Jerusalem, [ 1 ] [ 2 ] and educated at the Herzliya Hebrew Gymnasium [ 2 ] and Hebrew University of Jerusalem . [ 1 ] She completed her PhD on the perception of chance at the Hebrew University in 1975 under the supervision of Amos Tversky , [ 2 ] and became a professor there. [ 1 ] [ 3 ] [ 2 ] She was married to Raphael Falk , a geneticist and historian of science. [ 3 ] [ 2 ] [ 4 ]
Falk won the George Pólya Award of the Mathematical Association of America with Maya Bar-Hillel in 1984 for their joint work on probability. [ 5 ] She died on August 15, 2020. [ 4 ]
Falk was the author of books including:
She also created a board game, ברירה וסיכוי (Choice and Chance). [ 2 ]
Her other publications include: | https://en.wikipedia.org/wiki/Ruma_Falk |
Rumble strips (also known as sleeper lines or alert strips ) are a traffic calming feature to alert inattentive drivers of potential danger, by causing a tactile vibration and audible rumbling transmitted through a vehicle's wheels into its interior. A rumble strip is applied along the direction of travel following an edgeline or centerline, to alert drivers when they drift from their lane. Rumble strips may also be installed in a series across the direction of travel, to warn drivers of a stop or slowdown ahead, or of an approaching danger spot.
In favorable circumstances, rumble strips are effective (and cost-effective) at reducing accidents due to inattention. The effectiveness of shoulder rumble strips is largely dependent on a wide and stable road shoulder for a recovery, but there are several other less obvious factors that engineers consider during design.
Rumble strips are also known as audible lines , [ 1 ] sleepy bumps , wake up calls , ruffles strips (named after the potato chips ), growlers , drift lines , waker-uppers , and drunk bumps .
Rumble strips are divided into transverse rumble strips, shoulder rumble strips, and centerline rumble strips, depending on how they are used.
Transverse rumble strips are placed in the travel lanes where most if not all vehicles will cross them. They are used to alert the driver of an upcoming intersection, toll booth or similar hazard. They may cross the entire road from shoulder to shoulder, or they may only be in the wheel paths. [ 2 ] Portable rumble strips, also called Andreas strips, can be used to alert traffic to upcoming lane closures or road works to prevent collision with signage and barriers. [ 3 ] [ 4 ]
Shoulder and centerline rumble strips are used to reduce lane departure crashes. Centerline rumble strips are used on undivided highways to reduce cross-over incidents and resultant head-on collisions . Shoulder rumble strips are used primarily to reduce run-off-road collisions . They alert distracted or drowsy drivers that they are leaving the roadway or crossing the centerline of the road. In this application, they are narrower and outside of the wheelpaths. [ 5 ]
There are several different ways to install rumble strips:
Surface-mount raised pavement reflectors are easily scraped off by the blade on snowplows , and thus are not practical in many locations in the United States and Canada. [ 11 ] [ 12 ]
Rumble strips combined with pavement markings are sometimes called rumble stripes . They may be formed with raised textured plastic pavement markers, or they may use conventional pavement marking materials sprayed onto milled rumble strips. Rumble stripes have markedly increased visibility in wet nighttime conditions, when conventional markings on flat surfaces can be difficult to see.
An early use of this construction was in 1943 on New Jersey's Route 6 near Great Notch. The scoring in the pavement—at the dual-lane divisions—reflected drivers' headlights, while "the resonant whine or roar coming off the ridges as the vehicle's tires rolled over the strip let the motorist know he was getting out of his traffic lane." With the "singing lane" safety benefit recognized for nearly a decade, the New Jersey chair of its Highway Authority, Ransford J. Abbott, mandated pavement-edge scoring for the Garden State Parkway in the early 1950s. [ 13 ]
Rumble strips were first implemented on the Garden State Parkway in New Jersey in 1952. [ 14 ] [ 15 ]
Initially, shoulder rumble strip installation focused on freeways using rolled-in rumble strips of different designs using a modified roller on a pavement rolling machines. Later, paving contractors modified pavement rolling machines to mill rumble strips into existing hardened asphalt pavement. Specifically designed commercially available machines followed. The development of ceramic and plastic raised systems enabled installation on concrete pavement highways, and the smaller footprint was better suited for the dashed centerline. "Virtual" rumble strips followed.
As rumble strips produce audible rumbling in specific audio frequencies based on the spacing of the grooves and the speed of the automobile, they have been used to create novel musical roads . These are also known as "singing shoulders".
Rumble strip installation is widespread, and in some cases controversial. Residents near urban freeways complain of noise at night as vehicles change lanes; or when vehicles strike the transverse rumble strips. The encroachment of shoulder rumble strips onto highways with narrow shoulders may create a hazard for cyclists. US and Canadian guidelines have minimum standards for installation on known cycling routes. In 2009, in Michigan, the Amish claimed that the shoulder rumble strips were dangerous for horse-drawn carriages, and successfully lobbied to have them paved over. In 2010, Kansas has considered removing shoulder rumble strips from an interstate highway to allow buses to travel on the shoulder during periods of traffic congestion.
Single-vehicle crashes are classified into two groups: run-off-road (ROR) , and on-road (OR) crashes in which the vehicle remains on the road after the crash. ROR crashes can account for up to 70% of the fatal single-vehicle crashes.
ROR crashes are due to inattention, speeding, traction loss, overreaction, crash avoidance, and mechanical failure. [ 16 ] Rumble strips only prevent ROR crashes due to inattention.
Research indicates that 47% of RORs exited the highway to the left; while 53% exited the highway to the right (in the USA where driving is on the right-hand-side of the road). [ 11 ]
A US Federal Highway Administration (FHWA) sponsored study stated that driver inattention comes in many forms, including distraction, daydreaming/competing thoughts, fatigue/drowsiness, and alcohol/drug impairment. [ 17 ] Early evening low alcohol intake also worsens sleepiness-related driving impairment. [ 18 ]
In a 2008 survey in the US, 33% of fatally injured drivers tested were found to be legally impaired ( BAC > 80 mg %), and an additional 5% were found to have a legal amount of alcohol in their bodies. [ 19 ] Canada has similar statistics. [ 20 ]
Studies support the hypothesis that some crashes are not prevented, but merely "migrated" or displaced from vehicle to vehicle, season to season, or location to location (e.g., further downstream of rumble strips on the highway system), and that such crashes may be no less severe than ones prevented by rumble strips.
An FHWA sponsored study wrestled with the moral dilemma of rumble strips keeping "unsafe drivers" (which includes impaired drivers) on the highway. "This group of unsafe drivers temporarily saved by the rumble strips may have caused some multiple-vehicle crashes involving harm to innocent victims to occur downstream from the treated site where no rumble strips existed. Unfortunately, as noted above, an examination of downstream crashes could not be conducted." [ 17 ]
A 2008 Swedish study using a driving simulator and 35 sleep-deprived drivers concluded: "The main results showed an increase in sleepiness indicators from start to before hitting the rumble strip, an alerting effect in most parameters after hitting the strip. The alertness enhancing effect was, however, short and the sleepiness signs returned 5 min after the rumble strip hit. Essentially no effects were seen due to type of strip." [ 21 ]
A 2003 Montana study suggested that on Interstates, shoulder rumble reduced the roll-over accident rates but the severity of unprevented roll-over accidents increased. This was thought to be due to the rumble strip "scaring" sleeping drivers to the extent that they overreacted. This problem was more pronounced on primary highways (that have narrower shoulders) with rumble strips. [ 22 ]
The 'classic' one-car crash results when a vehicle slowly drifts to the right, hits dirt or rumble strips on the right shoulder of the road, and the driver becomes alert and overreacts, jerking the wheel left to bring the vehicle back onto the road. This motion causes the left front tire to strike the raised edge of the pavement at a sharp angle, often causing a rollover or a swerve into oncoming traffic. This form of one-car crash is "classic" because it occurs very often. [ 23 ] Raised edges of pavement (or "edge-drops") were once common, but are now recognized as a hazard; it is now standard practice to level the gravel shoulder with the pavement, although edge-drops may reform due to soil erosion . This "slowly drift to the right" scenario applies to jurisdictions with right-hand traffic , so in jurisdictions with left-hand traffic it would be a "slowly drift to the left" scenario.
This phenomenon implies that a sleeping driver often does not react and begin to recover, until all four wheels have struck a rumble strip; if the paved shoulder is narrower than the width of the vehicle wheel track, a rumble strip may not prevent a sleeping driver from going off the road.
On a single-lane highway, an overreacting driver has less room to regain control, which may exacerbate their initial overreaction after striking the strips, resulting in a roll-over or head-on collision. A crash investigating officer stated: "It's consistent with someone who falls asleep or overreacts to the rumble strips", which implied that this was not the first time the officer has witnessed this situation. [ 24 ] Note that in the KATU.com article photograph (in the upper left-hand corner) of the crash scene, the passenger-side tire print in the soft shoulder that suggests that all four wheels passed over the rumble strip before the driver attempted the unsuccessful recovery. [ 25 ]
Accident profiles can change over time, and this can be considered a form of migration. Studies from Canada shows that over one decade the rate of off-road ATV accidents requiring hospitalization increased by 66%, while the rate for snowmobile accidents decreased 20%. [ 26 ] Many of these recreational vehicle owners own both or choose one over the other. Data from the US shows that motorcycles are becoming more popular and that motorcycle fatalities are increasing, while car fatalities are decreasing. [ 19 ] Many motorcyclists own or have access to a car.
Rumble strips may gradually encourage inattentive driving – thereby partially negating any safety benefits in the long term. This is referred to as "behavior adaptation". [ 27 ] [ 28 ]
A 2006 US study suggested that airbags and antilock brakes can lead to unsafe driving. [ 29 ] A 2007 Canadian study suggested that unsafe drivers are habitual, and that unsafe driving is increasing. [ 30 ] A 2009 Canadian study indicated that, after a steady decline, drinking and driving has been on the increase since 2004. [ 31 ] These support the migration and behavioral adaptation rumble strip concerns.
A safe driver population has more potential for negative behavior adaptation than an extreme unsafe driver population; whereas, an extreme unsafe driver population has more potential for positive behavior adaptation than a safe driver population. [ citation needed ]
Different jurisdictions have different accident and fatality rates, as a function of various factors such as climate, road layout, demographics, educational programs, level of policing, driver attitudes toward night driving, promptness of emergency response, and level of medical intervention. [ 16 ] For example, the 2006 Canadian motor vehicle fatality rate per province varied between 8.8 and 26.8 per 100,000 licensed drivers per year, with a national average of 13. [ 32 ] The 2008 US rate is 20.05. [ 19 ] Installing rumble strips on a highway with a relatively low accident rate and low proportion of accidents due to inattention will be relatively ineffective, even if the highway has 12-foot (3.7 m) paved shoulders.
The FHWA states: "Long sections of relatively straight roadways that make few demands on motorists are the most likely candidates for the installation of shoulder rumble strips." The degree of engagement of a highway affects the accident rate. Implied in this statement is that highways that are twisty and hilly with a variable foreground have low rates of accidents due to inattention, and are therefore not likely candidates for the installation of rumble strips. [ 33 ] Installing rumble strips along a highway that is highly engaging, with a narrow shoulder, a low accident rate, and relatively low proportion of accidents due to fatigue or inattentive driving would have questionable value.
In addition, safety improvements are not linear; there are diminishing marginal returns with a safer driver population, in which it is more difficult to further reduce the accident rate. Within the industrialized countries the rate varies between about 8 and 27 (per 100,000 licensed drivers per year).
"Safety improvements are usually subject to the law of diminishing marginal returns. This means that for every improvement of a fixed amount, the safety benefit gained decreases a little each time. For example, increasing the width of the median from 50m to 60m will decrease the number of collisions less than increasing it from 10m to 20m. Eventually, a width will be reached at which widening the median further cannot be justified because the improvement in safety is too small." [ 34 ]
When the accident rate is close to the baseline of 8, there may already be several factors pushing it down so adding another safety factor (initiative) will only yield a very small improvement. Installing rumble strips on a highway with a high accident rate close to 27 should yield a relatively high accident reduction. This assumes that the road shoulder is adequate for a recovery, once a straying driver has been alerted by the rumble strips.
Montana undertook an extensive 10-year multi-site study of the effectiveness of CSRS on Interstate and primary highways (both types are divided pavements). This study also investigated the severity of crashes, which sets it apart from previous studies. The results indicated a 14% reduction in crashes on Interstate highways; however the effectiveness on primary highways indicated both improvements and worsening, and the results were considered inconclusive. It was found that "roll-overs" decreased in number, but increased in severity. The study only considered crashes in dry and wet conditions, not snow and ice. [ 22 ]
The FHWA undertook a multi-state study involving test sites from Illinois and California. The Illinois component indicated crash reduction from 7.3% to 21.7%. The California component indicated crash reductions of 7.3%. This study also indicated an overall reduction of about 14%. [ 17 ]
The 1997 New York State Thruway study indicated a 65% to 70% reduction. [ 12 ] However, in a 1999 New York Times article regarding the New York State Thruway study, an official stated that the experiment was not done completely "pure", due to Troop T concurrently conducting a campaign to reduce drunk driving and increase seat-belt use, and Troop T's campaign would also reduce the number of fatal vehicle crashes. [ 35 ] 10 to 24 percent of crashes are estimated to involve fatigue or inattention of some kind, but these numbers are based on guesswork. [ 35 ] Despite this, the New York State Thruway study indicating a 65% to 70% reduction continues to be cited in literature. [ 12 ] [ 22 ]
New Zealand used rumble strips in small applications since the late 1980s, and started a larger program in 2004. Research in the country indicated that lane delineation with rumble strips reduced crashes by an average of 27% over all crash types and studies, with types of crashes such as "run off road" being reduced by up to 80% in some studies. Centre-line rumble strips showed similar effects. However, it appears that there were other crash reduction initiatives that may have contributed to the relatively sizable results. [ 36 ]
The effects remained even after road users had become accustomed to the feature, while other road safety measures (when studied at specific installations) often showed declining effectiveness over time. [ 36 ] Cost-benefit analysis showed that even on relatively low-volume roads, the costs of applying the markings were quickly exceeded several-fold by the economic benefits of improved road safety (as counted by the reduction of crash rates weighted against the average social costs of a crash). [ 36 ]
Further research in New Zealand led to recommendations that strip edge lines and centre lines be marked over extended lengths of road, rather than just at focal points and crash black spots. Apart from the safety benefits of providing a consistent road environment, continuous markings provide valuable alerts to drivers long before the more common crash spots. [ 37 ]
A one-third reduction rate is commonly cited and is based on an average of early studies. It includes the New York State Thruway and Pennsylvania Turnpike results which produced a skewed result non-representative of typical situations. [ 7 ] [ 12 ]
The one-third reduction rate and the Pennsylvania Turnpike Study (with a 60% reduction) are the rule-of-thumb and the classic study , but these can be misleading as CSRS do not have a "fixed" effectiveness that may be applied to any highway. [ 38 ]
A 1999 FHWA study concluded that "a best guess" might be 20% to 30% reduction in single-vehicle run-off-road crashes on rural freeways, with less effective on urban freeways. [ 17 ]
Almost all before-and-after studies are based on Interstate (freeway, turnpikes, thruways) test sites have minimum 12-foot (3.7 m) paved shoulders and very high crash rates due to inattention.
The collision reduction attributed to the installation of CSRS is mainly a function of stable shoulder width, crash rate and profile, climate and diminishing marginal returns.
Centerline Rumble Strips are applied to single-lane undivided highways to help prevent head-on collisions. When present, these are often milled into the pavement.
A 2005 National Cooperative Highway Research Program (NCHRP) study concluded that overall motor vehicle crashes at sites treated with Centerline Rumble Strips were reduced overall by 14%. [ 11 ] In these situations the opposite lane and any paved shoulder would function as a generous recovery zone. However, this study did not investigate changes in crash severity, as did the 2005 Montana study.
It is interesting that the CRS reduction value is the same as the 2005 Montana CSRS study that indicated a 14% reduction in accidents on Interstate highways. This supports the hypothesis that the overall effectiveness of CSRS with a generous recovery zone is about 14%.
Ice and slush filled rumble strips can be a concern, particularly so for milled centerline rumble strips. For this reason, some jurisdictions are reluctant to install them. [ 39 ]
A 2015 Federal Highway Administration study evaluated the application of shoulder rumble strips and centerline rumble strips in combination by analyzing geometric, traffic, and crash data obtained at treated two-lane rural road locations in Kentucky, Missouri and Pennsylvania. The results suggested that the effect of combining centerline and shoulder rumble strips further reduces run-off-road crashes compared to shoulder rumble strips alone and both total and fatal+injury crashes compared to centerline rumble strips alone. However, it appeared that shoulder rumble strips do not further reduce head-on+sideswipe-opposite-direction crashes than applying centerline rumble strips in isolation. [ 40 ]
CLRS are applied to multiple lane highways to help prevent vehicles from drifting into the adjacent lane and possibility colliding with an overtaking vehicle. These are typically a raised reflective system.
Transverse rumble strips (TRS) may be used to warn drivers: of the need to stop (e.g. intersections, toll plazas); the need to slow down; the need to change lanes; of a change in roadway alignment; that they are leaving the traveled way; upcoming construction zones; wildlife crossings; and other potentially unexpected conditions. [ 7 ] [ 41 ]
As a speed reduction measure, TRS have been marginally successful. A 2003 Texas study concluded: "However, the actual reductions in speeds have been in the range of 2 to 8 mph (3 to 13 km/h), which may be barely perceptible to the traveling public. There have been no studies that evaluate the reduction of excessive speeds." [ 7 ]
As a construction zone safety measure, the effectiveness appears unclear. A 2007 Minnesota study concluded that while transverse rumble strips offer a low cost and easy-to-install option, they “did not seem to be successful at reducing approach speeds at the project sites”. [ 42 ] A 2005 Maryland study stated: "In conclusion, although in the present study rumble strips did not produce the desired speed reduction effect, its use for work zone applications is still highly encouraged; though, not as a speed control measure but as a driver's attention-catching device." [ 43 ]
As an approach stop-control crash reduction measure they have proven successful. The 2003 Texas indicated: "The majority of studies found reported large reductions (40% to 100%) of accidents after installing transverse rumble strips." [ 7 ]
In Ghana , rumble strips running across the entire carriageway were installed at Suhum Junction on the main Accra - Kumasi highway and reduced crashes by about 35% and fatalities by about 55%. By reducing speeds the environment for and safety of pedestrians was improved with a decline in the "hit pedestrian" crash rate of 51%. "While the enforcement of speed limits by traffic police may not be affordable for most developing countries, rumble strips and speed humps were found to be effective on Ghanaian roads." [ 44 ]
A 2009 FHWA intelligent systems study suggested that a combined infrastructure-based and in-vehicle warning could be highly effective in reducing crossing path crashes and fatalities at signalized intersections. [ 10 ]
Recent before-and-after studies suggest that the effectiveness of CSRS on Interstate highway (or freeways or thruways) with 12-foot (3.7 m) paved shoulders is about 7% to 21% with an overall effectiveness of about 14%.
The effectiveness of CSRS on the lower-standard primary highways (that are also divided) has not been given the same consideration as those on Interstate highways. The 2003 Montana study suggested that CSRS on primary highways can result in either worsening or improvement of crash rates. This may be due to variation in recovery zone width and condition, and other factors. The study also stated that unprevented crash severity may worsen, and the overall results were inconclusive. The study suggested that the differences in rumble strip-related crashes between Interstate highways and primary highways were due to the primaries having smaller shoulders than Interstates. [ 22 ]
Secondary highways are single-lane undivided highways, and CSRS would be expected to be less effective than on primary highways. The most serious problem would be an increase in crash severity. Also, there is the concern of drivers sometimes overreacting and crossing the centerline, resulting in a head-on collision. [ 25 ] The recovery zone width and condition of single-lane highways can vary greatly. It appears that there may be no published before-and-after CSRS studies for single-lane highways.
Given behavior adaptation and migration, the current rigorous Interstate effectiveness of 14%, and CLRS on single-lane highways effectiveness of 14% could be over-estimations of the actual "big-picture" reduction. In certain situations, such as an engaging single-lane highways that typically have narrow shoulders, high precipitation, in a northern climate with frequent freeze-thaw cycles, rumble strip effectiveness may be negative. [ 22 ]
As before-and-after studies become broader and more sophisticated, it appears the reduction estimates for both CSRS and CRS are less impressive. This may be due to the initial installations were on highways that had been identified as having very high accident rates due to inattention. Also, there may have been other accident reduction campaigns in concert with rumble strip programs." [ 35 ]
Also, as lane departure warning systems built into vehicles become more widespread, the physical CSRS, CRS, and CLRS in pavements may become increasingly redundant.
Research has found that on rural freeways, rumble strips are much more effective when placed at or near the edgeline than when placed closer to the shoulder edge. Edgeline rumble strips can be expected to reduce crashes by 28.8%, and non-edgeline rumble strips only reduce crashes by 8.9%.
On two-lane roads, there is little difference in effectiveness between edgeline and non-edgeline rumble strips, with crash reduction factors of 39.2% and 41.9%, respectively. [ 45 ] FHWA now recommends rumble strips on two lane roads if the edge of shoulder is more than 13 feet (4.0 m) from the centerline, especially if the road has high volumes, poor geometry , or a history of run-off-road crashes. [ 46 ]
The 2003 Montana study stated that in certain cases, the rumble strips may act only as a warning of an impending crash, and that sort of a situation is much more likely where less shoulder is available for recovery. [ 22 ]
A concern about highways with narrow paved shoulders is the condition of the adjacent gravel shoulder. Sometimes, the paved and gravel shoulders are combined as the "recovery zone" beyond the rumble strip. However, if the gravel is loose, soft, non-level, eroded, or there is an "edge-drop" from the pavement to the gravel, then the gravel shoulder portion will be ineffective for recovery, especially at highway speeds. When a vehicle's tires sink into a soft shoulder, thus compromising vehicle handling, it is known as "vehicle tripping". [ 38 ]
Virtual rumble strips require an adequate recovery zone as well.
Climate is another factor that affects the success of a rumble strips installation. If they are installed in a northern climate, they may be filled or partially filled with a deicing salt and traction sand mixture. They may also be filled with ice. This is a particular concern in regions with freeze-thaw cycles requiring frequent deicing. Furthermore, strips filled with water, snow, slush, and ice may cause or aggravate occasional accidents. Generally, air turbulence and vibration from passing large trucks keep rumble strips clear of debris and ice, but this process may take several days. [ 12 ] Moist traction sand tends to cake together or freezes, and is not easily dislodged by truck traffic. This is problematic on low-volume highways with frequent deicing, and can significantly reduce the effectiveness of rumble strips in winter months.
When rumble strips are installed on a very narrow paved shoulder, sometimes sand and gravel can fill the rumble strip which is usually a problem in the winter and early spring.
If the snow-cover is substantial, then the shoulder (including the rumble strip) is usually partially snow-covered as the snowplow's wing-blade doesn't clear the entire shoulder. Vehicles going off the road usually collide with the shoulder snow bank or go into a snow-filled ditch which reduces the possibility of serious damage and injury. In these situations, the rumble strip effectiveness can be negated but the crash implications are mitigated by the snow bank.
Generally, deterioration of the shoulder asphalt pavement due to rumble strip installation is not a problem. However, if the sub-grade under the CSRS is poorly compacted or has poor drainage characteristics; or the gravel shoulder has eroded, crack(s) may form in the CSRS. Sand tends to fall into these cracks resulting in "jacking" of the cracks. Water percolates vertically down through the soil, but it also creeps horizontally under the paved shoulder. This may be a particular problem with narrow paved shoulders in regions with frequent freeze-thaw cycles that may result in frequent frost-heaving of the paved shoulder. [ 47 ]
US and Canadian guidelines recommend not installing rumble strips in asphalt pavement displaying cracks, to avoid excessive break-up of pavement. It is also recommended that rumble strips be inspected in summer months for cracking, potholing, water ponding, and snowplow damage. If necessary, structural problems should be repaired. [ 12 ] If the cracks become wide enough, grass and weeds will grow in the cracks accentuating the deterioration.
The centerline of highway has a pavement joint and if milled CLRS are installed over this joint they will make pavement more vulnerable to deterioration. Truckers have reported deterioration of the joint and the CLRS. [ 11 ]
Also, road salt prematurely degrades asphalt, so having it retained and concentrated in rumble strips is not desirable. [ 48 ]
In February 2010, Johnson County , Kansas , considered legislation to allow buses to travel on the paved shoulder (which was rumble stripped) when traffic slows to less than 35 mph (56 km/h). The estimated cost was between $17.6 million and $20 million, including $2.4 million to remove the already-existing rumble strips along the shoulder of I-35. [ 49 ] The Kansas House Transportation Committee had said it would be modeled after a similar project in Minneapolis , Minnesota . [ 50 ] [ 51 ] [ 52 ]
Some residents living close to either newly installed lane or transverse rumble strips have complained about noise levels and were successful in having them removed at considerable expense. In 2004, the town of Chapel Hill , North Carolina , had transverse rumble strips removed as the measured noise from nighttime traffic on the rumble strips exceeded the Town's Noise Ordinance. The noise levels at the sidewalk ranged from 60 to 77 decibels, higher than the 60 decibel noise level limit in the Town's Noise Ordinance during nighttime hours. [ 53 ] In 2005, the London borough of Bromley removed transverse rumble strips after residents complained of the excessive "machine gun fire" noise. [ 54 ] In 2010, Reno County planned to remove rumble strips from a roundabout after residents complained about excessive noise levels. [ 55 ]
The Transportation Association of Canada and US FHWA guidelines basically specify that a width of 1.5 m (4.9 ft) of clear paved shoulder between the outside of the rumble strip and the edge of pavement is adequate to provide cyclists with a clear travel path. [ 12 ] [ 33 ]
However, in situations of parked vehicle on the shoulder, debris on the shoulder, or downhill sections even with the 1.5 m (4.9 ft) clear path requirement, rumble strips present a significant hazard particularly if the pavement is wet. The argument that rumble strips help protect cyclists is moot, as inattentive drivers' vehicles generally pass entirely over the rumble strip before recovery (if any).
Other related FHWA guidelines are: "Rumble strips should not normally be used in urban or suburban areas or along roadways where prevailing speeds are less than 50 mph (80 km/h)." and "All responsible agencies should work in cooperation with bicycle groups, enforcement agencies, emergency groups and other roadway users, to develop policies, design standards and implementation techniques that address the safety and operational needs of all roadway users." and "To provide a clear area beyond the rumble strip for bicycle travel, highway maintenance agencies should periodically sweep shoulders along identified bicycle routes of high bicycle usage." [ 33 ]
In the United States, the 1999 American Association of State Highway and Transportation Officials (AASHTO) Guide for the Development of Bicycle Facilities recommends minimum standards for road shoulders receiving rumble strips to accommodate all users of the roadway and make best use of funds. [ 56 ]
In New Jersey, a centerline rumble strip was placed in the vicinity of the D&R Canal [ 57 ] without a permit from the Delaware & Raritan Canal Commission in violation of state law. [ 58 ] The excessive noise through a residential area and the fact that the work was not appropriately permitted was complained about to the New Jersey Department of Transportation by a local homeowner, with no corrective action taken by the New Jersey Department of Transportation. [ 57 ]
Excessive noise is noted in a Canadian study as a reason not to install rumble strips, and it is advised not to install rumble strips within 200 metres (660 ft) of a residential area. The report states that "a balance is required between installing effective rumble strips and minimizing noise impacts. Studies show that rumble strips terminated approximately 200 m (660 ft) away from residential or urban areas produce tolerable noise impacts on residences. At an offset of 500 m (1,600 ft), the noise from rumble strips is negligible.” [ 59 ] In an Open Public Records Act Request, [ 60 ] this study was the only document provided by the New Jersey Department of Transportation when requested to provide policy documents and safety studies relating to its implementation of centerline rumble strips.
Numerous US and Canadian cycling associations have complained about encroachment of rumble strips. [ 61 ] [ 62 ] [ 63 ] [ 64 ] [ 65 ] One club even launched a lawsuit to have them paved over, [ 66 ] although the suit was dismissed for lack of standing. [ 67 ]
A 2005 Quebec study concluded: "Based on the results of the analyses, it was not possible to recommend a type of rumble strip that would provide sufficient warning to drivers who encroach on the shoulder while remaining safe for cyclists who ride over it." [ 68 ] A 2003 Montana study stated that bicyclists cannot operate on shoulders with rumble strips and that shoulders would have to be swept as needed. [ 22 ]
Once a section of highway with narrow paved shoulders is rumble-stripped, informed cyclists tend to avoid it, but unsuspecting cyclists occasionally have serious accidents. [ 69 ] Much bicyclist opposition to rumble strips stems from situations in which no quantitative data was used to justify their installation, or installation was not in accordance with guidelines. Rumble strips on narrow shoulders force cyclists into the travel lanes, where it is less safe to ride. [ 62 ] [ 63 ] [ 64 ] [ 65 ] Furthermore, this scenario forces drivers to make an otherwise unnecessary lane change to go around cyclists and there is a correlation with frequency of lane changes and accidents. "According to the National Highway Traffic Safety Administration, 9 percent (533,000) of all accidents occurred when vehicles were changing lanes or merging." [ 70 ] In certain incidents, a vehicle attempting to avoid cyclists (without striking the cyclists) may go off the road or even sideswipe a passing or an oncoming vehicle. Center-line rumble strips are a concern for cyclists as well, as motorists are less inclined to cross the centerline to provide sufficient space when passing bicyclists. [ 11 ]
Rumble strips are very inexpensive to install, so there is concern that some installations are frivolous. The 2009 economic stimulus infrastructure spending in the US and Canada has raised concerns that many new shoulder rumble strips will be frivolous as well. [ 62 ] [ 63 ] [ 64 ] [ 65 ]
In 2009 in St. Joseph County, Michigan (US), after a lobbying campaign by the local Amish community, a new $20,000 rumble strip installation was removed at a cost of $275,000 to the taxpayers. M-DOT says they are not removing the strips just to appease the Amish. They say "it is far more dangerous to have horses jumping out into the road that [sic] it is to not have the rumble strips on the road." [ 71 ]
Motor vehicle tires can become permanently damaged if a flat occurs in the traffic lane and the driver pulls over onto the shoulder with the flat tire passing over the rumble strip. This may cause the flat tire's sidewalls to be crushed or abraded between the metal wheel rim and rumble strip high-points. [ citation needed ]
Wildlife-vehicle collisions can be a significant problem when large animals are involved such as moose, elk, and deer, which can cause serious vehicle damage, injury, and fatalities. [ 72 ] [ 73 ] Separate studies in New Hampshire (US) and Quebec (Canada), of radio-collared moose found that home ranges were associated with salt licks formed by road salt runoff. These roadside salt licks were thought to increase moose-vehicle collisions. [ 74 ] [ 75 ] [ 76 ] Normally, salt would make its way off the pavement onto the gravel shoulder and into the soil, however, rumble strips will retain and create a salt lick on the road surface. Loose rock salt in the rumble strip subjected to evaporating moisture will cake and accumulate and is not easily dislodged by truck traffic. | https://en.wikipedia.org/wiki/Rumble_strip |
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