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Shape moiré is one type of moiré patterns demonstrating the phenomenon of moiré magnification. [ 1 ] [ 2 ] 1D shape moiré is the particular simplified case of 2D shape moiré. One-dimensional patterns may appear when superimposing an opaque layer containing tiny horizontal transparent lines on top of a layer containing a complex shape which is periodically repeating along the vertical axis .
Shape moiré is sometimes referred as band moiré . The opaque layer with transparent lines is called the revealing layer . The layer containing the periodically repeating shapes is called the base layer . The period of shapes in the base layer is denoted as p b . The period of transparent lines in the revealing layer is denoted as p r . The periods of both layers must be sufficiently close. The superimposition image reveals the shapes of the base layer stretched along the vertical axis. The magnified shapes appear periodically along the vertical axis. The dimensions along the horizontal axis are not changed. If the complex shape of the base layer is a sequence of symbols (e.g. a horizontal text) compressed along the vertical axis, then the superimposition of the revealing layer can restore the original proportions of these symbols. The size along the vertical axis, p m , of the magnified optical shape is expressed by the following formula:
Negative values of p m signify mirrored appearance (the magnified shapes will be inverted along the vertical axis) of the stretched shapes.
When the revealing layer is moved along the vertical axis, the magnified shapes move along the vertical axis at a faster speed. The speedup factor is expressed by the following formula:
Negative values of v m / v r signify the movement of optical shapes in reverse direction.
When p r > p b , the magnified shapes appear normally, but they move in reverse direction compared to the movement of the revealing layer. See the figure below:
When p r < p b , the magnified shapes appear inverted along the vertical axis, but they move in the same direction as the revealing layer. See the figure below:
Line moiré can be considered as a particular case of shape moiré when the shape embedded in the base layer is simply a straight or curved line. | https://en.wikipedia.org/wiki/Shape_moiré |
The shape of the atomic nucleus depends on the variety of factors related to the size and shape of its nucleon ( proton or neutron ) constituents and the nuclear force holding them together. The spatial extent of the prolate spheroid nucleon (and larger nuclides) is determined by root mean squared (RMS) charge radius of the proton, as determined mainly by electron and muon scattering experiments, as well as spectroscopic experiments. [ 2 ] An important factor in the internal structure of the nucleus is the nucleon-nucleon potential , which ultimately governs the distance between individual nucleons, [ 3 ] and the radial charge density of each nuclide. The charge density of some light nuclide indicates a lesser density of nucleonic matter in the center [ 4 ] which may have implications for a nucleonic nuclear structure. A surprising non-spherical expectation for the shape of the nucleus originated in 1939 in the spectroscopic analysis of the quadrupole moments [ 5 ] while the prolate spheroid shape of the nucleon arises from analysis of the intrinsic quadruple moment. [ 1 ] The simple spherical approximation of nuclear size and shape provides at best a textbook introduction to nuclear size and shape. [ 6 ] The unusual cosmic abundance of alpha nuclides has inspired geometric arrangements of alpha particles as a solution to nuclear shapes, although the atomic nucleus generally assumes a prolate spheroid shape. Nuclides can also be discus-shaped (oblate deformation), triaxial (a combination of oblate and prolate deformation) or pear-shaped. [ 7 ] [ 8 ]
The atomic nucleus is composed of protons and neutrons (collectively called nucleons). In the Standard Model of particle physics, nucleons are in the group called hadrons , the smallest known particles in the universe to have measurable size and shape. [ 1 ] Each is in turn composed of three quarks . The spatial extent and shape of nucleons (and nuclides assembled from them) ultimately involves quark interactions within and between nucleons. The quark itself does not have measurable size at the experimental limit set by the electron (≈ 10 −18 m in diameter). [ 9 ] The size, or RMS charge radius , of the proton (the smallest nuclide) has a 2018 CODATA recommended value of 0.8414 (19) fm (10 −15 m), although values may vary by a few percent according to the experimental method employed (see proton radius puzzle ). Nuclide size ranges up to ≈ 6 fm. The largest stable nuclide, lead-208 , has an RMS charge radius of 5.5012 fm, and the largest unstable nuclide americium-243 has an experimental RMS charge radius of 5.9048 fm. [ 2 ] The main source of nuclear radius values derives from elastic scattering experiments (electron and muon ), but nuclear radii data also come from experiments on spectroscopic isotope shifts (x-ray and optical), β decay by mirror nuclei , α decay , and neutron scattering . [ 10 ] Although the radius values delimit the spatial extent of the nucleus, spectroscopic and scattering experiments dating back to 1935 [ 11 ] in many cases indicate a deviation of the nuclear charge distribution or quadrupole moment consistent with non-spherical nuclear shapes for many nuclei.
The atomic nucleus been depicted as a compact bundle of the two types of nucleons depicted as hard-packed spheres. This depiction of the nucleus only approximates the empirical evidence for the size and shape of the nucleus. The RMS charge radius of most stable (and many unstable) nuclides have been experimentally determined. [ 2 ] If the nucleus is assumed to be spherically symmetric, an approximate relationship between nuclear radius and mass number arises above A=40 from the formula R=R o A 1/3 with R o = 1.2 ± 0.2 fm. [ 6 ] R is the predicted spherical nuclear radius, A is the mass number, and R o is a constant determined by experimental data. This radius to mass relationship has its roots in the liquid drop model as proposed by Gamow in 1930. [ 12 ] The graph on the right plots the radius-to-mass of the experimental charge radius (blue line) [ 2 ] as compared to the spherical approximation (green line). For light nuclides below A=40, the smooth curvilinear spherical radius plot contrasts with the erratic experimental radius-to-mass. For medium and heavy nuclides above A=40, the plots converge and run approximately parallel when R o = 1.
The empirical knowledge of nucleon shape originates from the study of the transition from the proton ground state N (938) to the first excited state ∆ + (1232). [ 1 ] Multiple studies using a variety of models have led to an expectation of non-spherical shape. The proton's RMS charge radius of 0.8414 fm only defines the spatial extent of its charge distribution, i.e. the distance from its center of mass to its farthest point. Examination of the angular dependence of the charge distribution indicates that the proton is not a perfect sphere. Model-dependent analyses of the intrinsic quadrupole moment suggests that the ground-state nucleon shape conforms to a prolate spheroid shape. [ 13 ]
The intrinsic quadrupole moment is distinct from the spectroscopic quadrupole moment, as realized more than 50 years ago. [ 14 ] The intrinsic quadrupole moment relates to a body-fixed coordinate system that rotates with the nucleon in contrast to the spectroscopically measured quadrupole moment. While the nucleon's spectroscopic quadrupole moment is zero due to angular moment selection rules related to spin, the non-zero intrinsic quadrupole is obtained by electromagnetic quadrupole transitions between the nucleon ground N (938) and ∆(1232) excited states. [ 15 ] The proton and neutron have nearly the same mass (938 MeV), [ 16 ] and may be regarded as one particle, the nucleon N (938),with two different charge states (proton +1, and neutron 0). [ 17 ] The proton's N (938) ground state and ∆ + (1232) excited state have different shapes. [ 18 ] The transition between the states supports a prolate spheroid deformation for the ground state, and an oblate spheroid deformation for the excited state.
The prolate shaped ground state reflects quark-to-quark interactions arising from the Pauli exclusion principle. The Pauli exclusion principle, sometimes referred to as the Pauli exclusion force, is a fundamental rule in quantum mechanics stating that no two fermions (particles with half-integer spin such as electrons or quarks) can occupy the same quantum state simultaneously. [ 19 ] In the ground state, the two down quarks of a ground-state neutron are in an isospin 1 state, and simultaneously in a spin 1 state in order that the spin-isospin wave function is symmetric. [ 17 ] The consequence of this quantum mechanical constraint is that the likelihood of finding the neutron's two identical down quarks near one another is small, but increases with distance between them. Thus, within the spatial extent of the prolate spheroid neutron, the two down quarks will most likely be at opposite ends of the prolate spheroid. A similar quantum mechanical constraint applies to the two identical up quarks of the proton. [ 17 ] Accordingly, the spin-spin interactions between identical fermions result in finding like-flavored quarks further apart. Conversely, when the spins of a pair of unlike fermions align, such as an up-/down-quark pair within a ground-state nucleon, the nuclear force draws the particles close to other each other without violating the Pauli exclusion principle. [ 15 ] Within the ground state neutron, this results in a picture of the spin interactions (above) in which the two down quarks (like fermions) qualitatively reside on either end of the prolate nucleon structure while simultaneously attracting to the up quark (unlike fermion) in the middle. Similar spin-spin interactions play out in the proton, considered identical to the neutron but existing in a different charge state. [ 19 ]
Electron scattering techniques pioneered by Robert Hofstadter gave the first indication of a deeper structure for the nucleon. [ 20 ] The technique is similar in principle to Rutherford's gold foil experiment in which alpha particles are directed at a thin gold foil, but Hofstadter's use of electrons, rather than alpha particles, enabled much higher resolution. The radial charge density of the neutron in particular was shown to have a complex internal structure consisting of a positive core and a negative skin, qualitatively consistent with the neutron's quark charge distribution shown above. [ 20 ] [ 21 ] [ 22 ] Hofstadter received a Nobel prize for this work in 1961, several years before Murray Gell-Mann posited the quark model in 1965. [ 21 ]
The atomic nucleus is a bound system of protons and neutrons . The spatial extent and shape of the nucleus depend not only on the size and shape of discrete nucleons, but also on the distance between them (the inter-nucleon distance). (Other factors include spin , alignment, orbital motion, and the local nuclear environment (see EMC effect ).) The proximity of adjacent nucleons is governed by the nucleon-nucleon potential , and the force between a pair of nucleons can be obtained by taking the derivative of the potential. The strong nuclear force between nucleons is short-range, and the interaction between a pair of nucleons depends on the distance between them . Below 0.5 fm, each nucleon has a repulsive hard core that prevents neighboring nucleons from approaching any closer. [ 23 ] Repulsive and attractive forces balance at ≈ 0.8 fm, and become maximally attractive at ≈ 1.0 fm, as illustrated in the diagram. [ 3 ] Because energy is required to separate them, the pair of nucleons are said to be in a bound state . The proton-neutron (p-n) bound state, or p-n pair, is stable and ubiquitous in baryonic matter. [ 24 ] The p-n pair contributes implicitly to the top ten most abundant isotopes in the universe, eight of which contain equal numbers of protons and neutrons (see Oddo-Harkins rule and abundance of the elements ). Conversely, the proton-proton ( diproton ) and neutron-neutron ( dineutron ) bound states are unstable and therefore rarely found in nature. The deuteron (the simplest p-n pair) has a prolate shape as indicated by its quadrupole moment . [ 5 ] The transverse charge density of the deuteron confirms this prolate or elongated shape. [ 25 ]
Electron scattering techniques have yielded clues as to the internal structure of light nuclides. Proton-neutron pairs experience a strongly repulsive component of the nuclear force within ≈ 0.5 fm (see "Space between nucleons" above). As nucleons cannot pack any closer, nearly all medium to heavy nuclei have the same central density. [ 6 ] This statement generally holds true for nuclides above calcium-40, but electron scattering experiments of many of the lighter nuclides reveal a nuclear core that is remarkably less dense then the rest of the nucleus. Model-independent analyses of nuclear charge densities for both He-3 and He-4, for example, indicate a hole or significant central depression within a radius of 0.8 fm. [ 4 ] Other light nuclides, including carbon-12 and oxygen-16, exhibit similar off-center charge density maxima. [ 20 ] [ 26 ] A lower radial charge density within the nuclear core reflects a lower likelihood that scattering electrons will encounter a nucleon near the center of the nucleus compared to the surrounding nuclear structure.
Although the proton and the neutron are the building blocks of the atomic nucleus, the unusual natural abundance of alpha nuclides has prompted investigations of the role of the alpha particle , or helium-4 nucleus, as a potential building block of matter. [ 27 ] Alpha cluster models envision the atomic nucleus as having discrete alpha particles that occupy average relative positions. Hydrogen makes up 74% of the ordinary baryonic matter of the universe, but 99% of the remaining matter is contained within just eight nuclides ( He 2 4 {\displaystyle {\ce {^{4}_{2}He}}} , C 6 12 {\displaystyle {\ce {^{12}_{6}C}}} , N 7 14 {\displaystyle {\ce {^{14}_{7}N}}} , O 8 16 {\displaystyle {\ce {^{16}_{8}O}}} , Ne 10 20 {\displaystyle {\ce {^{20}_{10}Ne}}} , Mg 12 24 {\displaystyle {\ce {^{24}_{12}Mg}}} , Si 14 28 {\displaystyle {\ce {^{28}_{14}Si}}} , and S 16 32 {\displaystyle {\ce {^{32}_{16}S}}} ), seven of which are alpha nuclides. In the table below, the shapes of these nuclides may correspond to simple geometric arrangements of alpha particles, with associated radius predictions. [ 28 ]
For many medium-to-heavy nuclides, in particular those far from the magic numbers of protons and neutrons, a spherical model of the atomic nucleus is incompatible with observed large quadrupole moments, indicating that lower potential energy is obtained for an ellipsoidal shape than for a spherical nucleus of the same volume. [ 32 ] In general, their ground states tend towards a prolate shape, [ 33 ] although experimental data hint at oblate ground-state shapes in certain nuclei, for example krypton-72. [ 34 ] Experiments also suggest that some heavy nuclei, such as barium-144 and radium-224, possess asymmetric pear shapes evidenced by their measured octupole moments. [ 35 ] [ 36 ] [ 37 ] It is also possible for a nucleus to adopt different shapes in states with a similar excitation energy, which is referred to as shape coexistence. [ 38 ] For example, the ground states of krypton-74 and krypton-76 have prolate shapes, but there is evidence for oblate-shape excited structures in these nuclei appearing at low excitation energy. In this particular case, the shapes of coexisting structures tend to mix together. [ 39 ] | https://en.wikipedia.org/wiki/Shape_of_the_atomic_nucleus |
In physical cosmology , the shape of the universe refers to both its local and global geometry. Local geometry is defined primarily by its curvature , while the global geometry is characterised by its topology (which itself is constrained by curvature). General relativity explains how spatial curvature (local geometry) is constrained by gravity . The global topology of the universe cannot be deduced from measurements of curvature inferred from observations within the family of homogeneous general relativistic models alone, due to the existence of locally indistinguishable spaces with varying global topological characteristics. For example; a multiply connected space like a 3 torus has everywhere zero curvature but is finite in extent, whereas a flat simply connected space is infinite in extent (such as Euclidean space ).
Current observational evidence ( WMAP , BOOMERanG , and Planck for example) imply that the observable universe is spatially flat to within a 0.4% margin of error of the curvature density parameter with an unknown global topology. [ 1 ] [ 2 ] It is currently unknown whether the universe is simply connected like euclidean space or multiply connected like a torus. To date, compelling evidence has been found suggesting the topology of the universe is simply connected, though multiplied connections can also be possible by astronomical observations.
The universe's structure can be examined from two angles:
The observable universe (of a given current observer) is a roughly spherical region extending about 46 billion light-years in every direction (from that observer, the observer being the current Earth, unless specified otherwise). [ 3 ] It appears older and more redshifted the deeper we look into space. In theory, we could look all the way back to the Big Bang , but in practice, we can only see up to the cosmic microwave background (CMB) (roughly 370 000 years after the Big Bang) as anything beyond that is opaque . Studies show that the observable universe is isotropic and homogeneous on the largest scales.
If the observable universe encompasses the entire universe, we might determine its structure through observation. However, if the observable universe is smaller, we can only grasp a portion of it, making it impossible to deduce the global geometry through observation. Different mathematical models of the universe's global geometry can be constructed, all consistent with current observations and general relativity. Hence, it is unclear whether the observable universe matches the entire universe or is significantly smaller, though it is generally accepted that the universe is larger than the observable universe.
The universe may be compact in some dimensions and not in others, similar to how a cuboid [ citation needed ] is longer in one dimension than the others. Scientists test these models by looking for novel implications – phenomena not yet observed but necessary if the model is accurate. For instance, a small closed universe would produce multiple images of the same object in the sky, though not necessarily of the same age. As of 2024, current observational evidence suggests that the observable universe is spatially flat with an unknown global structure.
The curvature is a quantity describing how the geometry of a space differs locally from flat space. The curvature of any locally isotropic space (and hence of a locally isotropic universe) falls into one of the three following cases:
Curved geometries are in the domain of non-Euclidean geometry . An example of a positively curved space would be the surface of a sphere such as the Earth. A triangle drawn from the equator to a pole will have at least two angles equal 90°, which makes the sum of the 3 angles greater than 180°. An example of a negatively curved surface would be the shape of a saddle or mountain pass. A triangle drawn on a saddle surface will have the sum of the angles adding up to less than 180°.
General relativity explains that mass and energy bend the curvature of spacetime and is used to determine what curvature the universe has by using a value called the density parameter , represented with Omega ( Ω ). The density parameter is the average density of the universe divided by the critical energy density, that is, the mass energy needed for a universe to be flat. Put another way,
Scientists could experimentally calculate Ω to determine the curvature two ways. One is to count all the mass–energy in the universe and take its average density, then divide that average by the critical energy density. Data from the Wilkinson Microwave Anisotropy Probe (WMAP) as well as the Planck spacecraft give values for the three constituents of all the mass–energy in the universe – normal mass ( baryonic matter and dark matter ), relativistic particles (predominantly photons and neutrinos ), and dark energy or the cosmological constant : [ 4 ] [ 5 ]
The actual value for critical density value is measured as ρ critical = 9.47 × 10 −27 kg⋅m −3 . From these values, within experimental error, the universe seems to be spatially flat.
Another way to measure Ω is to do so geometrically by measuring an angle across the observable universe. This can be done by using the CMB and measuring the power spectrum and temperature anisotropy . For instance, one can imagine finding a gas cloud that is not in thermal equilibrium due to being so large that light speed cannot propagate the thermal information. Knowing this propagation speed, we then know the size of the gas cloud as well as the distance to the gas cloud, we then have two sides of a triangle and can then determine the angles. Using a method similar to this, the BOOMERanG experiment has determined that the sum of the angles to 180° within experimental error, corresponding to Ω total ≈ 1.00 ± 0.12 . [ 6 ]
These and other astronomical measurements constrain the spatial curvature to be very close to zero, although they do not constrain its sign. This means that although the local geometries of spacetime are generated by the theory of relativity based on spacetime intervals , we can approximate 3-space by the familiar Euclidean geometry .
The Friedmann–Lemaître–Robertson–Walker (FLRW) model using Friedmann equations is commonly used to model the universe. The FLRW model provides a curvature of the universe based on the mathematics of fluid dynamics , that is, modeling the matter within the universe as a perfect fluid. Although stars and structures of mass can be introduced into an "almost FLRW" model, a strictly FLRW model is used to approximate the local geometry of the observable universe. Another way of saying this is that, if all forms of dark energy are ignored, then the curvature of the universe can be determined by measuring the average density of matter within it, assuming that all matter is evenly distributed (rather than the distortions caused by 'dense' objects such as galaxies). This assumption is justified by the observations that, while the universe is "weakly" inhomogeneous and anisotropic (see the large-scale structure of the cosmos ), it is on average homogeneous and isotropic when analyzed at a sufficiently large spatial scale.
Global structure covers the geometry and the topology of the whole universe—both the observable universe and beyond. While the local geometry does not determine the global geometry completely, it does limit the possibilities, particularly a geometry of a constant curvature. The universe is often taken to be a geodesic manifold , free of topological defects ; relaxing either of these complicates the analysis considerably. A global geometry is a local geometry plus a topology. It follows that a topology alone does not give a global geometry: for instance, Euclidean 3-space and hyperbolic 3-space have the same topology but different global geometries.
As stated in the introduction, investigations within the study of the global structure of the universe include:
One of the unanswered questions about the universe is whether it is infinite or finite in extent. For intuition, it can be understood that a finite universe has a finite volume that, for example, could be in theory filled with a finite amount of material, while an infinite universe is unbounded and no numerical volume could possibly fill it. Mathematically, the question of whether the universe is infinite or finite is referred to as boundedness . An infinite universe (unbounded metric space) means that there are points arbitrarily far apart: for any distance d , there are points that are of a distance at least d apart. A finite universe is a bounded metric space, where there is some distance d such that all points are within distance d of each other. The smallest such d is called the diameter of the universe, in which case the universe has a well-defined "volume" or "scale".
Assuming a finite universe, the universe can either have an edge or no edge. Many finite mathematical spaces, e.g., a disc , have an edge or boundary. Spaces that have an edge are difficult to treat, both conceptually and mathematically. Namely, it is difficult to state what would happen at the edge of such a universe. For this reason, spaces that have an edge are typically excluded from consideration.
However, there exist many finite spaces, such as the 3-sphere and 3-torus , that have no edges. Mathematically, these spaces are referred to as being compact without boundary. The term compact means that it is finite in extent ("bounded") and complete . The term "without boundary" means that the space has no edges. Moreover, so that calculus can be applied, the universe is typically assumed to be a differentiable manifold . A mathematical object that possesses all these properties, compact without boundary and differentiable, is termed a closed manifold . The 3-sphere and 3-torus are both closed manifolds.
In the 1990s and early 2000s, empirical methods for determining the global topology using measurements on scales that would show multiple imaging were proposed [ 8 ] and applied to cosmological observations. [ 9 ] [ 10 ]
In the 2000s and 2010s, it was shown that, since the universe is inhomogeneous as shown in the cosmic web of large-scale structure , acceleration effects measured on local scales in the patterns of the movements of galaxies should, in principle, reveal the global topology of the universe. [ 11 ] [ 12 ] [ 13 ]
The curvature of the universe places constraints on the topology. If the spatial geometry is spherical , i.e., possess positive curvature, the topology is compact. For a flat (zero curvature) or a hyperbolic (negative curvature) spatial geometry, the topology can be either compact or infinite. [ 8 ] Many textbooks erroneously state that a flat or hyperbolic universe implies an infinite universe; however, the correct statement is that a flat universe that is also simply connected implies an infinite universe. [ 8 ] For example, Euclidean space is flat, simply connected, and infinite, but there are tori that are flat, multiply connected, finite, and compact (see flat torus ).
In general, local to global theorems in Riemannian geometry relate the local geometry to the global geometry. If the local geometry has constant curvature, the global geometry is very constrained, as described in Thurston geometries .
The latest research shows that even the most powerful future experiments (like the SKA ) will not be able to distinguish between a flat, open and closed universe if the true value of cosmological curvature parameter is smaller than 10 −4 . If the true value of the cosmological curvature parameter is larger than 10 −3 we will be able to distinguish between these three models even now. [ 14 ]
Final results of the Planck mission, released in 2018, show the cosmological curvature parameter, 1 − Ω = Ω K = − Kc 2 / a 2 H 2 , to be 0.0007 ± 0.0019 , consistent with a flat universe. [ 15 ] (i.e. positive curvature: K = +1 , Ω K < 0 , Ω > 1 , negative curvature: K = −1 , Ω K > 0 , Ω < 1 , zero curvature: K = 0 , Ω K = 0 , Ω = 1 ).
In a universe with zero curvature, the local geometry is flat . The most familiar such global structure is that of Euclidean space, which is infinite in extent. Flat universes that are finite in extent include the torus and Klein bottle . Moreover, in three dimensions, there are 10 finite closed flat 3-manifolds, of which 6 are orientable and 4 are non-orientable. These are the Bieberbach manifolds . The most familiar is the aforementioned 3-torus universe .
In the absence of dark energy, a flat universe expands forever but at a continually decelerating rate, with expansion asymptotically approaching zero. With dark energy, the expansion rate of the universe initially slows down, due to the effect of gravity, but eventually increases. The ultimate fate of the universe is the same as that of an open universe in the sense that space will continue expanding forever.
A flat universe can have zero total energy . [ 16 ]
A positively curved universe is described by elliptic geometry , and can be thought of as a three-dimensional hypersphere , or some other spherical 3-manifold (such as the Poincaré dodecahedral space ), all of which are quotients of the 3-sphere.
Poincaré dodecahedral space is a positively curved space, colloquially described as "soccerball-shaped", as it is the quotient of the 3-sphere by the binary icosahedral group , which is very close to icosahedral symmetry , the symmetry of a soccer ball. This was proposed by Jean-Pierre Luminet and colleagues in 2003 [ 9 ] [ 17 ] and an optimal orientation on the sky for the model was estimated in 2008. [ 10 ]
A hyperbolic universe, one of a negative spatial curvature, is described by hyperbolic geometry, and can be thought of locally as a three-dimensional analog of an infinitely extended saddle shape. There are a great variety of hyperbolic 3-manifolds , and their classification is not completely understood. Those of finite volume can be understood via the Mostow rigidity theorem . For hyperbolic local geometry, many of the possible three-dimensional spaces are informally called "horn topologies", so called because of the shape of the pseudosphere , a canonical model of hyperbolic geometry. An example is the Picard horn , a negatively curved space, colloquially described as "funnel-shaped". [ 18 ]
When cosmologists speak of the universe as being "open" or "closed", they most commonly are referring to whether the curvature is negative or positive, respectively. These meanings of open and closed are different from the mathematical meaning of open and closed used for sets in topological spaces and for the mathematical meaning of open and closed manifolds, which gives rise to ambiguity and confusion. In mathematics, there are definitions for a closed manifold (i.e., compact without boundary) and open manifold (i.e., one that is not compact and without boundary). A "closed universe" is necessarily a closed manifold. An "open universe" can be either a closed or open manifold. For example, in the Friedmann–Lemaître–Robertson–Walker (FLRW) model, the universe is considered to be without boundaries, in which case "compact universe" could describe a universe that is a closed manifold. | https://en.wikipedia.org/wiki/Shape_of_the_universe |
In quantum mechanics , a shape resonance is a metastable state in which an electron is trapped due to the shape of a potential barrier . [ 1 ] Altunata [ 2 ] describes a state as being a shape resonance if, "the internal state of the system remains unchanged upon disintegration of the quasi- bound level."
A more general discussion of resonances and their taxonomies in molecular system can be found in the review article by Schulz; [ 3 ] [ 4 ] for the discovery of the Fano resonance line-shape [ 5 ] and for the Majorana pioneering work in this field [ 6 ] by Antonio Bianconi; and for
a mathematical review by Combes et al. [ 7 ]
In quantum mechanics , a shape resonance, in contrast to a Feshbach resonance , is a resonance which is not turned into a bound state if the coupling between some degrees of freedom and the degrees of freedom associated to the fragmentation ( reaction coordinates ) are set to zero. More simply, the shape resonance total energy is more than the separated fragment energy. [ 8 ] Practical implications of this difference for lifetimes and spectral widths are mentioned in works such as Zobel. [ 9 ]
Related terms include a special kind of shape resonance, the core-excited shape resonance , and trap-induced shape resonance. [ 10 ]
Of course in one-dimensional systems, resonances are shape resonances. In a system with more than one degree of freedom, this definition makes sense only if the separable model, which supposes the two groups of degrees of freedom uncoupled, is a meaningful approximation. When the coupling becomes large, the situation is much less clear.
In the case of atomic and molecular electronic structure problems, it is well known that the self-consistent field (SCF) approximation is relevant at least as a starting point of more elaborate methods. The Slater determinants built from SCF orbitals ( atomic or molecular orbitals ) are shape resonances if only one electronic transition is required to emit one electron .
Today, there is some debate about the definition and even existence of the shape resonance in some systems observed with molecular spectroscopy. [ 11 ] It has been experimentally observed in the anionic yields from photofragmentation of small molecules to provide details of internal structure. [ 12 ]
In nuclear physics the concept of "Shape Resonance" is described by Amos de-Shalit and Herman Feshbach in their book. [ 13 ]
"It is well known that the scattering from a potential shows characteristics peaks, as a function of energy, for such values of E that make the integral number of wave lengths sit within the potential. The resulting shape resonances are rather broad, their width being of the order of ...."
The shape resonances were observed around the years 1949–54 in nuclear scattering experiments. They indicate broad asymmetric peaks in the scattering cross section of neutrons or protons scattered by nuclei. The name "shape resonance" has been introduced to describe the fact that the resonance in the potential scattering for the particle of energy E is controlled by the shape of the nucleus. In fact the shape resonance occurs where the integral number of wavelengths of the particle sit within the potential of the nucleus of radius R. Therefore, the measure of the energies of the shape resonances in the neutron-nucleus scattering have been used in the years from 1947 to 1954 to measure the radii R of the nuclei with the precision of ±1×10 −13 cm as it can be seen in the chapter "Elastic Cross Sections" of A Textbook in Nuclear Physics by R. D. Evans. [ 14 ]
The "shape resonances" are discussed in general introductory academic courses of quantum mechanics in the frame of potential scattering phenomena. [ 15 ]
The shape resonances arise from the quantum interference between closed and an open scattering channels. At the resonance energy a quasi bound state is degenerate with a continuum. This quantum interference in many body system has been described using quantum mechanics by Gregor Wentzel , for the interpretation of the Auger effect, by Ettore Majorana for the dissociation processes and quasi bound states, by Ugo Fano for the atomic auto-ionization states in the continuum of helium atomic spectrum and by Victor Frederick Weisskopf . J. M. Blatt and Herman Feshbach for nuclear scattering experiments. [ 16 ]
The shape resonances are related with the existence of nearly stable bound states (that is, resonances) of two objects that dramatically influences how those two objects interact when their total energy is near that of the bound state. When the total energy of the objects is close to the energy of the resonance they interact strongly, and their scattering cross-section becomes very large.
A particular type of "shape resonance" occurs in multiband or two-band superconducting heterostructures at atomic limit called superstripes due to quantum interference of a first pairing channel in a first wide band and a second pairing channel in a second band where the chemical potential is tuned near a Lifshitz transition at the band edge or at the topological electronic transitions of the Fermi surface type "neck-collapsing" or "neck-disrupting" [ 17 ] | https://en.wikipedia.org/wiki/Shape_resonance |
Shape theory is a branch of topology that provides a more global view of the topological spaces than homotopy theory . The two coincide on compacta dominated homotopically by finite polyhedra . Shape theory associates with the Čech homology theory while homotopy theory associates with the singular homology theory.
Shape theory was invented and published by D. E. Christie in 1944; it was reinvented, further developed and promoted by the Polish mathematician Karol Borsuk in 1968. Actually, the name shape theory was coined by Borsuk.
Borsuk lived and worked in Warsaw , hence the name of one of the fundamental examples of the area, the Warsaw circle . [ 1 ] It is a compact subset of the plane produced by "closing up" a topologist's sine curve (also called a Warsaw sine curve ) with an arc. The homotopy groups of the Warsaw circle are all trivial , just like those of a point, and so any map between the Warsaw circle and a point induces a weak homotopy equivalence . However these two spaces are not homotopy equivalent . So by the Whitehead theorem , the Warsaw circle does not have the homotopy type of a CW complex .
Borsuk's shape theory was generalized onto arbitrary (non- metric ) compact spaces, and even onto general categories, by Włodzimierz Holsztyński in year 1968/1969, and published in Fund. Math. 70 , 157–168, y. 1971 (see Jean-Marc Cordier, Tim Porter, (1989) below). This was done in a continuous style , characteristic for the Čech homology rendered by Samuel Eilenberg and Norman Steenrod in their monograph Foundations of Algebraic Topology . Due to the circumstance [ clarification needed ] , Holsztyński's paper was hardly noticed, and instead a great popularity in the field was gained by a later paper by Sibe Mardešić and Jack Segal, Fund. Math. 72 , 61–68, y.1971. Further developments are reflected by the references below, and by their contents.
For some purposes, like dynamical systems , more sophisticated invariants were developed under the name strong shape . Generalizations to noncommutative geometry , e.g. the shape theory for operator algebras have been found. | https://en.wikipedia.org/wiki/Shape_theory_(mathematics) |
A shaped charge , commonly also hollow charge if shaped with a cavity, is an explosive charge shaped to focus the effect of the explosive's energy. Different types of shaped charges are used for various purposes such as cutting and forming metal, initiating nuclear weapons , penetrating armor , or perforating wells in the oil and gas industry .
A typical modern shaped charge, with a metal liner on the charge cavity, can penetrate armor steel to a depth of seven or more times the diameter of the charge (charge diameters, CD), though depths of 10 CD and above [ 1 ] [ 2 ] have been achieved. Contrary to a misconception, possibly resulting from the acronym HEAT ( high-explosive anti-tank ), the shaped charge does not depend in any way on heating or melting for its effectiveness; that is, the jet from a shaped charge does not melt its way through armor, as its effect is purely kinetic in nature [ 3 ] —however the process creates significant heat and often has a significant secondary incendiary effect after penetration.
The shock wave from an explosive is perpendicular to the surface of the explosive. The inside of a cone focuses and concentrates the shock wave to points along the axis of the cone. As the explosion progresses from the point of detonation, the concentrated shock wave progresses along the axis of the cone, gathering energy along the way. [ 4 ]
The addition of a liner, increases the effect of the explosion by providing a heavy mass that is ejected from the cone.
The Munroe or Neumann effect is the focusing of blast energy by a hollow or void cut on a surface of an explosive. The earliest mention of hollow charges were mentioned in 1792. Franz Xaver von Baader (1765–1841) was a German mining engineer at that time; in a mining journal, he advocated a conical space at the forward end of a blasting charge to increase the explosive's effect and thereby save powder. [ 5 ] The idea was adopted, for a time, in Norway and in the mines of the Harz mountains of Germany, although the only available explosive at the time was gunpowder, which is not a high explosive and hence incapable of producing the shock wave that the shaped-charge effect requires. [ 6 ]
The first true hollow charge effect was achieved in 1883, by Max von Foerster (1845–1905), [ 7 ] chief of the nitrocellulose factory of Wolff & Co. in Walsrode , Germany. [ 8 ] [ 9 ]
By 1886, Gustav Bloem of Düsseldorf , Germany, had filed U.S. patent 342,423 for hemispherical cavity metal detonators to concentrate the effect of the explosion in an axial direction. [ 10 ] The Munroe effect is named after Charles E. Munroe , who discovered it in 1888. As a civilian chemist working at the U.S. Naval Torpedo Station at Newport, Rhode Island , he noticed that when a block of explosive guncotton with the manufacturer's name stamped into it was detonated next to a metal plate, the lettering was cut into the plate. Conversely, if letters were raised in relief above the surface of the explosive, then the letters on the plate would also be raised above its surface. [ 11 ] In 1894, Munroe constructed his first crude shaped charge: [ 12 ] [ 13 ]
Among the experiments made ... was one upon a safe twenty-nine inches cube, with walls four inches and three quarters thick, made up of plates of iron and steel ... When a hollow charge of dynamite nine pounds and a half in weight and untamped was detonated on it, a hole three inches in diameter was blown clear through the wall ... The hollow cartridge was made by tying the sticks of dynamite around a tin can, the open mouth of the latter being placed downward. [ 14 ]
Although Munroe's experiment with the shaped charge was widely publicized in 1900 in Popular Science Monthly , the importance of the tin can "liner" of the hollow charge remained unrecognized for another 44 years. [ 15 ] Part of that 1900 article was reprinted in the February 1945 issue of Popular Science , [ 4 ] describing how shaped-charge warheads worked. It was this article that at last revealed to the general public how the United States Army bazooka actually worked against armored vehicles during WWII.
In 1910, Egon Neumann of Germany discovered that a block of TNT , which would normally dent a steel plate, punched a hole through it if the explosive had a conical indentation. [ 16 ] [ 17 ] The military usefulness of Munroe's and Neumann's work was unappreciated for a long time. Between the world wars, academics in several countries – Myron Yakovlevich Sukharevskii (Мирон Яковлевич Сухаревский) in the Soviet Union, [ 18 ] William H. Payment and Donald Whitley Woodhead in Britain, [ 19 ] and Robert Williams Wood in the U.S. [ 20 ] – recognized that projectiles could form during explosions.
In 1932 Franz Rudolf Thomanek, a student of physics at Vienna's Technische Hochschule , conceived an anti-tank round that was based on the hollow charge effect. When the Austrian government showed no interest in pursuing the idea, Thomanek moved to Berlin's Technische Hochschule , where he continued his studies under the ballistics expert Carl Julius Cranz. [ 21 ] There in 1935, he and Hellmuth von Huttern developed a prototype anti-tank round. Although the weapon's performance proved disappointing, Thomanek continued his developmental work, collaborating with Hubert Schardin at the Waffeninstitut der Luftwaffe (Air Force Weapons Institute) in Braunschweig. [ 22 ]
By 1937, Schardin believed that hollow-charge effects were due to the interactions of shock waves. It was during the testing of this idea that, on February 4, 1938, Thomanek conceived the shaped-charge explosive (or Hohlladungs-Auskleidungseffekt (hollow-charge liner effect)). [ 23 ] (It was Gustav Adolf Thomer who in 1938 first visualized, by flash radiography, the metallic jet produced by a shaped-charge explosion. [ 24 ] ) Meanwhile, Henry Hans Mohaupt , a chemical engineer in Switzerland, had independently developed a shaped-charge munition in 1935, which was demonstrated to the Swiss, French, British, and U.S. militaries. [ 25 ]
During World War II, shaped-charge munitions were developed by Germany ( Panzerschreck , Panzerfaust , Panzerwurfmine , Mistel ), Britain ( No. 68 AT grenade , PIAT , Beehive cratering charge), the Soviet Union ( RPG-43 , RPG-6 ), the U.S. ( M9 rifle grenade , bazooka ), [ 26 ] [ 27 ] and Italy ( Effetto Pronto Speciale shells for various artillery pieces). [ 28 ] The development of shaped charges revolutionized anti-tank warfare . Tanks faced a serious vulnerability from a weapon that could be carried by an infantryman or aircraft.
One of the earliest uses of shaped charges was by German glider-borne troops against the Belgian Fort Eben-Emael in 1940. [ 29 ] These demolition charges – developed by Dr. Wuelfken of the German Ordnance Office – were unlined explosive charges [ 30 ] and did not produce a metal jet like the modern HEAT warheads.
Due to the lack of metal liner they shook the turrets but they did not destroy them, and other airborne troops were forced to climb on the turrets and smash the gun barrels. [ 31 ]
The common term in military terminology for shaped-charge warheads is high-explosive anti-tank (HEAT) warhead. HEAT warheads are frequently used in anti-tank guided missiles , unguided rockets , gun-fired projectiles (both spun ( spin stabilized ) and unspun), rifle grenades , land mines , bomblets , torpedoes , and various other weapons.
During World War II , the precision of the charge's construction and its detonation mode were both inferior to modern warheads. This lower precision caused the jet to curve and to break up at an earlier time and hence at a shorter distance. The resulting dispersion decreased the penetration depth for a given cone diameter and also shortened the optimum standoff distance. Since the charges were less effective at larger standoffs, side and turret skirts (known as Schürzen ) fitted to some German tanks to protect against ordinary anti-tank rifles [ 32 ] were fortuitously found to give the jet room to disperse and hence also reduce HEAT penetration. [ citation needed ]
The use of add-on spaced armor skirts on armored vehicles may have the opposite effect and actually increase the penetration of some shaped-charge warheads. Due to constraints in the length of the projectile/missile, the built-in stand-off on many warheads is less than the optimum distance. In such cases, the skirting effectively increases the distance between the armor and the target, and the warhead detonates closer to its optimum standoff. [ 33 ] Skirting should not be confused with cage armor which is primarily used to damage the fusing system of RPG-7 projectiles, but can also cause a HEAT projectile to pitch up or down on impact, lengthening the penetration path for the shaped charge's penetration stream. If the nose probe strikes one of the cage armor slats, the warhead will function as normal.
In non-military applications shaped charges are used in explosive demolition of buildings and structures , in particular for cutting through metal piles, columns and beams [ 34 ] [ 35 ] [ 36 ] and for boring holes. [ 37 ] In steelmaking , small shaped charges are often used to pierce taps that have become plugged with slag. [ 37 ] They are also used in quarrying, breaking up ice, breaking log jams, felling trees, and drilling post holes. [ 37 ]
Shaped charges are used most extensively in the petroleum and natural gas industries, in particular in the completion of oil and gas wells , in which they are detonated to perforate the metal casing of the well at intervals to admit the influx of oil and gas. [ 38 ] [ 39 ] Another use in the industry is to put out oil and gas fires by depriving the fire of oxygen.
A 4.5 kg (9.9 lb) shaped charge was used on the Hayabusa2 mission on asteroid 162173 Ryugu . The spacecraft dropped the explosive device onto the asteroid and detonated it with the spacecraft behind cover. The detonation dug a crater about 10 meters wide, to provide access to a pristine sample of the asteroid. [ 40 ]
A typical device consists of a solid cylinder of explosive with a metal-lined conical hollow in one end and a central detonator , array of detonators, or detonation wave guide at the other end. Explosive energy is released directly away from ( normal to ) the surface of an explosive, so shaping the explosive will concentrate the explosive energy in the void. If the hollow is properly shaped, usually conically, the enormous pressure generated by the detonation of the explosive drives the liner in the hollow cavity inward to collapse upon its central axis.
The resulting collision forms and projects a high-velocity jet of metal particles forward along the axis. Most of the jet material originates from the innermost part of the liner, a layer of about 10% to 20% of the thickness. The rest of the liner forms a slower-moving slug of material, which, because of its appearance, is sometimes called a "carrot".
Because of the variation along the liner in its collapse velocity, the jet's velocity also varies along its length, decreasing from the front. This variation in jet velocity stretches it and eventually leads to its break-up into particles. Over time, the particles tend to fall out of alignment, which reduces the depth of penetration at long standoffs.
At the apex of the cone, which forms the very front of the jet, the liner does not have time to be fully accelerated before it forms its part of the jet. This results in its small part of jet being projected at a lower velocity than jet formed later behind it. As a result, the initial parts of the jet coalesce to form a pronounced wider tip portion.
Most of the jet travels at hypersonic speed. The tip moves at 7 to 14 km/s, the jet tail at a lower velocity (1 to 3 km/s), and the slug at a still lower velocity (less than 1 km/s). The exact velocities depend on the charge's configuration and confinement, explosive type, materials used, and the explosive-initiation mode. At typical velocities, the penetration process generates such enormous pressures that it may be considered hydrodynamic ; to a good approximation, the jet and armor may be treated as inviscid , compressible fluids (see, for example, [ 41 ] ), with their material strengths ignored.
A recent technique using magnetic diffusion analysis showed that the temperature of the outer 50% by volume of a copper jet tip while in flight was between 1100K and 1200K, [ 42 ] much closer to the melting point of copper (1358 K) than previously assumed. [ 43 ] This temperature is consistent with a hydrodynamic calculation that simulated the entire experiment. [ 44 ] In comparison, two-color radiometry measurements from the late 1970s indicate lower temperatures for various shaped-charge liner material, cone construction and type of explosive filler. [ 45 ]
A Comp-B loaded shaped charge with a copper liner and pointed cone apex had a jet tip temperature ranging from 668 K to 863 K over a five shot sampling. Octol-loaded charges with a rounded cone apex generally had higher surface temperatures with an average of 810 K, and the temperature of a tin-lead liner with Comp-B fill averaged 842 K. While the tin-lead jet was determined to be liquid, the copper jets are well below the melting point of copper. However, these temperatures are not completely consistent with evidence that soft recovered copper jet particles show signs of melting at the core while the outer portion remains solid and cannot be equated with bulk temperature. [ 46 ]
The location of the charge relative to its target is critical for optimum penetration for two reasons. If the charge is detonated too close there is not enough time for the jet to fully develop. But the jet disintegrates and disperses after a relatively short distance, usually well under two meters. At such standoffs, it breaks into particles which tend to tumble and drift off the axis of penetration, so that the successive particles tend to widen rather than deepen the hole. At very long standoffs, velocity is lost to air drag , further degrading penetration.
The key to the effectiveness of the hollow charge is its diameter. As the penetration continues through the target, the width of the hole decreases leading to a characteristic "fist to finger" action, where the size of the eventual "finger" is based on the size of the original "fist". In general, shaped charges can penetrate a steel plate as thick as 150% to 700% [ 47 ] of their diameter, depending on the charge quality. The figure is for basic steel plate, not for the composite armor , reactive armor , or other types of modern armor.
The most common shape of the liner is conical , with an internal apex angle of 40 to 90 degrees. Different apex angles yield different distributions of jet mass and velocity. Small apex angles can result in jet bifurcation , or even in the failure of the jet to form at all; this is attributed to the collapse velocity being above a certain threshold, normally slightly higher than the liner material's bulk sound speed. Other widely used shapes include hemispheres, tulips, trumpets, ellipses , and bi-conics; the various shapes yield jets with different velocity and mass distributions.
Liners have been made from many materials, including various metals [ 48 ] and glass. The deepest penetrations are achieved with a dense, ductile metal, and a very common choice has been copper . For some modern anti-armor weapons, molybdenum and pseudo-alloys of tungsten filler and copper binder (9:1, thus density is ≈18 Mg/m 3 ) have been adopted. Nearly every common metallic element has been tried, including aluminum , tungsten , tantalum , depleted uranium , lead , tin , cadmium , cobalt , magnesium , titanium , zinc , zirconium , molybdenum , beryllium , nickel , silver , and even gold and platinum . [ citation needed ] The selection of the material depends on the target to be penetrated; for example, aluminum has been found advantageous for concrete targets.
In early antitank weapons, copper was used as a liner material. Later, in the 1970s, it was found tantalum is superior to copper, due to its much higher density and very high ductility at high strain rates. Other high-density metals and alloys tend to have drawbacks in terms of price, toxicity, radioactivity, or lack of ductility. [ 49 ]
For the deepest penetrations, pure metals yield the best results, because they display the greatest ductility, which delays the breakup of the jet into particles as it stretches. In charges for oil well completion , however, it is essential that a solid slug or "carrot" not be formed, since it would plug the hole just penetrated and interfere with the influx of oil. In the petroleum industry, therefore, liners are generally fabricated by powder metallurgy , often of pseudo-alloys which, if unsintered , yield jets that are composed mainly of dispersed fine metal particles.
Unsintered cold pressed liners, however, are not waterproof and tend to be brittle , which makes them easy to damage during handling. Bimetallic liners, usually zinc-lined copper, can be used; during jet formation the zinc layer vaporizes and a slug is not formed; the disadvantage is an increased cost and dependency of jet formation on the quality of bonding the two layers. Low-melting-point (below 500 °C) solder - or braze -like alloys (e.g., Sn 50 Pb 50 , Zn 97.6 Pb 1.6 , or pure metals like lead, zinc, or cadmium) can be used; these melt before reaching the well casing, and the molten metal does not obstruct the hole. Other alloys, binary eutectics (e.g. Pb 88.8 Sb 11.1 , Sn 61.9 Pd 38.1 , or Ag 71.9 Cu 28.1 ), form a metal-matrix composite material with ductile matrix with brittle dendrites ; such materials reduce slug formation but are difficult to shape.
A metal-matrix composite with discrete inclusions of low-melting material is another option; the inclusions either melt before the jet reaches the well casing, weakening the material, or serve as crack nucleation sites, and the slug breaks up on impact. The dispersion of the second phase can be achieved also with castable alloys (e.g., copper) with a low-melting-point metal insoluble in copper, such as bismuth, 1–5% lithium, or up to 50% (usually 15–30%) lead; the size of inclusions can be adjusted by thermal treatment. Non-homogeneous distribution of the inclusions can also be achieved. Other additives can modify the alloy properties; tin (4–8%), nickel (up to 30% and often together with tin), up to 8% aluminium, phosphorus (forming brittle phosphides) or 1–5% silicon form brittle inclusions serving as crack initiation sites. Up to 30% zinc can be added to lower the material cost and to form additional brittle phases. [ 50 ]
Oxide glass liners produce jets of low density, therefore yielding less penetration depth. Double-layer liners, with one layer of a less dense but pyrophoric metal (e.g. aluminum or magnesium ), can be used to enhance incendiary effects following the armor-piercing action; explosive welding can be used for making those, as then the metal-metal interface is homogeneous, does not contain significant amount of intermetallics , and does not have adverse effects to the formation of the jet. [ 51 ]
The penetration depth is proportional to the maximum length of the jet, which is a product of the jet tip velocity and time to particulation. The jet tip velocity depends on bulk sound velocity in the liner material, the time to particulation is dependent on the ductility of the material. The maximum achievable jet velocity is roughly 2.34 times the sound velocity in the material. [ 52 ] The speed can reach 10 km/s, peaking some 40 microseconds after detonation; the cone tip is subjected to acceleration of about 25 million g. The jet tail reaches about 2–5 km/s. The pressure between the jet tip and the target can reach one terapascal. The immense pressure makes the metal flow like a liquid, though x-ray diffraction has shown the metal stays solid; one of the theories explaining this behavior proposes molten core and solid sheath of the jet. The best materials are face-centered cubic metals, as they are the most ductile, but even graphite and zero-ductility ceramic cones show significant penetration. [ 53 ]
For optimal penetration, a high explosive with a high detonation velocity and pressure is normally chosen. The most common explosive used in high performance anti-armor warheads is HMX (octogen), although never in its pure form, as it would be too sensitive. It is normally compounded with a few percent of some type of plastic binder, such as in the polymer-bonded explosive (PBX) LX-14, or with another less-sensitive explosive, such as TNT , with which it forms Octol . Other common high-performance explosives are RDX -based compositions, again either as PBXs or mixtures with TNT (to form Composition B and the Cyclotols ) or wax (Cyclonites). Some explosives incorporate powdered aluminum to increase their blast and detonation temperature, but this addition generally results in decreased performance of the shaped charge. There has been research into using the very high-performance but sensitive explosive CL-20 in shaped-charge warheads, but, at present, due to its sensitivity, this has been in the form of the PBX composite LX-19 (CL-20 and Estane binder).
A 'waveshaper' is a body (typically a disc or cylindrical block) of an inert material (typically solid or foamed plastic, but sometimes metal, perhaps hollow) inserted within the explosive for the purpose of changing the path of the detonation wave. The effect is to modify the collapse of the cone and resulting jet formation, with the intent of increasing penetration performance. Waveshapers are often used to save space; a shorter charge with a waveshaper can achieve the same performance as a longer charge without a waveshaper. Given that the space of possible waveshapes is infinite, machine learning methods have been developed to engineer more optimal waveshapers that can enhance the performance of a shaped charge via computational design. [ 54 ]
Another useful design feature is sub-calibration , the use of a liner having a smaller diameter (caliber) than the explosive charge. In an ordinary charge, the explosive near the base of the cone is so thin that it is unable to accelerate the adjacent liner to sufficient velocity to form an effective jet. In a sub-calibrated charge, this part of the device is effectively cut off, resulting in a shorter charge with the same performance.
There are several forms of shaped charge.
A linear shaped charge (LSC) has a lining with V-shaped profile and varying length. The lining is surrounded with explosive, the explosive then encased within a suitable material that serves to protect the explosive and to confine (tamp) it on detonation. "At detonation, the focusing of the explosive high pressure wave as it becomes incident to the side wall causes the metal liner of the LSC to collapse–creating the cutting force." [ 55 ] The detonation projects into the lining, to form a continuous, knife-like (planar) jet. The jet cuts any material in its path, to a depth depending on the size and materials used in the charge. Generally, the jet penetrates around 1 to 1.2 times [ 56 ] the charge width. For the cutting of complex geometries, there are also flexible versions of the linear shaped charge, these with a lead or high-density foam sheathing and a ductile/flexible lining material, which also is often lead. LSCs are commonly used in the cutting of rolled steel joists (RSJ) and other structural targets, such as in the controlled demolition of buildings. LSCs are also used to separate the stages of multistage rockets , and destroy them when they go errant. [ 57 ]
The explosively formed penetrator (EFP) is also known as the self-forging fragment (SFF), explosively formed projectile (EFP), self-forging projectile (SEFOP), plate charge, and Misnay-Schardin (MS) charge. An EFP uses the action of the explosive's detonation wave (and to a lesser extent the propulsive effect of its detonation products) to project and deform a plate or dish of ductile metal (such as copper, iron, or tantalum) into a compact high-velocity projectile, commonly called the slug. This slug is projected toward the target at about two kilometers per second. The chief advantage of the EFP over a conventional (e.g., conical) shaped charge is its effectiveness at very great standoffs, equal to hundreds of times the charge's diameter (perhaps a hundred meters for a practical device).
The EFP is relatively unaffected by first-generation reactive armor and can travel up to perhaps 1000 charge diameters (CD)s before its velocity becomes ineffective at penetrating armor due to aerodynamic drag, or successfully hitting the target becomes a problem. The impact of a ball or slug EFP normally causes a large-diameter but relatively shallow hole, of, at most, a couple of CDs. If the EFP perforates the armor, spalling and extensive behind armor effects (BAE, also called behind armor damage, BAD) will occur.
The BAE is mainly caused by the high-temperature and high-velocity armor and slug fragments being injected into the interior space and the blast overpressure caused by this debris. More modern EFP warhead versions, through the use of advanced initiation modes, can also produce long-rods (stretched slugs), multi-slugs and finned rod/slug projectiles. The long-rods are able to penetrate a much greater depth of armor, at some loss to BAE, multi-slugs are better at defeating light or area targets and the finned projectiles are much more accurate.
The use of this warhead type is mainly restricted to lightly armored areas of main battle tanks (MBT) such as the top, belly and rear armored areas. It is well suited for the attack of other less heavily protected armored fighting vehicles (AFV) and in the breaching of material targets (buildings, bunkers, bridge supports, etc.). The newer rod projectiles may be effective against the more heavily armored areas of MBTs. Weapons using the EFP principle have already been used in combat; the " smart " submunitions in the CBU-97 cluster bomb used by the US Air Force and Navy in the 2003 Iraq war employed this principle, and the US Army is reportedly experimenting with precision-guided artillery shells under Project SADARM (Seek And Destroy ARMor). There are also various other projectile (BONUS, DM 642) and rocket submunitions (Motiv-3M, DM 642) and mines (MIFF, TMRP-6) that use EFP principle. Examples of EFP warheads are US patents 5038683 [ 58 ] and US6606951. [ 59 ]
Some modern anti-tank rockets ( RPG-27 , RPG-29 ) and missiles ( TOW-2 , TOW-2A, Eryx , HOT , MILAN ) use a tandem warhead shaped charge, consisting of two separate shaped charges, one in front of the other, typically with some distance between them. TOW-2A was the first to use tandem warheads in the mid-1980s, an aspect of the weapon which the US Army had to reveal under news media and Congressional pressure resulting from the concern that NATO antitank missiles were ineffective against Soviet tanks that were fitted with the new ERA boxes . The Army revealed that a 40 mm precursor shaped-charge warhead was fitted on the tip of the TOW-2 and TOW-2A collapsible probe. [ 60 ]
Usually, the front charge is somewhat smaller than the rear one, as it is intended primarily to disrupt ERA boxes or tiles. Examples of tandem warheads are US patents 7363862 [ 61 ] and US 5561261. [ 62 ] The US Hellfire antiarmor missile is one of the few that have accomplished the complex engineering feat of having two shaped charges of the same diameter stacked in one warhead. Recently, a Russian arms firm revealed a 125mm tank cannon round with two same diameter shaped charges one behind the other, but with the back one offset so its penetration stream will not interfere with the front shaped charge's penetration stream. The reasoning behind both the Hellfire and the Russian 125 mm munitions having tandem same diameter warheads is not to increase penetration, but to increase the beyond-armour effect .
In 1964 a Soviet scientist proposed that a shaped charge originally developed for piercing thick steel armor be adapted to the task of accelerating shock waves. [ 63 ] The resulting device, looking a little like a wind tunnel, is called a Voitenko compressor. [ 64 ] The Voitenko compressor initially separates a test gas from a shaped charge with a malleable steel plate. When the shaped charge detonates, most of its energy is focused on the steel plate, driving it forward and pushing the test gas ahead of it. Ames Laboratory translated this idea into a self-destroying shock tube. A 66-pound shaped charge accelerated the gas in a 3-cm glass-walled tube 2 meters in length. The velocity of the resulting shock wave was 220,000 feet per second (67 km/s). The apparatus exposed to the detonation was completely destroyed, but not before useful data was extracted. [ 65 ]
In a typical Voitenko compressor, a shaped charge accelerates hydrogen gas which in turn accelerates a thin disk up to about 40 km/s. [ 66 ] [ 67 ] A slight modification to the Voitenko compressor concept is a super-compressed detonation, [ 68 ] [ 69 ] a device that uses a compressible liquid or solid fuel in the steel compression chamber instead of a traditional gas mixture. [ 70 ] [ 71 ] A further extension of this technology is the explosive diamond anvil cell , [ 72 ] [ 73 ] [ 74 ] [ 75 ] utilizing multiple opposed shaped-charge jets projected at a single steel encapsulated fuel, [ 76 ] such as hydrogen. The fuels used in these devices, along with the secondary combustion reactions and long blast impulse, produce similar conditions to those encountered in fuel-air and thermobaric explosives. [ 77 ] [ 78 ] [ 79 ] [ 80 ]
The proposed Project Orion nuclear propulsion system would have required the development of nuclear shaped charges for reaction acceleration of spacecraft. Shaped-charge effects driven by nuclear explosions have been discussed speculatively, but are not known to have been produced in fact. [ 81 ] [ 82 ] [ 83 ] For example, the early nuclear weapons designer Ted Taylor was quoted as saying, in the context of shaped charges, "A one-kiloton fission device, shaped properly, could make a hole ten feet (3.0 m) in diameter a thousand feet (305 m) into solid rock." [ 84 ] Also, a nuclear driven explosively formed penetrator was apparently proposed for terminal ballistic missile defense in the 1960s. [ 85 ] [ 86 ] | https://en.wikipedia.org/wiki/Shaped_charge |
In digital communications shaping codes are a method of encoding that changes the distribution of signals to improve efficiency.
Typical digital communication systems uses M- Quadrature Amplitude Modulation ( QAM ) to communicate through an analog channel (specifically a communication channel with Gaussian noise ). For Higher bit rates(M) the minimum signal-to-noise ratio (SNR) required by a QAM system with Error Correcting Codes is about 1.53 dB higher than minimum SNR required by a Gaussian source(>30% more transmitter power) as given in Shannon–Hartley theorem
where
This 1.53 dB difference is called the shaping gap . Typically digital system will encode bits with uniform probability to maximize the entropy . Shaping code act as buffer between digital sources and modulator communication system. They will receive uniformly distributed data and convert it to Gaussian like distribution before presenting to the modulator. Shaping codes are helpful in reducing transmit power and thus reduce the cost of Power amplifier and the interference caused to other users in the vicinity.
Some of the methods used for shaping are described in the trellis shaping paper by Dr. G. D. Forney Jr. [ 1 ]
Shell mapping [ 2 ] is used in V.34 modems to get a shaping gain of .8 dB .
All the shaping schemes in the literature try to reduce the transmitted signal power. In future this may have find application in wireless networks where the interference from other nodes are becoming the major issue. | https://en.wikipedia.org/wiki/Shaping_codes |
In mathematics , the Shapiro inequality is an inequality proposed by Harold S. Shapiro in 1954. [ 1 ]
Suppose n is a natural number and x 1 , x 2 , …, x n are positive numbers and:
Then the Shapiro inequality states that
where x n +1 = x 1 and x n +2 = x 2 . The special case with n = 3 is Nesbitt's inequality .
For greater values of n the inequality does not hold, and the strict lower bound is γ n / 2 with γ ≈ 0.9891… (sequence A245330 in the OEIS ).
The initial proofs of the inequality in the pivotal cases n = 12 [ 2 ] and n = 23 [ 3 ] rely on numerical computations. In 2002, P.J. Bushell and J.B. McLeod published an analytical proof for n = 12 . [ 4 ]
The value of γ was determined in 1971 by Vladimir Drinfeld . Specifically, he proved that the strict lower bound γ is given by ψ (0) , where the function ψ is the convex hull of f ( x ) = e − x and g ( x ) = 2 / ( e x + e x /2 ) . (That is, the region above the graph of ψ is the convex hull of the union of the regions above the graphs of f and g .) [ 5 ] [ 6 ]
Interior local minima of the left-hand side are always ≥ n / 2 . [ 7 ]
The first counter-example was found by Lighthill in 1956, for n = 20 : [ 8 ]
where ϵ {\displaystyle \epsilon } is close to 0. Then the left-hand side is equal to 10 − ϵ 2 + O ( ϵ 3 ) {\displaystyle 10-\epsilon ^{2}+O(\epsilon ^{3})} , thus lower than 10 when ϵ {\displaystyle \epsilon } is small enough.
The following counter-example for n = 14 is by Troesch (1985): | https://en.wikipedia.org/wiki/Shapiro_inequality |
In mathematics, the Shapiro polynomials are a sequence of polynomials which were first studied by Harold S. Shapiro in 1951 when considering the magnitude of specific trigonometric sums . [ 1 ] In signal processing , the Shapiro polynomials have good autocorrelation properties and their values on the unit circle are small. [ 2 ] The first few members of the sequence are:
where the second sequence, indicated by Q , is said to be complementary to the first sequence, indicated by P .
The Shapiro polynomials P n ( z ) may be constructed from the Golay–Rudin–Shapiro sequence a n , which equals 1 if the number of pairs of consecutive ones in the binary expansion of n is even, and −1 otherwise. Thus a 0 = 1, a 1 = 1, a 2 = 1, a 3 = −1, etc.
The first Shapiro P n ( z ) is the partial sum of order 2 n − 1 (where n = 0, 1, 2, ...) of the power series
The Golay–Rudin–Shapiro sequence { a n } has a fractal-like structure – for example, a n = a 2 n – which implies that the subsequence ( a 0 , a 2 , a 4 , ...) replicates the original sequence { a n }. This in turn leads to remarkable
functional equations satisfied by f ( z ).
The second or complementary Shapiro polynomials Q n ( z ) may be defined in terms of this sequence, or by the relation Q n ( z ) = (−1) n z 2 n −1 P n (−1/ z ), or by the recursions
The sequence of complementary polynomials Q n corresponding to the P n is uniquely characterized by the following properties:
The most interesting property of the { P n } is that the absolute value of P n ( z ) is bounded on the unit circle by the square root of 2 ( n + 1) , which is on the order
of the L 2 norm of P n . Polynomials with coefficients from the set {−1, 1} whose maximum modulus on the unit circle is close to their mean modulus are useful for various applications in communication theory (e.g., antenna design and data compression ). Property (iii) shows that ( P , Q ) form a Golay pair .
These polynomials have further properties: [ 3 ] | https://en.wikipedia.org/wiki/Shapiro_polynomials |
The Shapiro reaction or tosylhydrazone decomposition is an organic reaction in which a ketone or aldehyde is converted to an alkene through an intermediate hydrazone in the presence of 2 equivalents of organolithium reagent . [ 1 ] [ 2 ] [ 3 ] The reaction was discovered by Robert H. Shapiro in 1967. [ 4 ] The Shapiro reaction was used in the Nicolaou Taxol total synthesis . [ 5 ] This reaction is very similar to the Bamford–Stevens reaction , which also involves the basic decomposition of tosyl hydrazones.
In a prelude to the actual Shapiro reaction, a ketone or an aldehyde is converted to the tosylhydrazone . Two equivalents of n -butyllithium gives the carbanion, which produces a carbon–carbon double bond , ejecting the tosyl anion. The resulting diazonium anion loses molecular nitrogen giving the vinyllithium species.
The reaction's directionality is controlled by the stereochemistry of the hydrazone, with deprotonation occurring cis to the tosylamide group. This is due to coordination by the nitrogen atom. [ 6 ]
The position of the alkene in the product is controlled by the site of deprotonation by the organolithium base. In general, the kinetically favored, less substituted site of differentially substituted tosylhydrazones is deprotonated selectively, leading to the less substituted vinyllithium intermediate. Although many secondary reactions exist for the vinyllithium functional group , in the Shapiro reaction in particular water is added, resulting in protonation to the alkene . [ 7 ] Other reactions of vinyllithium compounds include alkylation reactions with for instance alkyl halides . [ 8 ]
Importantly, the Shapiro reaction cannot be used to synthesize 1-lithioalkenes (and the resulting functionalized derivatives), as sulfonylhydrazones derived from aldehydes undergo exclusive addition of the organolithium base to the carbon of the C–N double bond. [ 9 ]
Traditional Shapiro reactions require stoichiometric (sometimes excess) amounts of base to generate the alkenyllithium reagents. To combat this problem, Yamamoto and coworkers developed an efficient stereoselective and regioselective route to alkenes using a combination of ketone phenylaziridinylhydrazones as arenesulfonylhydrazone equivalents with a catalytic amount of lithium amides.
The required phenylaziridinylhydrazone was prepared from the condensation of undecan-6-one with 1-amino-2-phenylaziridine. Treatment of the phenylaziridinylhydrazone with 0.3 equivalents of LDA in ether resulted in the alkene shown below with a cis : trans ratio of 99.4:0.6. The ratio was determined by capillary GLC analysis after conversion to the corresponding epoxides with mCPBA. The catalyst loading can be reduced to 0.05 equivalents in the case of a 30mmol scale reaction.
The high stereoselectivity is obtained by the preferential abstraction of the α-methylene hydrogen syn to the phenylaziridine, and is also accounted for by the internal chelation of the lithiated intermediated. [ 10 ]
The Shapiro reaction can also be combined with the Suzuki reaction to produce a variety of olefin products. Keay and coworkers have developed methodology that combines these reactions in a one pot process that does not require the isolation of the boronic acid , a setback of the traditional Suzuki coupling. This reaction has a wide scope, tolerating a slew of trisylhydrazones and aryl halides, as well as several solvents and Pd sources. [ 11 ]
The Shapiro reaction has been used to generate olefins towards to complex natural products. K. Mori and coworkers wanted to determine the absolute configuration of the phytocassane group of a class of natural products called phytoalexins . This was accomplished by preparing the naturally occurring (–)-phytocassane D from ( R )- Wieland-Miescher ketone . On the way to (–)-phytocassane D, a tricyclic ketone was subjected to Shapiro reaction conditions to yield the cyclic alkene product. [ 12 ] | https://en.wikipedia.org/wiki/Shapiro_reaction |
The Shapiro — Senapathy algorithm (S&S) is an algorithm for predicting splice junctions in genes of animals and plants. [ 1 ] [ 2 ] This algorithm has been used to discover disease-causing splice site mutations and cryptic splice sites.
A splice site is the border between an exon and intron in a gene. These sites contain a particular sequence motif , which is necessary for recognition and processing by the RNA splicing machinery. [ 1 ]
The S&S algorithm uses sliding windows of eight nucleotides, corresponding to the length of the splice site sequence motif, to identify these conserved sequences and thus potential splice sites. [ 1 ] Using a weighted table of nucleotide frequencies, the S&S algorithm outputs a consensus -based percentage for the possibility of the window containing a splice site. [ 1 ]
The S&S algorithm serves as the basis of other software tools, such as Human Splicing Finder, [ 3 ] Splice-site Analyzer Tool, [ 4 ] dbass (Ensembl), [ 5 ] Alamut, [ 6 ] and SROOGLE. [ 7 ]
By using the S&S algorithm, mutations and genes that cause many different forms of cancer have been discovered. For example, genes causing commonly occurring cancers including breast cancer , [ 8 ] [ 9 ] [ 10 ] ovarian cancer , [ 11 ] [ 12 ] [ 13 ] colorectal cancer , [ 14 ] [ 15 ] [ 16 ] leukemia , [ 17 ] [ 18 ] head and neck cancers , [ 19 ] [ 20 ] prostate cancer , [ 21 ] [ 22 ] retinoblastoma , [ 23 ] [ 24 ] squamous cell carcinoma , [ 25 ] [ 26 ] [ 27 ] gastrointestinal cancer , [ 28 ] [ 29 ] melanoma , [ 30 ] [ 31 ] liver cancer , [ 32 ] [ 33 ] Lynch syndrome , [ 34 ] [ 35 ] [ 15 ] skin cancer , [ 25 ] [ 36 ] [ 37 ] and neurofibromatosis [ 38 ] [ 39 ] have been found. In addition, splicing mutations in genes causing less commonly known cancers including gastric cancer, [ 40 ] [ 41 ] [ 28 ] gangliogliomas , [ 42 ] [ 43 ] Li-Fraumeni syndrome , Loeys–Dietz syndrome , Osteochondromas (bone tumor), Nevoid basal cell carcinoma syndrome , [ 11 ] and Pheochromocytomas [ 13 ] have been identified.
Specific mutations in different splice sites in various genes causing breast cancer (e.g., BRCA1, PALB2), ovarian cancer (e.g., SLC9A3R1, COL7A1, HSD17B7), colon cancer (e.g., APC, MLH1, DPYD), colorectal cancer (e.g., COL3A1, APC, HLA-A), skin cancer (e.g., COL17A1, XPA, POLH), and Fanconi anemia (e.g., FANC, FANA) have been uncovered. The mutations in the donor and acceptor splice sites in different genes causing a variety of cancers that have been identified by S&S are shown in Table 1 .
Specific mutations in different splice sites in various genes that cause inherited disorders, including, for example, Type 1 diabetes (e.g., PTPN22, TCF1 (HCF-1A)), hypertension (e.g., LDL, LDLR, LPL), Marfan syndrome (e.g., FBN1, TGFBR2, FBN2), cardiac diseases (e.g., COL1A2, MYBPC3, ACTC1), eye disorders (e.g., EVC, VSX1) have been uncovered. A few example mutations in the donor and acceptor splice sites in different genes causing a variety of inherited disorders identified using S&S are shown in Table 2 .
causing a truncated protein [ 55 ]
site 17 nt upstream in the exon [ 56 ]
stop codon will produce a truncated protein lacking the binding sites for myosin and titin [ 57 ]
More than 100 immune system disorders affect humans, including inflammatory bowel diseases , multiple sclerosis , systemic lupus erythematosus , bloom syndrome , familial cold autoinflammatory syndrome , and dyskeratosis congenita . The Shapiro–Senapathy algorithm has been used to discover genes and mutations involved in many immune disorder diseases, including Ataxia telangiectasia , B-cell defects, epidermolysis bullosa , and X-linked agammaglobulinemia .
Xeroderma pigmentosum , an autosomal recessive disorder is caused by faulty proteins formed due to new preferred splice donor site identified using S&S algorithm and resulted in defective nucleotide excision repair. [ 31 ]
Type I Bartter syndrome (BS) is caused by mutations in the gene SLC12A1. S&S algorithm helped in disclosing the presence of two novel heterozygous mutations c.724 + 4A > G in intron 5 and c.2095delG in intron 16 leading to complete exon 5 skipping. [ 32 ]
Mutations in the MYH gene, which is responsible for removing the oxidatively damaged DNA lesion are cancer-susceptible in the individuals. The IVS1+5C plays a causative role in the activation of a cryptic splice donor site and the alternative splicing in intron 1, S&S algorithm shows, guanine (G) at the position of IVS+5 is well conserved (at the frequency of 84%) among primates. This also supported the fact that the G/C SNP in the conserved splice junction of the MYH gene causes the alternative splicing of intron 1 of the β type transcript. [ 33 ]
Splice site scores were calculated according to S&S to find EBV infection in X-linked lymphoproliferative disease. [ 61 ] Identification of Familial tumoral calcinosis (FTC) is an autosomal recessive disorder characterized by ectopic calcifications and elevated serum phosphate levels and it is because of aberrant splicing. [ 62 ]
Applying the S&S technology platform in modern clinical genomics research hasadvance diagnosis and treatment of human diseases.
In the modern era of Next Generation Sequencing (NGS) technology, S&S is applied in clinical practice extensively. Clinicians and molecular diagnostic laboratories apply S&S using various computational tools including HSF, [ 3 ] SSF, [ 4 ] and Alamut. [ 6 ] It is aiding in the discovery of genes and mutations in patients whose disease are stratified or when the disease in a patient is unknown based on clinical investigations.
In this context, S&S has been applied on cohorts of patients in different ethnic groups with various cancers and inherited disorders. A few examples are given below.
Dr. Senapathy's original objective in developing a method for identifying splice sites was to find complete genes in raw uncharacterized genomic sequence that could be used in the human genome project. [ 73 ] [ 2 ] In the landmark paper with this objective, [ 73 ] he described the basic method for identifying the splice sites within a given sequence based on the Position Weight Matrix (PWM) [ 1 ] of the splicing sequences in different eukaryotic organism groups for the first time. He also created the first exon detection method by defining the basic characteristics of an exon as the sequence bounded by an acceptor and a donor splice sites that had S&S scores above a threshold, and by an ORF that was mandatory for an exon. An algorithm for finding complete genes based on the identified exons was also described by Dr. Senapathy for the first time. [ 73 ] [ 2 ]
Dr. Senapathy demonstrated that only deleterious mutations in the donor or acceptor splice sites that would drastically make the protein defective would reduce the splice site score (later known as the Shapiro–Senapathy score), and other non-deleterious variations would not reduce the score. The S&S method was adapted for researching the cryptic splice sites caused by mutations leading to diseases. This method for detecting deleterious splicing mutations in eukaryotic genes has been used extensively in disease research in the humans, animals and plants over the past three decades, as described above.
The basic method for splice site identification, and for defining exons and genes was subsequently used by researchers in finding splice sites, exons and eukaryotic genes in a variety of organisms. These methods also formed the basis of all subsequent tools development for discovering genes in uncharacterized genomic sequences. It also was used in a different computational approaches including machine learning and neural network, and in alternative splicing research.
The Shapiro–Senapathy algorithm has been used to determine the various aberrant splicing mechanisms in genes due to deleterious mutations in the splice sites, which cause numerous diseases. Deleterious splice site mutations impair the normal splicing of the gene transcripts, and thereby make the encoded protein defective. A mutant splice site can become “weak” compared to the original site, due to which the mutated splice junction becomes unrecognizable by the spliceosomal machinery. This can lead to the skipping of the exon in the splicing reaction, resulting in the loss of that exon in the spliced mRNA (exon-skipping). On the other hand, a partial or complete intron could be included in the mRNA due to a splice site mutation that makes it unrecognizable (intron inclusion). A partial exon-skipping or intron inclusion can lead to premature termination of the protein from the mRNA, which will become defective leading to diseases. The S&S has thus paved the way to determine the mechanisms by which a deleterious mutation could lead to a defective protein, resulting in different diseases depending on which gene is affected.
An example of splicing aberration (exon skipping) caused by a mutation in the donor splice site in the exon 8 of MLH1 gene that led to colorectal cancer is given below. This example shows that a mutation in a splice site within a gene can lead to a profound effect in the sequence and structure of the mRNA, and the sequence, structure and function of the encoded protein, leading to disease.
The proper identification of splice sites has to be highly precise as the consensus splice sequences are very short and there are many other sequences similar to the authentic splice sites within gene sequences, which are known as cryptic, non-canonical, or pseudo splice sites. When an authentic or real splice site is mutated, any cryptic splice sites present close to the original real splice site could be erroneously used as authentic site, resulting in an aberrant mRNA. The erroneous mRNA may include a partial sequence from the neighboring intron or lose a partial exon, which may result in a premature stop codon. The result may be a truncated protein that would have lost its function completely.
Shapiro–Senapathy algorithm can identify the cryptic splice sites, in addition to the authentic splice sites. Cryptic sites can often be stronger than the authentic sites, with a higher S&S score. However, due to the lack of an accompanying complementary donor or acceptor site, this cryptic site will not be active or used in a splicing reaction. When a neighboring real site is mutated to become weaker than the cryptic site, then the cryptic site may be used instead of the real site, resulting in a cryptic exon and an aberrant transcript.
Numerous diseases have been caused by cryptic splice site mutations or usage of cryptic splice sites due to the mutations in authentic splice sites. [ 78 ] [ 79 ] [ 80 ] [ 81 ] [ 82 ]
S&S has also been used in RNA splicing research in many animals [ 83 ] [ 84 ] [ 85 ] [ 86 ] [ 87 ] and plants. [ 88 ] [ 89 ] [ 90 ] [ 91 ] [ 92 ]
The mRNA splicing plays a fundamental role in gene functional regulation. Very recently, it has been shown that A to G conversions at splice sites can lead to mRNA mis-splicing in Arabidopsis. [ 88 ] The splicing and exon–intron junction prediction coincided with the GT/AG rule (S&S) in the Molecular characterization and evolution of carnivorous sundew (Drosera rotundifolia L.) class V b-1,3-glucanase. [ 89 ] Unspliced (LSDH) and spliced (SSDH) transcripts of NAD+ dependent sorbitol dehydroge nase (NADSDH) of strawberry (Fragaria ananassa Duch., cv. Nyoho) were investigated for phytohormonal treatments. [ 90 ]
Ambra1 is a positive regulator of autophagy, a lysosome-mediated degradative process involved both in physiological and pathological conditions. Nowadays, this function of Ambra1 has been characterized only in mammals and zebrafish. [ 84 ] Diminution of rbm24a or rbm24b gene products by morpholino knockdown resulted in significant disruption of somite formation in mouse and zebrafish. [ 85 ] Dr.Senapathy algorithm used extensively to study intron-exon organization of fut8 genes. The intron-exon boundaries of Sf 9 fut8 were in agreement with the consensus sequence for the splicing donor and acceptor sites concluded using S&S. [ 86 ] | https://en.wikipedia.org/wiki/Shapiro–Senapathy_algorithm |
The Shapley–Sawyer Concentration Class is a classification system on a scale of one to twelve using Roman numerals for globular clusters according to their concentration. The most highly concentrated clusters such as M75 are classified as Class I, with successively diminishing concentrations ranging to Class XII, such as Palomar 12 . (The class is sometimes given with numbers [Class 1–12] rather than with Roman numerals.)
From 1927 to 1929, Harlow Shapley and Helen Sawyer Hogg began categorizing clusters according to the degree of concentration the system has toward the core using this scale. This became known as the Shapley–Sawyer Concentration Class . [ 1 ]
[ 2 ]
This astronomy -related article is a stub . You can help Wikipedia by expanding it .
This star cluster–related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Shapley–Sawyer_Concentration_Class |
The Shapley–Shubik power index was formulated by Lloyd Shapley and Martin Shubik in 1954 to measure the powers of players in a voting game. [ 1 ]
The constituents of a voting system, such as legislative bodies, executives, shareholders, individual legislators, and so forth, can be viewed as players in an n -player game . Players with the same preferences form coalitions. Any coalition that has enough votes to pass a bill or elect a candidate is called winning. The power of a coalition (or a player) is measured by the fraction of the possible voting sequences in which that coalition casts the deciding vote, that is, the vote that first guarantees passage or failure. [ 2 ]
The power index is normalized between 0 and 1. A power of 0 means that a coalition has no effect at all on the outcome of the game; and a power of 1 means a coalition determines the outcome by its vote. Also the sum of the powers of all the players is always equal to 1.
There are some algorithms for calculating the power index, e.g., dynamic programming techniques, enumeration methods and Monte Carlo methods. [ 3 ]
Since Shapley and Shubik have published their paper, several axiomatic approaches have been used to mathematically study the Shapley–Shubik power index, with the anonymity axiom, the null player axiom, the efficiency axiom and the transfer axiom being the most widely used.
Suppose decisions are made by majority rule in a body consisting of A, B, C, D, who have 3, 2, 1 and 1 votes, respectively. The majority vote threshold is 4. There are 4! = 24 possible orders for these members to vote:
For each voting sequence the pivot voter – that voter who first raises the cumulative sum to 4 or more – is bolded. Here, A is pivotal in 12 of the 24 sequences. Therefore, A has an index of power 1/2. The others have an index of power 1/6. Curiously, B has no more power than C and D. When you consider that A's vote determines the outcome unless the others unite against A, it becomes clear that B, C, D play identical roles. This reflects in the power indices.
Suppose that in another majority-rule voting body with n + 1 {\displaystyle n+1} members, in which a single strong member has k {\displaystyle k} votes and the remaining n {\displaystyle n} members have one vote each. In this case the strong member has a power index of k n + 1 {\displaystyle {\dfrac {k}{n+1}}} (unless k > n + 1 {\displaystyle k>n+1} , in which case the power index is simply 1 {\displaystyle 1} ). Note that this is more than the fraction of votes which the strong member commands. Indeed, this strong member has only a fraction k n + k {\displaystyle {\dfrac {k}{n+k}}} of the votes. Consider, for instance, a company which has 1000 outstanding shares of voting stock. One large shareholder holds 400 shares, while 600 other shareholders hold 1 share each. This corresponds to n = 600 {\displaystyle n=600} and k = 400 {\displaystyle k=400} . In this case the power index of the large shareholder is approximately 0.666 (or 66.6%), even though this shareholder holds only 40% of the stock. The remaining 600 shareholder have a power index of less than 0.0006 (or 0.06%). Thus, the large shareholder holds over 1000 times more voting power as each other shareholder, while holding only 400 times as much stock. [ 1 ]
The above can be mathematically derived as follows. Note that a majority is reached if at least t ( n , k ) = ⌊ n + k 2 ⌋ + 1 {\displaystyle t(n,k)=\left\lfloor {\dfrac {n+k}{2}}\right\rfloor +1} votes are cast in favor. If k ≥ n + 1 {\displaystyle k\geq n+1} , the strong member clearly holds all the power, since in this case k ≥ t ( n , k ) {\displaystyle k\geq t(n,k)} (i.e., the votes of the strong member alone meet the majority threshold). Suppose now that k ≤ n + 1 {\displaystyle k\leq n+1} and that in a randomly chosen voting sequence, the strong member votes as the r {\displaystyle r} th member. This means that after the first r − 1 {\displaystyle r-1} member have voted, r − 1 {\displaystyle r-1} votes have been cast in favor, while after the first r {\displaystyle r} members have voted, r − 1 + k {\displaystyle r-1+k} votes have been cast in favor. The vote of strong member is pivotal if the former does not meet the majority threshold, while the latter does. That is, r − 1 < t ( n , k ) {\displaystyle r-1<t(n,k)} , and r − 1 + k ≥ t ( n , k ) {\displaystyle r-1+k\geq t(n,k)} . We can rewrite this condition as t ( n , k ) + 1 − k ≤ r < t ( n , k ) + 1 {\displaystyle t(n,k)+1-k\leq r<t(n,k)+1} . Note that our condition of k ≤ n + 1 {\displaystyle k\leq n+1} ensures that 1 ≤ t ( n , k ) + 1 − k {\displaystyle 1\leq t(n,k)+1-k} and t ( n , k ) + 1 ≤ n + 2 {\displaystyle t(n,k)+1\leq n+2} (i.e., all of the permitted values of r {\displaystyle r} are feasible). Thus, the strong member is the pivotal voter if r {\displaystyle r} takes on one of the k {\displaystyle k} values of t ( n , k ) + 1 − k {\displaystyle t(n,k)+1-k} up to but not including t ( n , k ) + 1 {\displaystyle t(n,k)+1} . Since each of the n + 1 {\displaystyle n+1} possible values of r {\displaystyle r} is associated with the same number of voting sequences, this means that the strong member is the pivotal voter in a fraction k n + 1 {\displaystyle {\dfrac {k}{n+1}}} of the voting sequences. That is, the power index of the strong member is k n + 1 {\displaystyle {\dfrac {k}{n+1}}} .
The index has been applied to the analysis of voting in the Council of the European Union . [ 4 ]
The index has been applied to the analysis of voting in the United Nations Security Council . The UN Security Council is made up of fifteen member states, of which five (the United States of America, Russia, China, France and the United Kingdom) are permanent members of the council. For a motion to pass in the Council, it needs the support of every permanent member and the support of four non permanent members. This is equivalent to a voting body where the five permanent members have eight votes each, the ten other members have one vote each and there is a quota of forty four votes, as then there would be fifty total votes, so you need all five permanent members and then four other votes for a motion to pass.
Note that a non-permanent member is pivotal in a permutation if and only if they are in the ninth position to vote and all five permanent members have already voted. Suppose that we have a permutation in which a non-permanent member is pivotal. Then there are three non-permanent members and five permanent that have to come before this pivotal member in this permutation.
Therefore, there are ( 9 3 ) {\displaystyle \textstyle {\binom {9}{3}}} ways of choosing these members and so 8! × ( 9 3 ) {\displaystyle \textstyle {\binom {9}{3}}} different orders of the members before the pivotal voter. There would then
be 6! ways of choosing the remaining voters after the pivotal voter. As there are a total of 15! permutations of 15 voters, the Shapley-Shubik power index of a non-permanent member is: ( 9 3 ) ( 8 ! ) ( 6 ! ) 15 ! = 4 2145 {\displaystyle {\frac {{\binom {9}{3}}(8!)(6!)}{15!}}={\frac {4}{2145}}} .
Hence the power index of a permanent member is 421 2145 {\displaystyle {\frac {421}{2145}}} .
This is a simple implementation of the above example in Python. | https://en.wikipedia.org/wiki/Shapley–Shubik_power_index |
Shapr3D is 3D modeling software initially released for iPadOS to work with the Apple Pencil and multi-touch gesturing as a workflow. It has been ported to run on macOS and Windows . [ 1 ] [ 2 ] [ 3 ]
Shapr3D launched using the open source Open Cascade Engine in 2016 but switched over to Parasolid geometric modeling kernel. [ 4 ] [ 5 ] The founder is István Csanády and the company is headquartered in Budapest, Hungary . [ 6 ] In 2020, Shapr3D won the Apple Design Award . [ 7 ]
This software article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Shapr3D |
The Shared Source Common Language Infrastructure (SSCLI), previously codenamed Rotor , is Microsoft 's shared source implementation of the CLI , the core of .NET . Although the SSCLI is not suitable for commercial use due to its license, it does make it possible for programmers to examine the implementation details of many .NET libraries and to create modified CLI versions. Microsoft provides the Shared Source CLI as a reference CLI implementation suitable for educational use.
Beginning in 2001, Microsoft announced they would release part of the .NET Framework infrastructure source code in Shared source through ECMA , as part of the C# and CLI standardization process. [ 1 ]
In March 2002, Microsoft released version 1.0 of the Shared Source Common Language Infrastructure , also called Rotor . [ 2 ] The Shared Source CLI was initially pre-configured to run on Windows , but could also be built on FreeBSD (version 4.7 or newer), and Mac OS X 10.2. It was designed such that the only thing that needed to be customized to port the Shared Source CLI to a different platform was a thin Platform Abstraction Layer (PAL).
The last 2.0 version of SSCLI was released in March 2006, [ 3 ] and contains most of the classes and features of version 2.0 of the .NET Framework . [ 4 ] SSCLI 2.0 can be downloaded directly from Microsoft downloads and requires Perl and Visual Studio 2005 running on Windows XP SP2 to compile. [ 5 ] Microsoft has not updated the source and build requirements since 2006. Even Microsoft MVPs , important part of Microsoft community ecosystem, complained about the lack of support for other Visual Studio versions and operating systems. [ 6 ] However, a non-official patch for Visual Studio 2008 [ 7 ] was provided by a Microsoft employee in the MSDN Blog and another for Visual Studio 2010 was released by the community. [ 8 ]
Later versions of .NET, originally known as .NET Core and now referred to simply as .NET, have been open sourced under the more permissive MIT license .
The Shared Source CLI use the non-free Microsoft Shared Source Common Language Infrastructure license . This license allows modifications and redistribution of the code for personal or academic usages, but they can't be used for commercial products. [ 9 ] | https://en.wikipedia.org/wiki/Shared_Source_Common_Language_Infrastructure |
A shared mesh (also known as 'traditional' or 'best effort' mesh) is a wireless mesh network that uses a single radio to communicate via mesh backhaul links to all the neighboring nodes in the mesh. This is a first generation mesh where the total available bandwidth of the radio channel is ‘shared’ between all the neighboring nodes in the mesh. The capacity of the channel is further consumed by traffic being forwarded from one node to the next in the mesh – reducing the end to end traffic that can be passed. Because bandwidth is shared amongst all nodes in the mesh, and because every link in the mesh uses additional capacity, this type of network offers much lower end to end transmission rates than a switched mesh and degrades in capacity as nodes are added to the mesh.
Wireless mesh nodes typically include both mesh backhaul links and client access. A dual radio shared mesh node uses separate access and mesh backhaul radios. Only the mesh backhaul radio is shared. In a single radio shared mesh node, access and mesh backhaul are collapsed onto a single radio. Now the available bandwidth is shared between both the mesh links and client access, further reducing the end to end traffic available. | https://en.wikipedia.org/wiki/Shared_mesh |
Shark tourism is a form of eco-tourism that allows people to dive with sharks in their natural environment. This benefits local shark populations by educating tourists and through funds raised by the shark tourism industry. Communities that previously relied on shark finning to make their livelihoods are able to make a larger profit from diving tours while protecting the local environment. People can get close to the sharks by free- or scuba diving or by entering the water in a protective cage for more aggressive species. Many of these dives are done by private companies and are often baited to ensure shark sightings, a practice which is highly controversial and under review in many areas. [ citation needed ]
Species commonly targeted in shark tourism activities include:
Great white shark viewing is available at the Neptune Islands in South Australia , [ 2 ] South Africa , Isla Guadalupe in Mexico , and New Zealand . Great white sharks are usually viewed using shark cages to protect the diver. Because of the exceptional visibility underwater in Isla Guadalupe, more outside the cage diving is done than anywhere else. [ 3 ]
The great white shark viewing industry was founded in the 1970s by pioneer Australian diver and great white attack survivor Rodney Fox in South Australia. He was the sole worldwide operator until the South African industry was founded in early 1989 by Pieter van der Walt who was joined shortly thereafter by pioneer diver and underwater photographer George Askew who handled promotions and put South African cage diving "on the map" with the publicity he got – until they split in January 1992, after they, together with famous Australian divers Ron Taylor and Valerie Taylor , did the world's first dive amongst great white sharks without a cage and completely unprotected. [ 4 ]
This dive was directly responsible for the upsurge in shark tourism – especially free-diving (i.e. out of cage) swimming with big sharks. When operators around the world became aware that the great white was quite approachable and not likely to attack they considered whether the other sharks with bad reputations like tigers, bulls and oceanics' might be safe enough to swim with too. This proved to be the case and shark tourism has become a multi-million-dollar a year industry. [ 5 ] In attempts to protect the great white shark species, in some places such as South Australia, there is mandatory logbook reporting and photograph/identification required to monitor how cage-diving tourism may impact white sharks involved in these tourism interactions. [ 6 ]
The Bahamas is a favorite region for pelagic sharks. Divers in the Bahamas experience reef sharks and tiger sharks while they are hand-fed. Isla Guadalupe, Mexico , has been named a Biosphere Reserve in an effort to control the shark diving activities there. Although the practice of shark diving proves to be controversial, it has been proven very effective in attracting tourists. Whale sharks , while not traditionally harvested for their fins but are sometimes harvested for their meat, have also benefited from shark tourism because of snorkelers getting into the water with the gentle giants. In the Philippines snorkelers must maintain a distance of four feet from the sharks and there is a fine and possible jail time for anyone who touches the animals. [ 7 ]
Several shark species are known from shark feeding dive sites within the Pacific Region. Grey reef sharks are the main feeders in places such as the Great Barrier Reef , Micronesia and Tahiti . Silvertips and black tip reef sharks tend to be more seen around the Papua New Guinea coastlines. Bull sharks are found around Mexico, Playa del Carmen in particular. [ 8 ]
Whale sharks attract a large amount of tourists each year to South Ari Atoll in the Republic of Maldives, yet, there is still some ambiguity regarding the economic extent of the attraction of these animals. Thus, making conservation/ implementation of management methods difficult to conduct. [ 9 ]
Additionally, whale sharks in the waters of the small town of Oslob, on Cebu islands in the Philippines, The sharks have become a top tourist attraction, local governments in the Philippines have followed along in the legalization of feeding these animals in attempt to attract more tourists. Although a huge commercial success, there is growing concern for the implementation of regulation and protection for the whale sharks and its marine environment. [ 10 ]
The coral reefs in the Philippines are being harmed greatly by the overpopulation of sharks and people in the area. As the population increases immensely so does the opportunity for the coral reefs to diminish. Sharks are overpopulating because they are being fed by tour operators and it is attracting many more sharks to the area than there naturally would be. [ citation needed ] This is causing the sharks to be more aggressive with people because they are getting too comfortable with people because they are associating feeding time with the people that are tossing the food to them. [ clarification needed ] [ citation needed ]
This type of shark tourism is done by professionals who dive down with the individuals that are partaking in the tourism event. A diver takes a small group of people down approximately 40 meters deep where the shark actions takes place. [ citation needed ] [ dubious – discuss ] Often sharks do not pay much attention to the divers, but in rare cases when there are threatening times the operator uses his/her training skills to prevent an attack from occurring. [ dubious – discuss ] [ citation needed ]
Shark cage diving is scuba diving or snorkeling where the observer remains inside a protective cage designed to prevent sharks from making contact with the divers. Shark cage diving is used for scientific observation, underwater cinematography, and as a tourist activity. Sharks may be attracted to the vicinity of the cage by the use of bait, in a procedure known as chumming , which has attracted some controversy as it is claimed to potentially alter the natural behaviour of sharks in the vicinity of swimmers.
Similar cages are also used purely as a protective measure for divers working in waters where potentially dangerous shark species are known to be present. In this application the shark-proof cage may be used as a refuge, or as a diving stage during descent and ascent, particularly during staged decompression where the divers may be vulnerable while constrained to a specific depth in mid-water for several minutes. In other applications a mobile cage may be carried by the diver while harvesting organisms such as abalone .
Previous economic valuation of whale shark tourism (in US million dollars).
Valuations reported in other currencies were converted to US$ using the average official rate for the year of 2007.
(season duration)
expenditure
WS excursions
2007, unpublished data a
[ 11 ] [ clarification needed ]
Whale sharks are considered a vulnerable species, and in certain areas such as Ningaloo Marine Park, they are entirely protected. [ 12 ] The whale sharks in the area are considered highly valuable in the ecotourism industry, as the industry provides numerous jobs to local people and brings in US$12 million annually. Tourist interest in wildlife tourism continues to grow, and the whale shark tourism industry is expected to increase through the year 2020. [ 13 ]
Shark tourism opened up a beneficial economic opportunity all over the globe. This helps the poverty stricken areas of the Bahamas, Moorea, Maldives, Australia and many more places around the globe. A study done in French Polynesia concluded that a single reef shark is worth US$100,000 a year compared to the $100 an individual may receive for harvesting a sharks' body parts. [ 14 ] Shark tourism is positively impacting the lives of many, as companies are not only making money for themselves and the community, but many profits benefit reef conservation efforts. Tourism providers often provide food to attract sharks to areas where they can be more easily viewed, although this is controversial. [ 15 ] In Australia's Great Barrier Reef Marine Park and the states of Hawaii and Florida shark feeding is prohibited. [ 16 ] The initial law in Hawaii that prohibited shark feeding was passed in 2002, but many companies were not following this law and locals pushed for stricter enforcement. [ 17 ]
Ningaloo Marine Park in Western Australia is the site of an annual whale shark aggregation. This site is a very popular tourist site, as whale sharks are incredibly gentle creatures that pose very little threat to humans. Introduced in 1997 and revised to its current version in 2013, the Department of Parks and Wildlife is responsible for a whale shark management program designed to protect the whale shark species and regulate human interaction with them. [ 18 ]
The shark tourism industry is meant to educate and increase awareness of the natural environment as well as generate profits for the local people. Data from the years 2006 to 2010 on whale sharks at Ningaloo Reef, Western Australia, has been evaluated to determine the scale of the tourism operations and the spatial and temporal distribution of interactions between whale sharks and humans; for example: whale shark tours at Ningaloo increased by about 70%. [ 19 ] The whale shark management program of Ningaloo Marine Park relies on the Conservation and Land Management Act of 1984 (CALM Act) and the Wildlife Conservation Act of 1950 . The CALM Act requires tour operators to obtain a commercial tourist activity license, and the Wildlife Conservation Act requires a wildlife interaction license for each protected species a tour may come in contact with. This includes the whale sharks but is not limited to whales, other shark species, and dugongs . [ 20 ] Under these laws, the Western Australian government is able to regulate how tourists interact with whale sharks and to what extent. A maximum of 15 operators are allowed to obtain licenses at a given time. In addition, only one tour vessel is allowed to travel to the whale sharks while the rest must stay 250 meters away. Only ten swimmers are allowed in the water at a time, which controls the crowding of the area, and tourists are prohibited from feeding or touching the whale sharks. [ 21 ] The shark tourism industry conducted a search, using a global questionnaire; detecting that 42% of operators conducting shark tourism used an attractant to lure sharks, and that 93% of operators surveyed regulated their practices using codes of conduct. [ 22 ]
Sharks , or "mano" as they are called by the local Hawaiians, are viewed as sacred. Early Hawaiians worshiped and protected the sharks which they saw as family gods or "aumaka". [ 23 ] In recent years, shark cage diving has become a very profitable tourist attraction in the state. Native Hawaiians were not pleased with this at first due to the fact that the companies were luring in the sharks using bait; they viewed these animals as sacred and feeding them for entertainment was said to be unjust. [ 24 ] There was also speculations that by feeding them, the sharks would begin to associate the boats and humans with food. For this reason, a law was passed in Hawaii in 2002 that banned the feeding of sharks in state waters, which is about three miles off shore. [ 25 ]
Beqa Lagoon is home to eight species of sharks, each of which are very prominent around feeding sites. Shark diving and shark feeding is very popular in the area, locals have been swimming with the sharks for close to three thousand years. The local people have many myths about these creatures passed down from antiquity. They are easily spotted in the waters of Beqa Lagoon Resort, which is their primary feeding ground. Shark tourism in places such as this is very profitable in Fiji, generating around US$42 million. [ clarification needed ] [ 26 ]
Palau is home to three species of sharks; the grey reef shark, the leopard shark, and the whitetip reef sharks. Palau's waters have many coral reefs, which are home to grey reef sharks, the most commonly seen of the three. Whitetip reef sharks are also seen around coral reefs, and are much more curious than the other sharks. Many tourists and locals are fascinated by these creatures, so that shark diving has become a big part of many tourists incentive to go to Palau. Studies have shown that shark diving and shark tourism in general is a major contributor to the economy of Palau. Over US$18 million is generated every year, which accounts for close to 10% of all domestic product in the country. The local communities and government benefit, receiving over $1 million and US$1.5 million respectively. [ citation needed ]
South African is known for conservation of sharks and diversity of species on the coastline. Cape Town is known for Great whites and Seven-gill sharks and Aliwal Shoal and Protea Banks are known for ragged-tooth sharks (also known as grey nurse or spotted sand tiger sharks), hammerhead schools, white tips reef sharks, oceanic black tip sharks, bull sharks (Zambezi), tiger sharks and the occasional great white sighting. These sites providing experiences to scuba divers and cage divers. [ 27 ]
Many people are involved in interest groups such as the late iDive Sharks Network [ 28 ] that aim to celebrate and promote safe and responsible shark diving activities. [ 29 ] | https://en.wikipedia.org/wiki/Shark_tourism |
Sharkbook is a global database for identifying and tracking sharks , particularly whale sharks , using uploaded photos and videos.In addition to identifying and tracking sharks, the site allows people to "adopt a shark" and get updates on specific animals.
Sharkbook is the result of collaboration between Simon J Pierce of the Marine Megafauna Foundation and Jason Holmberg of Wild Me. The software is Open Source and is now being used by other biology projects. [ 1 ] [ 2 ] [ 3 ]
Whale sharks have unique spot patterning on their sides, similar to a human fingerprint , which allows for individual identification. Scuba divers around the world can photograph sharks and upload their identification photographs to the Sharkbook website, supporting global research and conservation efforts. [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] Additionally, the software automatically searches social media sites like YouTube and Instagram to look for images of whale sharks and adds them to the database. [ 2 ]
Sharkbook software uses special pattern-matching software to identify the unique spots on each shark. This software and algorithms were originally adapted from NASA star tracking software [ 2 ] used on the Hubble Space Telescope . [ 3 ] [ 9 ] This software uses a scale-invariant feature transform (SIFT) algorithm, which can cope with complications presented by highly variable spot patterns and low contrast photographs. [ 4 ] [ 10 ] [ 11 ]
This citizen science tool is free to use by researchers worldwide. Sharkbook represents a global initiative to centralize shark sightings and facilitate research on these vulnerable species. [ 12 ] [ 13 ] [ 14 ] [ 15 ] | https://en.wikipedia.org/wiki/Sharkbook |
Sharklet , manufactured by Sharklet Technologies, is a bio-inspired plastic sheet product structured to impede microorganism growth, particularly bacterial growth . It is marketed for use in hospitals and other places with a relatively high potential for bacteria to spread and cause infections. [ 1 ]
The inspiration for Sharklet's texture came through analysis of the texture of shark skin , which does not attract barnacles or other biofouling , unlike ship hulls and other smooth surfaces. The texture was later found to also repel microbial activity. [ 2 ]
Sharklet is a bio-inspired material that was invented by Anthony Brennan, a materials science and engineering professor at the University of Florida , while working to improve antifouling technology for ships and submarines at Pearl Harbor . [ 3 ]
Brennan noticed that sharks do not get fouled. He discovered that shark skin denticles are structured in a characteristic diamond -repeating micro-pattern with millions of small ribs [ 3 ] at the micrometer scale. His mathematical model for the texture of a substance that would deter microorganisms from settling corresponds to the width-to-height ratio of shark denticle riblets. When compared to smooth surfaces, [ 4 ] the first test resulted in an 85% reduction in green algae settlement.
Adherence prevention and translocation restriction have been demonstrated and are believed to significantly reduce the risk of device-associated infections. Sharklet's topography creates mechanical stress on settling bacteria, a phenomenon known as mechanotransduction . The surface variations induce stress gradients within the plane, which disrupt normal cell functions, forcing the microorganism to adjust its contact area on each topographical feature to equalize the stresses. [ 5 ] Sharklet is made, however, with the same material as other plastics.
Sharklet micro-patterns can be incorporated onto the surfaces of a variety of medical devices during the manufacturing process. Sharklet micro-patterns have been tested to control the bio-adhesion of marine microorganisms , pathogenic bacteria , and eukaryotic cells . They reduce S. aureus and S. epidermidis colonization in a simulated vascular environment by around 70% when compared to smooth controls. This micro-pattern similarly reduces platelet adhesion and fibrin sheath formation by approximately 80%. [ 6 ] An in vitro study found that it reduced the colonization of S. aureus and P. aeruginosa bacterial pathogens in a central venous catheters -relevant thermoplastic polyurethane . [ 7 ] | https://en.wikipedia.org/wiki/Sharklet_(material) |
In mathematics , Sharkovskii's theorem (also spelled Sharkovsky , Sharkovskiy , Šarkovskii or Sarkovskii ), named after Oleksandr Mykolayovych Sharkovsky , who published it in 1964, is a result about discrete dynamical systems . [ 1 ] One of the implications of the theorem is that if a discrete dynamical system on the real line has a periodic point of period 3, then it must have periodic points of every other period.
For some interval I ⊂ R {\displaystyle I\subset \mathbb {R} } , suppose that f : I → I {\displaystyle f:I\to I} is a continuous function . The number x {\displaystyle x} is called a periodic point of period m {\displaystyle m} if f ( m ) ( x ) = x {\displaystyle f^{(m)}(x)=x} , where f ( m ) {\displaystyle f^{(m)}} denotes the iterated function obtained by composition of m {\displaystyle m} copies of f {\displaystyle f} . The number x {\displaystyle x} is said to have least period m {\displaystyle m} if, in addition, f ( k ) ( x ) ≠ x {\displaystyle f^{(k)}(x)\neq x} for all 0 < k < m {\displaystyle 0<k<m} . Sharkovskii's theorem concerns the possible least periods of periodic points of f {\displaystyle f} . Consider the following ordering of the positive integers , sometimes called the Sharkovskii ordering: [ 2 ] 3 5 7 9 11 … ( 2 n + 1 ) ⋅ 2 0 … 3 ⋅ 2 5 ⋅ 2 7 ⋅ 2 9 ⋅ 2 11 ⋅ 2 … ( 2 n + 1 ) ⋅ 2 1 … 3 ⋅ 2 2 5 ⋅ 2 2 7 ⋅ 2 2 9 ⋅ 2 2 11 ⋅ 2 2 … ( 2 n + 1 ) ⋅ 2 2 … 3 ⋅ 2 3 5 ⋅ 2 3 7 ⋅ 2 3 9 ⋅ 2 3 11 ⋅ 2 3 … ( 2 n + 1 ) ⋅ 2 3 … ⋮ … 2 n … 2 4 2 3 2 2 2 1 {\displaystyle {\begin{array}{cccccccc}3&5&7&9&11&\ldots &(2n+1)\cdot 2^{0}&\ldots \\3\cdot 2&5\cdot 2&7\cdot 2&9\cdot 2&11\cdot 2&\ldots &(2n+1)\cdot 2^{1}&\ldots \\3\cdot 2^{2}&5\cdot 2^{2}&7\cdot 2^{2}&9\cdot 2^{2}&11\cdot 2^{2}&\ldots &(2n+1)\cdot 2^{2}&\ldots \\3\cdot 2^{3}&5\cdot 2^{3}&7\cdot 2^{3}&9\cdot 2^{3}&11\cdot 2^{3}&\ldots &(2n+1)\cdot 2^{3}&\ldots \\&\vdots \\\ldots &2^{n}&\ldots &2^{4}&2^{3}&2^{2}&2&1\end{array}}}
It consists of:
This ordering is a total order : every positive integer appears exactly once somewhere on this list. However, it is not a well-order . In a well-order, every subset would have an earliest element, but in this order there is no earliest power of two.
Sharkovskii's theorem states that if f {\displaystyle f} has a periodic point of least period m {\displaystyle m} , and m {\displaystyle m} precedes n {\displaystyle n} in the above ordering, then f {\displaystyle f} has also a periodic point of least period n {\displaystyle n} .
One consequence is that if f {\displaystyle f} has only finitely many periodic points, then they must all have periods that are powers of two. Furthermore, if there is a periodic point of period three, then there are periodic points of all other periods.
Sharkovskii's theorem does not state that there are stable cycles of those periods, just that there are cycles of those periods. For systems such as the logistic map , the bifurcation diagram shows a range of parameter values for which apparently the only cycle has period 3. In fact, there must be cycles of all periods there, but they are not stable and therefore not visible on the computer-generated picture.
The assumption of continuity is important. Without this assumption, the discontinuous piecewise linear function f : [ 0 , 3 ) → [ 0 , 3 ) {\displaystyle f:[0,3)\to [0,3)} defined as: f : x ↦ { x + 1 f o r 0 ≤ x < 2 x − 2 f o r 2 ≤ x < 3 {\displaystyle f:x\mapsto {\begin{cases}x+1&\mathrm {for\ } 0\leq x<2\\x-2&\mathrm {for\ } 2\leq x<3\end{cases}}} for which every value has period 3, would be a counterexample. Similarly essential is the assumption of f {\displaystyle f} being defined on an interval. Otherwise f : x ↦ ( 1 − x ) − 1 {\displaystyle f:x\mapsto (1-x)^{-1}} , which is defined on real numbers except the one: R ∖ { 1 } , {\displaystyle \mathbb {R} \setminus \{1\},} and for which every non-zero value has period 3, would be a counterexample.
Sharkovskii also proved the converse theorem: every upper set of the above order is the set of periods for some continuous function from an interval to itself. In fact all such sets of periods are achieved by the family of functions T h : [ 0 , 1 ] → [ 0 , 1 ] {\displaystyle T_{h}:[0,1]\to [0,1]} , x ↦ min ( h , 1 − 2 | x − 1 / 2 | ) {\displaystyle x\mapsto \min(h,1-2|x-1/2|)} for h ∈ [ 0 , 1 ] {\displaystyle h\in [0,1]} , except for the empty set of periods which is achieved by T : R → R {\displaystyle T:\mathbb {R} \to \mathbb {R} } , x ↦ x + 1 {\displaystyle x\mapsto x+1} . [ 3 ] [ 4 ]
On the other hand, with additional information on the combinatorial structure of the interval map acting on the points in a periodic orbit, a period-n point may force period-3 (and hence all periods). Namely, if the orbit type (the cyclic permutation generated by the map acting on the points in the periodic orbit) has a so-called stretching pair, then this implies the existence of a periodic point of period-3. It can be shown (in an asymptotic sense) that almost all cyclic permutations admit at least one stretching pair, and hence almost all orbit types imply period-3. [ 5 ]
Tien-Yien Li and James A. Yorke showed in 1975 that not only does the existence of a period-3 cycle imply the existence of cycles of all periods, but in addition it implies the existence of an uncountable infinitude of points that never map to any cycle ( chaotic points )—a property known as period three implies chaos . [ 6 ]
Sharkovskii's theorem does not immediately apply to dynamical systems on other topological spaces. It is easy to find a circle map with periodic points of period 3 only: take a rotation by 120 degrees, for example. But some generalizations are possible, typically involving the mapping class group of the space minus a periodic orbit. For example, Peter Kloeden showed that Sharkovskii's theorem holds for triangular mappings, i.e., mappings for which the component f i depends only on the first i components x 1 ,..., x i . [ 7 ] | https://en.wikipedia.org/wiki/Sharkovskii's_theorem |
Sharon Beder is an environmentalist [ 1 ] and former professor in the Faculty of Arts at the University of Wollongong in New South Wales , Australia. [ 2 ] Her research has focused on how power relationships are maintained and challenged, particularly by corporations and professions. She has written 11 books, and many articles, book chapters and conference papers, as well as designing teaching resources and educational websites. [ 2 ]
Beder was born in 1956 in Wellington, New Zealand , granddaughter of Jewish immigrants from Scotland, England and eastern Europe, before the second world war, and daughter of Jacqui and Yoss Beder. [ 1 ]
Beder initially trained and worked as a civil engineer in New Zealand [ 3 ] before becoming interested in the social, political and philosophical aspects of engineering and then environmental politics. She completed a PhD in Science and Technology Studies at the University of New South Wales in 1989 based on research into the process of engineering decision-making using a case study on the development of Sydney's sewerage system. [ 4 ] [ 5 ]
Before joining the University of Wollongong in 1992, Beder was Environmental Education Co-ordinator at the University of Sydney . She has also been Chairperson of the Environmental Engineering Branch of the Institution of Engineers , Sydney, President of the Society for Social Responsibility in Engineering, and a director of the Earth Foundation Australia.
Beder was included in a list of "Australia's most influential engineers", published by Engineers Australia in 2004. [ 6 ] She was also included in Bulletin Magazine's "Smart 100" in 2003. [ 7 ] Her awards include: | https://en.wikipedia.org/wiki/Sharon_Beder |
The Sharp Actius MM10 Muramasas was a laptop computer ( subnotebook ) developed by Sharp Corporation which started selling in 2003.
It was named after a sword master, Muramasa Tenji, and is one of the thinnest computers in the world at 20 mm thick at its maximum. It had a battery life of 2.5 hours, a 1 GHz Transmeta Crusoe processor, 256 MB of memory, a Wi-Fi module (incorporated into the laptop), a 15 GB hard drive and a $1,499 price tag. [ 1 ]
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Sharp_Actius_MM10_Muramasas |
The Sharp PC-3000 was an MS-DOS -based palmtop computer introduced in 1991. [ 1 ] [ 2 ] The "SPC" was designed and developed by Distributed Information Processing Research Ltd. ("DIP") in the UK. DIP had earlier designed the Atari Portfolio and the two machines shared many design features both in hardware and software.
As with desktop IBM PCs , this one-pound device's [ 3 ] [ 4 ] screen displayed 80-column 25 lines. [ 5 ]
The machine was one of the first to support the PC card interface , at the time known as PCMCIA.
Printers, floppy drives, dial-up modems, Fax modems were among the supported peripheral devices.
Choice were MS-DOS 3.3 and Microsoft Windows 3.0 (running in real mode with a mouse). [ 6 ]
The machine came with a suite of built in application providing a simple word processor, calculator and 1-2-3 compatible spreadsheet.
With some tweaking, it was also possible to run WordPerfect , Microsoft Word and Microsoft Excel .
A 2 MB model was produced: the 3100. [ 7 ] [ 6 ]
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Sharp_PC-3000 |
Sharpless asymmetric dihydroxylation (also called the Sharpless bishydroxylation ) is the chemical reaction of an alkene with osmium tetroxide in the presence of a chiral quinine ligand to form a vicinal diol . The reaction has been applied to alkenes of virtually every substitution, often high enantioselectivities are realized, with the chiral outcome controlled by the choice of dihydroquinidine (DHQD) vs dihydroquinine (DHQ) as the ligand. Asymmetric dihydroxylation reactions are also highly site selective, providing products derived from reaction of the most electron-rich double bond in the substrate. [ 1 ] [ 2 ] [ 3 ]
It is common practice to perform this reaction using a catalytic amount of osmium tetroxide, which after reaction is regenerated with reoxidants such as potassium ferricyanide [ 4 ] [ 5 ] or N -methylmorpholine N -oxide . [ 6 ] [ 7 ] This dramatically reduces the amount of the highly toxic and very expensive osmium tetroxide needed. These four reagents are commercially available premixed (" AD-mix "). The mixture containing (DHQ) 2 -PHAL is called AD-mix-α, and the mixture containing (DHQD) 2 -PHAL is called AD-mix-β. [ 8 ]
Such chiral diols are important in organic synthesis . The introduction of chirality into nonchiral reactants through usage of chiral catalysts is an important concept in organic synthesis . This reaction was developed principally by K. Barry Sharpless building on the already known racemic Upjohn dihydroxylation , for which he was awarded a share of the 2001 Nobel Prize in Chemistry .
Alkene dihydroxylation by osmium tetroxide is an old and extremely useful method for the functionalization of alkenes. However, since osmium(VIII) reagents like osmium tetroxide (OsO 4 ) are expensive and extremely toxic, it has become desirable to develop catalytic variants of this reaction. Some stoichiometric terminal oxidants that have been employed in these catalytic reactions include potassium chlorate , hydrogen peroxide ( Milas hydroxylation ), N -Methylmorpholine N -oxide (NMO, Upjohn dihydroxylation ), tert -butyl hydroperoxide ( t BHP), and potassium ferricyanide (K 3 Fe(CN) 6 ). K. Barry Sharpless was the first to develop a general, reliable enantioselective alkene dihydroxylation, referred to as the Sharpless asymmetric dihydroxylation (SAD). Low levels of OsO 4 are combined with a stoichiometric ferricyanide oxidant in the presence of chiral nitrogenous ligands to create an asymmetric environment around the oxidant.
The reaction mechanism of the Sharpless dihydroxylation begins with the formation of the osmium tetroxide – ligand complex ( 2 ). A [3+2]-cycloaddition with the alkene ( 3 ) gives the cyclic intermediate 4 . [ 9 ] [ 10 ] Basic hydrolysis liberates the diol ( 5 ) and the reduced osmate ( 6 ). Methanesulfonamide (CH 3 SO 2 NH 2 ) has been identified as a catalyst to accelerate this step of the catalytic cycle and if frequently used as an additive to allow non-terminal alkene substrates to react efficiently at 0 °C. [ 8 ] Finally, the stoichiometric oxidant regenerates the osmium tetroxide – ligand complex ( 2 ).
The mechanism of the Sharpless asymmetric dihydroxylation has been extensively studied and a potential secondary catalytic cycle has been identified (see below). [ 11 ] [ 12 ] If the osmylate ester intermediate is oxidized before it dissociates, then an osmium(VIII)-diol complex is formed which may then dihydroxylate another alkene. [ 13 ] Dihydroxylations resulting from this secondary pathway generally suffer lower enantioselectivities than those resulting from the primary pathway. A schematic showing this secondary catalytic pathway is shown below. This secondary pathway may be suppressed by using a higher molar concentration of ligand.
In his original report Sharpless suggested the reaction proceeded via a [2+2] cycloaddition of OsO 4 onto the alkene to give an osmaoxetane intermediate (see below). [ 14 ] This intermediate would then undergo a 1,1- migratory insertion to form an osmylate ester which after hydrolysis would give the corresponding diol. In 1989 E. J. Corey published a slightly different variant of this reaction and suggested that the reaction most likely proceeded via a [3+2] cycloaddition of OsO 4 with the alkene to directly generate the osmylate ester. [ 15 ] Corey's suggestion was based on a previous computational study done by Jorgensen and Hoffmann which determined the [3+2] reaction pathway to be the lower energy pathway. In addition Corey reasoned that steric repulsions in the octahedral intermediate would disfavor the [2+2] pathway.
The next ten years saw numerous publications by both Corey and Sharpless, each supporting their own version of the mechanism. While these studies were not able to distinguish between the two proposed cyclization pathways, they were successful in shedding light on the mechanism in other ways. For example, Sharpless provided evidence for the reaction proceeding via a step-wise mechanism. [ 16 ] Additionally both Sharpless and Corey showed that the active catalyst possesses a U-shaped chiral binding pocket. [ 17 ] [ 18 ] [ 19 ] Corey also showed that the catalyst obeys Michaelis-Menten kinetics and acts like an enzyme pocket with a pre-equilibrium. [ 20 ] In the February 1997 issue of the Journal of the American Chemical Society Sharpless published the results of a study (a Hammett analysis) which he claimed supported a [2+2] cyclization over a [3+2]. [ 21 ] In the October issue of the same year, however, Sharpless also published the results of another study conducted in collaboration with Ken Houk and Singleton which provided conclusive evidence for the [3+2] mechanism. [ 10 ] Thus Sharpless was forced to concede the decade-long debate.
Crystallographic evidence has shown that the active catalyst possesses a pentacoordinate osmium species held in a U-shaped binding pocket. The nitrogenous ligand holds OsO 4 in a chiral environment making approach of one side of the olefin sterically hindered while the other is not. [ 20 ]
Numerous catalytic systems and modifications have been developed for the SAD. Given below is a brief overview of the various components of the catalytic system:
In general Sharpless asymmetric dihydroxylation favors oxidation of the more electron-rich alkene (scheme 1). [ 22 ]
In this example SAD gives the diol of the alkene closest to the (electron-withdrawing) para-methoxybenzoyl group, albeit in low yield. This is likely due to the ability of the aryl ring to interact favorably with the active site of the catalyst via π-stacking. In this manner the aryl substituent can act as a directing group. [ 23 ]
The diastereoselectivity of SAD is set primarily by the choice of ligand (i.e. AD-mix-α versus AD-mix-β), however factors such as pre-existing chirality in the substrate or neighboring functional groups may also play a role. In the example shown below, the para-methoxybenzoyl substituent serves primarily as a source of steric bulk to allow the catalyst to differentiate the two faces of the alkene. [ 23 ]
It is often difficult to obtain high diastereoselectivity on cis -disubstituted alkenes when both ends of the olefin have similar steric environments. | https://en.wikipedia.org/wiki/Sharpless_asymmetric_dihydroxylation |
The Sharpless epoxidation reaction is an enantioselective chemical reaction to prepare 2,3-epoxyalcohols from primary and secondary allylic alcohols . The oxidizing agent is tert -butyl hydroperoxide . The method relies on a catalyst formed from titanium tetra(isopropoxide) and diethyl tartrate . [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ]
2,3-Epoxyalcohols can be converted into diols , aminoalcohols, and ethers . The reactants for the Sharpless epoxidation are commercially available and relatively inexpensive. [ 6 ] K. Barry Sharpless published a paper on the reaction in 1980 and was awarded the 2001 Nobel Prize in Chemistry for this and related work on asymmetric oxidations . The prize was shared with William S. Knowles and Ryōji Noyori .
5–10 mol% of the catalyst is typical. The presence of 3Å molecular sieves (3Å MS) is necessary. [ 7 ] The structure of the catalyst is uncertain although it is thought to be a dimer of [Ti(tartrate)(OR) 2 ]. [ 8 ]
The epoxidation of allylic alcohols is a well-utilized conversion in fine chemical synthesis. The chirality of the product of a Sharpless epoxidation is sometimes predicted with the following mnemonic . A rectangle is drawn around the double bond in the same plane as the carbons of the double bond (the xy-plane ), with the allylic alcohol in the bottom right corner and the other substituents in their appropriate corners. In this orientation, the (−) diester tartrate preferentially interacts with the top half of the molecule, and the (+) diester tartrate preferentially interacts with the bottom half of the molecule. This model seems to be valid despite substitution on the olefin. Selectivity decreases with larger R 1 , but increases with larger R 2 and R 3 (see introduction). [ 1 ]
However, this method incorrectly predicts the product of allylic 1,2-diols. [ 9 ]
The Sharpless epoxidation can also give kinetic resolution of a racemic mixture of secondary 2,3-epoxyalcohols. While the yield of a kinetic resolution process cannot be higher than 50%, the enantiomeric excess approaches 100% in some reactions. [ 10 ] [ 11 ]
The Sharpless epoxidation is viable with a large range of primary and secondary alkenic alcohols. Furthermore, with the exception noted above, a given dialkyl tartrate will preferentially add to the same face independent of the substitution on the alkene .To demonstrate the synthetic utility of the Sharpless epoxidation, the Sharpless group created synthetic intermediates of various natural products: methymycin, erythromycin , leukotriene C-1, and (+)- disparlure . [ 12 ]
As one of the few highly enantioselective reactions during its time, many manipulations of the 2,3-epoxyalcohols have been developed. [ 13 ]
The Sharpless epoxidation has been used for the total synthesis of various saccharides , terpenes , leukotrienes , pheromones , and antibiotics . [ 6 ]
The main drawback of this protocol is the necessity of the presence of an allylic alcohol . The Jacobsen epoxidation , an alternative method to enantioselectively oxidise alkenes, overcomes this issue and tolerates a wider array of functional groups . [ citation needed ] For specifically glycidic epoxides , the Jørgensen-Córdova epoxidation avoids the need to reduce the carbonyl and then reoxidize, and has more efficient catalyst turnover. [ 14 ] | https://en.wikipedia.org/wiki/Sharpless_epoxidation |
The Sharpless oxyamination (often known as Sharpless aminohydroxylation ) is the chemical reaction that converts an alkene to a vicinal amino alcohol . The reaction is related to the Sharpless dihydroxylation , which converts alkenes to vicinal diols. [ 1 ] Vicinal amino-alcohols are important products in organic synthesis and recurring pharmacophores in drug discovery .
Akin to the dihydroxylation, the oxyamination involves the cycloaddition of the alkene to an imido Os(VIII) intermediate of the type OsO 3 (NR). Such species are generated by treatment of osmium tetroxide with the sodium chloramines. Typical procedures combine chloramine-T , alkene, an osmium catalyst, and a chiral ligand. [ 2 ] Related procedures use benzyl carbamate (CbzNH 2 ), sodium hydroxide, tert-butyl hypochlorite to give CbzNCl(Na). [ 3 ]
Early papers in the development of this methodology. | https://en.wikipedia.org/wiki/Sharpless_oxyamination |
Sharps waste is a form of biomedical waste composed of used "sharps", which includes any device or object used to puncture or lacerate the skin. Sharps waste is classified as biohazardous waste and must be carefully handled. Common medical materials treated as sharps waste are hypodermic needles ,
disposable scalpels and blades,
contaminated glass and certain plastics , and
guidewires used in surgery. [ 1 ]
In addition to needles and blades, anything attached to them, such as syringes and injection devices, is also considered sharps waste.
Blades can include razors , scalpels , X-Acto knives , scissors , or any other items used for cutting in a medical or biological research setting, regardless of whether they have been contaminated with biohazardous material. While glass and sharp plastic are considered sharps waste, their handling methods can vary.
Glass items which have been contaminated with a biohazardous material are treated with the same concern as needles and blades, even if unbroken. If glass is contaminated, it is still often treated as a sharp, because it can break during the disposal process. Contaminated plastic items which are not sharp can be disposed of in a bio hazardous waste receptacle instead of a sharps container.
Injuries from sharps waste can pose a large public health concern, as used sharps may contain biohazardous material. It is possible for this waste to spread blood-borne pathogens if contaminated sharps penetrate the skin. The spread of these pathogens is directly responsible for the transmission of blood-borne diseases , such as hepatitis B (HBV), hepatitis C (HCV), and HIV . Health care professionals expose themselves to the risk of transmission of these diseases when handling sharps waste. The large volume handled by health care professionals on a daily basis increases the chance that an injury may occur.
The general public can occasionally be at risk of sustaining injuries from sharps waste as well when hypodermic needles are improperly disposed of by injection drug users.
Hard plastic containers known as sharps containers are used to safely dispose of hypodermic needles and other sharp medical instruments, such as IV catheters and disposable scalpels. They are often sealable and self-locking, as well as rigid, which prevents waste from penetrating or damaging the sides of the container. In the United States, sharps containers are usually red and marked with the universal biohazard symbol for ease of recognition. Elsewhere, they are often yellow. Waste is loaded into the container until it reaches a certain height, which is usually around three-quarters of the way full. At that point, the container is emptied or disposed of.
Sharps containers may be single use, in which case they are disposed of along with the waste they contain, or reusable, in which case they are robotically emptied and sterilized before being returned for re-use. Airports and large institutions commonly have sharps containers available in restrooms for safe disposal for users of injection drugs, such as insulin-dependent diabetics . Medical facilities and laboratories are also equipped with sharps containers, as well as the equipment required to safely sterilize or dispose of them. This minimizes the distance the containers have to travel and the number of people to come in contact with the sharps waste. Smaller clinics or offices in the US without such facilities are required by federal regulations to hire the services of a company that specializes in transporting and properly disposing of the hazardous wastes.
Extreme care must be taken in the management and disposal of sharps waste. The goal in sharps waste management is to safely handle all materials until they can be properly disposed of. The final step in the disposal of sharps waste is to dispose of them in an autoclave . [ further explanation needed ] A less common approach is to incinerate them; typically only chemotherapy sharps waste is incinerated. Steps must be taken along the way to minimize the risk of injury from this material, while maximizing the amount of sharps material disposed. Strict hospital protocols and government regulations that instruct health care providers on how to manage sharps waste help ensure that the waste is handled as effectively and safely as possible.
Disposal methods vary by country and locale, but common methods of disposal are either by truck service or, in the United States , by disposal of sharps through the mail. Truck service involves trained personnel collecting sharps waste, and often medical waste , at the point of generation, and hauling it away by truck to a destruction facility. Similarly, the mail-back sharps disposal method allows generators to ship sharps waste to the disposal facility directly through the U.S. mail in specially designed and approved shipping containers. Mail-back sharps disposal allows waste generators to dispose of smaller amounts of sharps more economically than if they were to hire out a truck service. Recent [ when? ] legislation in France has stated that pharmaceutical companies supplying self injection medications are responsible for the disposal of spent needles. Previously popular needle clippers and caps are no longer acceptable as safety devices, and either sharps box or needle destruction devices are required. [ citation needed ]
A report by the Canadian Mental Health Association found that supervised injection sites help reduce the amount of discarded needles on streets. [ 2 ]
With more than sixteen billion injections administered annually worldwide, [ 3 ] needles are the largest contributor to sharps waste. For this reason, many new technologies surrounding injections have been developed, mostly related to safety mechanisms. As these technologies have been developed, governments have attempted to make them commonplace to ensure sharps waste safety. In 2000, the Needlestick Safety and Prevention Act was passed, along with the 2001 Bloodborne Pathogens Standard . [ 4 ]
Safety syringes help reduce occurrences of accidental needlesticks. One of the most recent developments has been the auto-disable injection device. These injection devices automatically disable after a single use. This can be done by retracting the needle back into the syringe or rendering the syringe plunger inoperable. With the injection device now inoperable, it cannot be reused. Shielding the needle after the injection is another approach for safe management of sharps. These are hands free methods usually involving a hinging cap that can be pressed on a table to seal the needle. Another technology in sharps waste management relating to injections is the needle remover . Varying approaches can be taken with the main goal to separate the needle from the syringe. This allows the sharp needle to be quarantined and disposed of separately from the syringe. There is debate around the use of these devices, as they involve an additional step in the handling of sharps waste.
Sharps waste is of great concern in developing and transitional regions of the world. Factors such as high disease prevalence and lack of health care professionals amplify the dangers involved with sharps waste, and the cost of newer disposal technology makes them unlikely to be used.
As with the rest of the world, injection waste make up the largest portion of sharps waste. However, injection use is much more prevalent in the developing world. One of the contributors to this increase is a larger emphasis placed on injections for therapeutic purposes. It has been estimated that 95% of all injections in developing regions are for therapeutic purposes. [ 5 ] The average person has been estimated to receive 1.5 injections per year. [ 5 ] Newly developed injection technologies are rarely used to provide these injections due to added costs. Therefore, the majority of injections are given with standard disposable syringes in developing regions. [ 6 ]
The infrastructure of developing regions is not equipped to deal with this large volume of contaminated sharps waste. Contrary to the industrialized world, disposal incinerators and transportation networks are not always available. Cost restraints make the purchase of single use disposable containers unrealistic. Facilities are often overwhelmed with patients and understaffed with educated workers. Demand on these facilities can limit the emphasis or enforcement of waste disposal protocols. These factors leave a dangerous quantity of sharps waste in the environment. Contrasts between the industrialized and developing world segment can be seen in accidental needle stick injuries. These occur at a rate of .18 to .74 per person per year in industrialized nations and .93 to 4.68 per person per year in developing and transitional nations (Hutin, Hauri, Armstrong, 2003). [ citation needed ]
Improper sharps management is a major factor involved in what is categorized as unsafe injections. Annually these account for 21 million, 2 million, and 260,000 of new HBV, HCV, and HIV infections annually. [ 7 ] 40-65% of new HBV and HCV infections are due to percutaneous occupational exposure. [ 8 ] | https://en.wikipedia.org/wiki/Sharps_waste |
In high energy physics detectors , shashlik is a layout for a sampling calorimeter . It refers to a stack of alternating slices of absorber (e.g. lead , brass ) and scintillator materials (crystal or plastic), which is penetrated by a wavelength shifting fiber running perpendicular to the absorber and scintillator tiles. [ 1 ]
The absorber has a small interaction length, so that a particle radiates energy in a short track. The scintillator material produces visible light when transversed by the particle's radiated energy. This occurs with an electromagnetic calorimeter , in the form of photons and/or electron + positron pairs. The energy of the particle may be then measured by the intensity of scintillation light produced by the various scintillator slices. An example detector that uses a shashlik electromagnetic calorimeter is the LHCb detector. [ 2 ]
This type of calorimeter was likely named after the shashlik , a popular form of shish kebab sold by street vendors in the former Soviet Union , by the Russian and Ukrainian scientists who first proposed it. [ 3 ]
This particle physics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Shashlik_(physics) |
In computing, a shatter attack is a programming technique employed by hackers on Microsoft Windows operating systems to bypass security restrictions between processes in a session . A shatter attack takes advantage of a design flaw in Windows's message-passing system whereby arbitrary code could be injected into any other running application or service in the same session, that makes use of a message loop . This could result in a privilege escalation exploit. [ 1 ]
Shatter attacks became a topic of intense conversation in the security community in August 2002 after the publication of Chris Paget's paper "Exploiting design flaws in the Win32 API for privilege escalation". [ 2 ] The paper, which coined the term "shatter attack", explained the process by which an application could execute arbitrary code in another application. This could occur because Windows allows unprivileged applications to send messages to message loops of higher-privileged application—and some messages can have the address of a callback function in the application's address space as their parameters. If an attacker manages to put their own string into the memory of the higher-privileged application (say by pasting shellcode to an edit box) at a known location, they could then send WM_TIMER messages with callback function parameters set to point to the attacker's string.
A few weeks after the publication of this paper, Microsoft responded, noting that: "The paper is correct that this situation exists, and it does correctly describe its effect. ... Where the paper errs is in claiming that this is a flaw in Windows. In reality, the flaw lies in the specific, highly privileged service. By design, all services within the interactive desktop are peers, and can levy requests upon each other. As a result, all services in the interactive desktop effectively have privileges commensurate with the most highly privileged service there." [ 3 ]
In December 2002, Microsoft issued a patch for Windows NT 4.0 , Windows 2000 , and Windows XP that closed off some avenues of exploitation. [ 4 ] This was only a partial solution, however, as the fix was limited to services included with Windows that could be exploited using this technique; the underlying design flaw still existed and could still be used to target other applications or third-party services. [ 5 ] With Windows Vista , Microsoft aimed to solve the problem in two ways: First, local users no longer log into Session 0, thus separating the message loop of a logged-in user's session from high-privilege system services, which are loaded into Session 0. Second, a new feature called User Interface Privilege Isolation (UIPI) was introduced, whereby processes can be further protected against shatter attacks by assigning an Integrity Level to each process. [ 6 ] Attempts to send messages to a process with a higher Integrity Level will fail, even if both processes are owned by the same user. However, not all interactions between processes at different Integrity Levels are prevented by UIPI. [ 6 ] Internet Explorer 7 , for example, uses the UIPI feature to limit the extent to which its rendering components interact with the rest of the system.
The way sessions are instantiated was redesigned in Windows Vista and Windows Server 2008 to provide additional protection against shatter attacks. Local user logins were moved from Session 0 to Session 1, thus separating the user's processes from system services that could be vulnerable. [ 7 ] [ 8 ]
This creates backward compatibility issues, however, as some software was designed with the assumption that the service is running in the same session as the logged-in user. To support this view, Windows Vista and Windows Server 2008 introduced a Windows service called " Interactive Services Detection " that enables access to dialogs created by interactive services when they appear. The interactive user is shown a dialog box and is offered the ability to switch to Session 0 to access the dialog box. [ 9 ] This capability was removed in the Windows 10 Creators Update . [ 10 ] | https://en.wikipedia.org/wiki/Shatter_attack |
In mathematics, a sheaf of planes is the set of all planes that have the same common line . [ 1 ] [ 2 ] It may also be known as a fan of planes or a pencil of planes .
When extending the concept of line to the line at infinity , a set of parallel planes can be seen as a sheaf of planes intersecting in a line at infinity. To distinguish it from the more general definition, the adjective parallel can be added to it, resulting in the expression parallel sheaf of planes . [ 3 ] | https://en.wikipedia.org/wiki/Sheaf_of_planes |
In geology , shear is the response of a rock to deformation usually by compressive stress and forms particular textures. Shear can be homogeneous or non-homogeneous, and may be pure shear or simple shear . Study of geological shear is related to the study of structural geology , rock microstructure or rock texture and fault mechanics .
The process of shearing occurs within brittle , brittle-ductile, and ductile rocks. Within purely brittle rocks, compressive stress results in fracturing and simple faulting .
Rocks typical of shear zones include mylonite , cataclasite , S-tectonite and L-tectonite , pseudotachylite , certain breccias and highly foliated versions of the wall rocks .
A shear zone is a tabular to sheetlike, planar or curviplanar zone composed of rocks that are more highly strained than rocks adjacent to the zone. Typically this is a type of fault , but it may be difficult to place a distinct fault plane into the shear zone. Shear zones may form zones of much more intense foliation , deformation , and folding . En echelon veins or fractures may be observed within shear zones.
Many shear zones host ore deposits as they are a focus for hydrothermal flow through orogenic belts . They may often show some form of retrograde metamorphism from a peak metamorphic assemblage and are commonly metasomatised .
Shear zones can be only inches wide, or up to several kilometres wide. Often, due to their structural control and presence at the edges of tectonic blocks, shear zones are mappable units and form important discontinuities to separate terranes. As such, many large and long shear zones are named, identical to fault systems.
When the horizontal displacement of this faulting can be measured in the tens or hundreds of kilometers of length, the fault is referred to as a megashear. Megashears often indicate the edges of ancient tectonic plates. [ 1 ]
The mechanisms of shearing depend on the pressure and temperature of the rock and on the rate of shear which the rock is subjected to. The response of the rock to these conditions determines how it accommodates the deformation.
Shear zones which occur in more brittle rheological conditions (cooler, less confining pressure ) or at high rates of strain, tend to fail by brittle failure; breaking of minerals, which are ground up into a breccia with a milled texture.
Shear zones which occur under brittle-ductile conditions can accommodate much deformation by enacting a series of mechanisms which rely less on fracture of the rock and occur within the minerals and the mineral lattices themselves. Shear zones accommodate compressive stress by movement on foliation planes.
Shearing at ductile conditions may occur by fracturing of minerals and growth of sub-grain boundaries, as well as by lattice glide . This occurs particularly on platy minerals, especially micas.
Mylonites are essentially ductile shear zones.
During the initiation of shearing, a penetrative planar foliation is first formed within the rock mass. This manifests as realignment of textural features, growth and realignment of micas and growth of new minerals.
The incipient shear foliation typically forms normal to the direction of principal shortening, and is diagnostic of the direction of shortening. In symmetric shortening, objects flatten on this shear foliation much the same way that a round ball of treacle flattens with gravity.
Within asymmetric shear zones, the behavior of an object undergoing shortening is analogous to the ball of treacle being smeared as it flattens, generally into an ellipse. Within shear zones with pronounced displacements a shear foliation may form at a shallow angle to the gross plane of the shear zone. This foliation ideally manifests as a sinusoidal set of foliations formed at a shallow angle to the main shear foliation, and which curve into the main shear foliation. Such rocks are known as L-S tectonites.
If the rock mass begins to undergo large degrees of lateral movement, the strain ellipse lengthens into a cigar shaped volume. At this point shear foliations begin to break down into a rodding lineation or a stretch lineation. Such rocks are known as L-tectonites.
Very distinctive textures form as a consequence of ductile shear. An important group of microstructures observed in ductile shear zones are S-planes, C-planes and C' planes.
The sense of shear shown by both S-C and S-C' structures matches that of the shear zone in which they are found.
Other microstructures which can give sense of shear include:
Transpression regimes are formed during oblique collision of tectonic plates and during non-orthogonal subduction . Typically a mixture of oblique-slip thrust faults and strike-slip or transform faults are formed. Microstructural evidence of transpressional regimes can be rodding lineations , mylonites , augen-structured gneisses , mica fish and so on.
A typical example of a transpression regime is the Alpine Fault zone of New Zealand , where the oblique subduction of the Pacific Plate under the Indo-Australian Plate is converted to oblique strike-slip movement. Here, the orogenic belt attains a trapezoidal shape dominated by oblique splay faults , steeply-dipping recumbent nappes and fault-bend folds.
The Alpine Schist of New Zealand is characterised by heavily crenulated and sheared phyllite . It is being pushed up at the rate of 8 to 10 mm per year, and the area is prone to large earthquakes with a south block up and west oblique sense of movement.
Transtension regimes are oblique tensional environments. Oblique, normal geologic fault and detachment faults in rift zones are the typical structural manifestations of transtension conditions. Microstructural evidence of transtension includes rodding or stretching lineations , stretched porphyroblasts , mylonites, etc.
Diagrams and definitions of shear ( Wayback Machine ), by University of the West of England , Bristol. Archive copy incomplete, 12/31/2012. | https://en.wikipedia.org/wiki/Shear_(geology) |
In solid mechanics , a shear band (or, more generally, a strain localization ) is a narrow zone of intense strain due to shearing , usually of plastic nature, developing during severe deformation of ductile materials.
As an example, a soil (overconsolidated silty-clay) specimen is shown in Fig. 1, after an axialsymmetric compression test. Initially the sample was cylindrical in shape and, since symmetry was tried to be preserved during the test, the cylindrical shape was maintained for a while during the test and the deformation was homogeneous, but at extreme loading two X-shaped shear bands had formed and the subsequent deformation was strongly localized (see also the sketch on the right of Fig. 1).
Although not observable in brittle materials (for instance glass at room temperature), shear bands or, more generally, ‘localized deformations’ usually develop within a broad range of ductile materials (alloys, metals, granular materials, plastics, polymers, and soils) and even in quasi-brittle materials (concrete, ice, rock, and some ceramics).
The relevance of the shear banding phenomena is that they precede failure, since extreme deformations occurring within shear bands lead to intense damage and fracture. Therefore, the formation of shear bands is the key to the understanding of failure in ductile materials, a research topic of great importance for the design of new materials and for the exploiting of existing materials in extreme conditions. As a consequence, localization of deformation has been the focus of an intense research activity since the middle of the 20th century.
Shear band formation is an example of a material instability, corresponding to an abrupt loss of homogeneity of deformation occurring in a solid sample subject to a loading path compatible with continued uniform deformation. In this sense, it may be interpreted as a deformation mechanism ‘alternative’ to a trivial one and therefore a bifurcation or loss of uniqueness of a ‘perfect’ equilibrium path. The distinctive character of this bifurcation is that it may occur even in an infinite body (or under the extreme constraint of smooth contact with a rigid constraint).
Consider an infinite body made up of a nonlinear material, quasi-statically deformed in a way that stress and strain may remain homogeneous. The incremental response of this nonlinear material is assumed for simplicity linear, so that it can be expressed as a relation between a stress increment σ ˙ {\displaystyle {\dot {\sigma }}} and a strain increment ε ˙ {\displaystyle {\dot {\varepsilon }}} , through a fourth-order constitutive tensor C {\displaystyle \mathbb {C} } as
where the fourth-order constitutive tensor C {\displaystyle \mathbb {C} } depends on the current state, i.e. the current stress, the current strain and, possibly, other constitutive parameters (for instance, hardening variables for metals, or density for granular materials).
Conditions are sought for the emergence of a surface of discontinuity (of unit normal vector n {\displaystyle \mathbf {n} } ) in the incremental stress and strain. These conditions are identified with the conditions for the occurrence of localization of deformation. In particular, incremental equilibrium requires that the incremental tractions (not the stresses!) remain continuous
(where + and - denote the two sides of the surface) and geometrical compatibility imposes a strain compatibility restriction on the form of incremental strain:
where the symbol ⊗ {\displaystyle \otimes } denotes tensor product and g {\displaystyle \mathbf {g} } is a vector defining the deformation discontinuity mode (orthogonal to n {\displaystyle \mathbf {n} } for incompressible materials). A substitution of the incremental constitutive law (1) and of the strain compatibility ( 3 ) into the continuity of incremental tractions ( 2 ) yields the necessary condition for strain localization:
Since the second-order tensor A ( n ) {\displaystyle \mathbb {A} (\mathbf {n} )} defined for every vector g {\displaystyle {\textbf {g}}} as A ( n ) g = C ( g ⊗ n ) n {\displaystyle \mathbb {A} ({\textbf {n}}){\textbf {g}}=\mathbb {C} \left({\textbf {g}}\otimes {\textbf {n}}\right){\textbf {n}}}
is the so-called 'acoustic tensor', defining the condition of propagation of acceleration waves, we can conclude that the condition for strain localization coincides with the condition of singularity (propagation at null speed) of an acceleration wave. This condition represents the so-called 'loss of ellipticity' of the differential equations governing the rate equilibrium.
The state-of-the-art of the research on shear bands is that the phenomenon is well understood from the theoretical [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ] and experimental [ 10 ] [ 11 ] [ 12 ] [ 13 ] point of view and available constitutive models give nice qualitative predictions, although quantitative predictions are often poor. [ 14 ] Moreover, great progresses have been made on numerical simulations, [ 15 ] [ 16 ] [ 17 ] [ 18 ] so that shear band nucleation and propagation in relatively complex situations can be traced numerically with finite element models, although still at the cost of a great computational effort. Of further interest are simulations that reveal the crystallographic orientation dependence of shear banding in single crystal and polycrystals. These simulations show that certain orientations are much more prone to undergo shear localization than others. [ 19 ]
Most polycrystalline metals and alloys usually deform via shear caused by dislocations, twins , and / or shear bands. This leads to pronounced plastic anisotropy at the grain scale and to preferred grain orientation distributions, i.e. crystallographic textures. Cold rolling textures of most face centered cubic metals and alloys for instance range between two types, i.e. the brass-type texture and the copper-type texture . The stacking fault energy plays an important role for the prevailing mechanisms of plastic deformation and the resultant textures. For aluminum and other fcc materials with high SFE, dislocation glide is the main mechanism during cold rolling and the {112}<111> (copper) and {123}<634> (S) texture components (copper-type textures) are developed. In contrast, in Cu–30 wt.% Zn (alpha-brass) and related metals and alloys with low SFE, mechanical twinning and shear banding occur together with dislocation glide as main deformation carriers, particularly at large plastic deformations. The resulting rolling textures are characterized by the {011}<211> (brass) and {01 1}<100> (Goss) texture components (brass-type texture). In either case non-crystallographic shear banding plays an essential role for the specific type of deformation texture evolved. [ 20 ] [ 21 ]
Closed-form solutions disclosing the shear band emergence can be obtained through the perturbative approach, [ 22 ] [ 23 ] consisting in the superimposition of a perturbation field upon an unperturbed deformed state.
In particular, an infinite, incompressible, nonlinear elastic material, homogeneously deformed under the plane strain condition can be perturbed through superposition of concentrated forces or by the presence of cracks or rigid line inclusions .
It has been shown that, when the unperturbed state is taken close to the localization condition (4), the perturbed fields self-arrange in the form of localized fields, taking extreme values in the neighbourhood of the introduced perturbation and focussed along the shear bands directions. In particular, in the case of cracks and rigid line inclusions such shear bands emerge from the linear inclusion tips. [ 24 ]
Within the perturbative approach, an incremental model for a shear band of finite length has been introduced [ 25 ] prescribing the following conditions along its surface:
Employing this model, the following main features of shear banding have been demonstrated: | https://en.wikipedia.org/wiki/Shear_band |
In solid mechanics , shear flow is the shear stress over a distance in a thin-walled structure. [ 1 ] In fluid dynamics , shear flow is the flow induced by a force in a fluid.
For thin-walled profiles, such as that through a beam or semi-monocoque structure, the shear stress distribution through the thickness can be neglected. [ 2 ] Furthermore, there is no shear stress in the direction normal to the wall, only parallel. [ 2 ] In these instances, it can be useful to express internal shear stress as shear flow, which is found as the shear stress multiplied by the thickness of the section. An equivalent definition for shear flow is the shear force V per unit length of the perimeter around a thin-walled section. Shear flow has the dimensions of force per unit of length. [ 1 ] This corresponds to units of newtons per meter in the SI system and pound-force per foot in the US.
When a transverse force is applied to a beam, the result is variation in bending normal stresses along the length of the beam. This variation causes a horizontal shear stress within the beam that varies with distance from the neutral axis in the beam. The concept of complementary shear then dictates that a shear stress also exists across the cross section of the beam, in the direction of the original transverse force. [ 3 ] As described above, in thin-walled structures, the variation along the thickness of the member can be neglected, so the shear stress across the cross section of a beam that is composed of thin-walled elements can be examined as shear flow, or the shear stress multiplied by the thickness of the element. [ 2 ]
The concept of shear flow is particularly useful when analyzing semi-monocoque structures, which can be idealized using the skin-stringer model. In this model, the longitudinal members, or stringers, carry only axial stress, while the skin or web resists the externally applied torsion and shear force. [ 3 ] In this case, since the skin is a thin-walled structure, the internal shear stresses in the skin can be represented as shear flow. In design, the shear flow is sometimes known before the skin thickness is determined, in which case the skin thickness can simply be sized according to allowable shear stress.
For a given structure, the shear center is the point in space at which shear force could be applied without causing torsional deformation (e.g. twisting) of the cross-section of the structure. [ 4 ] The shear center is an imaginary point, but does not vary with the magnitude of the shear force - only the cross-section of the structure. The shear center always lies along the axis of symmetry, and can be found using the following method: [ 3 ]
By definition, shear flow through a cross section of thickness t is calculated using q = τ t {\displaystyle q=\tau t} , where τ = V Q I t {\displaystyle \tau ={\frac {VQ}{It}}} . Thus the equation for shear flow at a particular depth in a particular cross-section of a thin-walled structure that is symmetric across its width is
where
Unlike in solid mechanics where shear flow is the shear stress force per unit length, in fluid mechanics , shear flow (or shearing flow ) refers to adjacent layers of fluid moving parallel to each other with different speeds. Viscous fluids resist this shearing motion. For a Newtonian fluid , the stress exerted by the fluid in resistance to the shear is proportional to the strain rate or shear rate .
A simple example of a shear flow is Couette flow , in which a fluid is trapped between two large parallel plates, and one plate is moved with some relative velocity to the other. Here, the strain rate is simply the relative velocity divided by the distance between the plates.
Shear flows in fluids tend to be unstable at high Reynolds numbers , when fluid viscosity is not strong enough to dampen out perturbations to the flow. For example, when two layers of fluid shear against each other with relative velocity, the Kelvin–Helmholtz instability may occur. | https://en.wikipedia.org/wiki/Shear_flow |
In solid mechanics , shearing forces are unaligned forces acting on one part of a body in a specific direction, and another part of the body in the opposite direction. When the forces are collinear (aligned with each other), they are called tension forces or compression forces . Shear force can also be defined in terms of planes : "If a plane is passed through a body, a force acting along this plane is called a shear force or shearing force ." [ 1 ]
This section calculates the force required to cut a piece of material with a shearing action. The relevant information is the area of the material being sheared, i.e. the area across which the shearing action takes place, and the shear strength of the material. A round bar of steel is used as an example. The shear strength is calculated from the tensile strength using a factor which relates the two strengths. In this case 0.6 applies to the example steel, known as EN8 bright, although it can vary from 0.58 to 0.62 depending on application.
EN8 bright has a tensile strength of 800 MPa and mild steel, for comparison, has a tensile strength of 400 MPa.
To calculate the force to shear a 25 mm diameter bar of EN8 bright steel;
When working with a riveted or tensioned bolted joint , the strength comes from friction between the materials bolted together. Bolts are correctly torqued to maintain the friction. The shear force only becomes relevant when the bolts are not torqued.
A bolt with property class 12.9 has a tensile strength of 1200 MPa (1 MPa = 1 N/mm 2 ) or 1.2 kN/mm 2 and the yield strength is 0.90 times tensile strength, 1080 MPa in this case.
A bolt with property class 4.6 has a tensile strength of 400 MPa (1 MPa = 1 N/mm 2 ) or 0.4 kN/mm 2 and yield strength is 0.60 times tensile strength, 240 MPa in this case. | https://en.wikipedia.org/wiki/Shear_force |
In plane geometry , a shear mapping is an affine transformation that displaces each point in a fixed direction by an amount proportional to its signed distance from a given line parallel to that direction. [ 1 ]
This type of mapping is also called shear transformation , transvection , or just shearing . The transformations can be applied with a shear matrix or transvection , an elementary matrix that represents the addition of a multiple of one row or column to another. Such a matrix may be derived by taking the identity matrix and replacing one of the zero elements with a non-zero value.
An example is the linear map that takes any point with coordinates ( x , y ) {\displaystyle (x,y)} to the point ( x + 2 y , y ) {\displaystyle (x+2y,y)} . In this case, the displacement is horizontal by a factor of 2 where the fixed line is the x -axis, and the signed distance is the y -coordinate. Note that points on opposite sides of the reference line are displaced in opposite directions.
Shear mappings must not be confused with rotations . Applying a shear map to a set of points of the plane will change all angles between them (except straight angles ), and the length of any line segment that is not parallel to the direction of displacement. Therefore, it will usually distort the shape of a geometric figure, for example turning squares into parallelograms , and circles into ellipses . However a shearing does preserve the area of geometric figures and the alignment and relative distances of collinear points. A shear mapping is the main difference between the upright and slanted (or italic) styles of letters .
The same definition is used in three-dimensional geometry , except that the distance is measured from a fixed plane. A three-dimensional shearing transformation preserves the volume of solid figures, but changes areas of plane figures (except those that are parallel to the displacement).
This transformation is used to describe laminar flow of a fluid between plates, one moving in a plane above and parallel to the first.
In the general n -dimensional Cartesian space R n , {\displaystyle \mathbb {R} ^{n},} the distance is measured from a fixed hyperplane parallel to the direction of displacement. This geometric transformation is a linear transformation of R n {\displaystyle \mathbb {R} ^{n}} that preserves the n -dimensional measure (hypervolume) of any set.
In the plane R 2 = R × R {\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } , a horizontal shear (or shear parallel to the x -axis) is a function that takes a generic point with coordinates ( x , y ) {\displaystyle (x,y)} to the point ( x + m y , y ) {\displaystyle (x+my,y)} ; where m is a fixed parameter, called the shear factor .
The effect of this mapping is to displace every point horizontally by an amount proportionally to its y -coordinate. Any point above the x -axis is displaced to the right (increasing x ) if m > 0 , and to the left if m < 0 . Points below the x -axis move in the opposite direction, while points on the axis stay fixed.
Straight lines parallel to the x -axis remain where they are, while all other lines are turned (by various angles) about the point where they cross the x -axis. Vertical lines, in particular, become oblique lines with slope 1 m . {\displaystyle {\tfrac {1}{m}}.} Therefore, the shear factor m is the cotangent of the shear angle φ {\displaystyle \varphi } between the former verticals and the x -axis. [ citation needed ] In the example on the right the square is tilted by 30°, so the shear angle is 60°.
If the coordinates of a point are written as a column vector (a 2×1 matrix ), the shear mapping can be written as multiplication by a 2×2 matrix:
A vertical shear (or shear parallel to the y -axis) of lines is similar, except that the roles of x and y are swapped. It corresponds to multiplying the coordinate vector by the transposed matrix :
The vertical shear displaces points to the right of the y -axis up or down, depending on the sign of m . It leaves vertical lines invariant, but tilts all other lines about the point where they meet the y -axis. Horizontal lines, in particular, get tilted by the shear angle φ {\displaystyle \varphi } to become lines with slope m .
Two or more shear transformations can be combined.
If two shear matrices are ( 1 λ 0 1 ) {\textstyle {\begin{pmatrix}1&\lambda \\0&1\end{pmatrix}}} and ( 1 0 μ 1 ) {\textstyle {\begin{pmatrix}1&0\\\mu &1\end{pmatrix}}}
then their composition matrix is ( 1 λ 0 1 ) ( 1 0 μ 1 ) = ( 1 + λ μ λ μ 1 ) , {\displaystyle {\begin{pmatrix}1&\lambda \\0&1\end{pmatrix}}{\begin{pmatrix}1&0\\\mu &1\end{pmatrix}}={\begin{pmatrix}1+\lambda \mu &\lambda \\\mu &1\end{pmatrix}},} which also has determinant 1, so that area is preserved.
In particular, if λ = μ {\displaystyle \lambda =\mu } , we have
( 1 + λ 2 λ λ 1 ) , {\displaystyle {\begin{pmatrix}1+\lambda ^{2}&\lambda \\\lambda &1\end{pmatrix}},}
which is a positive definite matrix .
A typical shear matrix is of the form S = ( 1 0 0 λ 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 ) . {\displaystyle S={\begin{pmatrix}1&0&0&\lambda &0\\0&1&0&0&0\\0&0&1&0&0\\0&0&0&1&0\\0&0&0&0&1\end{pmatrix}}.}
This matrix shears parallel to the x axis in the direction of the fourth dimension of the underlying vector space.
A shear parallel to the x axis results in x ′ = x + λ y {\displaystyle x'=x+\lambda y} and y ′ = y {\displaystyle y'=y} . In matrix form: ( x ′ y ′ ) = ( 1 λ 0 1 ) ( x y ) . {\displaystyle {\begin{pmatrix}x'\\y'\end{pmatrix}}={\begin{pmatrix}1&\lambda \\0&1\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}.}
Similarly, a shear parallel to the y axis has x ′ = x {\displaystyle x'=x} and y ′ = y + λ x {\displaystyle y'=y+\lambda x} . In matrix form: ( x ′ y ′ ) = ( 1 0 λ 1 ) ( x y ) . {\displaystyle {\begin{pmatrix}x'\\y'\end{pmatrix}}={\begin{pmatrix}1&0\\\lambda &1\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}.}
In 3D space this matrix shear the YZ plane into the diagonal plane passing through these 3 points: ( 0 , 0 , 0 ) {\displaystyle (0,0,0)} ( λ , 1 , 0 ) {\displaystyle (\lambda ,1,0)} ( μ , 0 , 1 ) {\displaystyle (\mu ,0,1)} S = ( 1 λ μ 0 1 0 0 0 1 ) . {\displaystyle S={\begin{pmatrix}1&\lambda &\mu \\0&1&0\\0&0&1\end{pmatrix}}.}
The determinant will always be 1, as no matter where the shear element is placed, it will be a member of a skew-diagonal that also contains zero elements (as all skew-diagonals have length at least two) hence its product will remain zero and will not contribute to the determinant. Thus every shear matrix has an inverse , and the inverse is simply a shear matrix with the shear element negated, representing a shear transformation in the opposite direction. In fact, this is part of an easily derived more general result: if S is a shear matrix with shear element λ , then S n is a shear matrix whose shear element is simply n λ . Hence, raising a shear matrix to a power n multiplies its shear factor by n .
If S is an n × n shear matrix, then:
For a vector space V and subspace W , a shear fixing W translates all vectors in a direction parallel to W .
To be more precise, if V is the direct sum of W and W′ , and we write vectors as
correspondingly, the typical shear L fixing W is
where M is a linear mapping from W′ into W . Therefore in block matrix terms L can be represented as
The following applications of shear mapping were noted by William Kingdon Clifford :
The area-preserving property of a shear mapping can be used for results involving area. For instance, the Pythagorean theorem has been illustrated with shear mapping [ 3 ] as well as the related geometric mean theorem .
Shear matrices are often used in computer graphics . [ 4 ] [ 5 ] [ 6 ]
An algorithm due to Alan W. Paeth uses a sequence of three shear mappings (horizontal, vertical, then horizontal again) to rotate a digital image by an arbitrary angle. The algorithm is very simple to implement, and very efficient, since each step processes only one column or one row of pixels at a time. [ 7 ]
In typography , normal text transformed by a shear mapping results in oblique type . [ citation needed ]
In pre-Einsteinian Galilean relativity , transformations between frames of reference are shear mappings called Galilean transformations . These are also sometimes seen when describing moving reference frames relative to a "preferred" frame, sometimes referred to as absolute time and space . [ citation needed ] | https://en.wikipedia.org/wiki/Shear_mapping |
In plane geometry , a shear mapping is an affine transformation that displaces each point in a fixed direction by an amount proportional to its signed distance from a given line parallel to that direction. [ 1 ]
This type of mapping is also called shear transformation , transvection , or just shearing . The transformations can be applied with a shear matrix or transvection , an elementary matrix that represents the addition of a multiple of one row or column to another. Such a matrix may be derived by taking the identity matrix and replacing one of the zero elements with a non-zero value.
An example is the linear map that takes any point with coordinates ( x , y ) {\displaystyle (x,y)} to the point ( x + 2 y , y ) {\displaystyle (x+2y,y)} . In this case, the displacement is horizontal by a factor of 2 where the fixed line is the x -axis, and the signed distance is the y -coordinate. Note that points on opposite sides of the reference line are displaced in opposite directions.
Shear mappings must not be confused with rotations . Applying a shear map to a set of points of the plane will change all angles between them (except straight angles ), and the length of any line segment that is not parallel to the direction of displacement. Therefore, it will usually distort the shape of a geometric figure, for example turning squares into parallelograms , and circles into ellipses . However a shearing does preserve the area of geometric figures and the alignment and relative distances of collinear points. A shear mapping is the main difference between the upright and slanted (or italic) styles of letters .
The same definition is used in three-dimensional geometry , except that the distance is measured from a fixed plane. A three-dimensional shearing transformation preserves the volume of solid figures, but changes areas of plane figures (except those that are parallel to the displacement).
This transformation is used to describe laminar flow of a fluid between plates, one moving in a plane above and parallel to the first.
In the general n -dimensional Cartesian space R n , {\displaystyle \mathbb {R} ^{n},} the distance is measured from a fixed hyperplane parallel to the direction of displacement. This geometric transformation is a linear transformation of R n {\displaystyle \mathbb {R} ^{n}} that preserves the n -dimensional measure (hypervolume) of any set.
In the plane R 2 = R × R {\displaystyle \mathbb {R} ^{2}=\mathbb {R} \times \mathbb {R} } , a horizontal shear (or shear parallel to the x -axis) is a function that takes a generic point with coordinates ( x , y ) {\displaystyle (x,y)} to the point ( x + m y , y ) {\displaystyle (x+my,y)} ; where m is a fixed parameter, called the shear factor .
The effect of this mapping is to displace every point horizontally by an amount proportionally to its y -coordinate. Any point above the x -axis is displaced to the right (increasing x ) if m > 0 , and to the left if m < 0 . Points below the x -axis move in the opposite direction, while points on the axis stay fixed.
Straight lines parallel to the x -axis remain where they are, while all other lines are turned (by various angles) about the point where they cross the x -axis. Vertical lines, in particular, become oblique lines with slope 1 m . {\displaystyle {\tfrac {1}{m}}.} Therefore, the shear factor m is the cotangent of the shear angle φ {\displaystyle \varphi } between the former verticals and the x -axis. [ citation needed ] In the example on the right the square is tilted by 30°, so the shear angle is 60°.
If the coordinates of a point are written as a column vector (a 2×1 matrix ), the shear mapping can be written as multiplication by a 2×2 matrix:
A vertical shear (or shear parallel to the y -axis) of lines is similar, except that the roles of x and y are swapped. It corresponds to multiplying the coordinate vector by the transposed matrix :
The vertical shear displaces points to the right of the y -axis up or down, depending on the sign of m . It leaves vertical lines invariant, but tilts all other lines about the point where they meet the y -axis. Horizontal lines, in particular, get tilted by the shear angle φ {\displaystyle \varphi } to become lines with slope m .
Two or more shear transformations can be combined.
If two shear matrices are ( 1 λ 0 1 ) {\textstyle {\begin{pmatrix}1&\lambda \\0&1\end{pmatrix}}} and ( 1 0 μ 1 ) {\textstyle {\begin{pmatrix}1&0\\\mu &1\end{pmatrix}}}
then their composition matrix is ( 1 λ 0 1 ) ( 1 0 μ 1 ) = ( 1 + λ μ λ μ 1 ) , {\displaystyle {\begin{pmatrix}1&\lambda \\0&1\end{pmatrix}}{\begin{pmatrix}1&0\\\mu &1\end{pmatrix}}={\begin{pmatrix}1+\lambda \mu &\lambda \\\mu &1\end{pmatrix}},} which also has determinant 1, so that area is preserved.
In particular, if λ = μ {\displaystyle \lambda =\mu } , we have
( 1 + λ 2 λ λ 1 ) , {\displaystyle {\begin{pmatrix}1+\lambda ^{2}&\lambda \\\lambda &1\end{pmatrix}},}
which is a positive definite matrix .
A typical shear matrix is of the form S = ( 1 0 0 λ 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 ) . {\displaystyle S={\begin{pmatrix}1&0&0&\lambda &0\\0&1&0&0&0\\0&0&1&0&0\\0&0&0&1&0\\0&0&0&0&1\end{pmatrix}}.}
This matrix shears parallel to the x axis in the direction of the fourth dimension of the underlying vector space.
A shear parallel to the x axis results in x ′ = x + λ y {\displaystyle x'=x+\lambda y} and y ′ = y {\displaystyle y'=y} . In matrix form: ( x ′ y ′ ) = ( 1 λ 0 1 ) ( x y ) . {\displaystyle {\begin{pmatrix}x'\\y'\end{pmatrix}}={\begin{pmatrix}1&\lambda \\0&1\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}.}
Similarly, a shear parallel to the y axis has x ′ = x {\displaystyle x'=x} and y ′ = y + λ x {\displaystyle y'=y+\lambda x} . In matrix form: ( x ′ y ′ ) = ( 1 0 λ 1 ) ( x y ) . {\displaystyle {\begin{pmatrix}x'\\y'\end{pmatrix}}={\begin{pmatrix}1&0\\\lambda &1\end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}.}
In 3D space this matrix shear the YZ plane into the diagonal plane passing through these 3 points: ( 0 , 0 , 0 ) {\displaystyle (0,0,0)} ( λ , 1 , 0 ) {\displaystyle (\lambda ,1,0)} ( μ , 0 , 1 ) {\displaystyle (\mu ,0,1)} S = ( 1 λ μ 0 1 0 0 0 1 ) . {\displaystyle S={\begin{pmatrix}1&\lambda &\mu \\0&1&0\\0&0&1\end{pmatrix}}.}
The determinant will always be 1, as no matter where the shear element is placed, it will be a member of a skew-diagonal that also contains zero elements (as all skew-diagonals have length at least two) hence its product will remain zero and will not contribute to the determinant. Thus every shear matrix has an inverse , and the inverse is simply a shear matrix with the shear element negated, representing a shear transformation in the opposite direction. In fact, this is part of an easily derived more general result: if S is a shear matrix with shear element λ , then S n is a shear matrix whose shear element is simply n λ . Hence, raising a shear matrix to a power n multiplies its shear factor by n .
If S is an n × n shear matrix, then:
For a vector space V and subspace W , a shear fixing W translates all vectors in a direction parallel to W .
To be more precise, if V is the direct sum of W and W′ , and we write vectors as
correspondingly, the typical shear L fixing W is
where M is a linear mapping from W′ into W . Therefore in block matrix terms L can be represented as
The following applications of shear mapping were noted by William Kingdon Clifford :
The area-preserving property of a shear mapping can be used for results involving area. For instance, the Pythagorean theorem has been illustrated with shear mapping [ 3 ] as well as the related geometric mean theorem .
Shear matrices are often used in computer graphics . [ 4 ] [ 5 ] [ 6 ]
An algorithm due to Alan W. Paeth uses a sequence of three shear mappings (horizontal, vertical, then horizontal again) to rotate a digital image by an arbitrary angle. The algorithm is very simple to implement, and very efficient, since each step processes only one column or one row of pixels at a time. [ 7 ]
In typography , normal text transformed by a shear mapping results in oblique type . [ citation needed ]
In pre-Einsteinian Galilean relativity , transformations between frames of reference are shear mappings called Galilean transformations . These are also sometimes seen when describing moving reference frames relative to a "preferred" frame, sometimes referred to as absolute time and space . [ citation needed ] | https://en.wikipedia.org/wiki/Shear_matrix |
In materials science , shear modulus or modulus of rigidity , denoted by G , or sometimes S or μ , is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain : [ 1 ]
where
The derived SI unit of shear modulus is the pascal (Pa), although it is usually expressed in gigapascals (GPa) or in thousand pounds per square inch (ksi). Its dimensional form is M 1 L −1 T −2 , replacing force by mass times acceleration .
The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law :
These moduli are not independent, and for isotropic materials they are connected via the equations [ 9 ]
The shear modulus is concerned with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences an opposing force (such as friction). In the case of an object shaped like a rectangular prism, it will deform into a parallelepiped . Anisotropic materials such as wood , paper and also essentially all single crystals exhibit differing material response to stress or strain when tested in different directions. In this case, one may need to use the full tensor-expression of the elastic constants, rather than a single scalar value.
One possible definition of a fluid would be a material with zero shear modulus.
In homogeneous and isotropic solids, there are two kinds of waves, pressure waves and shear waves . The velocity of a shear wave, ( v s ) {\displaystyle (v_{s})} is controlled by the shear modulus,
where
The shear modulus of metals is usually observed to decrease with increasing temperature. At high pressures, the shear modulus also appears to increase with the applied pressure. Correlations between the melting temperature, vacancy formation energy, and the shear modulus have been observed in many metals. [ 13 ]
Several models exist that attempt to predict the shear modulus of metals (and possibly that of alloys). Shear modulus models that have been used in plastic flow computations include:
The Varshni-Chen-Gray model (sometimes referred to as the Varshni equation) has the form:
where μ 0 {\displaystyle \mu _{0}} is the shear modulus at T = 0 K {\displaystyle T=0K} , and D {\displaystyle D} and T 0 {\displaystyle T_{0}} are material constants.
The Steinberg-Cochran-Guinan (SCG) shear modulus model is pressure dependent and has the form
where, μ 0 is the shear modulus at the reference state ( T = 300 K, p = 0, η = 1), p is the pressure, and T is the temperature.
The Nadal-Le Poac (NP) shear modulus model is a modified version of the SCG model. The empirical temperature dependence of the shear modulus in the SCG model is replaced with an equation based on Lindemann melting theory . The NP shear modulus model has the form:
where
and μ 0 is the shear modulus at absolute zero and ambient pressure, ζ is an area, m is the atomic mass , and f is the Lindemann constant .
The shear relaxation modulus G ( t ) {\displaystyle G(t)} is the time-dependent generalization of the shear modulus [ 18 ] G {\displaystyle G} :
There are two valid solutions. The plus sign leads to ν ≥ 0 {\displaystyle \nu \geq 0} . | https://en.wikipedia.org/wiki/Shear_modulus |
A shear pin is a mechanical detail designed to allow a specific outcome to occur once a predetermined force is applied. It can either function as a safeguard designed to break to protect other parts, or as a conditional operator that will not allow a mechanical device to operate until the correct force is applied.
In the role of a mechanical safeguard, a shear pin is a safety device designed to shear in the case of a mechanical overload, preventing other, more expensive or less-easily replaced parts from being damaged. As a mechanical sacrificial part , it is analogous to an electric fuse .
They are most commonly used in drive trains , such as a snow blower 's auger or the propellers attached to marine engines.
Another use is in pushback bars used for large aircraft . In this device, shear pins are frequently used to connect the "head" of the towbar – the portion that attaches to the aircraft – to the main shaft of the towbar. In this way, the failure of the shear pin will physically separate the aircraft and the tractor. The design may be such that the shear pin will have several different causes of failure – towbar rotation about its long axis, sudden braking or acceleration, excessive steering force, etc. – all of which could otherwise be extremely damaging to the aircraft.
In the role as a conditional operator, a shear pin will be used to prevent a mechanical device from operating before the criteria for operation are met. A shear pin gives a distinct threshold for the force required for operation. It is very cheap and easy to produce delivering a very high reliability and predictable tolerance. They are almost maintenance-free and can remain ready for operation for years with little to no decrease in reliability. Shear pins are only useful for a single operating cycle, after each operation they have to be replaced. A common example is the plastic or wire loop securing the pin to the handles of common fire extinguishers . The presence of the pin prevents accidental discharge by only allowing the handle to be depressed once the pin is removed. The loop prevents the inadvertant removal of the pin, which could otherwise easily fall out. A significant amount of force is applied to the plastic or wire loop; by breaking, it allows the pin to subsequently be removed, thus allowing the handles to be depressed, discharging the fire extinguisher.
Many designs take advantage of the maintenance-free state of constant readiness. For example, a hydraulic damper protecting a structure from earthquake damage could be secured with a shear pin. During normal conditions the system would be completely rigid, but when acted upon by the force of an earthquake the shear pin would break and the hydraulic damping system would operate.
Their high reliability and low cost make them very popular for use in weapons. A typical example is using shear pins in an explosive device. A shear pin can here hold a striker pin in place, preventing the striker pin from striking an initiator (primer) unless the correct force is applied. That force can be the acceleration of a rifle grenade being launched. The force would snap the shear pin, allowing the striker pin to move backwards onto a primer, which in turn ignites a pyrotechnic delay composition for auto destruction. In this use shear pins prevent the striker pin from hitting the primer during handling or if the grenade was dropped by accident. Additionally, shear-pins are frequently used in anti-tank mine fuzes , to prevent them from being triggered by much lighter, non-target vehicles such as motorcycles. Typically, the shear-pin in an anti-tank mine is designed to snap (and release the spring-loaded firing pin ) when a weight in excess of 1500 kilograms is applied to the pressure plate.
A shear pin could potentially be made from any material although metal is the most common.
When making a metal object for a mechanical application, an alloy and tempering is usually selected to make the construction resistant to damage. This can for example be achieved by giving the material a high degree of elasticity so that, like a spring, the metal returns to its original shape after being deformed by an external force. A shear pin however is often tempered to make the metal brittle , so that it breaks or shatters rather than bends when the required force is applied.
The material of a shear pin is selected and treated so that it is relatively resistant to fatigue . That is, when subjected to small forces, each one insufficient to break the pin, the pin does not retain damage. If material fatigue were to weaken a shear pin, the pin could potentially be broken by a force smaller than the original threshold force causing the mechanism to operate unintentionally, or a safety shear pin to break during normal operation of the machinery it protects.
The pin itself may be as simple as a metal rod inserted into a channel drilled through two moving parts, locking them in place as long as the pin is intact.
It may also be a plain metal rod inserted through a hub and axle; the diameter of the rod, alloy and tempering of the metal, are all carefully chosen to allow the pin to shear only when the predetermined threshold force or shock is reached.
A split pin ( cotter pin in American usage) can also be used as a shear pin. | https://en.wikipedia.org/wiki/Shear_pin |
The shear strength of a discontinuity in a soil or rock mass may have a strong impact on the mechanical behavior of a soil or rock mass. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] The shear strength of a discontinuity is often considerably lower than the shear strength of the blocks of intact material in between the discontinuities, and therefore influences, for example, tunnel , foundation , or slope engineering, but also the stability of natural slopes . Many slopes, natural and man-made, fail due to a low shear strength of discontinuities in the soil or rock mass in the slope. The deformation characteristics of a soil or rock mass are also influenced by the shear strength of the discontinuities. For example, the modulus of deformation is reduced, and the deformation becomes plastic (i.e. non-reversible deformation on reduction of stress) rather than elastic (i.e. reversible deformation). This may cause, for example, larger settlement of foundations, which is also permanent even if the load is only temporary. Furthermore, the shear strength of discontinuities influences the stress distribution in a soil or rock mass. [ 7 ]
The shear strength along a discontinuity in a soil or rock mass in geotechnical engineering is governed by the persistence of the discontinuity, roughness of discontinuity surfaces, [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] infill material in the discontinuity, [ 13 ] presence and pressure of gasses and fluids (e.g. water, oil), and possible solution (e.g. karst ) and cementation along the discontinuity. Further the shear strength is dependent on whether the discontinuity has moved before in the geological history (i.e. are the asperities on opposing walls of the discontinuity fitting or non-fitting , or have the asperities been sheared off).
Only for simple models of discontinuities the shear strength can be analytically calculated. [ 8 ] For real discontinuities no analytical calculation method exists. Testing on various scales in the laboratory or in the field, or empirical calculations based on characterizing the discontinuity [ 12 ] [ 14 ] [ 15 ] are used to establish the shear strength. | https://en.wikipedia.org/wiki/Shear_strength_(discontinuity) |
In rheology , shear thinning is the non-Newtonian behavior of fluids whose viscosity decreases under shear strain . It is sometimes considered synonymous for pseudo- plastic behaviour, [ 1 ] [ 2 ] and is usually defined as excluding time-dependent effects, such as thixotropy . [ 3 ]
Shear thinning is the most common type of non-Newtonian behavior of fluids and is seen in many industrial and everyday applications. [ 4 ] Although shear thinning is generally not observed in pure liquids with low molecular mass or ideal solutions of small molecules like sucrose or sodium chloride , it is often observed in polymer solutions and molten polymers, as well as complex fluids and suspensions like ketchup , whipped cream , blood , [ 5 ] paint , and nail polish .
Though the exact cause of shear thinning is not fully understood, it is widely regarded to be the effect of small structural changes within the fluid, such that microscale geometries within the fluid rearrange to facilitate shearing . [ 6 ] In colloid systems, phase separation during flow leads to shear thinning. In polymer systems such as polymer melts and solutions, shear thinning is caused by the disentanglement of polymer chains during flow. At rest, high molecular weight polymers are entangled and randomly oriented. However, when undergoing agitation at a high enough rate, these highly anisotropic polymer chains start to disentangle and align along the direction of the shear force. [ 7 ] This leads to less molecular/particle interaction and a larger amount of free space, decreasing the viscosity. [ 4 ]
At both sufficiently high and very low shear rates, viscosity of a polymer system is independent of the shear rate. At high shear rates, polymers are entirely disentangled and the viscosity value of the system plateaus at η ∞ , or the infinite shear viscosity plateau. At low shear rates, the shear is too low to be impeded by entanglements and the viscosity value of the system is η 0 , or the zero shear rate viscosity. The value of η ∞ represents the lowest viscosity attainable and may be orders of magnitude lower than η 0 , depending on the degree of shear thinning.
Viscosity is plotted against shear rate in a log(η) vs. log( γ ˙ {\displaystyle {\dot {\gamma }}} ) plot, where the linear region is the shear-thinning regime and can be expressed using the Ostwald and de Waele power law equation: [ 8 ]
The Ostwald and de Waele equation can be written in a logarithmic form:
The apparent viscosity is defined as η = τ γ ˙ {\displaystyle \eta ={\tau \over {\dot {\gamma }}}} , and this may be plugged into the Ostwald equation to yield a second power-law equation for apparent viscosity:
This expression can also be used to describe dilatant (shear thickening) behaviour, where the value of n is greater than 1.
Bingham plastics require a critical shear stress to be exceeded in order to start flowing. This behaviour is usually seen in polymer/silica micro- and nanocomposites, where the formation of a silica network in the material provides a solid-like response at low shear stress. The shear-thinning behavior of plastic fluids can be described with the Herschel-Bulkley model, which adds a threshold shear stress component to the Ostwald equation: [ 8 ]
Some authors consider shear thinning to be a special case of thixotropic behaviour, because the recovery of the microstructure of the liquid to its initial state will always require a non-zero time. When the recovery of viscosity after disturbance is very rapid however, the observed behaviour is classic shear thinning or pseudoplasticity, because as soon as the shear is removed, the viscosity returns to normal. When it takes a measurable time for the viscosity to recover, thixotropic behaviour is observed. [ 9 ] When describing the viscosity of liquids, however, it is therefore useful to distinguish shear-thinning (pseudoplastic) behaviour from thixotropic behaviour, where the viscosity at all shear rates is decreased for some duration after agitation: both of these effects can often be seen separately in the same liquid. [ 10 ]
Wall paint is a pseudoplastic material. [ 11 ] When modern wall paint is applied, the shear created by the brush or roller will allow it to thin and wet out the surface evenly. Once applied, the paint regains its higher viscosity, which avoids drips and runs.
Ketchup is a shear-thinning material, viscous when at rest, but flowing at speed when agitated by squeezing, shaking, or striking the bottle. [ 11 ]
Whipped cream is also a shear-thinning material. [ 6 ] When whipped cream is sprayed out of its canister, it flows out smoothly from the nozzle due to the low viscosity at high flow rate. However, after whipped cream is sprayed into a spoon, it does not flow and its increased viscosity allows it to be rigid. | https://en.wikipedia.org/wiki/Shear_thinning |
A shear wall is an element of a structurally engineered system that is designed to resist in- plane lateral forces, typically wind and seismic loads.
A shear wall resists loads parallel to the plane of the wall. Collectors, also known as drag members, transfer the diaphragm shear to shear walls and other vertical elements of the seismic-force-resisting system. Shear walls are typically made of light framed or braced wood sheathed in shear-resisting material such as plywood or other structurally rigid panels, reinforced concrete , reinforced masonry , or steel plates.
While plywood is the conventional material used in wood (timber) shear walls, advances in technology and modern building methods have produced prefabricated options such as sheet steel and steel-backed shear panels used for narrow walls bracketing an opening that have proven to provide stronger seismic resistance.
In many jurisdictions, the International Building Code and International Residential Code govern the design of shear walls.
A shear wall is stiffer in its principal X and Y axes than it is in its Z axis. It is considered as a primary structure which provides relatively stiff resistance to vertical and horizontal forces acting in its plane. Under this combined loading condition, a shear wall develops compatible axial, shear, torsional and flexural strains, resulting in a complicated internal stress distribution. In this way, loads are transferred vertically to the building's foundation. Therefore, there are four critical failure mechanisms; as shown in Figure 1. The factors determining the failure mechanism include geometry, loading, material properties, restraint, and construction. Shear walls may also be constructed using light-gauge steel diagonal bracing members tied to collector and ancor points.
The slenderness ratio of a wall is defined as the ratio of its effective height divided its effective thickness. [ 1 ] It is highly related to the slenderness limit that is the cut-off between elements being classed "slender" or "stocky". Slender walls are vulnerable to buckling failure modes, including Euler in-plane buckling due to axial compression, Euler out-of-plane buckling due to axial compression and lateral torsional buckling due to bending moment. In the design process, structural engineers need to consider all these failure modes to ensure that the wall design is safe under various kinds of possible loading conditions.
In actual structural systems, the shear walls may function as a coupled system instead of isolated walls depending on their arrangements and connections. Two neighboring wall panels can be considered coupled when the interface transfers longitudinal shear to resist the deformation mode. This stress arises whenever a section experiences a flexural or restrained warping stress and its magnitude is dependent on the stiffness of the coupling element. Depending on this stiffness, the performance of a coupled section will fall between that of an ideal uniform element of similar gross plan cross-section and the combined performance of the independent component parts. Another advantage of coupling is that it enhances the overall flexural stiffness dis-proportionally to shear stiffness, resulting in smaller shear deformation.
The location of a shear wall significantly affects the building function, such as natural ventilation and daylighting performance. The performance requirements vary for buildings of different functions.
Hotel or dormitory buildings require many partitions, allowing insertions of shear walls. In these structures, traditional cellular construction (Figure 2) is preferred and a regular wall arrangement with transverse cross walls between rooms and longitudinal spine walls flanking a central corridor is used.
A structure of shear walls in the center of a large building—often encasing an elevator shaft or stairwell—form a shear core . In multi-storey commercial buildings, shear walls form at least one core (Figure 3). From a building services perspective, the shear core houses communal services including stairs, lifts, toilets and service risers. Building serviceability requirements necessitates a proper arrangement of a shear core. From the structural point of view, a shear core could strengthen the building's resistance to lateral loads, i.e., wind load and seismic load, and significantly increase the building safety.
Concrete shear walls are reinforced with both horizontal and vertical reinforcement (Figure 4). A reinforcement ratio is defined as the ratio of the gross concrete area for a section taken orthogonal to the reinforcement. Construction codes of practice define maximum and minimum amounts of reinforcement as well as the detailing of steel bars. Common construction methods for in-situ reinforced concrete walls include traditional shuttered lifts, slip form, jump form and tunnel form.
The traditional shuttered lifts method should be used when the total number of walls is small or the arrangement is irregular. In this method, walls are formed one story at one time together with the columns. Although it is slow, this technique may produce a premium finish quality or texture.
Slip forming is method of concrete placement whereby a moving form is used to create a continuous wall extrusion. This method is very efficient for well-suited structures, such as flanged and core wall systems. A very accurate wall thickness can be achieved but the surface is rough because of the abrasion of the form on the walls.
Jump forming, also known as climbing forming, is a method of construction whereby the walls are cast in discrete lifts. It is a stop-start process with day joints formed at each lift level. Similar to slip forming, jump forming is only efficient for structures with repetition of wall arrangement. Moreover, it is convenient for adding connections and extrusions at the floor level due to the discrete features. Nevertheless, the inclusion of day joints leaves higher chances for defects and imperfections.
Tunnel form construction uses a formwork system to cast slabs and walls as a single pour operation. It is suitable for cellular structures with regular repetition of both horizontal and vertical members. The advantage of this method is that the construction can progress vertically and horizontally at the same time, thereby increasing the integrity and stability of the structure.
Due to functional requirements, the designer may choose non planar sections like C,L [ clarification needed ] as opposed to the planar sections like rectangular/bar bell sections. Nonplanar sections require 3D analysis and are a research area.
Modeling techniques have been progressively updated during the last two decades, moving from linear static to nonlinear dynamic, enabling more realistic representation of global behavior, and different failure modes . Different modeling techniques shear walls span from macro models such as modified beam-column elements, to micro models such as 3D finite element models. An appropriate modeling technique should:
Different models have been developed over time, including macro-models, vertical line element models, finite-element models , and multi-layer models. More recently, fiber-section beam-columns elements have become popular, as they can model most of the global response and failure modes properly, while avoiding sophistications associated with finite element models. [ 2 ] | https://en.wikipedia.org/wiki/Shear_wall |
Shearer's inequality or also Shearer's lemma, in mathematics , is an inequality in information theory relating the entropy of a set of variables to the entropies of a collection of subsets. It is named for mathematician James B. Shearer .
Concretely, it states that if X 1 , ..., X d are random variables and S 1 , ..., S n are subsets of {1, 2, ..., d } such that every integer between 1 and d lies in at least r of these subsets, then
where H {\displaystyle H} is entropy and ( X j ) j ∈ S i {\displaystyle (X_{j})_{j\in S_{i}}} is the Cartesian product of random variables X j {\displaystyle X_{j}} with indices j in S i {\displaystyle S_{i}} . [ 1 ]
Let F {\displaystyle {\mathcal {F}}} be a family of subsets of [n] (possibly with repeats) with each i ∈ [ n ] {\displaystyle i\in [n]} included in at least t {\displaystyle t} members of F {\displaystyle {\mathcal {F}}} . Let A {\displaystyle {\mathcal {A}}} be another set of subsets of [ n ] {\displaystyle [n]} . Then
where trace F ( A ) = { A ∩ F : A ∈ A } {\displaystyle \operatorname {trace} _{F}({\mathcal {A}})=\{A\cap F:A\in {\mathcal {A}}\}} the set of possible intersections of elements of A {\displaystyle {\mathcal {A}}} with F {\displaystyle F} . [ 2 ] | https://en.wikipedia.org/wiki/Shearer's_inequality |
Sheath current filters are electronic components that can prevent noise signals travelling in the sheath of sheathed cables, which can cause interference. Using sheath current filters, ground loops causing mains hum and high frequency common-mode signals can be prevented.
Depending on the type, sheath current filters can remove or ameliorate hum in audio equipment, scanning frequencies in AV equipment and unwanted common-mode signals in coaxial cables .
There are various types of sheath current filter. Different types have different characteristics and are used to combat different forms of sheath current.
Isolation transformers are transformers for low frequency analog and digital audio connections or rarely for high-frequencies in antenna cables between TV outlets and devices (tuner, VCR, TV, etc.). This filter then suppresses low-frequency ground loop currents on the sheath and core of coaxial cables, which can result from multiple grounds at different potentials. They affect the signal because of their upper and lower frequency limits and therefore can not transmit DC . In addition, analog signals can suffer from nonlinear distortion, especially near the frequency limits of the device.
The propagation of (low-frequency) ripple current through antenna cables may be prevented by capacitive coupling of the two conductors. Such elements are available as adapters called braid-breakers or ground breakers and have, in both the signal and ground connection, coupling capacitors (with a capacitance of approximately 1 nF ). They are generally only capable of passing frequencies greater than approximately 50 MHz - ripple current cannot flow. Capacitive coupling adapters have an upper limit frequency of around 1 GHz, so UHF signals can pass through. A passband of approximately 50 MHz to 1 GHz makes the devices useful for analog and digital television reception, and broadcast FM radio reception. Such ground breakers cannot be used in commercial satellite receivers, since low-frequency control signals and the supply voltage for the low-noise block converter have to be transferred.
Ferrite sheath current filters consist of a ferrite sleeve around the line or cable bundle. These are common mode chokes, damping high-frequency common-mode noise on cables.
They block to high-frequency common-mode currents above about 50 MHz and affect the signal and the ground connection is not in terms of their Low frequency properties or protective function. Ferrite sheath current filters cannot effectively attenuate ground loop noise.
Cables for connection of computer peripherals often have a ferrite bead. The cable can be used to increase the inductance also repeatedly passed through a ferrite core.
Ferrite sheath current filters can only work effectively if a common-mode signal can flow on a line. This is generally the case when a cable bundle or a coaxial cable has a ground connection at both ends to the grounded equipment.
For a cable bundle between two devices but grounded at only one device, in general a ferrite sheath current filter is not effective. With such an arrangement, a ferrite bead would only be effective to reduce sheath current standing waves . When used to eliminate standing waves, the ferrite sheath current filter must be placed at a current antinode , but not at standing wave nodes.
Ferrite beads are available for different frequency ranges and power capacity.
Transformer sheath current filters are used in low-frequency signal lines, where a ground loop otherwise can not be prevented. They are galvanically isolated .
Capacitive coupling filters can be used to prevent hum loops in antennas and radio frequency cables. They also have a galvanic separation.
Ferrite sheath current filters are used for noise suppression, combating noise such as radio frequency interference. They have no electrical isolation and cannot prevent ground loops. | https://en.wikipedia.org/wiki/Sheath_current_filter |
Shedun is a family of malware software (also known as Kemoge, Shiftybug and Shuanet [ 1 ] [ 2 ] [ 3 ] ) targeting the Android operating system first identified in late 2015 by mobile security company Lookout , affecting roughly 20,000 [ 4 ] popular Android applications. [ 3 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ] Lookout claimed the HummingBad malware was also a part of the Shedun family, however, these claims were refuted. [ 9 ] [ 10 ]
Avira Protection Labs stated that Shedun family malware is detected to cause approximately 1500-2000 infections per day. [ 11 ] All three variants of the virus are known to share roughly ~80% of the same source code. [ 12 ] [ 13 ]
In mid 2016, arstechnica reported that approximately 10.000.000 devices would be infected by this malware [ 14 ] and that new infections would still be surging. [ 15 ] [ 16 ]
The malware's primary attack vector is repackaging legitimate Android applications (e.g. Facebook , Twitter , WhatsApp , Candy Crush, Google Now, Snapchat [ 17 ] ) [ 4 ] [ 18 ] [ 19 ] with adware included. The app which remains functional is then released to a third party app store; [ 20 ] once downloaded, the application generates revenue by serving ads (estimated to amount to $2 US per installation [ 19 ] ), most users cannot get rid of the virus without getting a new device, as the only other way to get rid of the malware is to root affected devices and re-flash a custom ROM . [ 21 ] [ 22 ]
In addition, Shedun-type malware has been detected pre-installed on 26 different types [ 23 ] of Chinese Android-based hardware such as Smartphones and Tablet computers . [ 24 ] [ 25 ] [ 26 ] [ 27 ] [ 28 ] [ 29 ] [ 30 ] [ 31 ] [ 32 ] [ 33 ] [ 34 ] [ 35 ] [ 36 ]
Shedun-family malware is known for auto- rooting the Android OS [ 18 ] [ 37 ] using well-known exploits like ExynosAbuse, Memexploit and Framaroot [ 38 ] (causing a potential privilege escalation [ 19 ] [ 39 ] [ 40 ] ) [ 41 ] and for serving trojanized adware and installing themselves within the system partition of the operating system , so that not even a factory reset can remove the malware from infected devices. [ 42 ] [ 43 ]
Shedun malware is known for targeting the Android Accessibility Service, [ 2 ] [ 42 ] [ 44 ] [ 45 ] [ 46 ] [ 47 ] [ 48 ] as well as for downloading and installing arbitrary applications [ 49 ] (usually adware ) without permission. [ 3 ] It is classified as "aggressive adware" for installing potentially unwanted program [ 50 ] [ 51 ] [ 52 ] applications and serving ads. [ 53 ]
As of April 2016, Shedun malware is considered by most security researchers to be next to impossible to entirely remove. [ 54 ] [ 55 ] [ 56 ] [ 57 ] [ 58 ] [ 59 ]
Avira Security researcher Pavel Ponomariov, who specializes in Android malware detection tools, mobile threat detection, and mobile malware detection automation research, [ 60 ] has published an in-depth analysis of this malware. [ 11 ]
The countries most infected by this virus were in Asia including China, India, Philippines, Indonesia and Turkey. [ 61 ] | https://en.wikipedia.org/wiki/Shedun |
The Sheild Professorship of Pharmacology is the senior professorship in pharmacology at the University of Cambridge . It is named in honour of Marmaduke Sheild . [ 1 ]
The position was originally established on 7 June 1946 as a personal chair for the tenure of Ernest Basil Verney . On 11 March 1961 the professorship was re-established on a permanent basis. [ 2 ] | https://en.wikipedia.org/wiki/Sheild_Professor_of_Pharmacology |
The Shelby Gem Factory was the production facility of ICT Incorporated, a company in Shelby, Michigan , United States, that manufactured artificial gemstones through proprietary processes. ICT began operations in 1970 and closed in December 2019.
Larry Paul Kelley established ICT (International Crystal Technology [ 1 ] ) in 1970 with Craig Hardy and Tom VanBergen. [ 2 ] [ 3 ] Kelley had worked for Dow Chemical in Ludington and at a factory in Ann Arbor that produced laser crystals. [ 4 ] The facility was sited in Shelby because the town had a new industrial park. [ 5 ] By 2015, Kelley was ICT's sole owner. [ 6 ]
The Shelby Gem Factory initially produced only synthetic ruby , with ruby lasers being the principal application, primarily sold to firms in California. However, laser technology was in its infancy, [ 1 ] and the far greater profit potential of converting ruby rods into a variety of artificial gemstones of various colors led to a change in the factory's focus. [ 2 ] Larry Kelley built on Soviet research into cubic zirconia and became its first commercial producer, having solved issues of temperature control that had impeded its production. [ 1 ] For a time, cubic zirconia was a lucrative product line; Shelby opened factories outside the United States to keep up with demand. [ 7 ] [ 8 ] However, the value of cubic zirconia soon declined to the point that it was used as fill when the factory was expanded. [ 1 ] In 1983, ICT opened a faceting factory in southern China to create gemstones for jewelry use from the crystals produced in Shelby; this closed in 1991, and separate companies in China and South Korea were contracted to continue faceting. The South Korean market represented up to 40 percent of the factory's sales until a precipitous decline caused by the 1997 Asian financial crisis . [ 1 ] In 1994, the factory entered the business of recrystallizing rubies, buying low-grade gems from Myanmar to be melted down in the process. [ 1 ]
A 50-seat theater ran a presentation for visitors, [ 3 ] and jewelry was sold on site. [ 5 ]
The factory closed in 2019 after Kelley was diagnosed in 2017 with Alzheimer's disease . Other issues that contributed to the closing were worldwide competition and online markets. [ 8 ] Larry Kelley died on October 24, 2020. [ 9 ]
Some of the furnaces burned at 5,040 °F (2,780 °C). [ 10 ] Factory tours were discontinued due to liability concerns attendant to the "very high temperatures and extremely bright light" and the unavailability of affordable insurance to cover the risk. [ 5 ]
The gems were synthesized in a furnace . [ 5 ] The Shelby Gem Factory's diamonds were simulants . [ 2 ] The factory also manufactured simulated citrine and topaz , along with other birthstone substitutes. [ 5 ] | https://en.wikipedia.org/wiki/Shelby_Gem_Factory |
The Sheldon spectrum is an empirically-observed feature of marine life by which the size of an organism is inversely correlated with its abundance in the ocean. The spectrum is named after Ray Sheldon, a marine ecologist at Canada’s Bedford Institute of Oceanography in Dartmouth , Nova Scotia . Sheldon and colleagues first suggested the existence of the inverse correlation based on seagoing measurements of plankton made with a Coulter counter in the late 1960s, most notably during the first circum-navigation of the Americas aboard the CCGS Hudson . [ 1 ]
The inverse correlation implies that biomass density as a function of logarithmic body mass is approximately constant over many orders of magnitude . [ 2 ] For example, when Sheldon and his colleagues analyzed a plankton sample in a bucket of seawater, they would tend to find that one third of the plankton mass was between 1 and 10 micrometers , another third was between 10 and 100 micrometers, and a third was between 100 micrometers and 1 millimeter. To make up for the differences of size, there must be a remarkably accurate mathematically correlative decrease in number of organisms as they become larger, in order for the biomass to remain constant. Thus, the rule predicts that krill which are a million times smaller than tuna are a million times more abundant in the ocean, a prediction which appears to be true. [ 3 ]
There is strong evidence that human behavior, particularly overfishing and whaling , have modified the Sheldon spectrum for larger species, and it is unknown what long term effects such global alteration may have. [ 4 ] | https://en.wikipedia.org/wiki/Sheldon_spectrum |
Shelf-Break Fronts are a process by which stratification of the water column occurs. This stratification normally results in thermoclines, since they occur where a sudden change in water depth causes a constriction of the current flow. They can be expressed as a ratio of their potential energy due to maintaining mixed (non-stratified) conditions, to the dissipated energy produced by the current being forced across the sudden change in depth. This can be expressed as:
The energy terms can be expressed in very detailed equations, but with constant terms factored out, the important terms are water velocity (average velocity, | U ¯ | {\displaystyle \left\vert {\bar {U}}\right\vert } ) and water depth (h).
The equation for the stratification index can be expressed as:
Where C D {\displaystyle C_{D}} is a friction coefficient , approximated as 0.003 for a sandy bottom. This index can be calculated for any coastal region, usually in the range of +3 (highly stratified) to -2 (highly turbulent).
The stratification index for a Shelf Break Front is an indication of how productive phytoplankton will be. When the stratification index is approximately 1.5, this produces a nutrient-rich environment for the growth of phytoplankton. Too much higher, and the stratification of the water column will not cause the upwellings of nutrients needed for the phytoplankton to prosper, too much lower, and the water will be too turbulent for the phytoplankton to use the nutrients available.
Stability of the front, in addition to nutrients, [ 2 ] is a key to phytoplankton production.
An illustration of the stratification index for Narragansett Bay is shown here, with the average speeds estimated, using actual bathymetry for the bay, and an estimated C D {\displaystyle C_{D}} for silt , which composes much of the bay's bottom. Using the Stokes Spreadsheet, [ 3 ] and some customization on the size of silt particles, I used a C D {\displaystyle C_{D}} = 0.0011. More accurate speed measurements and detailed C D {\displaystyle C_{D}} values for the Bay's bottom could yield a higher fidelity image.
Notice the green color (a stratification index of approximately 1.5) along the edges of the Northern Bay and near some of the islands. These areas are favorable to the formation of algal blooms in the Narraganset Bay habitat due to the stratification index being approximately 1.5. Algae have been observed in high concentration in some of these areas, but not all of them.
Using flow cytometry , results [ 5 ] have determined that the relative abundance of picophytoplankton (< 2 μ {\displaystyle \mu } m), small nanophytoplankton (2 to 10 μ {\displaystyle \mu } m) and large nanophytoplankton (10-20 μ {\displaystyle \mu } m) are greatly affected by the stratification index of the water column. Cell diversity was greatest in the presence of moderate levels of stratification.
If the turbulence is too high, their numbers remain stable or fall, but if there is no turbulence, their numbers do fall. It is postulated that the nutrient-rich boundary layer around each phytoplankton cell is not exhausted, but renewed, by this moderate level of turbulence. [ 2 ] | https://en.wikipedia.org/wiki/Shelf-break_front |
In masonry veneer building construction, a shelf angle or masonry support is a steel angle which supports the weight of brick or stone veneer and transfers that weight onto the main structure of the building so that a gap or space can be created beneath to allow building movements to occur.
Traditional masonry buildings had thick Load-bearing walls that supported the weight of the building. Openings in these load bearing walls such as doors and windows were typically small and spanned by steel lintels or masonry arches .
The invention of skeleton frame buildings made it possible to reduce the thickness of the walls and have wide openings such as ribbon windows extending across most or all of the building facade . In these buildings, brick, stone, or other masonry cladding is often just a single wythe of material called a veneer since it is non-loadbearing. The only way to support the weight of this veneer across a wide opening is by providing a shelf angle on which the masonry bears. [ 1 ] The shelf angle, in turn, is attached to major elements of the building structure such as floor beams or structural columns . Shelf angles are in reality a horizontal expansion joint which allows growth of the brick below the shelf angle and to allow movement or shrinkage of the frame without putting stresses on the brick veneer. [ 2 ] In the United States, common sizes for steel shelf angles include L 3" x 3" x 1/4" and L 4" x 4" x 1/4".In the UK and Europe shelf angles / masonry support are predominantly manufactured in stainless steel to prevent corrosion and failure. These are bespoke to the building's frame and engineered to take the loads required.
Ramsey, Charles (2000). Hoke, John Ray Jr. (ed.). Architectural Graphics Standards (10th ed.). John Wiley & Sons, Inc. ISBN 0-471-34816-3 . | https://en.wikipedia.org/wiki/Shelf_angle |
Shelf life is the length of time that a commodity may be stored without becoming unfit for use, consumption, or sale. [ 1 ] In other words, it might refer to whether a commodity should no longer be on a pantry shelf (unfit for use), or no longer on a supermarket shelf (unfit for sale, but not yet unfit for use). It applies to cosmetics , foods and beverages , medical devices , medicines , explosives , pharmaceutical drugs , [ 2 ] chemicals , tyres , batteries , and many other perishable items. In some regions, an advisory best before , mandatory use by or freshness date is required on packaged perishable foods. The concept of expiration date is related but legally distinct in some jurisdictions. [ 3 ]
Shelf life is the recommended maximum time for which products or fresh (harvested) produce can be stored, during which the defined quality of a specified proportion of the goods remains acceptable under expected (or specified) conditions of distribution, storage and display. [ 4 ]
According to the United States Department of Agriculture (USDA), "canned foods are safe indefinitely as long as they are not exposed to freezing temperatures, or temperatures above 90 °F (32.2 °C)". [ citation needed ] If the cans look okay, they are safe to use. Discard cans that are dented, rusted, or swollen. High-acid canned foods (tomatoes, fruits) will keep their best quality for 12 to 18 months; low-acid canned foods (meats, vegetables) for 2 to 5 years. [ 5 ]
"Sell by date" is a less ambiguous term for what is often referred to as an "expiration date". Most food is still edible after the expiration date. [ 6 ] A product that has passed its shelf life might still be safe, but quality is no longer guaranteed. In most food stores, waste is minimized by using stock rotation , which involves moving products with the earliest sell by date from the warehouse to the sales area, and then to the front of the shelf, so that most shoppers will pick them up first and thus they are likely to be sold before the end of their shelf life. Some stores can be fined for selling out of date products; most if not all would have to mark such products down as wasted , resulting in a financial loss.
Shelf life depends on the degradation mechanism of the specific product. Most can be influenced by several factors: exposure to light , heat , moisture, transmission of gases , mechanical stresses , and contamination by things such as micro-organisms. Product quality is often mathematically modelled around a parameter (concentration of a chemical compound, a microbiological index, or moisture content). [ 7 ]
For some foods, health issues are important in determining shelf life. Bacterial contaminants are ubiquitous, and foods left unused too long will often be contaminated by substantial amounts of bacterial colonies and become dangerous to eat, leading to food poisoning . However, shelf life alone is not an accurate indicator of how long the food can safely be stored. For example, pasteurized milk can remain fresh for five days after its sell-by date if it is refrigerated properly. However, improper storage of milk may result in bacterial contamination or spoilage before the expiration date. [ 8 ]
The expiration date of pharmaceuticals specifies the date the manufacturer guarantees the full potency and safety of a drug. Most medications continue to be effective and safe for a time after the expiration date. A rare exception is a case of renal tubular acidosis purportedly caused by expired tetracycline . [ 9 ] A study conducted by the U.S. Food and Drug Administration covered over 100 drugs, prescription and over-the-counter. The study showed that about 90% of them were safe and effective as long as 15 years past their expiration dates. Joel Davis, a former FDA expiration-date compliance chief, said that with a handful of exceptions - notably nitroglycerin, insulin and some liquid antibiotics - most expired drugs are probably effective. [ 10 ]
Shelf life is not significantly studied during drug development [ dubious – discuss ] , and drug manufacturers have economic and liability incentives to specify shorter shelf lives so that consumers are encouraged to discard and repurchase products. One major exception is the Shelf Life Extension Program (SLEP) of the U.S. Department of Defense (DoD), which commissioned a major study of drug efficacy from the FDA starting in the mid-1980s. One criticism is that the U.S. Food and Drug Administration (FDA) refused to issue guidelines based on SLEP research for normal marketing of pharmaceuticals even though the FDA performed the study. The SLEP and FDA signed a memorandum that scientific data could not be shared with the public, public health departments, other government agencies, and drug manufacturers. [ 11 ] State and local programs are not permitted to participate. [ 12 ] The failure to share data has caused foreign governments to refuse donations of expired medications. [ 13 ] One exception occurred during the 2010 Swine Flu Epidemic when the FDA authorized expired Tamiflu based on SLEP Data. [ 14 ] The SLEP discovered that drugs such as Cipro remained effective nine years after their shelf life, and, as a cost-saving measure, the US military routinely uses a wide range of SLEP tested products past their official shelf life if drugs have been stored properly. [ 15 ]
Preservatives and antioxidants may be incorporated into some food and drug products to extend their shelf life. Some companies use induction sealing and vacuum /oxygen-barrier pouches to assist in the extension of the shelf life of their products where oxygen causes the loss.
The DoD Shelf-Life Program defines shelf-life as
The total period of time beginning with the date of manufacture, date of cure (for elastomeric and rubber products only), date of assembly, or date of pack (subsistence only), and terminated by the date by which an item must be used (expiration date) or subjected to inspection, test, restoration, or disposal action; or after inspection/laboratory test/restorative action that an item may remain in the combined wholesale (including manufacture's) and retail storage systems and still be suitable for issue or use by the end user. Shelf-life is not to be confused with service-life (defined as, A general term used to quantify the average or standard life expectancy of an item or equipment while in use. When a shelf-life item is unpacked and introduced to mission requirements, installed into intended application, or merely left in storage, placed in pre-expended bins, or held as bench stock , shelf-life management stops and service life begins.) [ 16 ]
Shelf life is often specified in conjunction with a specific product, package, and distribution system. For example, an MRE field ration is designed to have a shelf life of three years at 80 °F (27 °C) and six months at 100 °F (38 °C). [ 17 ]
Nearly all chemical reactions can occur at normal temperatures (although different reactions proceed at different rates). However most reactions are accelerated by high temperatures, and the degradation of foods and pharmaceuticals is no exception. The same applies to the breakdown of many chemical explosives into more unstable compounds. Nitroglycerine is notorious. Old explosives are thus more dangerous (i.e. liable to be triggered to explode by very small disturbances, even trivial jiggling) than more recently manufactured explosives. Rubber products also degrade as sulphur bonds induced during vulcanization revert; this is why old rubber bands and other rubber products soften and get crispy, and lose their elasticity as they age.
The often quoted rule of thumb is that chemical reactions double their rate for each temperature increase of 10 °C (18 °F) because activation energy barriers are more easily surmounted at higher temperatures. However, as with many rules of thumb, there are many caveats and exceptions. The rule works best for reactions with activation energy values around 50 kJ/mole; many of these are important at the usual temperatures we encounter. It is often applied in shelf life estimation, sometimes wrongly. There is a widespread impression, for instance in industry, that "triple time" can be simulated in practice by increasing the temperature by 15 °C (27 °F), e.g., storing a product for one month at 35 °C (95 °F) simulates three months at 20 °C (68 °F). This is mathematically incorrect (if the rule was precisely accurate the required temperature increase would be about 15.8 °C (28.4 °F)), and in any case the rule is only a rough approximation and cannot always be relied on. Chemists often use the more comprehensive Arrhenius equation for better estimations.
The same is true, up to a point, of the chemical reactions of living things. They are usually catalyzed by enzymes which change reaction rates, but with no variation in catalytic action, the rule of thumb is still mostly applicable. In the case of bacteria and fungi , the reactions needed to feed and reproduce speed up at higher temperatures, up to the point that the proteins and other compounds in their cells themselves begin to break down, or denature , so quickly that they cannot be replaced. This is why high temperatures kill bacteria and other micro-organisms: 'tissue' breakdown reactions reach such rates that they cannot be compensated for and the cell dies. On the other hand, 'elevated' temperatures short of these result in increased growth and reproduction; if the organism is harmful, perhaps to dangerous levels.
Just as temperature increases speed up reactions, temperature decreases reduce them. Therefore, to make explosives stable for longer periods, or to keep rubber bands springy, or to force bacteria to slow down their growth, they can be cooled. That is why shelf life is generally extended by temperature control: ( refrigeration , insulated shipping containers , controlled cold chain , etc.) and why some medicines and foods must be refrigerated. Since such storing of such goods is temporal in nature and shelf life is dependent on the temperature controlled environment, they are also referred to as cargo even when in special storage to emphasize the inherent time-temperature sensitivity matrix.
Temperature data loggers and time temperature indicators can record the temperature history of a shipment to help estimate their remaining shelf life. [ 18 ]
According to the USDA , "foods kept frozen continuously are safe indefinitely". [ 5 ]
Passive barrier packaging can often help control or extend shelf life by blocking the transmission of deleterious substances, like moisture or oxygen, across the barrier. [ 2 ] Active packaging , on the other hand, employs the use of substances that scavenge, capture, or otherwise render harmless deleterious substances. [ 2 ] When moisture content is a mechanism for product degradation, packaging with a low moisture vapor transmission rate and the use of desiccants help keep the moisture in the package within acceptable limits. When oxidation is the primary concern, packaging with a low oxygen transmission rate and the use of oxygen absorbers can help extend the shelf life. Produce and other products with respiration often require packaging with controlled barrier properties. The use of a modified atmosphere in the package can extend the shelf life for some products.
The concept of shelf life applies to other products besides food and drugs. Gasoline has a shelf life, although it is not normally necessary to display a sell-by date. Exceeding this time-frame will introduce harmful varnishes [ clarification needed ] , etc. into equipment designed to operate with these products, i.e. a gasoline lawn mower that has not been properly winterized [ clarification needed ] could incur damage that will prevent use in the spring, and require expensive servicing to the carburetor.
Some glues and adhesives also have a limited storage life, and will stop working in a reliable and usable manner if their safe shelf life is exceeded.
Rather different is the use of a time limit for the use of items like vouchers, gift certificates and pre-paid phone cards, so that after the displayed date the voucher etc. will no longer be valid. Bell Mobility and its parent company, BCE Inc. have been served with notice of a $100-million class-action lawsuit alleging that expiry dates on its pre-paid wireless services are illegal. [ 19 ] | https://en.wikipedia.org/wiki/Shelf_life |
A shell-and-tube heat exchanger is a class of heat exchanger designs. [ 1 ] [ 2 ] It is the most common type of heat exchanger in oil refineries and other large chemical processes, and is suited for higher-pressure applications. As its name implies, this type of heat exchanger consists of a shell (a large pressure vessel ) with a bundle of tubes inside it. One fluid runs through the tubes, and another fluid flows over the tubes (through the shell) to transfer heat between the two fluids. The set of tubes is called a tube bundle, and may be composed of several types of tubes: plain, longitudinally finned, etc.
Two fluids, of different starting temperatures, flow through the heat exchanger. One flows through all the tubes in parallel and the other flows outside the tubes, but inside the shell, typically in counterflow. Heat is transferred from one fluid to the other through the tube walls, either from tube side to shell side or vice versa. Cross-baffles can be used to force the shell fluid to flow perpendicularly across the tubes to develop a more turbulent flow, increasing the heat-transfer coefficient. The fluids can be either liquids or gases on either the shell or the tube side. [ 3 ]
In order to transfer heat efficiently, a large heat transfer area should be used, leading to the use of many tubes. In this way, waste heat can be put to use. This is an efficient way to conserve energy.
Heat exchangers with only one phase (liquid or gas) on each side can be called one-phase or single-phase heat exchangers. Two-phase heat exchangers can be used to heat a liquid to boil it into a gas (vapor), sometimes called boilers , or to cool the vapors and condense it into a liquid (called condensers ), with the phase change usually occurring on the shell side. Boilers in steam engine locomotives are typically large, usually cylindrically-shaped shell-and-tube heat exchangers. In large power plants with steam-driven turbines , shell-and-tube surface condensers are used to condense the exhaust steam exiting the turbine into condensate water which is recycled back to be turned into steam in the steam generator.
They are also used in liquid-cooled chillers for transferring heat between the refrigerant and the water in both the evaporator and condenser , and in air-cooled chillers for only the evaporator.
There can be many variations on the shell-and tube-design. Typically, the ends of each tube are connected to plenums (sometimes called water boxes ) through holes in tubesheets . The tubes may be straight or bent in the shape of a U, called U-tubes.
In nuclear power plants called pressurized water reactors , large heat exchangers called steam generators are two-phase, shell-and-tube heat exchangers which typically have U-tubes. They are used to boil water recycled from a surface condenser into steam to drive a turbine to produce power. Most shell-and-tube heat exchangers are either 1, 2, or 4 pass designs on the tube side. This refers to the number of times the fluid in the tubes passes through the fluid in the shell. In a single pass heat exchanger, the fluid goes in one end of each tube and out the other.
Surface condensers in power plants are often 1-pass straight-tube heat exchangers (see surface condenser for diagram). Two and four pass designs are common because the fluid can enter and exit on the same side. This makes construction much simpler.
There are often baffles directing flow through the shell side so the fluid does not take a short cut through the shell side leaving ineffective low flow volumes. These are generally attached to the tube bundle rather than the shell in order that the bundle is still removable for maintenance.
Countercurrent heat exchangers are most efficient because they allow the highest log mean temperature difference between the hot and cold streams. Many companies however do not use two pass heat exchangers with a u-tube because they can break easily in addition to being more expensive to build. Often multiple heat exchangers can be used to simulate the countercurrent flow of a single large exchanger.
To be able to transfer heat well, the tube material should have good thermal conductivity . Because heat is transferred from a hot to a cold side through the tubes, there is a temperature difference through the width of the tubes. Because of the tendency of the tube material to thermally expand differently at various temperatures, thermal stresses occur during operation. This is in addition to any stress from high pressures from the fluids themselves. The tube material also should be compatible with both the shell-and-tube side fluids for long periods under the operating conditions ( temperatures , pressures, pH , etc.) to minimize deterioration such as corrosion . All of these requirements call for careful selection of strong, thermally-conductive, corrosion-resistant, high quality tube materials, typically metals , including aluminium , copper alloy , stainless steel , carbon steel , non-ferrous copper alloy, Inconel , nickel , Hastelloy and titanium . [ 4 ] Fluoropolymers such as Perfluoroalkoxy alkane (PFA) and Fluorinated ethylene propylene (FEP) are also used to produce the tubing material due to their high resistance to extreme temperatures. [ 5 ] Poor choice of tube material could result in a leak through a tube between the shell-and-tube sides causing fluid cross-contamination and possibly loss of pressure.
The simple design of a shell-and-tube heat exchanger makes it an ideal cooling solution for a wide variety of applications. One of the most common applications is the cooling of hydraulic fluid and oil in engines, transmissions and hydraulic power packs . With the right choice of materials they can also be used to cool or heat other mediums, such as swimming pool water or charge air. [ 6 ] There are many advantages to shell-and-tube technology over plates
In shell-and-tube heat exchangers there is a potential for a tube to rupture and for high pressure (HP) fluid to enter and over-pressurise the low pressure (LP) side of the heat exchanger. [ 8 ] The usual configuration of exchangers is for the HP fluid to be in the tubes and for LP water, cooling or heating media to be on the shell side. There is a risk that a tube rupture could compromise the integrity of the shell and the release flammable gas or liquid, with a risk to people and financial loss. The shell of an exchanger must be protected against over-pressure by rupture discs or relief valves. The opening time of protection devices has been found to be critical for exchanger protection. [ 9 ] Such devices are fitted directly on the shell of the exchanger and discharge into a relief system.
Shell-and-tube heat exchangers are integral components in thermal engineering , primarily used for efficient heat transfer. The design and arrangement of the tubes within these exchangers are fundamental to their operation and effectiveness. [ 10 ] The precise design and specification of tubes in shell and tube heat exchangers underscore the complexities of thermal engineering . Each design aspect, from material selection to tube arrangement and fluid flow , plays a vital role in the exchanger's performance, showcasing the intricacies and precision required in this field. [ 10 ]
Tubes in these exchangers, often termed as condenser tubes, are distinct from typical water tubing. They adhere to the Birmingham Wire Gage (BWG) standard, which dictates specific dimensions such as the outside diameter . For example, a 1-inch tube according to BWG will have an exact outside diameter of 1 inch. [ 11 ] Detailed specifications are available in specialized references.
The tubes in shell and tube heat exchanger [1] s are constructed from a range of materials, selected based on factors such as thermal conductivity, mechanical strength, corrosion resistance, and compatibility with the process fluids. The selection of tube material is crucial for optimizing heat exchanger performance, ensuring durability, and preventing issues such as corrosion and fouling.
Common materials used for the tubes include:
Stainless Steel (e.g., 304, 316L, 904L): Stainless steel is commonly used in shell and tube heat exchangers due to its favorable combination of thermal conductivity, corrosion resistance, and mechanical strength. These alloys are suitable for a wide range of industries, including chemical, petrochemical, and food processing. Stainless steel's resistance to corrosion in both high and low temperatures makes it a popular choice.
Titanium and Titanium Alloys: Titanium is highly resistant to corrosion, particularly in harsh environments such as seawater and acidic conditions. Its excellent strength-to-weight ratio and resistance to chloride stress corrosion cracking make it ideal for applications in the chemical and marine industries, where corrosion resistance is critical.
Nickel Alloys (e.g., Inconel, Hastelloy): Nickel alloys are often used in high-temperature and highly corrosive environments. These materials, such as Inconel and Hastelloy, provide excellent resistance to oxidation and corrosion, making them ideal for power generation, aerospace, and chemical processing industries.
Copper and Copper Alloys (e.g., CuNi, Brass): Copper and copper alloys are chosen primarily for their high thermal conductivity, which enhances heat transfer. These materials are often used in applications such as HVAC systems, refrigeration, and desalination processes, where efficient heat exchange is essential.
Carbon Steel: Carbon steel is a cost-effective material commonly used in less corrosive environments. It is often selected for applications where cost is a major consideration, but protective coatings or internal linings are usually required to reduce the risk of corrosion.
Aluminum: Aluminum offers good thermal conductivity and is lightweight, making it suitable for applications that require both high heat transfer rates and reduced weight, such as in certain heat recovery and aerospace applications.
The choice of material for the tubes in a shell and tube heat exchanger is influenced by the operating conditions, including temperature, pressure, and the chemical nature of the fluids involved. Proper material selection helps prevent premature failure, corrosion, and inefficiency, thus ensuring the heat exchanger operates effectively throughout its service life.
The arrangement of tubes is a crucial design aspect. They are positioned in holes drilled in tube sheets, with the spacing between holes - known as tube pitch - being a key factor for both structural integrity and efficiency. [ 10 ] Tubes are typically organized in square or triangular patterns, and specific layouts are detailed in engineering references.
Tube count refers to the maximum number of tubes that can fit within a shell of a specific diameter without weakening the tube sheet. [ 10 ] This aspect is crucial for ensuring the structural integrity and efficiency of the heat exchanger. Information on tube counts for various shell sizes can be found in specialized literature.
Shell and tube ===Fluid Flow===
In shell and tube heat exchangers, there are two distinct fluid streams for heat transfer . The tube fluid circulates inside the tubes, while the shell fluid flows around them, guided by various types of baffles (e.g., segmental, helical, or disc-and-doughnut). The movement of the shell fluid, designed to enhance turbulence and heat transfer, can be arranged in different flow configurations, such as counter-current, co-current, or cross-flow. The number of passes, whether single or multiple, made by the shell and tube fluids over the heat exchange surfaces plays a key role in optimizing the exchanger's overall performance. These aspects are detailed in specialized references. | https://en.wikipedia.org/wiki/Shell-and-tube_heat_exchanger |
A shell is a three-dimensional solid structural element whose thickness is very small compared to its other dimensions. It is characterized in structural terms by mid-plane stress which is both coplanar and normal to the surface. A shell can be derived from a plate in two steps: by initially forming the middle surface as a singly or doubly curved surface, [ 1 ] then by applying loads which are coplanar to the plate's plane thus generating significant stresses.
Materials range from concrete (a concrete shell ) to fabric (as in fabric structures ).
Thin-shell structures (also called plate and shell structures ) are lightweight constructions using shell elements . These elements, typically curved, are assembled to make large structures. Typical applications include aircraft fuselages , boat hulls, and the roofs of large buildings.
A thin shell is defined as a shell with a thickness which is small compared to its other dimensions and in which deformations are not large compared to thickness. A primary difference between a shell structure and a plate structure is that, in the unstressed state, the shell structure has curvature as opposed to the plates structure which is flat. Membrane action in a shell is primarily caused by in-plane forces ( plane stress ), but there may be secondary forces resulting from flexural deformations. Where a flat plate acts similar to a beam with bending and shear stresses , shells are analogous to a cable which resists loads through tensile stresses. The ideal thin shell must be capable of developing both tension and compression. [ 2 ]
The most popular types of thin-shell structures are:
Persons related:
This article about a civil engineering topic is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Shell_(structure) |
Shell Rotella is a line of heavy-duty engine lubrication products produced by Shell plc . The line includes engine oils, gear oils and coolants. The oil carries both the American Petroleum Institute (API) diesel "C" rating as well as the API gasoline engine "S" rating. Ratings differ based on the oil. Rotella oils, like the T3 15W-40, meet both the API CJ-4 and SM specifications, and may be used in both gasoline and diesel engines. However, it is formulated specifically for vehicles without catalytic converters , containing phosphorus levels beyond the 600–800 ppm range. [ 1 ] Therefore, Rotella is not recommended for gasoline vehicles with catalytic converters due to the higher risk of damaging these emission controls. [ citation needed ] [ 2 ] Newer formulations of Rotella T6 however are API SM rated as safe for pre-2011 gasoline vehicles.
The Rotella product family is categorized by Shell into the following product families:
In the engine oil family, there are four basic oil sub-families:
Shell is marketing their new CJ-4/SM oil as "Triple Protection," meaning it provides enhanced qualities for engine wear, soot control and engine cleanliness. Shell's Rotella website indicates that on-road testing confirms the new Triple Protection technology produces better anti-wear characteristics than their existing CI-4+ rated Rotella oil. This is achieved despite a lower zinc and phosphorus additive level as called for by the API CJ-4 specification. (The 15W-40 Rotella T with Triple Protection oil has approximately 1200 ppm of zinc and 1100 ppm phosphorus at the time of manufacture.)
The Shell Rimula brand is multi-national and comparable in all aspects, including the classification names. (i.e. T-5, T-6, Etc.)
Rotella competes with similar lubrication products from other oil manufacturers. Some notable competitive products are:
Though marketed as an engine oil for diesel trucks, Rotella oil has found popularity with motorcyclists as well. The lack of " friction modifiers " in Rotella means they do not interfere with wet clutch operations. This is called a "shared sump" design, which is unlike automobiles which maintain separate oil reservoirs – one for the engine and one for the transmission. Used oil analysis reports on BobIsTheOilGuy.com have shown wear metals levels comparable to oils marketed as motorcycle-specific.
Rotella oil is ideal for older cars without catalytic converters and for which zinc was a requirement at the time for engine oil. It eliminates the need for adding a zinc additive to modern oils. [ 4 ]
Both Rotella T4 15W-40 conventional and, Rotella T6 5W-40 and 15w-40 Synthetic both list the JASO MA/MA 2 standard; this information can be found on the bottle adjacent to the SAE/API rating stamp. JASO is an acronym that stands for Japanese Automotive Standards Organization . Note that the 10W-30 conventional oil does not list JASO-MA.
Likewise with motorcycles, though marketed as an engine oil for diesel trucks, Rotella T6 5W-40 synthetic oil has also found popularity with drivers and tuners of gasoline powered vehicles that utilize turbocharging or other forms of forced induction . Several owners of high performance model cars have adopted its use due to its high heat tolerance and its resistance to shearing. Rotella T6 is a Non Energy Conserving Oil, and does not meet GF-5 Oil specifications. When Rotella T6 was revised for the API specification (for use in spark ignition engines), its zinc levels were effectively reduced. Higher (content) zinc additives ( ZDDP ) are required for flat tappet engines and cartridge bearings, which in previous formulations Rotella T6 had desirable levels of zinc (ZDDP).
In December 2016 Shell Rotella Oils were updated to the newer API CK-4 Oil specification (Previously CJ-4).
″The new API CK-4 and FA-4 categories are driven by changes in engine technology to meet emissions, renewable fuel and fuel economy standards for reduced CO2 and other greenhouse gas emissions″ [ 5 ]
Upon Release of CK-4 API Licensing (Dec/2016) FORD issued a statement stating ″Ford testing has shown some CK-4 type formulations have shown inadequate wear protection compared to CJ-4 formulations developed and licensed before 2016″ [ 6 ] Similarly, Stellantis also issued a TSB citing Oil requirements that eliminated CK-4 Rotella from being an approved option in the 6.7L Diesel engines. [ 7 ] .And RAM's 3rd Gen ECO-Diesel equipped trucks no longer recommend CK-4 in their Diesel engines.
Rotella has since gained Fords updated oil specification by raising the phosphorus level of Rotella products. Rotella does not meet Stellantis' new oil specification as of Jan/2024.
With Rotella's CK-4 offerings under a new light, their robustness for use in Gasoline engines has come into question. Many users that once relied on Rotella in their gasoline engines have moved onto Motor oils that meet more stringent Gasoline Motor oil tests such as Porsche A40, BMW LL01, and MB229.5. Another Shell product that meets these specifications would be Pennzoil Platinum® Euro. | https://en.wikipedia.org/wiki/Shell_Rotella |
The Shell Spher process ( Shell Pellet Heat Exchange Retorting ) is an above ground fluidization bed retorting technology for shale oil extraction . It is classified as a hot recycled solids technology. [ 1 ] [ 2 ]
Raw oil shale is crushed to a fine particles. Heat is transferred to oil shale by heat-carrying ceramic balls of size 6 to 8 millimetres (0.24 to 0.31 in). Raw oil shale is preheated in fluidized bed at the temperature of 600 °F (320 °C) in the case if oxygen is used as fluidizing medium, or at 650 °F (340 °C) if non-oxidizing gases are used. Heated ceramic balls fall then through the bed in counter-current direction. The preheated oil shale is further heated in the retorting vessel. The retorted spent shale is cooled in a fast-fluidized bed by the recirculated cool pellets from the preheater; while cooling the spent shale ceramic balls are heated by the spent shale. [ 3 ] | https://en.wikipedia.org/wiki/Shell_Spher_process |
The Shell Technology Centre was a chemical and oil products research institute in northern Cheshire, near Stanlow , owned by Anglo-Dutch Shell .
The site was first set up, in 1941, by Shell for the Ministry of Aircraft Production as the Aero Engine Research Laboratory .
It tested a BMW 801 engine with different octane ratings of fuel in the early 1940s.
It returned to Shell ownership in April 1947. [ 1 ] The site had 70 scientists, and around 250 technicians working on quartz combustion tubes, direct fuel injection, butane fuel and the atomisation of fuel. It claimed to be the largest oil research centre in the British Empire . The site was 30 acres and 730,000 square feet, with 900 staff. The site had developed synthetic rubber, paint, varnish and soap. [ 2 ] A new 85-acre chemicals plant was to open in 1948 (the Stanlow refinery). [ 3 ]
Stanlow made around 24,000 tons of chemicals per year. The neighbouring oil refinery opened in 1949, although a smaller plant had been there since 1924. The Shellhaven plant, in Essex , would make 30,000 tons of chemicals. [ 4 ] It opened officially on Thursday 20 May 1948 as Shell Research Centre, by George Legh-Jones. [ 5 ] Also attending the opening was Lt-Gen Jimmy Doolittle , known for his strategy of bombing Germany, John Cunningham (Royal Navy officer) , First Sea Lord, and Air Chief Marshal Arthur Barratt [ 6 ]
In the 1950s it was one of three main Shell research sites in the UK, the others being in Kent and Buckinghamshire.
In 1962, Shell spent £25m on research, with 19 worldwide research centres, 8 in Europe, and 11 in the US. [ 7 ] Pre-ignition was prevented by Ignition Control Additive (ICA), developed at the centre, which was added to Shell petrol, in the UK, from Monday 11 January 1954. ICA contained tricresyl phosphate .
Vehicle testing was conducted at the former RAF Poulton , but in 1957, this was moved to the former RAF Hooton Park , when flying operations ceased. [ 8 ] The site had 1000 staff, with 200 graduates in 1957. [ 9 ]
In October 1960 a three-day international symposium held entitled Wear in the gasoline engine . Prof Frank Philip Bowden FRS spoke at the meeting. [ 10 ]
Testing work in the 1960s took place at the Autodrome de Linas-Montlhéry in France, and MIRA in Leicestershire .
By the early 1960s Shell also had its Central Laboratories in Surrey (which opened in 1956), the Tunstall Laboratory, and Chemical Enzymology Laboratory at Sittingbourne in Kent. Shell X-100 was Europe's top selling motor oil (lubrication).
North Sea oil was produced from 1975.
In the mid 1970s Shell had around 5,000 worldwide research staff. In 1975 it closed two of its four British research sites, and one in Delft in the Netherlands. The Surrey research site closed with its 430 employees, with its work transferred work to Amsterdam, the Netherlands, and Cheshire with the centre's 850 employees. Before the closures, Shell had 2080 employees at British research centres.
The main Dutch research sites were at Amsterdam (Royal Shell Laboratory Amsterdam) and Rijswijk. [ 11 ]
It has had much contact with local schools. In the 1960s it worked informally with Ellesmere Port County Grammar School for Boys [ 17 ] In the 1990s it worked with Stanney High School (now Ellesmere Port Church of England College ), Pensby High School , [ 18 ] and Helsby High School . [ 19 ]
Shell closed its research centres in the UK in 2014, moving the research to Germany. Shell had sold the neighbouring oil refinery. 280 staff moved to London and Manchester, with 170 to northern Germany.
The site was largely an automotive engineering research facility. [ 20 ] Work was carried out on direct fuel injection and butane-powered engines.
A 5 kW fuel cell had been first demonstrated at Cambridge in 1959 by Francis Thomas Bacon ; the site looked into fuel cell technology. A methanol fuel cell was demonstrated in December 1964. [ 21 ] The world's first liquid fuel cell in 1964 was made by the Surface Reactions Division, with K.R. Williams; it was a direct methanol fuel cell , with a sulphuric acid electrolyte, with a palladium -silver membrane.
Work was also conducted at the Koninklijke Shell Laboratorium (now called the Energy Transition Campus Amsterdam ). The proton-exchange membrane fuel cell (PEMFC) took over in the late 1980s.
In 1972 it made the world's first fuel cell car, a converted DAF 44 .
The site had worked on early jet engines in the war, on work for the Comet , and would work on lubrication and fuel for Concorde . By 1961 around 500 scientists and 350 technicians. [ 22 ]
In 1977 made a record-breaking vehicle that did 1141 mpg, with bicycle wheels. In 1977 it was predicted that oil would run out by 1990. [ 23 ] A competition run by the centre for fuel efficient vehicles took place on 5 July 1977 at Mallory Park , with teams from 23 universities - the Shell Mileage Marathon . The Shell vehicle had a Honda 50cc engine, and consumed 1252 mpg.
At a Deutsche Shell Mileage Marathon at Hockenheim , it managed 1373 mpg, but three German vehicles consumed less, with one managing 1904 mpg. [ 24 ] Shell now run the Shell Eco-marathon , which largely the only international event of its kind.
In 1994, Shell decided to invest £70m in new buildings at the site, when it moved out from its Kent site at the end of 1995, so environmental research and 140 scientists moved to Cheshire. [ 25 ] Alfred McAlpine started construction in August 1994. [ 26 ] In 1997, Shell took fuel additive research away from Cheshire, when it undertook joint research work with Esso. [ 27 ]
Its scientists researched lubrication with the Ubbelohde viscometer . In 1949 Britain's first diesel train, with an English Electric engine, had Shell lubricating oil. Two-thirds of the lubricating oil made in UK was Shell, with Shell conducting £6m of research in 1949. The centre researched tyres, paint, textiles, and detergents. [ 28 ] BEA airliners only had Shell lubricants.
In the 1960s automotive companies from Europe would test automotive engines there. [ 29 ]
In May 1985, an automated £14m lubrication oil laboratory opened, called ELMA - Engine Laboratory Modernisation and Automation, with sixteen engine test beds , for different driving cycles . [ 30 ] [ 31 ] With ELMA, it developed the petrol known as Formula Shell, sold from 19 May 1986. [ 32 ]
The site conducted work with British Leyland on pollution in the late 1960s, due to increasing legislation in the US, costing £100,000 a year, overlooked by Morris Sugden. [ 33 ] BP conducted similar research at its Sunbury Research Centre .
The site researched fuel for the Ferrari F1 team ( Scuderia Ferrari ).
The site is 66 acres. It was situated north of the M56 , north-west of junction 14, at the Hapsford services (a Shell services), to the north of the A5117 . It is directly east of the large oil refinery, south of the neighbouring Hooton–Helsby line . | https://en.wikipedia.org/wiki/Shell_Technology_Centre |
The Shell higher olefin process ( SHOP ) is a chemical process for the production of linear alpha olefins via ethylene oligomerization and olefin metathesis invented and exploited by Shell plc . [ 1 ] The olefin products are converted to fatty aldehydes and then to fatty alcohols , which are precursors to plasticizers and detergents . The annual global production of olefins through this method is over one million tonnes . [ 2 ]
The process was discovered by chemists at Shell Development Emeryville in 1968. At the time ecological considerations demanded the replacement of branched fatty alcohols used widely in detergents by linear fatty alcohols because the biodegradation of the branched compounds was slow, causing foaming of surface water. [ 2 ] At the same time new gas oil crackers were being commissioned and ethylene supply was outpacing demand. [ 2 ]
The process was commercialized in 1977 by Shell plc and following an expansion of the Geismar, Louisiana (USA) plant in 2002 global annual production capacity was 1.2 million tons. [ 3 ]
Ethylene reacts by the catalyst to give longer chains. Unlike the Ziegler–Natta process , which aims to produce very long polymers, the oligomer stops growing after addition of 1–10 repeating units of ethylene. The fraction containing C 12 to C 18 olefins (40–50%) has direct commercial value in detergent production and is removed. [ 2 ] For the remaining fraction to be of commercial interest two additional steps are required. The first step is liquid-phase isomerization using alkaline alumina catalyst leading to internal double bonds. For example, 1-octene is converted to 4- octene and 1-eicocene (a C20 hydrocarbon) is converted to 10-eicocene. In the second step olefin metathesis converts mixtures like these to 2-tetradecene which is a C14 component and again within commercial range. [ 2 ]
The internal olefins can also be reacted with an excess of ethylene with rhenium(VII) oxide supported on alumina as catalyst in an ethenolysis reaction, which causes the internal double bond to break up to form a mixture of α-olefins with odd and even carbon chain-length of the desired molecular weight. [ 4 ]
The C 12 to C 18 olefins subsequently are subjected to hydroformylation (oxo process) to give aldehydes . The aldehyde is hydrogenated to give fatty alcohols, which are suitable for manufacturing detergents. [ 4 ]
The first step in this process is the ethylene oligomerization to a mixture of even-numbered α-olefins at 80 to 120 °C and 70 to 140 bar (7 to 14 MPa) catalyzed by a nickel - phosphine complex. Such catalysts are typically prepared from diarylphosphino carboxylic acids, such as (C 6 H 5 ) 2 PCH 2 CO 2 H. [ 5 ] The process and its mechanism was elucidated by the group of Wilhelm Keim , first at Shell and later at the RWTH Aachen . [ 6 ]
In another olefin application of Shell cyclododecatriene is partially hydrogenated to cyclododecene and then subjected to ethenolysis to the terminal linear open-chain diene . The process was still in use at Essar Stanlow refinery until a serious explosion and following fire lead to the closure of the plant and the alcohols units it fed in 2018. | https://en.wikipedia.org/wiki/Shell_higher_olefin_process |
The Shell in situ conversion process ( Shell ICP ) is an in situ shale oil extraction technology to convert kerogen in oil shale to shale oil . It is developed by the Shell Oil Company .
Shell's in situ conversion process has been under development since the early 1980s. [ 1 ] In 1997, the first small scale test was conducted on the 30-by-40-foot (9.1 by 12.2 m) Mahogany property test site, located 200 miles (320 km) west of Denver on Colorado's Western Slope in the Piceance Creek Basin . Since 2000, additional research and development activities have carried on as a part of the Mahogany Research Project. [ 2 ] The oil shale heating at Mahogany started early 2004. [ 3 ] From this test site, Shell has recovered 1,700 barrels (270 m 3 ) of shale oil. [ 4 ] [ 5 ]
The process heats sections of the vast oil shale field in situ , releasing the shale oil and oil shale gas from the rock so that it can be pumped to the surface and made into fuel . In this process, a freeze wall is first to be constructed to isolate the processing area from surrounding groundwater. [ 1 ] To maximize the functionality of the freeze walls, adjacent working zones will be developed in succession. 2,000 feet (610 m) wells, eight feet apart, are drilled and filled with a circulating super-chilled liquid to cool the ground to −60 °F (−50 °C). [ 4 ] [ 6 ] [ 7 ] Water is then removed from the working zone. Heating and recovery wells are drilled at 40 feet (12 m) intervals within the working zone. Electrical heating elements are lowered into the heating wells and used to heat oil shale to between 650 °F (340 °C) and 700 °F (370 °C) over a period of approximately four years. [ 2 ] [ 6 ] Kerogen in oil shale is slowly converted into shale oil and gases, which then flow to the surface through recovery wells. [ 4 ] [ 6 ]
A RAND study in 2005 estimated that production of 100,000 barrels per day (16,000 m 3 /d) of oil (5.4 million tons/year) would theoretically require a dedicated power generating capacity of 1.2 gigawatts (10 billion kWh/year), assuming deposit richness of 25 US gallons (95 L; 21 imp gal) per ton, with 100% pyrolysis efficiency, and 100% extraction of pyrolysis products. [ 1 ] If this amount of electricity were to be generated by a coal-fired power plant, it would consume five million ton of coal annually (about 2.2 million toe ). [ 8 ]
In 2006, Shell estimated that over the project life cycle, for every unit of energy consumed, three to four units would be produced. [ 4 ] [ 6 ] Such an " energy returned on energy invested " would be significantly better than that achieved in the Mahogany trials. For the 1996 trial, Shell applied 440,000 kWh (which would require about 96 toe energy input in a coal-fired plant), to generate 250 barrels (40 m 3 ) of oil (37 toe output). [ 9 ]
Shell's underground conversion process requires significant development on the surface. The separation between drilled wells is less than five meters and wells must be connected by electrical wiring and by piping to storage and processing facilities. Shell estimates that the footprint of extraction operations would be similar to that for conventional oil and gas drilling. [ 4 ] [ 6 ] However, the dimensions of Shell's 2005 trial indicate that a much larger footprint is required. Production of 50,000 bbl/day would require that land be developed at a rate on the order of 1 square kilometre (0.39 sq mi) per year. [ 10 ]
Extensive water use and the risk of groundwater pollution are the technology's greatest challenges. [ 11 ]
In 2006, Shell received a Bureau of Land Management lease to pursue a large demonstration with a capacity of 1,500 barrels per day (240 m 3 /d); Shell has since dropped those plans and is planning a test based on ICP that would produce a total of minimum 1,500 barrels (240 m 3 ), together with nahcolite , over a seven-year period. [ 12 ] [ 13 ]
In Israel, IEI, a subsidiary of IDT Corp. is planning a shale pilot based on ICP technology. The project would produce a total of 1,500 barrels. However, IEI has also announced that any subsequent projects would not use ICP technology, but would instead utilize horizontal wells and hot gas heating methods. [ 14 ]
In Jordan, Shell subsidiary JOSCO plans to use ICP technology to achieve commercial production by the "late 2020s." [ 15 ] In October, 2011, it was reported that JOSCO had drilled more than 100 test holes over the prior two years, apparently for the sake of testing shale samples. [ 16 ]
The Mahogany Oil Shale Project has been abandoned by Shell in 2013 due to unfavorable project economics [ 17 ] | https://en.wikipedia.org/wiki/Shell_in_situ_conversion_process |
Shell integration (the shell method in integral calculus ) is a method for calculating the volume of a solid of revolution , when integrating along an axis perpendicular to the axis of revolution. This is in contrast to disc integration which integrates along the axis parallel to the axis of revolution.
The shell method goes as follows: Consider a volume in three dimensions obtained by rotating a cross-section in the xy -plane around the y -axis. Suppose the cross-section is defined by the graph of the positive function f ( x ) on the interval [ a , b ] . Then the formula for the volume will be:
If the function is of the y coordinate and the axis of rotation is the x -axis then the formula becomes:
If the function is rotating around the line x = h then the formula becomes: [ 1 ]
and for rotations around y = k it becomes
The formula is derived by computing the double integral in polar coordinates .
Consider the function f ( x ) {\displaystyle f(x)} which describes our cross-section of the solid, now the integral of the function can be described as a Riemann integral: ∫ a b f ( x ) d x = lim n → ∞ ∑ i = 1 n f ( a + i Δ x ) Δ x {\displaystyle \int \limits _{a}^{b}f(x)dx=\lim _{n\to \infty }\sum _{i=1}^{n}f(a+i\Delta x)\Delta x}
Where Δ x = b − a n {\displaystyle \Delta x={\frac {b-a}{n}}} is a small difference in x {\displaystyle x}
The Riemann sum can be thought up as a sum of a number n of rectangles with ever shrinking bases, we might focus on one of them:
f ( a + k Δ x ) Δ x {\displaystyle f(a+k\Delta x)\Delta x}
Now, when we rotate the function around the axis of revolution, it is equivalent to rotating all of these rectangles around said axis, these rectangles end up becoming a hollow cylinder, composed by the difference of two normal cylinders. For our chosen rectangle, its made by obtaining a cylinder of radius a + ( k + 1 ) Δ x {\displaystyle a+(k+1)\Delta x} with height f ( a + k Δ x ) {\displaystyle f(a+k\Delta x)} , and substracting it another smaller cylinder of radius a + k Δ x {\displaystyle a+k\Delta x} , with the same height of f ( a + k Δ x ) {\displaystyle f(a+k\Delta x)} , this difference of cylinder volumes is:
π ( a + ( k + 1 ) Δ x ) 2 f ( a + k Δ x ) − π ( a + k Δ x ) 2 f ( a + k Δ x ) {\displaystyle \pi (a+(k+1)\Delta x)^{2}f(a+k\Delta x)-\pi (a+k\Delta x)^{2}f(a+k\Delta x)}
= π f ( a + k Δ x ) ( ( a + ( k + 1 ) Δ x ) 2 − ( a + k Δ x ) 2 ) {\displaystyle =\pi f(a+k\Delta x)((a+(k+1)\Delta x)^{2}-(a+k\Delta x)^{2})}
By difference of squares , the last factor can be reduced as:
π f ( a + k Δ x ) ( 2 a + 2 k Δ x + Δ x ) Δ x {\displaystyle \pi f(a+k\Delta x)(2a+2k\Delta x+\Delta x)\Delta x}
The third factor can be factored out by two, ending up as:
2 π f ( a + k Δ x ) ( a + k Δ x + Δ x 2 ) Δ x {\displaystyle 2\pi f(a+k\Delta x)(a+k\Delta x+{\frac {\Delta x}{2}})\Delta x}
This same thing happens with all terms, so our total sum becomes:
lim n → ∞ 2 π ∑ i = 1 n f ( a + i Δ x ) ( a + i Δ x + Δ x 2 ) Δ x {\displaystyle \lim _{n\to \infty }2\pi \sum _{i=1}^{n}f(a+i\Delta x)(a+i\Delta x+{\frac {\Delta x}{2}})\Delta x}
In the limit of n → ∞ {\displaystyle n\rightarrow \infty } , we can clearly identify that:
Thus, at the limit of infinity, the sum becomes the integral:
2 π ∫ a b x f ( x ) d x {\displaystyle 2\pi \int \limits _{a}^{b}xf(x)dx}
QED ◻ {\displaystyle \square } .
Consider the volume, depicted below, whose cross section on the interval [1, 2] is defined by:
With the shell method we simply use the following formula:
By expanding the polynomial, the integration is easily done giving 8 / 10 π {\displaystyle \pi } cubic units.
Much more work is needed to find the volume if we use disc integration . First, we would need to solve y = 8 ( x − 1 ) 2 ( x − 2 ) 2 {\displaystyle y=8(x-1)^{2}(x-2)^{2}} for x . Next, because the volume is hollow in the middle, we would need two functions: one that defined an outer solid and one that defined the inner hollow. After integrating each of these two functions, we would subtract them to yield the desired volume. | https://en.wikipedia.org/wiki/Shell_integration |
In classical mechanics , the shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetrical body. This theorem has particular application to astronomy .
Isaac Newton proved the shell theorem [ 1 ] and stated that:
A corollary is that inside a solid sphere of constant density, the gravitational force within the object varies linearly with distance from the center, becoming zero by symmetry at the center of mass . This can be seen as follows: take a point within such a sphere, at a distance r {\displaystyle r} from the center of the sphere. Then you can ignore all of the shells of greater radius, according to the shell theorem (2). But the point can be considered to be external to the remaining sphere of radius r, and according to (1) all of the mass of this sphere can be considered to be concentrated at its centre. The remaining mass m {\displaystyle m} is proportional to r 3 {\displaystyle r^{3}} (because it is based on volume). The gravitational force exerted on a body at radius r will be proportional to m / r 2 {\displaystyle m/r^{2}} (the inverse square law ), so the overall gravitational effect is proportional to r 3 / r 2 = r {\displaystyle r^{3}/r^{2}=r} , so is linear in r {\displaystyle r} .
These results were important to Newton's analysis of planetary motion; they are not immediately obvious, but they can be proven with calculus . ( Gauss's law for gravity offers an alternative way to state the theorem.)
In addition to gravity , the shell theorem can also be used to describe the electric field generated by a static spherically symmetric charge density , or similarly for any other phenomenon that follows an inverse square law . The derivations below focus on gravity, but the results can easily be generalized to the electrostatic force .
There are three steps to proving Newton's shell theorem (1). First, the equation for a gravitational field due to a ring of mass will be derived. Arranging an infinite number of infinitely thin rings to make a disc, this equation involving a ring will be used to find the gravitational field due to a disk. Finally, arranging an infinite number of infinitely thin discs to make a sphere, this equation involving a disc will be used to find the gravitational field due to a sphere.
The gravitational field E {\displaystyle E} at a position called P {\displaystyle P} at ( x , y ) = ( − p , 0 ) {\displaystyle (x,y)=(-p,0)} on the x -axis due to a point of mass M {\displaystyle M} at the origin is E point = G M p 2 {\displaystyle E_{\text{point}}={\frac {GM}{p^{2}}}} Suppose that this mass is moved upwards along the y -axis to the point ( 0 , R ) {\displaystyle (0,R)} . The distance between P {\displaystyle P} and the point mass is now longer than before; It becomes the hypotenuse of the right triangle with legs p {\displaystyle p} and R {\displaystyle R} which is p 2 + R 2 {\textstyle {\sqrt {p^{2}+R^{2}}}} . Hence, the gravitational field of the elevated point is: E elevated point = G M p 2 + R 2 {\displaystyle E_{\text{elevated point}}={\frac {GM}{p^{2}+R^{2}}}}
The magnitude of the gravitational field that would pull a particle at point P {\displaystyle P} in the x -direction is the gravitational field multiplied by cos ( θ ) {\displaystyle \cos(\theta )} where θ {\displaystyle \theta } is the angle adjacent to the x -axis. In this case, cos ( θ ) = p p 2 + R 2 {\displaystyle \cos(\theta )={\frac {p}{\sqrt {p^{2}+R^{2}}}}} . Hence, the magnitude of the gravitational field in the x -direction, E x {\displaystyle E_{x}} is: E x = G M cos θ p 2 + R 2 {\displaystyle E_{x}={\frac {GM\cos {\theta }}{p^{2}+R^{2}}}} Substituting in cos ( θ ) {\displaystyle \cos(\theta )} gives E x = G M p ( p 2 + R 2 ) 3 / 2 {\displaystyle E_{x}={\frac {GMp}{\left(p^{2}+R^{2}\right)^{3/2}}}} Suppose that this mass is evenly distributed in a ring centered at the origin and facing point P {\displaystyle P} with the same radius R {\displaystyle R} . Because all of the mass is located at the same angle with respect to the x -axis, and the distance between the points on the ring is the same distance as before, the gravitational field in the x -direction at point P {\displaystyle P} due to the ring is the same as a point mass located at a point R {\displaystyle R} units above the y -axis: E ring = G M p ( p 2 + R 2 ) 3 / 2 {\displaystyle E_{\text{ring}}={\frac {GMp}{\left(p^{2}+R^{2}\right)^{3/2}}}}
To find the gravitational field at point P {\displaystyle P} due to a disc, an infinite number of infinitely thin rings facing P {\displaystyle P} , each with a radius y {\displaystyle y} , width of d y {\displaystyle dy} , and mass of d M {\displaystyle dM} may be placed inside one another to form a disc. The mass of any one of the rings d M {\displaystyle dM} is the mass of the disc multiplied by the ratio of the area of the ring 2 π y d y {\displaystyle 2\pi y\,dy} to the total area of the disc π R 2 {\displaystyle \pi R^{2}} . So, d M = M ⋅ 2 y d y R 2 {\textstyle dM={\frac {M\cdot 2y\,dy}{R^{2}}}} . Hence, a small change in the gravitational field, E {\displaystyle E} is: d E = G p d M ( p 2 + y 2 ) 3 / 2 {\displaystyle dE={\frac {Gp\,dM}{(p^{2}+y^{2})^{3/2}}}}
Substituting in d M {\displaystyle dM} and integrating both sides gives the gravitational field of the disk: E = ∫ G M p ⋅ 2 y d y R 2 ( p 2 + y 2 ) 3 / 2 {\displaystyle E=\int {\frac {GMp\cdot {\frac {2y\,dy}{R^{2}}}}{(p^{2}+y^{2})^{3/2}}}} Adding up the contribution to the gravitational field from each of these rings will yield the expression for the gravitational field due to a disc. This is equivalent to integrating this above expression from y = 0 {\displaystyle y=0} to y = R {\displaystyle y=R} , resulting in: E disc = 2 G M R 2 ( 1 − p p 2 + R 2 ) {\displaystyle E_{\text{disc}}={\frac {2GM}{R^{2}}}\left(1-{\frac {p}{\sqrt {p^{2}+R^{2}}}}\right)} To find the gravitational field at point P {\displaystyle P} due to a sphere centered at the origin, an infinite amount of infinitely thin discs facing P {\displaystyle P} , each with a radius R {\displaystyle R} , width of d x {\displaystyle dx} , and mass of d M {\displaystyle dM} may be placed together.
These discs' radii R {\displaystyle R} follow the height of the cross section of a sphere (with constant radius a {\displaystyle a} ) which is an equation of a semi-circle: R = a 2 − x 2 {\textstyle R={\sqrt {a^{2}-x^{2}}}} . x {\displaystyle x} varies from − a {\displaystyle -a} to a {\displaystyle a} .
The mass of any of the discs d M {\displaystyle dM} is the mass of the sphere M {\displaystyle M} multiplied by the ratio of the volume of an infinitely thin disc divided by the volume of a sphere (with constant radius a {\displaystyle a} ). The volume of an infinitely thin disc is π R 2 d x {\displaystyle \pi R^{2}\,dx} , or π ( a 2 − x 2 ) d x {\textstyle \pi \left(a^{2}-x^{2}\right)dx} . So, d M = π M ( a 2 − x 2 ) d x 4 3 π a 3 {\textstyle dM={\frac {\pi M(a^{2}-x^{2})\,dx}{{\frac {4}{3}}\pi a^{3}}}} . Simplifying gives d M = 3 M ( a 2 − x 2 ) d x 4 a 3 {\textstyle dM={\frac {3M(a^{2}-x^{2})\,dx}{4a^{3}}}} .
Each discs' position away from P {\displaystyle P} will vary with its position within the 'sphere' made of the discs, so p {\displaystyle p} must be replaced with p + x {\displaystyle p+x} .
Replacing M {\displaystyle M} with d M {\displaystyle dM} , R {\displaystyle R} with a 2 − x 2 {\displaystyle {\sqrt {a^{2}-x^{2}}}} , and p {\displaystyle p} with p + x {\displaystyle p+x} in the 'disc' equation yields: d E = ( 2 G [ 3 M ( a 2 − x 2 ) ] 4 a 3 ) a 2 − x 2 2 ⋅ ( 1 − p + x ( p + x ) 2 + a 2 − x 2 2 ) d x {\displaystyle dE={\frac {\left({\frac {2G\left[3M\left(a^{2}-x^{2}\right)\right]}{4a^{3}}}\right)}{{\sqrt {a^{2}-x^{2}}}^{2}}}\cdot \left(1-{\frac {p+x}{\sqrt {(p+x)^{2}+{\sqrt {a^{2}-x^{2}}}^{2}}}}\right)\,dx} Simplifying, ∫ d E = ∫ − a a 3 G M 2 a 3 ( 1 − p + x p 2 + a 2 + 2 p x ) d x {\displaystyle \int dE=\int _{-a}^{a}{\frac {3GM}{2a^{3}}}\left(1-{\frac {p+x}{\sqrt {p^{2}+a^{2}+2px}}}\right)dx} Integrating the gravitational field of each thin disc from x = − a {\displaystyle x=-a} to x = + a {\displaystyle x=+a} with respect to x {\displaystyle x} , and doing some careful algebra, yields Newton's shell theorem: E = G M p 2 {\displaystyle E={\frac {GM}{p^{2}}}} where p {\displaystyle p} is the distance between the center of the spherical mass and an arbitrary point P {\displaystyle P} . The gravitational field of a spherical mass may be calculated by treating all the mass as a point particle at the center of the sphere.
A solid, spherically symmetric body can be modeled as an infinite number of concentric , infinitesimally thin spherical shells. If one of these shells can be treated as a point mass, then a system of shells (i.e. the sphere) can also be treated as a point mass. Consider one such shell (the diagram shows a cross-section):
(Note: the d θ {\displaystyle d\theta } in the diagram refers to the small angle, not the arc length . The arc length is R d θ {\textstyle R\,d\theta } .)
Applying Newton's Universal Law of Gravitation , the sum of the forces due to the mass elements in the shaded band is
However, since there is partial cancellation due to the vector nature of the force in conjunction with the circular band's symmetry, the leftover component (in the direction pointing towards m {\displaystyle m} ) is given by
The total force on m {\displaystyle m} , then, is simply the sum of the force exerted by all the bands. By shrinking the width of each band, and increasing the number of bands, the sum becomes an integral expression:
Since G {\displaystyle G} and m {\displaystyle m} are constants, they may be taken out of the integral:
To evaluate this integral, one must first express d M {\displaystyle dM} as a function of d θ {\displaystyle d\theta }
The total surface of a spherical shell is
while the surface area of the thin slice between θ {\displaystyle \theta } and θ + d θ {\displaystyle \theta +d\theta } is
If the mass of the shell is M {\displaystyle M} , one therefore has that
and
By the law of cosines ,
and
These two relations link the three parameters θ {\displaystyle \theta } , φ {\displaystyle \varphi } and s {\displaystyle s} that appear in the integral together. As θ {\displaystyle \theta } increases from 0 {\displaystyle 0} to π {\displaystyle \pi } radians, φ {\displaystyle \varphi } varies from the initial value 0 to a maximal value before finally returning to zero at θ = π {\displaystyle \theta =\pi } . At the same time, s {\displaystyle s} increases from the initial value r − R {\displaystyle r-R} to the final value r + R {\displaystyle r+R} as θ {\displaystyle \theta } increases from 0 to π {\displaystyle \pi } radians. This is illustrated in the following animation:
(Note: As viewed from m {\displaystyle m} , the shaded blue band appears as a thin annulus whose inner and outer radii converge to R sin ( θ ) {\displaystyle R\sin(\theta )} as d θ {\displaystyle d\theta } vanishes.)
To find a primitive function to the integrand, one has to make s {\displaystyle s} the independent integration variable instead of θ {\displaystyle \theta } .
Performing an implicit differentiation of the second of the "cosine law" expressions above yields
and thus
It follows that
where the new integration variable s {\displaystyle s} increases from r − R {\displaystyle r-R} to r + R {\displaystyle r+R} .
Inserting the expression for cos ( φ ) {\displaystyle \cos(\varphi )} using the first of the "cosine law" expressions above, one finally gets that
A primitive function to the integrand is
and inserting the bounds r − R {\displaystyle r-R} and r + R {\displaystyle r+R} for the integration variable s {\displaystyle s} in this primitive function, one gets that
saying that the gravitational force is the same as that of a point mass in the center of the shell with the same mass.
It is possible to use this spherical shell result to re-derive the solid sphere result from earlier. This is done by integrating an infinitesimally thin spherical shell with mass of d M {\displaystyle dM} , and we can obtain the total gravity contribution of a solid ball to the object outside the ball
Uniform density means between the radius of x {\displaystyle x} to x + d x {\displaystyle x+dx} , d M {\displaystyle dM} can be expressed as a function of x {\displaystyle x} , i.e.,
Therefore, the total gravity is
As found earlier, this suggests that the gravity of a solid spherical ball to an exterior object can be simplified as that of a point mass in the center of the ball with the same mass.
For a point inside the shell, the difference is that when θ is equal to zero, ϕ takes the value π radians and s the value R − r . When θ increases from 0 to π radians, ϕ decreases from the initial value π radians to zero and s increases from the initial value R − r to the value R + r .
This can all be seen in the following figure
Inserting these bounds into the primitive function
one gets that, in this case
saying that the net gravitational forces acting on the point mass from the mass elements of the shell, outside the measurement point, cancel out.
Generalization: If f = k r p {\displaystyle f={\frac {k}{r^{p}}}} , the resultant force inside the shell is:
The above results into F ( r ) {\displaystyle F(r)} being identically zero if and only if p = 2 {\displaystyle p=2}
Outside the shell (i.e. r > R {\displaystyle r>R} or r < − R {\displaystyle r<-R} ):
The shell theorem is an immediate consequence of Gauss's law for gravity saying that
where M is the mass of the part of the spherically symmetric mass distribution that is inside the sphere with radius r and
is the surface integral of the gravitational field g {\displaystyle \mathbf {g} } over any closed surface inside which the total mass is M , the unit vector n ^ {\displaystyle {\hat {\mathbf {n} }}} being the outward normal to the surface.
The gravitational field of a spherically symmetric mass distribution like a mass point, a spherical shell or a homogeneous sphere must also be spherically symmetric. If n ^ {\displaystyle {\hat {\mathbf {n} }}} is a unit vector in the direction from the point of symmetry to another point the gravitational field at this other point must therefore be
where g ( r ) only depends on the distance r to the point of symmetry
Selecting the closed surface as a sphere with radius r with center at the point of symmetry the outward normal to a point on the surface, n ^ {\displaystyle {\hat {\mathbf {n} }}} , is precisely the direction pointing away from the point of symmetry of the mass distribution.
One, therefore, has that
and
as the area of the sphere is 4 π r 2 .
From Gauss's law it then follows that
or,
It is natural to ask whether the converse of the shell theorem is true, namely whether the result of the theorem implies the law of universal gravitation, or if there is some more general force law for which the theorem holds. If we require only that the force outside of a spherical shell is the same as for an equal point mass at its center, then there is one additional degree of freedom for force laws. [ 2 ] [ 3 ] The most general force, as given by the Gurzadyan theorem , is: [ 2 ]
where G {\displaystyle G} and Λ {\displaystyle \Lambda } can be constants taking any value. The first term is the familiar law of universal gravitation; the second is an additional force, analogous to the cosmological constant term in general relativity . However, the inverse-square potential is the only potential such that the net force inside the shell is also zero. [ 2 ]
The force described by the Yukawa potential
has the property that the force outside of a spherical shell is also a Yukawa potential with the same range 1 / λ {\displaystyle 1/\lambda } and centered at the shell's center, but for λ > 0 {\displaystyle \lambda >0} the equivalent point mass is not the same as the mass of the shell. [ 4 ] [ 5 ] [ 6 ] For a shell of radius R {\displaystyle R} and mass M {\displaystyle M} , the equivalent point mass is:
For an ellipsoidal shell, the two halves of the shell theorem are generalized by different types of shells. The shell bound by two concentric , similar , and aligned ellipsoids (a homoeoid ) exters no gravitational force on a point inside of it. [ 7 ] Meanwhile, the shell bound by two concentric, confocal ellipsoids (a focaloid ) has the property that the gravitational force outside of two concentric, confocal focaloids is the same. [ 8 ]
Propositions 70 and 71 consider the force acting on a particle from a hollow sphere with an infinitesimally thin surface, whose mass density is constant over the surface. The force on the particle from a small area of the surface of the sphere is proportional to the mass of the area and inversely as the square of its distance from the particle. The first proposition considers the case when the particle is inside the sphere, the second when it is outside. The use of infinitesimals and limiting processes in geometrical constructions are simple and elegant and avoid the need for any integrations. They well illustrate Newton's method of proving many of the propositions in the Principia .
His proof of Propositions 70 is trivial. In the following, it is considered in slightly greater detail than Newton provides.
The proof of Proposition 71 is more historically significant. It forms the first part of his proof that the gravitational force of a solid sphere acting on a particle outside it is inversely proportional to the square of its distance from the center of the sphere, provided the density at any point inside the sphere is a function only of its distance from the center of the sphere.
Although the following are completely faithful to Newton's proofs, very minor changes have been made to attempt to make them clearer.
Fig. 2 is a cross-section of the hollow sphere through the center, S and an arbitrary point, P, inside the sphere. Through P draw two lines IL and HK such that the angle KPL is very small. JM is the line through P that bisects that angle. From the inscribed angle theorem , the triangles IPH and KPL are similar. The lines KH and IL are rotated about the axis JM to form two cones that intersect the sphere in two closed curves. In Fig. 1 the sphere is seen from a distance along the line PE and is assumed transparent so both curves can be seen.
The surface of the sphere that the cones intersect can be considered to be flat, and ∠ P J I = ∠ P M K {\displaystyle \angle PJI=\angle PMK} .
Since the intersection of a cone with a plane is an ellipse, in this case the intersections form two ellipses with major axes IH and KL, where I H K L = P J P M {\displaystyle {\frac {IH}{KL}}={\frac {PJ}{PM}}} .
By a similar argument, the minor axes are in the same ratio. This is clear if the sphere is viewed from above. Therefore, the two ellipses are similar, so their areas are as the squares of their major axes. As the mass of any section of the surface is proportional to the area of that section, for the two elliptical areas the ratios of their masses ∝ P J 2 P M 2 {\displaystyle \propto {\frac {PJ^{2}}{PM^{2}}}} .
Since the force of attraction on P in the direction JM from either of the elliptic areas, is direct as the mass of the area and inversely as the square of its distance from P, it is independent of the distance of P from the sphere. Hence, the forces on P from the two infinitesimal elliptical areas are equal and opposite and there is no net force in the direction JM.
As the position of P and the direction of JM are both arbitrary, it follows that any particle inside a hollow sphere experiences no net force from the mass of the sphere.
Note: Newton simply describes the arcs IH and KL as 'minimally small' and the areas traced out by the lines IL and HK can be any shape, not necessarily elliptic, but they will always be similar.
Fig. 1 is a cross-section of the hollow sphere through the center, S with an arbitrary point, P, outside the sphere. PT is the tangent to the circle at T which passes through P. HI is a small arc on the surface such that PH is less than PT. Extend PI to intersect the sphere at L and draw SF to the point F that bisects IL. Extend PH to intersect the sphere at K and draw SE to the point E that bisects HK, and extend SF to intersect HK at D. Drop a perpendicular IQ on to the line PS joining P to the center S. Let the radius of the sphere be a and the distance PS be D.
Let arc IH be extended perpendicularly out of the plane of the diagram, by a small distance ζ. The area of the figure generated is I H ⋅ ζ {\displaystyle IH\cdot \zeta } , and its mass is proportional to this product.
The force due to this mass on the particle at P ∝ I H ⋅ ζ P I 2 {\displaystyle \propto {\frac {IH\cdot \zeta }{PI^{2}}}} and is along the line PI.
The component of this force towards the center ∝ I H ⋅ P Q ⋅ ζ P I 3 {\displaystyle \propto {\frac {IH\cdot PQ\cdot \zeta }{PI^{3}}}} .
If now the arc HI is rotated completely about the line PS to form a ring of width HI and radius IQ , the length of the ring is 2 π · IQ and its area is 2 π · IQ · IH . The component of the force due to this ring on the particle at P in the direction PS becomes ∝ I H ⋅ I Q ⋅ P Q P I 3 {\displaystyle \propto {\frac {IH\cdot IQ\cdot PQ}{PI^{3}}}} .
The perpendicular components of the force directed towards PS cancel out since the mass in the ring is distributed symmetrically about PS . Therefore, the component in the direction PS is the total force on P due to the ring formed by rotating arc HI about PS .
From similar triangles: I Q P I = F S D {\displaystyle {\frac {IQ}{PI}}={\frac {FS}{D}}} ; P Q P I = P F D {\displaystyle {\frac {PQ}{PI}}={\frac {PF}{D}}} , and R I P I = D F P F {\displaystyle {\frac {RI}{PI}}={\frac {DF}{PF}}} .
If HI is sufficiently small that it can be taken as a straight line, ∠ S I H {\displaystyle \angle SIH} is a right angle, and ∠ R I H = ∠ F I S {\displaystyle \angle RIH=\angle FIS} , so that H I R I = a I F {\displaystyle {\frac {HI}{RI}}={\frac {a}{IF}}} .
Hence the force on P due to the ring ∝ I H ⋅ I Q ⋅ P Q P I 3 = a ⋅ D F ⋅ F S ⋅ P F I F ⋅ P F ⋅ D ⋅ D = a ⋅ D F ⋅ F S I F ⋅ D 2 {\displaystyle \propto {\frac {IH\cdot IQ\cdot PQ}{PI^{3}}}={\frac {a\cdot DF\cdot FS\cdot PF}{IF\cdot PF\cdot D\cdot D}}={\frac {a\cdot DF\cdot FS}{IF\cdot D^{2}}}} .
Assume now in Fig. 2 that another particle is outside the sphere at a point p , a different distance d from the center of the sphere, with corresponding points lettered in lower case. For easy comparison, the construction of P in Fig. 1 is also shown in Fig. 2. As before, ph is less than pt .
Generate a ring with width ih and radius iq by making angle f i S = F I S {\displaystyle fiS=FIS} and the slightly larger angle d h S = D H S {\displaystyle dhS=DHS} , so that the distance PS is subtended by the same angle at I as is pS at i. The same holds for H and h, respectively.
The total force on p due to this ring is
Clearly f S = F S {\displaystyle fS=FS} , i f = I F {\displaystyle if=IF} , and e S = E S {\displaystyle eS=ES} .
Newton claims that DF and df can be taken as equal in the limit as the angles DPF and dpf 'vanish together'. Note that angles DPF and dpf are not equal. Although DS and dS become equal in the limit, this does not imply that the ratio of DF to df becomes equal to unity, when DF and df both approach zero. In the finite case DF depends on D, and df on d, so they are not equal.
Since the ratio of DF to df in the limit is crucial, more detailed analysis is required. From the similar right triangles, D F P F = E D E S {\textstyle {\frac {DF}{PF}}={\frac {ED}{ES}}} and E D 2 = ( D F + F S ) 2 − E S 2 {\displaystyle ED^{2}=(DF+FS)^{2}-ES^{2}} , giving ( P F 2 − E S 2 ) D F 2 P F 2 + 2 ⋅ F S ⋅ D F + F S 2 − E S 2 = 0 {\displaystyle {\frac {\left(PF^{2}-ES^{2}\right)DF^{2}}{PF^{2}}}+2\cdot FS\cdot DF+FS^{2}-ES^{2}=0} . Solving the quadratic for DF, in the limit as ES approaches FS, the smaller root, D F = E S − F S {\displaystyle DF=ES-FS} . More simply, as DF approaches zero, in the limit the D F 2 {\displaystyle DF^{2}} term can be ignored: 2 ⋅ F S ⋅ D F + F S 2 − E S 2 = 0 {\displaystyle 2\cdot FS\cdot DF+FS^{2}-ES^{2}=0} leading to the same result. Clearly df has the same limit, justifying Newton's claim.
Comparing the force from the ring HI rotated about PS to the ring hi about pS, the ratio of these 2 forces equals d 2 D 2 {\textstyle {\frac {d^{2}}{D^{2}}}} .
By dividing up the arcs AT and Bt into corresponding infinitesimal rings, it follows that the ratio of the force due to the arc AT rotated about PS to that of Bt rotated about pS is in the same ratio, and similarly, the ratio of the forces due to arc TB to that of tA both rotated are in the same ratio.
Therefore, the force on a particle any distance D from the center of the hollow sphere is inversely proportional to D 2 {\displaystyle D^{2}} , which proves the proposition.
An analogue for shell theorem exists in general relativity (GR).
Spherical symmetry implies that the metric has time-independent Schwarzschild geometry, even if a central mass is undergoing gravitational collapse (Misner et al. 1973; see Birkhoff's theorem ). The metric thus has form
(using geometrized units , where G = c = 1 {\displaystyle G=c=1} ). For r > R > 0 {\displaystyle r>R>0} (where R {\displaystyle R} is the radius of some mass shell), mass acts as a delta function at the origin. For r < R {\displaystyle r<R} , shells of mass may exist externally, but for the metric to be non-singular at the origin, M {\displaystyle M} must be zero in the metric. This reduces the metric to flat Minkowski space ; thus external shells have no gravitational effect.
This result illuminates the gravitational collapse leading to a black hole and its effect on the motion of light-rays and particles outside and inside the event horizon (Hartle 2003, chapter 12). | https://en.wikipedia.org/wiki/Shell_theorem |
Shellac ( / ʃ ə ˈ l æ k / ) [ 1 ] is a resin secreted by the female lac bug on trees in the forests of India and Thailand. Chemically, it is mainly composed of aleuritic acid , jalaric acid, shellolic acid, and other natural waxes. [ 2 ] It is processed and sold as dry flakes and dissolved in alcohol to make liquid shellac, which is used as a brush-on colorant, food glaze and wood finish . Shellac functions as a tough natural primer , sanding sealant , tannin -blocker, odour -blocker, stain , and high-gloss varnish . Shellac was once used in electrical applications as it possesses good insulation qualities and seals out moisture. Phonograph and 78 rpm gramophone records were made of shellac until they were gradually replaced by vinyl .
From the time shellac replaced oil and wax finishes in the 19th century, it was one of the dominant wood finishes in the western world until it was largely replaced by nitrocellulose lacquer in the 1920s and 1930s. Besides wood finishing, shellac is used as an ingredient in food, medication and candy as confectioner's glaze , [ 3 ] as well as a means of preserving harvested citrus fruit . [ 4 ]
Shellac comes from shell and lac , a partial calque of French laque en écailles , 'lac in thin pieces', later gomme-laque , 'gum lac'. [ 5 ] Most European languages (except Romance ones and Greek) have borrowed the word for the substance from English or from the German equivalent Schellack . [ 6 ]
Shellac is scraped from the bark of the trees where the female lac bug, Kerria lacca (order Hemiptera, family Kerriidae , also known as Laccifer lacca ), secretes it to form a tunnel-like tube as it traverses the branches of the tree. Though these tunnels are sometimes referred to as " cocoons ", they are not cocoons in the entomological sense. [ 7 ] This insect is in the same superfamily as the insect from which cochineal is obtained. The insects suck the sap of the tree and excrete " sticklac " almost constantly. The least-coloured shellac is produced when the insects feed on the kusum tree ( Schleichera ). [ 8 ]
The number of lac bugs required to produce 1 kilogram (2.2 lb) of shellac has variously been estimated between 50,000 and 300,000. [ 9 ] [ 10 ] The root word lakh is a unit in the Indian numbering system for 100,000 and presumably refers to the huge numbers of insects that swarm on host trees, up to 150 per square inch (23/cm 2 ). [ 11 ]
The raw shellac, which contains bark shavings and lac bugs removed during scraping, is placed in canvas tubes (much like long socks) and heated over a fire. This causes the shellac to liquefy, and it seeps out of the canvas, leaving the bark and bugs behind. The thick, sticky shellac is then dried into a flat sheet and broken into flakes, or dried into "buttons" (pucks/cakes), then bagged and sold. The end-user then crushes it into a fine powder and mixes it with ethyl alcohol before use, to dissolve the flakes and make liquid shellac. [ 12 ]
Liquid shellac has a limited shelf life (about 1 year), so is sold in dry form for dissolution before use. Liquid shellac sold in hardware stores is often marked with the production (mixing) date, so the consumer can know whether the shellac inside is still good. Some manufacturers (e.g., Zinsser) have ceased labeling shellac with the production date, but the production date may be discernible from the production lot code. Alternatively, old shellac may be tested to see if it is still usable: a few drops on glass should dry to a hard surface in roughly 15 minutes. Shellac that remains tacky for a long time is no longer usable. Storage life depends on peak temperature, so refrigeration extends shelf life. [ 13 ]
The thickness (concentration) of shellac is measured by the unit "pound cut", referring to the amount (in pounds) of shellac flakes dissolved in a gallon of denatured alcohol. For example: a 1-lb. cut of shellac is the strength obtained by dissolving one pound of shellac flakes in a gallon of alcohol (equivalent to 120 grams per litre). [ 14 ] Most pre-mixed commercial preparations come at a 3-lb. cut. Multiple thin layers of shellac produce a significantly better end result than a few thick layers. Thick layers of shellac do not adhere to the substrate or to each other well, and thus can peel off with relative ease; in addition, thick shellac will obscure fine details in carved designs in wood and other substrates. [ citation needed ]
Shellac naturally dries to a high-gloss sheen. For applications where a flatter (less shiny) sheen is desired, products containing amorphous silica, such as "Shellac Flat", may be added to the dissolved shellac. [ 15 ]
Shellac naturally contains a small amount of wax (3%–5% by volume), which comes from the lac bug. In some preparations, this wax is removed (the resulting product being called "dewaxed shellac"). This is done for applications where the shellac will be coated with something else (such as paint or varnish), so the topcoat will adhere. Waxy (non-dewaxed) shellac appears milky in liquid form, but dries clear. [ citation needed ]
Shellac comes in many warm colours, ranging from a very light blonde ("platina") to a very dark brown ("garnet"), with many varieties of brown, yellow, orange and red in between. The colour is influenced by the sap of the tree the lac bug is living on and by the time of harvest. Historically, the most commonly sold shellac is called "orange shellac", and was used extensively as a combination stain and protectant for wood panelling and cabinetry in the 20th century. [ citation needed ]
Shellac was once very common anywhere paints or varnishes were sold (such as hardware stores). However, cheaper and more abrasion- and chemical-resistant finishes, such as polyurethane , have almost completely replaced it in decorative residential wood finishing such as hardwood floors, wooden wainscoting plank panelling, and kitchen cabinets. These alternative products, however, must be applied over a stain if the user wants the wood to be coloured; clear or blonde shellac may be applied over a stain without affecting the colour of the finished piece, as a protective topcoat. "Wax over shellac" (an application of buffed-on paste wax over several coats of shellac) is often regarded as a beautiful, if fragile, finish for hardwood floors. Luthiers still use shellac to French polish fine acoustic stringed instruments, but it has been replaced by synthetic plastic lacquers and varnishes in many workshops, especially high-volume production environments. [ 16 ]
Shellac dissolved in alcohol, typically more dilute than as used in French polish, is now commonly sold as "sanding sealer" by several companies. It is used to seal wooden surfaces, often as preparation for a final more durable finish; it reduces the amount of final coating required by reducing its absorption into the wood. [ citation needed ]
Shellac is a natural bioadhesive polymer and is chemically similar to synthetic polymers. [ 17 ] It can thus be considered a natural form of plastic .
With a melting point of 75 °C (167 °F), it can be classed as a thermoplastic used to bind wood flour , the mixture can be moulded with heat and pressure.
Shellac scratches more easily than most lacquers and varnishes, and application is more labour-intensive, which is why it has been replaced by plastic in most areas. Shellac is much softer than Urushi lacquer, for instance, which is far superior with regard to both chemical and mechanical resistance. [ citation needed ] But damaged shellac can easily be touched up with another coat of shellac (unlike polyurethane, which chemically cures to a solid) because the new coat merges with and bonds to the existing coat(s).
Shellac is soluble in alkaline solutions of ammonia , sodium borate , sodium carbonate , and sodium hydroxide , and also in various organic solvents . When dissolved in alcohol (typically denatured ethanol ) for application, shellac yields a coating of good durability and hardness. [ 18 ]
Upon mild hydrolysis shellac gives a complex mix of aliphatic and alicyclic hydroxy acids and their polymers that varies in exact composition depending upon the source of the shellac and the season of collection. The major component of the aliphatic component is aleuritic acid , whereas the main alicyclic component is shellolic acid . [ 19 ]
Shellac is UV-resistant, and does not darken as it ages (though the wood under it may do so, as in the case of pine). [ 20 ]
The earliest written evidence of shellac goes back 3,000 years, but shellac is known to have been used earlier. [ 20 ] According to the ancient Indian epic poem, the Mahabharata , an entire palace was coated with dried shellac. [ 20 ]
Shellac was uncommonly used as a dyestuff for as long as there was a trade with the East Indies . According to Merrifield, [ 21 ] shellac was first used as a binding agent in artist's pigments in Spain in the year 1220.
The use of overall paint or varnish decoration on large pieces of furniture was first popularised in Venice (then later throughout Italy). There are a number of 13th-century references to painted or varnished cassone , often dowry cassone that were made deliberately impressive as part of dynastic marriages. The definition of varnish is not always clear, but it seems to have been a spirit varnish based on gum benjamin or mastic , both traded around the Mediterranean. At some time, shellac began to be used as well. An article from the Journal of the American Institute of Conservation describes using infrared spectroscopy to identify shellac coating on a 16th-century cassone. [ 22 ] This is also the period in history where "varnisher" was identified as a distinct trade, separate from both carpenter and artist. [ citation needed ]
Another use for shellac is sealing wax . [ 23 ] The widespread use of shellac seals in Europe dates back to the 17th century , thanks to the increasing trade with India. [ 24 ]
In the early- and mid-twentieth century, orange shellac was used as a one-product finish (combination stain and varnish-like topcoat) on decorative wood panelling used on walls and ceilings in homes, particularly in the US. In the American South , use of knotty pine plank panelling covered with orange shellac was once as common in new construction as drywall is today. It was also often used on kitchen cabinets and hardwood floors, prior to the advent of polyurethane . [ citation needed ]
Until the advent of vinyl , most gramophone records were pressed from shellac compounds. [ 25 ] [ 26 ] From 1921 to 1928, 18,000 tons of shellac were used to create 260 million records for Europe. [ 11 ] In the 1930s, it was estimated that half of all shellac was used for gramophone records . [ 27 ] Use of shellac for records was common until the 1950s and continued into the 1970s in some non-Western countries, as well as for some children's records. [ 28 ] [ 29 ]
Until recent advances in technology, shellac ( French polish ) was the only glue used in the making of ballet dancers' pointe shoes , to stiffen the box (toe area) to support the dancer en pointe. Many manufacturers of pointe shoes still use the traditional techniques, and many dancers use shellac to revive a softening pair of shoes. [ 30 ]
Shellac was historically used as a protective coating on paintings. [ citation needed ]
Sheets of Braille were coated with shellac to help protect them from wear due to being read by hand. [ citation needed ]
Shellac was used from the mid-nineteenth century to produce small moulded goods such as picture frames , boxes , toilet articles, jewelry , inkwells and even dentures . Advances in plastics have rendered shellac obsolete as a moulding compound. [ 31 ]
Shellac (both orange and white varieties) was used both in the field and laboratory to glue and stabilise dinosaur bones until about the mid-1960s. While effective at the time, the long-term negative effects of shellac (being organic in nature) on dinosaur bones and other fossils is debated, and shellac is very rarely used by professional conservators and fossil preparators today. [ 32 ]
Shellac was used for fixing inductor , motor , generator and transformer windings. It was applied directly to single-layer windings in an alcohol solution. For multi-layer windings, the whole coil was submerged in shellac solution, then drained and placed in a warm location to allow the alcohol to evaporate. The shellac locked the wire turns in place, provided extra insulation, prevented movement and vibration and reduced buzz and hum. In motors and generators it also helps transfer force generated by magnetic attraction and repulsion from the windings to the rotor or armature . In more recent times, shellac has been replaced in these applications by synthetic resins such as polyester resin . Some applications use shellac mixed with other natural or synthetic resins, such as pine resin or phenol- formaldehyde resin, of which Bakelite is the best known, for electrical use. Mixed with other resins, barium sulfate , calcium carbonate , zinc sulfide , aluminium oxide and/or cuprous carbonate ( malachite ), shellac forms a component of heat-cured capping cement used to fasten the caps or bases to the bulbs of electric lamps. [ citation needed ]
It is the central element of the traditional " French polish " method of finishing furniture, fine string instruments , and pianos . [ 33 ]
Shellac, being edible, is used as a glazing agent on pills (see excipient ) and sweets, in the form of pharmaceutical glaze (or, "confectioner's glaze"). Because of its acidic properties (resisting stomach acids), shellac-coated pills may be used for a timed enteric or colonic release. [ 34 ] Shellac is used as a 'wax' coating on citrus fruit to prolong its shelf/storage life. It is also used to replace the natural wax of the apple , which is removed during the cleaning process. [ 35 ] When used for this purpose, it has the food additive E number E904. [ 36 ]
Shellac is an odour and stain blocker and so is often used as the base of "all-purpose" primers. Although its durability against abrasives and many common solvents is not very good, shellac provides an excellent barrier against water vapour penetration. Shellac-based primers are an effective sealant to control odours associated with fire damage. [ 37 ]
Shellac has traditionally been used as a dye for cotton and, especially, silk cloth in Thailand, particularly in the north-eastern region. [ 38 ] It yields a range of warm colours from pale yellow through to dark orange-reds and dark ochre. [ 39 ] Naturally dyed silk cloth, including that using shellac, is widely available in the rural northeast, especially in Ban Khwao District , Chaiyaphum province . The Thai name for the insect and the substance is "khrang" (Thai: ครั่ง). [ citation needed ]
Wood finishing is one of the most traditional and still popular uses of shellac mixed with solvents or alcohol. This dissolved shellac liquid, applied to a piece of wood, is an evaporative finish: the alcohol of the shellac mixture evaporates, leaving behind a protective film. [ 40 ]
Shellac as wood finish is natural and non-toxic in its pure form. A finish made of shellac is UV-resistant. For water-resistance and durability, it does not keep up with synthetic finishing products. [ 41 ]
Because it is compatible with most other finishes, shellac is also used as a barrier or primer coat on wood to prevent the bleeding of resin or pigments into the final finish, or to prevent wood stain from blotching. [ 42 ]
Shellac is used: | https://en.wikipedia.org/wiki/Shellac |
In mathematics , a shelling of a simplicial complex is a way of gluing it together from its maximal simplices (simplices that are not a face of another simplex) in a well-behaved way. A complex admitting a shelling is called shellable .
A d -dimensional simplicial complex is called pure if its maximal simplices all have dimension d . Let Δ {\displaystyle \Delta } be a finite or countably infinite simplicial complex. An ordering C 1 , C 2 , … {\displaystyle C_{1},C_{2},\ldots } of the maximal simplices of Δ {\displaystyle \Delta } is a shelling if, for all k = 2 , 3 , … {\displaystyle k=2,3,\ldots } , the complex
is pure and of dimension one smaller than dim C k {\displaystyle \dim C_{k}} . That is, the "new" simplex C k {\displaystyle C_{k}} meets the previous simplices along some union B k {\displaystyle B_{k}} of top-dimensional simplices of the boundary of C k {\displaystyle C_{k}} . If B k {\displaystyle B_{k}} is the entire boundary of C k {\displaystyle C_{k}} then C k {\displaystyle C_{k}} is called spanning .
For Δ {\displaystyle \Delta } not necessarily countable, one can define a shelling as a well-ordering of the maximal simplices of Δ {\displaystyle \Delta } having analogous properties. | https://en.wikipedia.org/wiki/Shelling_(topology) |
A shellworld is any of several types of hypothetical megastructures : | https://en.wikipedia.org/wiki/Shellworld |
The Shell–Paques process , also known by the trade name of Thiopaq O&G , [ 1 ] is a gas desulfurization technology for the removal of hydrogen sulfide from natural-, refinery-, synthesis- and biogas . The process was initially named after the Shell Oil and Paques purification companies. After accession of a dedicated joint venture by the founders, Paqell B.V., the trade name for applications in the Oil & Gas industry was changed to "THIOPAQ O&G". It is based on the biocatalytical conversion of sulfide into elemental sulfur . It operates at near-ambient conditions of temperature, about 30-40 °C, and pressure which results in inherent safety. It is an alternative to, for example, the Claus process .
Each reaction can be applied individually or sequentially as dictated by the characteristics of the stream to be treated. The process consist of three main sections: An absorber (gas washing section), a bioreactor (sulfide oxidation and regeneration of washing liquid) and Sulfur handling section as shown in the figure below:
The washing step uses a dilute alkaline solution to remove hydrogen sulfide (H 2 S) from the sour gas according to:
The loaded washing liquid is transported to a bioreactor where a biocatalyst oxidises the aqueous NaHS to elemental sulfur with about 95% selectivity according to:
Combined reaction equation:
The regenerated washing liquid is sent back to the washing column.
The controlled partial oxidation of sulfide to elemental sulfur (2) is catalyzed by naturally occurring microorganisms of the genus Halothiobacillus in the bioreactor. These natural, living microorganisms present in the bioreactor catalyse the sulfur conversions and are, by their nature, resilient and adaptive.
In many situations the process can be used for sulfur removal and recovery. When sulfur recovery is desired, the elemental sulfur produced in the aerobic bioreactor will be separated from the aqueous effluent in a separator inside of the reactor. The excess sulfur will be removed as aqueous slurry or cake of up to 65% dry solids content. There are several options for handling this slurry and to convert it into products for sulfuric acid generation, fertiliser or fungicide.
The system is flexible and has several processing options that have ready application in the petroleum refinery or petrochemical complex for managing a variety of sulfur-containing streams including sulfidic caustic , LPG , hydrotreater offgas and fuel gas. | https://en.wikipedia.org/wiki/Shell–Paques_process |
Shemen ( Hebrew : שמן , romanized : šemen ) is the most commonly used word for oil in the Hebrew scriptures , used around 170 times in a variety of contexts.
In Exodus 29:1–9 describing the ordination of Aaron and his sons, unleavened challah ( חלה ) made with oil, translated as 'cakes', and wafers ( רקיק ) spread with oil are among the required offerings. The cakes, wafers and bread offering ( לחם ) made of the best quality of wheat are placed in a basket. After Aaron and his sons are anointed with oil and blood, the ram's tail fat , kidneys and other parts are burned as an offering, along with one oil cake, one wafer, and a piece of the unleavened bread. Then the remaining ram flesh is boiled for Aaron and his sons to eat along with the remainder of the bread and cakes.
In the Deuteronomy 8:8 it is mentioned as eretz zeit shemen in the description of the "good land": "A land of wheat and barley and the vine and figs and pomegranates, a land of olives for oil, and (date) honey ". [ 1 ] Based on this verse and additional descriptions given in Deuteronomy 6:11 , Deuteronomy 28:40 , Joshua 24:13 and 2 Kings 18:32 , olive oil appears to have been plentiful. Excavations at Tel Miqne-Ekron revealed over a hundred oil presses, and the region seems to have been central to a major olive oil industry. [ 2 ]
Genesis 49:20 describes the wealth of the lands of Asher : "From Asher shall come fat bread [rich foods], and he will provide delicacies of a king". [ 3 ] The relationship between fat ( Hebrew : שמנה , shemeneh ) and oil ( Hebrew : שהנ , shemen ) has been discussed by Ibn Ezra . [ 4 ] The blessings of Asher's exceptionally fertile lands is given by Moses in Deuteronomy 33:24 : "May he dip his foot in oil". [ 5 ]
Describing the hardships of the wilderness, in Numbers 11:8 the Israelites have only manna to eat, which they prepare into flat cakes called uggah ( עוגה ) that according to the passage tasted like lesad hassamen ( לשד השמן ). Translated as rich cream by the JPS , the certain meaning is not known. Aside from Psalms 32:4 , this verse is the only known use of lesad . It was translated into Greek as cake with oil ( ενκρις εζ ελαιου ), enkris having also been used for the Hebrew tzappihhit in place of wafers in Exodus 16:31 (where the taste is described "like a cake made with honey"). [ 6 ]
In Exodus 29:21 two unblemished rams are brought before Aaron and his sons for their ordination as priests. One is sacrificed as a burnt offering , while the second is slaughtered and some of the blood mixed with anointing oil and sprinkled on the priestly vestments. It was also used to anoint kings. [ 7 ]
It is used for anointing oil in conjunction with Bethel and other sites that were "anointed" in the narrative of Jacob's Ladder and subsequent second visit to Bethel ( Genesis 35:9–15 ). [ 7 ] [ 8 ] It is one of the offerings God demands of the Israelites for the Tabernacle in Exodus 25:3–8 in the context of spices to be used to make anointing oil and incense, as well as for use in lamps. [ 7 ] It is also used in the context of offerings in Micah 6:7 : "Will the Lord be pleased with thousands of rams, With ten thousands of rivers of oil? Shall I give my first born for my transgression, The fruit of my body for the sin of my soul?" [ 9 ]
Leviticus 24:1–9 discusses Israel's obligations to provide the daily oil for the lamps at the Tabernacle , and the weekly bread for the priests. [ 2 ]
There are various additional rules on the use of oil for lighting in different contexts such as searching for chametz during Pesach . Sometimes the shamash candle is made of wax, while olive oil is used for the other candles. [ 1 ]
According to Ezekiel 27:17 oil is exchanged with Tyre : "Judah, and the land of Israel, they were thy merchants: they traded in thy market wheat of Minnith, and Pannag, and honey, and oil, and balm." Hosea 12:1 discusses the context of relations between Ephraim and Egypt: "Ephraim feedeth on wind, and followeth after the east wind: he daily increaseth lies and desolation; and they do make a covenant with the Assyrians, and oil is carried into Egypt". [ 5 ]
There are several biblical references to non-ritual cosmetic use. [ 7 ] | https://en.wikipedia.org/wiki/Shemen_(bible) |
Shemen afarsimon ( Hebrew : שֶׁמֶן אֲפַרְסְמוֹן šemen ʾăp̄arsəmōn ) was a prized oil used in antiquity. The ancient Jewish community of Ein Gedi was known for its cultivation of the afarsimon. [ 1 ]
The Hebrew Bible does not mention persimmons, but in the Talmud and Midrash the Hebrew term [ which? ] may also stand for balsam , which occurs once in the Hebrew Bible as Hebrew besami (בְּשָׂמִי) "my spice" ( pronounced [bə.ɬaːˈmiː] ) in Song of Songs 5:1, which is indirect evidence of the form basam (בָּשָׂם; pronounced [baːˈɬaːm] ). [ 2 ]
In modern Hebrew , the word afarsimon is translated as persimmon . However, some doubt that persimmons would have been known to the peoples of the Bible, although being a traditional Jewish New Year 's food in the Diaspora . [ 3 ]
According to Adin Steinsaltz , the afarsimon of the
Talmud was considered very valuable, and worth its weight in gold. [ 4 ]
It is not known exactly what plant was used to produce the biblical oil. According to one theory, it is the plant Commiphora opobalsamum - a small shrub, 10 to 12 feet high, with wandlike, spreading branches. The oil extracted from the seeds or branches of this plant has been used as a medicine, but more commonly as incense or perfumed oil. [ citation needed ]
In April 1988, archeologists working with the former Baptist minister Vendyl Jones discovered a small jug of oil in the Qumran region that Jones announced was the oil used in the Temple. The find was announced by the New York Times on February 15, 1989, [ 5 ] and a feature article was published in National Geographic Magazine in October of that year. [ 6 ] After testing by the Pharmaceutical Department of the Hebrew University of Jerusalem (the results of which were never detailed or revealed), the substance inside the juglet was claimed by Jones to be the shemen afarsimon hinted at in Psalm 133. According to Jones, it was the first artifact discovered from the First Temple Period , and one of the treasures listed in the Copper Scroll . However, this identification remains controversial. [ 7 ] | https://en.wikipedia.org/wiki/Shemen_Afarsimon |
The Shenzhen Metro ( 深圳地铁 ) is the rapid transit system for the city of Shenzhen in Guangdong province, China . The newest lines and extensions which opened on December 27, 2024 put the network at 595.1 kilometres (369.8 miles) [ 5 ] [ b ] of trackage. It currently operates on 17 lines with 398 stations. [ 1 ] Despite having only opened on December 28, 2004, the Shenzhen Metro is the 5th longest metro system in the world . By 2035, the network is planned to comprise 8 express and 24 non-express lines totaling 1,142 kilometres (710 miles) of trackage.
Currently the network has 595.1 kilometres (369.8 miles) of route, operating on 17 lines with 398 stations. Line 1, Line 4 and Line 10 run to the border crossings between the Shenzhen Special Economic Zone and the Hong Kong Special Administrative Region at Luohu / Lo Wu and Futian Checkpoint / Lok Ma Chau , where riders can transfer to Hong Kong's MTR East Rail line for travel onwards to Hong Kong.
Partial: Luohu ↔ Zhuzilin , Zhuzilin ↔ Airport East , Luohu ↔ Qianhaiwan , Luohu ↔ Xixiang
6B
7
9
10
11
12
13
14
16
Line 1, formerly known as Luobao line, runs westward from Luohu to Airport East . Trains operate every 2 minutes during peak hours and every 4 minutes at other times. The line is operated by SZMC (Shenzhen Metro Group). Line 1's color is green .
Line 2, formerly known as Shekou line, runs from Chiwan to Liantang. Line 2 is connected with Line 8 at Liantang station. The line is operated by SZMC (Shenzhen Metro Group). Line 2's color is dark orange , the same as Line 8.
Line 3, formerly known as Longgang line, runs from Futian Bonded Area to Pingdi Liulian in Longgang , in the north-east part of the city. Construction began on December 26, 2005. [ 12 ] The line is operated by Shenzhen Metro Line 3 Operations, which has been a subsidiary of SZMC (Shenzhen Metro Group) since April 11, 2011, when an 80% stake was transferred to SZMC. Line 3's color is sky blue .
Line 4, formerly known as Longhua line, runs northward from Futian Checkpoint to Niuhu . Trains operate every 2.5 minutes at peak hours and every 6 minutes during off-peak hours. Stations from Futian Checkpoint to Shangmeilin Station are underground . The line has been operated by MTR Corporation (Shenzhen), a subsidiary of MTR Corporation , since July 1, 2010. Line 4's color is red .
Line 5, formerly known as Huanzhong line, runs from Chiwan in the west to Huangbeiling in the east. Construction began in May 2009 and the line opened on June 22, 2011. [ 14 ] Line 5 required a total investment of 20.6 billion RMB. The line is operated by SZMC (Shenzhen Metro Group). Line 5's color is purple .
Line 6, formerly known as Guangming line, runs from Songgang in the north to Science Museum in the south, with a length of 49.4 km (30.7 mi) and a total of 27 stations. Construction began in August 2015 and the line opened on August 18, 2020. The line is operated by SZMC (Shenzhen Metro Group). Line 6's color is mint green .
Line 6 Branch, also known as Branch Line 6, runs from Guangming to SIAT in the north. The line opened on November 28, 2022. Line 6 Branch's color is teal .
Line 7, formerly known as Xili line of the Shenzhen Metro, opened on October 28, 2016, with a length of 32.84 km (20.41 mi) [ 15 ] and a total of 29 stations. It connects SZU Lihu Campus at Shenzhen University to Tai'an. The line travels East–West across Shenzhen in a "V" shape. The line is operated by SZMC (Shenzhen Metro Group). Line 7's color is navy blue .
Line 8, formerly known as Yantian line of the Shenzhen Metro, opened on October 28, 2020, with a length of 20.377 km (12.662 mi) [ 15 ] and a total of 11 stations. It connects the eastern suburbs of Liantang to Yantian Road , then towards the beach resorts at Dameisha and Xiaomeisha . However, this line serves as the extension of Line 2 in actual operation. The line is operated by SZMC (Shenzhen Metro Group). Line 8's color is dark orange , the same as Line 2.
Line 9, formerly known as Meilin line or Neihuan line of the Shenzhen Metro, opened on October 28, 2016. The line runs eastward from Qianwan to Wenjin . It has 10 transfer stations. The line is 36.18 km (22.48 mi) long, running through the districts of Nanshan, Futian and Luohu. The line is operated by SZMC (Shenzhen Metro Group). Line 9's color is grey brown .
Line 10 formerly known as Bantian line, runs from Futian Checkpoint in the south to Shuangyong Street in the north, with a length of 29.3 km (18.2 mi) and a total of 24 stations. Construction began in September 2015 and the line opened on August 18, 2020. The line is operated by SZMC (Shenzhen Metro Group). Line 10's color is pink .
Line 11, also known as the Airport Express, runs from Bitou in the northwest to Huaqiang South in the city centre via Shenzhen Bao'an International Airport. Construction began in April 2012 and the line opened on June 28, 2016. Line 11 runs at a higher speed of 120 km/h (75 mph), however, the current line speed is limited to 80 km/h (50 mph). The line is operated by SZMC (Shenzhen Metro Group). Line 11's color is maroon .
Line 12, also known as Nanbao Line, runs from Zuopaotai East in the southwest to Songgang in the northwest. Construction began in 2018 and the line opened on November 28, 2022. Line 12's color is light purple .
Line 13, also known as Shiyan Line, runs from Shenzhen Bay Checkpoint at the Shenzhen Bay Port in Nanshan to Shangwu in northeast Bao'an. Construction began in 2018 and the first phase of the line between Shenzhen Bay Checkpoint and Hi-Tech Central opened on December 28, 2024. Line 13's color is light orange .
Line 14, also known as the Eastern Express, runs from Gangxia North in the city centre to Shatian in the northeast. Construction began in 2018 and the line opened on October 28, 2022. The line is operated by SZMC (Shenzhen Metro Group). Line 14's color is yellow .
Line 16, also known as Longping Line, runs from Universiade in the centre of Longgang to Tianxin in the northeast. Construction began in 2018 and the line opened on December 28, 2022. The line is operated by SZMC (Shenzhen Metro Group). Line 16's color is dark blue .
Line 20, formerly known as Fuyong line, runs from Airport North in the north-west to Convention & Exhibition City near Shenzhen World. Construction began in September 2016 and the line opened on December 28, 2021. Line 20 runs at the same top speed as line 11, at 120 km/h (75 mph). The line is operated by SZMC (Shenzhen Metro Group). Line 20's color is light blue .
In late 1983, Party Secretary of Shenzhen Mayor Liang Xiang led a team to Singapore to study its mass transit system. Upon returning it was decided that 30 metres (98 ft 5 in) on each side of Shennan Avenue should be protected as a green belt, and to set aside a 16-metre (52 ft 6 in) wide median reserved for a light rail or light metro line. [ 17 ] In 1984, the "Shenzhen Special Economic Zone Master Plan (1985–2000)" pointed out that, with the growing population and traffic in Shenzhen, a light metro system would not have sufficient capacity to meet future demand. Instead the report proposed a heavy rail subway line to be built along Shennan Avenue. [ 18 ] The project was finally approved by the Central Planning Department in 1992. [ 19 ]
In August 1992, during and re-feasibility and rail network planning, The Shenzhen Municipal Government decided to move from building a light metro line to a heavy rail subway line. The rapid growth of Shenzhen City made a lower capacity light metro line impractical. [ 20 ] In 1994, Shenzhen organized the preparation of the "Shenzhen urban rail network master plan" to be incorporated into the "Shenzhen City Master Plan (1996–2010)". [ 21 ] The city's vision for an urban rail network would consists of nine lines. Of the nine transit lines, three of them would be commuter rail lines upgraded from existing national mainline railways. The total length of the proposed network would be about 270 km (170 mi). The three upgraded commuter rail lines would overlap the Guangzhou–Shenzhen railway , Pinghu–Nanshan railway and Pingyan railway. [ 21 ] This plan established the basic framework for the Shenzhen Metro network. [ 22 ]
In December 1995, the State Council issued the "moratorium on approval of urban rapid transit projects" to suspend approval of rail transit projects in all Chinese cities except Beijing, Shanghai, and Guangzhou. The Shenzhen Metro project was postponed. [ 23 ] In 1996, prior to the handover of Hong Kong, authorities attempted to restart construction by renaming the project "The Luohu, Huanggang / Lok Ma Chau border crossing passenger rail connection project", stressing that the project is designed to meet the potential growing demand for cross-border passenger traffic after the handover. [ 21 ]
In 1997, Shenzhen reapplied its Subway plans to the State Planning Commission, and received approval in May 1998. [ 20 ] The project was renamed the "Shenzhen Metro first phase". [ 24 ] In July 1998, SZMC (Shenzhen Metro Group). was formally established. [ 24 ] By April 1999, the subway project feasibility study report has been approved by the state.
Construction of the first sections of Line 1 and Line 4 began in 1999. The grand opening of the Shenzhen Metro system occurred at 5:00 pm on Tuesday, December 28, 2004. This made Shenzhen the seventh city in mainland China to have a subway after Beijing , Tianjin , Shanghai , Guangzhou , Dalian and Wuhan .
Initially the trains operated at 15-minute frequencies and consisted of Line 1 services between Luohu and Shijie Zhi Chuang (now Window of the World) and the Line 4 services between Fumin and Shaonian Gong (now Children's Palace). Initially the English names of the stations were rendered in Hanyu Pinyin , but some of the names were changed to English translation with American spelling like the rest of mainland China , despite being close to the Hong Kong, which uses British spelling and ongoing political tensions with the US , in mid-2011.
The Futian Checkpoint station opened on June 28, 2007, using the name Huanggang. [ 25 ]
On April 23, 2008, Shenzhen Municipal Planning Bureau announced that it would change the nomenclature of Shenzhen's subway lines according to the "2007 Urban Rail Transit Plan Scheme". Instead of using numbers as the lines official designation, as typically used in other mainland Chinese metro systems, lines would be given Chinese names more akin to the Hong Kong MTR. [ 26 ] In 2010, the Scheme was reviewed and adjusted with new routes and names in addition to newly proposed lines. On October 23, 2013, the SZMC (Shenzhen Metro Group) decided that current operational lines will have their number and names combined, while future lines will only be numbered. [ 27 ] Due to the change in the construction order of several lines, some numerical names have been reviewed in order to prevent big jump between numbers. By 2016, only numerical names are used.
Lines currently in operation:
Lines under construction:
From 2004 to 2007, there was a lack of official government interest and attention to expanding the subway after completion of Phase 1 with little or no active projects. [ 28 ] Subway construction speed was ridiculed as "earthworm speed". [ 29 ] On January 17, 2007, Shenzhen won the right to host the 2011 Universiade . In the bid Shenzhen committed to complete 155 km (96 mi) of subway lines before the games. [ 28 ] The mayor of Shenzhen at the time, Xu Zongheng, sharply criticized the speed and efficiency of Shenzhen's subway construction procedures and calls for reform. [ 30 ] Subsequently, the Shenzhen municipal government and various departments signed a liability form, requiring Phase II subway expansion to be completed in time for the Universiade. [ 31 ] Shenzhen Metro increased to over a hundred operating metro stations in June 2011, just before the Shenzhen Universiade games. In the span of two weeks, the network expanded from 64 km (40 mi) to 177 km (110 mi). This expansion increased rail transit's share of total public transit trips from 6% to 29% in 2014. [ 32 ] [ 33 ] [ 34 ] [ 35 ]
In 2010, the Shenzhen Urban Planning and Land Resources Committee proposed a building program (Phase III) between 2011 and 2020. In 2011 this plan was approved by the NDRC . Phase III formally commenced in May 2011 with an expected cost of 125.6 billion yuan. It will cover Lines 6, 7, 8, 9, and 11 and will extend the length of the Shenzhen Metro to 348 kilometres (216 mi) and 10 lines. [ 36 ] [ 37 ] In June 2011, the Shenzhen Urban Planning and Land Resources Commission started gather public input on Phase III station names. [ 38 ] On June 28, 2016, Line 11 opened being the first subway line in Shenzhen with 8 car trains and 120 km/h (75 mph) maximum service speed and the first in China with a First Class service. Lines 7 and 9 followed on October 28, 2016. South extension of Line 5 opened on September 28, 2019, and west extension of Line 9 opened on December 8, 2019. Line 6 and Line 10 opened on August 18, 2020, bringing the length of the Shenzhen Metro to 382.1 km (237.4 mi) and the fourth longest in China. Second east extension of Line 2, second south extension of Line 3, second north extension of Line 4 and phase 1 of Line 8 opened on October 28, 2020, bringing the length of the Shenzhen Metro to 411 km (255 mi). Phase III is also the first phase in which the lines are officially numbered instead of named and colored.
With the shortening of the Phase III implementation period, [ 44 ] a number of lines (Lines 16 and 12) planned in 2007's Phase III moved into the next phase. [ 45 ] By 2016, it was determined that Phase IV will have an implementation period between 2017 and 2022 and consist of 274 km (170 mi) of new subway. [ 46 ] Lines 13 and 14 which originally had a long term 2030 completion deadline were moved into Phase IV expansion. In addition, a branch line of Line 6 will connect with the neighboring Dongguan Rail Transit system. [ 47 ] Lines 12, 13, 14, and 16 and branch of Line 6 was approved by the NDRC in July 2017 and started construction in January 2018. [ 48 ] [ 35 ] The first phase of Line 20 was fast tracked from Phase IV to provide a shuttle between Line 11 and a new International Convention Center, now called Convention & Exhibition City. The construction started in September 2016, but as for early 2019, the construction is paused because the Development and Reform Commission did not approve the project. The Phase IV revised plan approved by the NDRC on March 26, 2020, approved the first Phase of Line 20 allowing for construction to continue. The line eventually opened on December 28, 2021. Futian to Gangxia North in the first section of Phase 2 of Line 11 opened on October 28, 2022 in tandem with Line 14 Phase I.
The Phase IV revised plan approved by the NDRC on March 26, 2020, added a number of extension projects. [ 49 ]
Line 5 west extension is part of Phase II expansion.
In the Shenzhen Metro 2007 masterplan proposed four more lines (Lines 13, 14, 15 and 16) which have a planned completion target of 2030. [ 50 ] In 2016, all aforementioned lines but Line 15 were designated as part of the Phase IV expansion, moving the completion date forward from 2030 to 2022. In 2012, four further lines Qiannan (Line 17), Pinghu (Line 18), Pingshan (Line 19) and Fuyong (Line 20) where unveiled, making the total planned length of the Shenzhen Metro to 720 km (447 mi) spread out over 20 lines. The first phase of Line 20 was fast-tracked and included in the Phase III revised expansion with a completion date of 2018. This leaves Line 15, 17–19 and the rest of Line 20 available for the next phase (Phase V) of subway expansion. In September 2022, the Shenzhen municipal government confirmed the projects proposed to be included in its phase V expansion. A total of 227 km (141 mi) of new lines are proposed. [ 51 ]
On March 31, 2023, the Bureau of Housing and Urban Rural Development of Shenzhen Metro Municipality will open the bidding for the fifth phase planning of Shenzhen Metro Metro, including Line 15, Line 17 Phase I, Line 19 Phase I, Line 20 Phase II (Airport East—Baishizhou), Line 22 Phase I, Line 25 Phase I, Line 27 Phase I, Line 29 Phase I and Line 32 Phase I, This means that these 9 lines have been approved with an investment amount of 191.1 billion yuan. However, Line 18 Phase I, Line 21 Phase I, Line 10 East Extension (Shenzhen Section) and Metro Line 11 North Extension (Shenzhen Section), which were previously proposed to be included in the fifth phase plan of Shenzhen Metro, were not included in this announcement. [ 52 ]
In June 2023, the Fifth Phase Construction Plan of Shenzhen Urban Rail Transit (2023–2028) has been approved for a total of 11 construction projects, including Line 15, Line 17 Phase I, Line 19 Phase I, Line 20 Phase II (Airport East—Baishizhou), Line 22 Phase I, Line 25 Phase I, Line 27 Phase I, Line 29 Phase I, Line 32 Phase I, Line 10 East Extension (Shenzhen Section) and Metro Line 11 North Extension (Shenzhen Section). [ 53 ]
Aside from the set masterplan, at the 12th Guangdong Provincial People's Congress in January 2014, [ 63 ] it was proposed to extend Line 4 beyond the planned Phase III terminus at the Songyuan Bus Terminal in Guanlan. The proposal wanted to further extend this line to reach the future planned Dongguan Metro Line 4 at Tangxia station. This proposal aims to shorten the distance between the two cities in residents' minds, boost tourism industries in both cities and expand housing options. It would also allow for direct connection between Hong Kong and Dongguan . As the area in the proposed area is less developed, the cost in building the line is expected to be lower, with a feasibility study yet to be conducted. In addition to metro lines, 5 Pearl River Delta Rapid Transit lines connecting neighboring urban centers in the Pearl River Delta such as Dongguan , Huizhou , Foshan and Guangzhou , totaling 146 km (91 mi), have also been revealed. [ 64 ] In 2016, an even more ambitious masterplan, expanding the previously planned 20 lines to 32, was unveiled. The new plan envisions a 1,142 km (710 mi) subway network to be completed by 2030. This will allow for travel between the central and suburban districts to be shortened to 45 minutes and for public transit to make up more than 70% of all motorized trips in Shenzhen. [ 65 ]
Since the opening of the first phase in 2004, there has been a steady growth in passenger traffic. In 2009 and 2010, passenger traffic soared with major openings of new phase 2 lines, with a three-fold increase in passenger traffic in 2010. [ 84 ] On July 12, 2019, it set a new record for its peak ridership at 6.63 million. [ 2 ]
July is the busiest month of the year for the Shenzhen Metro, accounting for 9.3% of annual passenger traffic, while January is the least busy month, accounting for only 6.7%. This is caused by Shenzhen's large migrant worker population. [ 85 ]
Metro rides are priced according to distance travelled, and fares vary from 2 RMB to 14 RMB. [ 86 ] Since December 2010 fares are based on a usage fee (2 RMB) + a distance fee. The distance fee is 1 RMB for each 4 km (2.5 mi) from 4 km (2.5 mi) to 12 km (7.5 mi); after that 1 RMB for each 6 km (3.7 mi) from 12 km (7.5 mi) to 24 km (15 mi) and finally 1 RMB for every 8 km (5.0 mi) over 24 km (15 mi) distance. [ 87 ] For passengers who wish to ride on business coach in line 11, they have to pay 3 times the amount of price that calculated by the regulations above.
Children under the height of 120 cm (3 ft 11 in) or aged below 6 may ride for free when accompanied by an adult. [ 89 ] The metro also offers free rides to senior citizens over the age of 65, the physically disabled and military personnel. Tickets for children between 120 cm (3 ft 11 in) and 150 cm (4 ft 11 in), or aged between 6 and 14 years, or middle school students, are half priced.
Metro fares can be paid for with single-ride tokens, multiple-ride Shenzhen Tong cards or 1- day passes. [ 90 ]
When using cash, a RFID token ( NXP Mifare Classic ) is purchased and used for a single, non-returnable journey. There are two different types of tokens, with green tokens for Standard Class, and yellow tokens used for Business Class which is only available on Line 11. All ticket vending machines offer both English and Chinese interface. The purchaser touches a station name to calculate the fare. After payment, a green token is dispensed, which must be scanned at the entrance station and deposited at the exit station. A penalty applies should a token be lost. Purchasers of green tokens cannot ride Business Class on Line 11 directly. Instead, they must get off at any transfer stations with Line 11 and purchase a separate yellow token.
Note that as of 2015, many machines accept only 5 or 10 RMB notes. The token(s) are only valid at the station where issued. Passengers are unable to buy an extra token for return journey prior to departure. Baggage X-Ray machines are located at each station, and may be staffed during peak hours.
Shenzhen Tong is a pre-paid currency card similar to Oyster card system in London and the Octopus card system used in Hong Kong. The multiple fare card stores credit purchased at stations. The card can be used by waving it in front of the card reader located at all entrances and exits to the subway system. Riders who pay for metro fare with a card receive a 5% discount. Since March 1, 2008, riders who pay for a bus fare with a card and then a subway fare within 90 minutes receive an additional 0.4 RMB discount on the subway fare. Card users pay a distance based fare.
Since June 30, 2011, cards containing both a Shenzhen Tong and Hong Kong Octopus chip have been available in both Shenzhen and Hong Kong. There are plans to further integrate the two systems, and for a new card which will be accepted all over Guangdong province and China's two SARs . [ 91 ] [ 92 ]
Unlike Hong Kong Octopus Cards, Shenzhen Tong cards cannot be sold back to the stations or have faults dealt with by SZMC. Instead, the customer must go to the offices of Shenzhen Tong. Students studying in Shenzhen can use the Shenzhen Tong to receive a 50% discount.
Note that discounts are not applicable for people who ride Business Class carriages on Line 11.
Metro cards can also be used on Shenzhen's public bus system.
Metro 1-day pass is a smart card that allowed the card holder have unlimited access of the metro system in 24 continuous hours. Passengers can purchase a 1-day pass for RMB 25 in the service center in any metro station. The pass will be activated and the passenger will have 24 continuous hour for unlimited access after the first entrance. When the pass expired, the pass is no longer available for entering a station but able to exiting a station and finish a journey in 27.5 hours. The 1-day passes are not applicable for Business Class carriages on Line 11.
Some stations have toilets (free of charge), and public telephones. SZMC also operates luggage storage facilities in the concourse above Luohu Station. Mobile phone service is available throughout the system provided by China Mobile , China Telecom , and China Unicom . [ 93 ]
Like the Hong Kong MTR , Guangzhou , and Foshan metros, station announcements are in Mandarin, Cantonese and English. Some announcements, such as train arrival, are in Mandarin and English only. Cantonese, an important local language, is chosen for the local Cantonese population as well as Cantonese speakers in Guangdong , Hong Kong and Macau .
The stations of Line 6 and Line 10 are the first metro stations in China to have 5G coverage. [ 94 ]
On Line 1 and Line 4, Siemens supplied 7 (Phase 1) and 6 (Phase 2) LZB 700 M continuous automatic control systems; 7 (Phase 1) and 6 (Phase 2) electronic Sicas ESTT interlockings; the Vicos OC 501 operations control system with 2 operations control centers, fall-back level with Vicos OC 101 and RTU (FEP), 230 (Phase 1) and 240 (Phase 2) FTG S track vacancy detection units. [ 95 ]
Line 2 and Line 5 use Casco CBTC system with 2.4 GHz frequencies, and so the system has suffered frequent problems with interference from consumer Wi-Fi equipment. [ 96 ] By the end of November 2012, CASCO solved the problem on Lines 2 and 5 by switching to their standard solution with frequency diversity on 2 different channels.
Pingshan Center station on Line 14 connects to Line 1 of the Pingshan Skyshuttle. This 8.5 km monorail line opened on December 28, 2022, with 11 stations, all in Pingshan district. Two of the stations will eventually connect to Line 16 stations.
The mascot of Shenzhen Metro named "Tiebao" (Simplified Chinese: 铁宝; Traditional Chinese: 鐵寳) was unveiled on December 27, 2023. It is a cute anthropomorphic of a Shenzhen Metro train's front. [ 104 ]
Macau (MFM)
Macau Ferry Terminal
Jieyang Chaoshan (SWA)
Bao'an (SZX)
Shekou Cruise Center | https://en.wikipedia.org/wiki/Shenzhen_Metro |
Howard Sheperd " Shep " Paine was a military historian and a collector of militaria best known for the more than three decades he spent as a modeler, sculptor, miniature figure painter , and champion of the diorama . Paine arguably did more than anyone else to forward the unique hobby/art form of military miniatures around the world, through his own pieces, numerous "how-to" hobby books, and championing of the "open system" of judging in use at many of the most prestigious modeling shows and exhibitions today. [ 2 ] [ 3 ]
Sheperd Paine was the first child born to American parents in Berlin after the end of World War II. [ 2 ] After leaving Berlin, his family moved to London for a year, during which period he attended Eaton House School . [ 4 ] [ 5 ] Paine's family then moved again to New England, where he attended St. Paul's School . [ 6 ] After service as a sergeant in the U.S. Army, he received a BA from the University of Chicago, and lived in the Windy City for most of his life.
For many years, Paine worked in the military history field as a free-lance artist, sculptor, and writer. His commissions included dioramas for private collections (notably those of Andrew Wyeth and Forbes Magazine), museum projects, and several large commemorative sculptures for the Franklin Mint. [ 2 ] [ 6 ]
Special displays of his work have been seen at the Brandywine River Museum, the Campbell Museum, and the St. Louis Museum of Science and Natural History. He was the author of four books; his work has been featured in articles in Sports Illustrated and Fortune (along with many hobby magazines), and he is the subject of a hardcover biography/career overview entitled Sheperd Paine: The Life and Work of a Master Modeler and Military Historian written by Chicago rock critic and fellow miniaturist Jim DeRogatis . [ 7 ] [1]
Paine had a broad knowledge of military history (particularly uniforms and equipment) with proficiency in the American Civil War, Napoleonic Wars, and the two World Wars. For thirty years he was an active collector of military antiques, specializing in the Victorian and Napoleonic periods. He was a director of the Napoleonic Historical Society, and had been a member of the Company of Military Historians since 1972, being elected a fellow of that organization in 1980. He remained active with the Military Miniature Society of Illinois (MMSI) , a Chicago-area club devoted to the miniatures hobby and many other aspects of military history, until his sudden death from a stroke in 2015. [ 8 ]
Most modelers and miniaturists first became aware of Paine's work through the series of "How to Build a Diorama" tip sheets included with Monogram models of tanks, military vehicles, and airplanes in the 1970s and '80s. He later did dioramas that were included in the catalogs published by Tamiya models , as well as a few projects for Dragon Models .
Paine also is well known for his box dioramas or shadow boxes , scratchbuilt scenes (usually with figures 100mm tall) set inside a box, which enabled him to control the viewpoint and set the mood via internal lighting and occasionally special effects such as mirrors. His boxes include "In the Turret of the Monitor, 1862"; "The Gun Deck of the HMS Victory at Trafalgar, 1805"; "Napoleon at the Tomb of Frederick the Great, 1806"; "The Remnants of an Army, 1812"; "To a Fair Wind... and Victory! Nelson on the Eve of Copenhagen, 1801," and "Rembrandt's Night Watch." [ 2 ] [ 6 ]
Paine told the Chicago Sun-Times: "When you get into dioramas, you are creating a work of art. I don't use the word with a capital 'A' but you are creating a 3-D painting, and the satisfaction you get is much the same. In some ways, dioramas are so interesting because they combine so many elements in different forms: You are basically telling a story without words. It's like silent movies, except you don't have anybody moving." [ 9 ] | https://en.wikipedia.org/wiki/Sheperd_Paine |
Shephard's lemma is a result in microeconomics having applications in the theory of the firm and in consumer choice . [ 1 ] The lemma states that if indifference curves of the expenditure or cost function are convex , then the cost-minimizing point of a given good ( i {\displaystyle i} ) with price p i {\displaystyle p_{i}} is unique. The idea is that a consumer will buy a unique ideal amount of each item to minimize the price for obtaining a certain level of utility given the price of goods in the market .
The lemma is named after Ronald Shephard , who proved it using the distance formula in his book Theory of Cost and Production Functions in 1953. The equivalent result in the context of consumer theory was first derived by Lionel W. McKenzie in 1957. [ 2 ] It states that the partial derivatives of the expenditure function with respect to the prices of goods equal the Hicksian demand functions for the relevant goods. Similar results had already been derived by John Hicks (1939) and Paul Samuelson (1947).
In consumer theory, Shephard's lemma states that the demand for a particular good i {\displaystyle i} for a given level of utility u {\displaystyle u} and given prices p {\displaystyle \mathbf {p} } , equals the derivative of the expenditure function with respect to the price of the relevant good:
where h i ( p , u ) {\displaystyle h_{i}(\mathbf {p} ,u)} is the Hicksian demand for good i {\displaystyle i} , e ( p , u ) {\displaystyle e(\mathbf {p} ,u)} is the expenditure function , and both functions are in terms of prices (a vector p {\displaystyle \mathbf {p} } ) and utility u {\displaystyle u} .
Likewise, in the theory of the firm , the lemma gives a similar formulation for the conditional factor demand for each input factor: the derivative of the cost function c ( w , y ) {\displaystyle c(\mathbf {w} ,y)} with respect to the factor price:
where x i ( w , y ) {\displaystyle x_{i}(\mathbf {w} ,y)} is the conditional factor demand for input i {\displaystyle i} , c ( w , y ) {\displaystyle c(\mathbf {w} ,y)} is the cost function. Both functions are in terms of factor prices (a vector w {\displaystyle \mathbf {w} } ) and output y {\displaystyle y} .
Although Shephard's original proof used the distance formula, modern proofs of Shephard's lemma use the envelope theorem . [ 3 ]
The proof is stated for the two good cases for ease of notation. The expenditure function e ( p 1 , p 2 , u ) {\displaystyle e(p_{1},p_{2},u)} is the value function of the constrained optimization problem characterized by the following Lagrangian:
By the envelope theorem the derivatives of the value function e ( p 1 , p 2 , u ) {\displaystyle e(p_{1},p_{2},u)} with respect to the parameter p 1 {\displaystyle p_{1}} are:
where x 1 h {\displaystyle x_{1}^{h}} is the minimizer (i.e. the Hicksian demand function for good 1). This completes the Proof.
Shephard's lemma gives a relationship between expenditure (or cost) functions and Hicksian demand. The lemma can be re-expressed as Roy's identity , which gives a relationship between an indirect utility function and a corresponding Marshallian demand function . | https://en.wikipedia.org/wiki/Shephard's_lemma |
In mathematics , Shephard's problem , is the following geometrical question asked by Geoffrey Colin Shephard in 1964: if K and L are centrally symmetric convex bodies in n - dimensional Euclidean space such that whenever K and L are projected onto a hyperplane , the volume of the projection of K is smaller than the volume of the projection of L , then does it follow that the volume of K is smaller than that of L ? [ 1 ]
In this case, "centrally symmetric" means that the reflection of K in the origin, −K , is a translate of K , and similarly for L . If π k : R n → Π k is a projection of R n onto some k -dimensional hyperplane Π k (not necessarily a coordinate hyperplane) and V k denotes k -dimensional volume, Shephard's problem is to determine the truth or falsity of the implication
V k ( π k ( K )) is sometimes known as the brightness of K and the function V k o π k as a ( k -dimensional) brightness function .
In dimensions n = 1 and 2, the answer to Shephard's problem is "yes". In 1967, however, Petty and Schneider showed that the answer is "no" for every n ≥ 3. [ 2 ] [ 3 ] The solution of Shephard's problem requires Minkowski's first inequality for convex bodies and the notion of projection bodies of convex bodies. | https://en.wikipedia.org/wiki/Shephard's_problem |
Sherardising or Zinc thermal diffusion is a process of galvanization of ferrous metal surfaces, also called vapour galvanising and dry galvanizing . The process is named after British metallurgist Sherard Osborn Cowper-Coles (son of naval inventor Cowper Phipps Coles ) who invented and patented the method c. 1900. [ 1 ] [ 2 ] [ 3 ] [ 4 ] This process involves heating the steel parts up to 500 °C in a closed rotating drum that contains metallic zinc dust and possibly an inert filler, such as sand. [ 5 ] At temperatures above 300 °C, zinc evaporates and diffuses into the steel substrate forming diffusion bonded Zn-Fe-phases.
Sherardising is ideal for small parts and parts that require coating of inner surfaces, such as batches of small items. Part size is limited by drum size. It is reported that pipes up to 6 m in length for the oil industry are sherardised. [ citation needed ] If the metal surface is free of scale or oxides, no pretreatment is needed. The process is hydrogen-free, hence hydrogen embrittlement is prevented.
During and shortly after World War I , German 5 pfennig and 10 pfennig coins were sherardised. | https://en.wikipedia.org/wiki/Sherardising |
Sherborne Sensors is a designer and manufacturer of precision inclinometers, accelerometers and load cells. Technologies utilized include mechanical servo , solid state and strain gauge . These precision measurement tools are available as both off-the-shelf and bespoke for use in military, aerospace, civil and industrial engineering applications.
Sherborne Sensors is based in ‘transducer valley’ in Hampshire, UK, [ 2 ] and supplies its products to over 50 countries across the world.
Many of the inertial products currently offered have evolved from the Schaevitz brand that innovated sensor design during the 1940s and 1950s. The current LSOC/LSOP range of Linear Servo Inclinometers originate from the genuine Schaevitz units. The Force Transducers have their roots with the Maywood brand founded in the 1970s.
Sherborne Sensors began life in 1945 as Schaevitz Engineering, a New Jersey–based manufacturer of LVDTs and other precision sensors. The business operated solely in the United States until an association formed with Electro-Mechanisms (EM) in 1963. This allowed their products to be distributed in the UK and also to be manufactured under licence.
Prompted by the success overseas, Schaevitz Engineering acquired the majority shareholding in EM and began manufacturing a UK range of inertial products in 1974.
The Schaevitz name traded until 1986 when the company was acquired by Lucas who changed the name of the business to Lucas Control Systems.
In 1997 the company became Lucas Varty [ sic ] and in 1999 was acquired by TRW. Throughout all of this time the Schaevitz brand remained strong and at the cutting edge of sensors technologies.
This business model continued until August 2000 when the Schaevitz Sensors and Components division of TRW was acquired by Measurement Specialities Inc (MSI). In 2002 the Measurement Specialties UK group was put into financial receivership and its assets sold. A group of former Schaevitz employees purchased the Inertial Products Division from MSI and formed the Sherborne Sensors Limited Company in July 2002 thus continuing the design, development and manufacture of precision sensors.
In 2007, Sherborne Sensors extended its product range beyond inertial sensors by obtaining the former Maywood Instruments force transducer product lines and intellectual property from FTSA Holdings Limited.
Following this expansion, Sherborne Sensors has extended its operation globally, establishing a sales and stocking location in North American in 2009. [ 3 ]
2012 NOVA METRIX LLC, Woburn MA, acquires Sherborne Sensors Ltd. | https://en.wikipedia.org/wiki/Sherborne_Sensors |
Sherifah Tumusiime (Born July 13, 1988) , alias "Chief Hustler" is a Ugandan Computer scientist , businesswoman , entrepreneur, and technology advocate. [ 1 ] [ 2 ] [ 3 ] She is the founder and Chief Executive Officer of Zimba Group Ltd flagship project, Zimba Women, a technology social enterprise supports and resources women entrepreneurs in East Africa , founder of The Baby Store UG, and Senior Systems Officer at Uganda Financial Intelligence Authority(FIA) in Uganda . [ 2 ] [ 4 ] [ 5 ] [ 6 ]
She is a 2015 Mandela Washington Fellow and the regional winner ( Africa and Europe ) for the Commonwealth Youth Award 2018, a speaker at international conferences, such as RightsCon in Silicon Valley and the Shoko Digital Festival in Harare , Zimbabwe . [ 7 ] [ 8 ] [ 9 ]
Tumusiime attended Mount Saint Mary's College Namagunga , then did a Bachelor of Computer Science at Makerere University from 2008–2011 and Business and Entrepreneurship at Clark Atlanta University in 2015. [ 8 ] [ 10 ]
Tumusiime is the Founder, CEO of Zimba Zimba Group Ltd from December 2014 to date, which currently collaborates with over 15,000 female entrepreneurs and Senior Systems Officer at Uganda Financial Intelligence Authority (FIA). [ 11 ] [ 12 ] [ 13 ] [ 4 ] [ 14 ] [ 5 ] She founded Baby Store started 2012 as an e-commerce store selling baby products, worked at Wipro Info Tech as Data Centre monitoring team lead in 2011 till she became a Tools team lead in 2014, and a Service Desk Administrator at MTN Uganda , April 2009 – Nov 2011. [ 12 ] [ 15 ] | https://en.wikipedia.org/wiki/Sherifah_Tumusiime |
Sherlock Biosciences is a biotechnology company based in Cambridge, Massachusetts developing diagnostic tests using CRISPR - Cas13 . The company was founded in 2019 [ 1 ] by Feng Zhang , Jim Collins , Omar Abudayyeh, and Jonathan Gootenberg of the Broad Institute . [ 2 ]
Cas13 was discovered by Zheng and Eugene Koonin using computational biology methods, and then further characterized by Jennifer Doudna 's team at the University of California, Berkeley . In 2020, both Sherlock Biosciences and Mammoth Biosciences from Doudna's lab at UC Berkeley used their similar CRISPR technologies to develop tests for COVID-19 . [ 3 ] [ 4 ]
In 2021, Sherlock Biosciences and The Forsyth Institute entered into a strategic partnership with its focus being on the research and development of products related to the “detection of human biomarkers in oral cavity and other oral health applications." [ citation needed ]
This United States corporation or company article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Sherlock_Biosciences |
The Sherman function describes the dependence of electron-atom scattering events on the spin of the scattered electrons . [ 1 ] It was first evaluated theoretically by the physicist Noah Sherman and it allows the measurement of polarization of an electron beam by Mott scattering experiments. [ 2 ] A correct evaluation of the Sherman function associated to a particular experimental setup is of vital importance in experiments of spin polarized photoemission spectroscopy , which is an experimental technique which allows to obtain information about the magnetic behaviour of a sample. [ 3 ]
When an electron beam is polarized, an unbalance between spin-up, n u p {\displaystyle n_{up}} , and spin-down electrons , n d o w n {\displaystyle n_{down}} , exists. The unbalance can be evaluated through the polarization P {\displaystyle P} [ 4 ] defined as
It is known that, when an electron collides against a nucleus, the scattering event is governed by Coulomb interaction . This is the leading term in the Hamiltonian , but a correction due to spin-orbit coupling can be taken into account and the effect on the Hamiltonian can be evaluated with the perturbation theory . Spin orbit interaction can be evaluated, in the rest reference frame of the electron, as the result of the interaction of the spin magnetic moment of the electron
with the magnetic field that the electron sees, due to its orbital motion around the nucleus, whose expression in the non-relativistic limit is:
In these expressions S {\displaystyle \mathbf {S} } is the spin angular-momentum, μ B {\displaystyle \mu _{\text{B}}} is the Bohr magneton , g s {\displaystyle g_{\text{s}}} is the g-factor , ℏ {\displaystyle \hbar } is the reduced Planck constant , m e {\displaystyle m_{\text{e}}} is the electron mass , e {\displaystyle e} is the elementary charge , c {\displaystyle c} is the speed of light , U = e V {\displaystyle U=eV} is the potential energy of the electron and L = r × p {\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} } is the angular momentum .
Due to spin orbit coupling, a new term will appear in the Hamiltonian, whose expression is [ 5 ] [ page needed ]
Due to this effect, electrons will be scattered with different probabilities at different angles. Since the spin-orbit coupling is enhanced when the involved nuclei possess a high atomic number Z , the target is usually made of heavy metals , such as mercury, [ 1 ] gold [ 6 ] and thorium . [ 7 ]
If we place two detectors at the same angle from the target, one on the right and one on the left, they will generally measure a different number of electrons n R {\displaystyle n_{R}} and n L {\displaystyle n_{L}} . Consequently it is possible to define the asymmetry A {\displaystyle A} , as [ 2 ]
The Sherman function S ( θ ) {\displaystyle S(\theta )} is a measure of the probability of a spin-up electron to be scattered, at a specific angle θ {\displaystyle \theta } , to the right or to the left of the target, due to spin-orbit coupling. [ 8 ] [ 9 ] It can assume values ranging from -1 (spin-up electron is scattered with 100% probability to the left of the target) to +1 (spin-up electron is scattered with 100% probability to the right of the target). The value of the Sherman function depends on the energy of the incoming electron, evaluated via the parameter β = v c {\displaystyle \beta ={\frac {v}{c}}} . [ 1 ] When S ( θ ) = 0 {\displaystyle S(\theta )=0} , spin-up electrons will be scattered with the same probability to the right and to the left of the target. [ 1 ]
Then it is possible to write
Plugging these formulas inside the definition of asymmetry, it is possible to obtain a simple expression for the evaluation of the asymmetry at a specific angle θ {\displaystyle \theta } , [ 10 ] i.e. :
Theoretical calculations are available for different atomic targets [ 1 ] [ 11 ] and for a specific target, as a function of the angle. [ 8 ]
To measure the polarization of an electron beam, a Mott detector is required. [ 12 ] In order to maximize the spin-orbit coupling, it is necessary that the electrons arrive near to the nuclei of the target. To achieve this condition, a system of electron optics is usually present, in order to accelerate the beam up to keV [ 13 ] or to MeV [ 14 ] energies. Since standard electron detectors count electrons being insensitive to their spin, [ 15 ] after the scattering with the target any information about the original polarization of the beam is lost. Nevertheless, by measuring the difference in the counts of the two detectors, the asymmetry can be evaluated and, if the Sherman function is known from previous calibration, the polarization can be calculated by inverting the last formula. [ 10 ]
In order to characterize completely the in-plane polarization, setups are available, with four channeltrons , two devoted to the left-right measure and two devoted to the up-right measure. [ 7 ]
In the panel it is shown an example of the working principle of a Mott detector, supposing a value for S ( θ ) = 0.5 {\displaystyle S(\theta )=0.5} . If an electron beam with a 3:1 ratio of spin-up over spin-down electrons collide with the target, it will be splitted with a ratio 5:3, according to previous equation, with an asymmetry of 25%. | https://en.wikipedia.org/wiki/Sherman_function |
The Sherman trap is a box-style animal trap designed for the live capture of small mammals . It was invented by Dr. H. B. Sherman in the 1920s and became commercially available in 1955. Since that time, the Sherman trap has been used extensively by researchers in the biological sciences for capturing animals such as mice , voles , shrews , and chipmunks . The Sherman trap consists of eight hinged pieces of sheet metal (either galvanized steel or aluminium ) that allow the trap to be collapsed for storage or transport. Sherman traps are often set in grids and may be baited with grains and seed.
The hinged design allows the trap to fold up flat into something only the width of one side panel. This makes it compact for storage and easy to transport to field locations (e.g. in a back pack). Both ends are hinged, but in normal operation the rear end is closed and the front folds inwards and latches the treadle, trigger plate, in place. When an animal enters far enough to be clear of the front door, their weight releases the latch and the door closes behind them.
The lure or bait is placed at the far end and can be dropped in place through the rear hinged door.
Later, other variants that built upon the basic design, appeared - such as the Elliott trap used in Europe and Australasia. The Elliott trap has simplified the design slightly and is made from just 7 hinged panels. | https://en.wikipedia.org/wiki/Sherman_trap |
In linear algebra , the Sherman–Morrison formula , named after Jack Sherman and Winifred J. Morrison, computes the inverse of a " rank -1 update" to a matrix whose inverse has previously been computed. [ 1 ] [ 2 ] [ 3 ] That is, given an invertible matrix A {\displaystyle A} and the outer product u v T {\displaystyle uv^{\textsf {T}}} of vectors u {\displaystyle u} and v , {\displaystyle v,} the formula cheaply computes an updated matrix inverse ( A + u v T ) ) − 1 . {\textstyle \left(A+uv^{\textsf {T}}\right){\vphantom {)}}^{\!-1}.}
The Sherman–Morrison formula is a special case of the Woodbury formula . Though named after Sherman and Morrison, it appeared already in earlier publications. [ 4 ]
Suppose A ∈ R n × n {\displaystyle A\in \mathbb {R} ^{n\times n}} is an invertible square matrix and u , v ∈ R n {\displaystyle u,v\in \mathbb {R} ^{n}} are column vectors . Then A + u v T {\displaystyle A+uv^{\textsf {T}}} is invertible if and only if 1 + v T A − 1 u ≠ 0 {\displaystyle 1+v^{\textsf {T}}A^{-1}u\neq 0} . In this case,
Here, u v T {\displaystyle uv^{\textsf {T}}} is the outer product of two vectors u {\displaystyle u} and v {\displaystyle v} . The general form shown here is the one published by Bartlett. [ 5 ]
( ⇐ {\displaystyle \Leftarrow } ) To prove that the backward direction 1 + v T A − 1 u ≠ 0 ⇒ A + u v T {\displaystyle 1+v^{\textsf {T}}A^{-1}u\neq 0\Rightarrow A+uv^{\textsf {T}}} is invertible with inverse given as above) is true, we verify the properties of the inverse. A matrix Y {\displaystyle Y} (in this case the right-hand side of the Sherman–Morrison formula) is the inverse of a matrix X {\displaystyle X} (in this case A + u v T {\displaystyle A+uv^{\textsf {T}}} ) if and only if X Y = Y X = I {\displaystyle XY=YX=I} .
We first verify that the right hand side ( Y {\displaystyle Y} ) satisfies X Y = I {\displaystyle XY=I} .
To end the proof of this direction, we need to show that Y X = I {\displaystyle YX=I} in a similar way as above:
(In fact, the last step can be avoided since for square matrices X {\displaystyle X} and Y {\displaystyle Y} , X Y = I {\displaystyle XY=I} is equivalent to Y X = I {\displaystyle YX=I} .)
( ⇒ {\displaystyle \Rightarrow } ) Reciprocally, if 1 + v T A − 1 u = 0 {\displaystyle 1+v^{\textsf {T}}A^{-1}u=0} , then via the matrix determinant lemma , det ( A + u v T ) = ( 1 + v T A − 1 u ) det ( A ) = 0 {\displaystyle \det \!\left(A+uv^{\textsf {T}}\right)=(1+v^{\textsf {T}}A^{-1}u)\det(A)=0} , so ( A + u v T ) {\displaystyle \left(A+uv^{\textsf {T}}\right)} is not invertible.
If the inverse of A {\displaystyle A} is already known, the formula provides a numerically cheap way to compute the inverse of A {\displaystyle A} corrected by the matrix u v T {\displaystyle uv^{\textsf {T}}} (depending on the point of view, the correction may be seen as a perturbation or as a rank-1 update). The computation is relatively cheap because the inverse of A + u v T {\displaystyle A+uv^{\textsf {T}}} does not have to be computed from scratch (which in general is expensive), but can be computed by correcting (or perturbing) A − 1 {\displaystyle A^{-1}} .
Using unit columns (columns from the identity matrix ) for u {\displaystyle u} or v {\displaystyle v} , individual columns or rows of A {\displaystyle A} may be manipulated and a correspondingly updated inverse computed relatively cheaply in this way. [ 6 ] In the general case, where A − 1 {\displaystyle A^{-1}} is an n {\displaystyle n} -by- n {\displaystyle n} matrix and u {\displaystyle u} and v {\displaystyle v} are arbitrary vectors of dimension n {\displaystyle n} , the whole matrix is updated [ 5 ] and the computation takes 3 n 2 {\displaystyle 3n^{2}} scalar multiplications. [ 7 ] If u {\displaystyle u} is a unit column, the computation takes only 2 n 2 {\displaystyle 2n^{2}} scalar multiplications. The same goes if v {\displaystyle v} is a unit column. If both u {\displaystyle u} and v {\displaystyle v} are unit columns, the computation takes only n 2 {\displaystyle n^{2}} scalar multiplications.
This formula also has application in theoretical physics . Namely, in quantum field theory , one uses this formula to calculate the propagator of a spin-1 field. [ 8 ] [ circular reference ] The inverse propagator (as it appears in the Lagrangian) has the form A + u v T {\displaystyle A+uv^{\textsf {T}}} . One uses the Sherman–Morrison formula to calculate the inverse (satisfying certain time-ordering boundary conditions) of the inverse propagator—or simply the (Feynman) propagator—which is needed to perform any perturbative calculation [ 9 ] involving the spin-1 field.
One of the issues with the formula is that little is known about its numerical stability. There are no published results concerning its error bounds. Anecdotal evidence [ 10 ] suggests that the Woodbury matrix identity (a generalization of the Sherman–Morrison formula) may diverge even for seemingly benign examples (when both the original and modified matrices are well-conditioned ).
Following is an alternate verification of the Sherman–Morrison formula using the easily verifiable identity
Let
then
Substituting w = A − 1 u {\displaystyle w=A^{-1}u} gives
Given a square invertible n × n {\displaystyle n\times n} matrix A {\displaystyle A} , an n × k {\displaystyle n\times k} matrix U {\displaystyle U} , and a k × n {\displaystyle k\times n} matrix V {\displaystyle V} , let B {\displaystyle B} be an n × n {\displaystyle n\times n} matrix such that B = A + U V {\displaystyle B=A+UV} . Then, assuming ( I k + V A − 1 U ) {\displaystyle \left(I_{k}+VA^{-1}U\right)} is invertible, we have | https://en.wikipedia.org/wiki/Sherman–Morrison_formula |
The Sheth–Tormen approximation is a halo mass function .
The Sheth–Tormen approximation extends the Press–Schechter formalism by assuming that halos are not necessarily spherical, but merely elliptical. The distribution of the density fluctuation is as follows: f ( σ r ) = A 2 a π [ 1 + ( σ r 2 a δ c 2 ) 0.3 ] δ c σ r exp ( − a δ c 2 2 σ r 2 ) {\displaystyle f(\sigma _{r})=A{\sqrt {\frac {2a}{\pi }}}[1+({\frac {\sigma _{r}^{2}}{a\delta _{c}^{2}}})^{0.3}]{\frac {\delta _{c}}{\sigma _{r}}}\exp(-{\frac {a\delta _{c}^{2}}{2\sigma _{r}^{2}}})} , where δ c = 1.686 {\displaystyle \delta _{c}=1.686} , a = 0.707 {\displaystyle a=0.707} , and A = 0.3222 {\displaystyle A=0.3222} . [ 1 ] The parameters were empirically obtained from the five-year release of WMAP . [ 2 ]
In 2010, the Bolshoi cosmological simulation predicted that the Sheth–Tormen approximation is inaccurate for the most distant objects. Specifically, the Sheth–Tormen approximation overpredicts the abundance of haloes by a factor of 10 {\displaystyle 10} for objects with a redshift z > 10 {\displaystyle z>10} , but is accurate at low redshifts. [ 3 ] [ 2 ] | https://en.wikipedia.org/wiki/Sheth–Tormen_approximation |
The Shi epoxidation is a chemical reaction described as the asymmetric epoxidation of alkenes with oxone (potassium peroxymonosulfate) and a fructose -derived catalyst ( 1 ). This reaction is thought to proceed via a dioxirane intermediate, generated from the catalyst ketone by oxone (potassium peroxymonosulfate). The addition of the sulfate group by the oxone facilitates the formation of the dioxirane by acting as a good leaving group during ring closure. It is notable for its use of a non-metal catalyst and represents an early example of organocatalysis . [3] [4]
The reaction was first reported by Yian Shi (史一安, pinyin : Shǐ Yī-ān) is derived from D-fructose and has a stereogenic center close to the reacting center (ketone)- the rigid six-membered ring structure of the catalyst and adjacent quaternary ring group minimizes epimerization of this stereocenter. Oxidation by the active dioxirane catalyst takes place from the si-face , due to steric hindrance of the opposing re-face. This catalyst functions efficiently as an asymmetric catalyst for unfunctionalized trans-olefins. [5]
Under normal pH conditions, an excess of 3 stoichiometric amounts of ketone catalyst are needed due to a high rate of decomposition. At basic pH conditions greater than 10 (pH 10.5) substoichiometric amounts (0.2–0.3) are needed for epoxidations, lowering the decomposition of reagents by disfavoring the Baeyer-Villiger side reaction. Higher temperatures result in further decomposition; thus a low temperature of zero degrees Celsius is used.
Decomposition of reagents is bimolecular ( second-order reaction rate), so low amounts of oxone and catalyst are used.
The reaction is mediated by a D-fructose derived catalyst, which produces the (R,R) enantiomer of the resulting epoxide. Solubilities of olefin organic substrate and oxidant (oxone) differ, and thus a biphasic medium is needed. The generation of the active catalyst species takes place in the aqueous layer, and is shuttled to the organic layer with the reactants by tetrabutylammonium sulfate. The ketone catalyst is continuously regenerated in a catalytic cycle, and thus can catalyze the epoxidation in small amounts.
The first step in the catalytic cycle reaction is the nucleophilic addition reaction of the oxone with the ketone group on the catalyst (intermediate 1). This forms the reactive intermediate number 2 species, the Criegee intermediate that can potentially lead to unwanted side reactions, such as the Baeyer-Villiger reaction (see below). The generation of intermediate species number 3 occurs under basic conditions, with a removal of the hydrogen from the hydroxy group to form a nucleophilic oxygen anion. The sulfate group facilitates the subsequent formation of the dioxirane, intermediate species number 4, by acting as a good leaving group during the 3-exo-tet cyclization. The activated dioxirane catalytic species then transfers an oxygen atom to the alkene, leading to a regeneration of the original catalyst. [6]
A potential side reaction that may occur is the Baeyer-Villiger reaction of intermediate 2, where there is a rearrangement of the peroxy group that results in the formation of the relative ester. The extent of this side reaction declines with the rise of pH, and increases the nucleophilicity of the oxone, making basic conditions favorable for the overall epoxidation and reactivity of the catalytic species.
The oxygen from the dioxirane group generated on the organic catalyst is transferred to the alkene, in what is thought to be a concerted mechanism, although the presence of an oxygen anion intermediate through an S n 2 mechanism may transpire.
The catalyst is formed by reaction with acetone under basic conditions, with the hydroxyl groups of the fructose ring acting as nucleophiles, their nucleophilicity increased by the basic conditions created by potassium carbonate . The electron withdrawing substituents (alpha-ether groups) encourage the formation of the ketone from the oxidizing agent pyridinium chlorochromate by increasing the electrophilicity of the carbonyl carbon, via a stabilizing delocalization of the forming π C-C bonds into the σ* C-O bonds of the adjacent ethers. [7]
Enantioselective dioxirane oxidations may rely on chiral, non-racemic dioxiranes, such as Shi's fructose-based dioxirane. Enantioselective oxidation of meso -diols with Shi's catalyst, for instance, produces chiral α-hydroxy ketones with moderate enantioselectivity. [ 1 ]
(4)
There are two proposed transition states , whose geometries are speculated and not corroborated by experimental evidence, but are attributed to stereoelectronic effects . The spiro transition state is favored over the planar due to the non-bonding orbitals of the superior oxygen donating into the π* anti-bonding C-C orbitals of the reacting alkene, providing a stabilizing delocalization of electrons.
Donation of these electrons into the forming C-O σ bonds of the epoxide bonds also encourages the formation of the
spiro-product (the geometry of the product is aligned as well). The planar configuration is disfavored due to lack of pi-backbonding and steric hindrance of the alkyl groups with large alkyl functional groups of the catalytic ring. [8]
The previously mentioned configurations are favored over the transition states of the opposing enantiomers because of unfavorable steric interactions between the R-alkyl groups (see below) and the ether-alkyl functional groups of the catalyst ring.
The enantiomeric success of this epoxidation is relatively high compared to metal catalysts, and generally results in a high enantiomeric excess exceeding 80 percent. [9]
This procedure generates epoxides with high enantiomeric excesses from trans-disubstituted alkenes and trisubstituted alkenes. Cis-disubstituted alkenes [10] and styrenes [11] are asymmetrically epoxidized using a similar catalyst. Generation of (R,R) epoxides from corresponding alkenes increases in stereoselectivity with increased steric bulk of substituent R groups (especially in trans-olefins). | https://en.wikipedia.org/wiki/Shi_epoxidation |
Shield lichen is the common name for lichens in either the genus Heterodermia or genus Parmelia . [ 1 ]
This article about lichens or lichenology is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Shield_lichen |
A shielded data link (SDL) connector is a type of electrical connector in which the signal pins are surrounded by a metal shield . The connector was designed by AMP (now TE Connectivity) and is available with a range of pins (4 to 16). It also features a locking mechanism and is available in differently keyed plugs that correspond to the proper socket.
It has been used by several different products, most notably on the original IBM Model M keyboard with a detachable cable, on the IBM SurePos line of devices, and on HP HIL devices (such as keyboards and mice). The connector was also used by AMF for their line of Accuscore automatic scoring systems for bowling. Some of the SDL connectors are still manufactured but are no longer common on consumer electronic devices.
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Shielded_data_link_connector |
In chemistry , the shielding effect sometimes referred to as atomic shielding or electron shielding describes the attraction between an electron and the nucleus in any atom with more than one electron . The shielding effect can be defined as a reduction in the effective nuclear charge on the electron cloud, due
to a difference in the attraction forces on the electrons in the atom. It is a special case of electric-field screening .
This effect also has some significance in many projects in material sciences.
The wider the electron shells are in space, the weaker is the electric interaction between the electrons and the nucleus due to screening. Further, because of differences in orbital penetration, we can order the screening strength, S , that electrons in a given orbital (s, p, d, or f) provide to the rest of the electrons thus: S ( s ) > S ( p ) > S ( d ) > S ( f ) . {\displaystyle S(\mathrm {s} )>S(\mathrm {p} )>S(\mathrm {d} )>S(\mathrm {f} ).}
In hydrogen , or any other atom in group 1A of the periodic table (those with only one valence electron ), the force on the electron is just as large as the electromagnetic attraction from the nucleus of the atom. However, when more electrons are involved, each electron (in the n th - shell ) experiences not only the electromagnetic attraction from the positive nucleus, but also repulsion forces from other electrons in shells from 1 to n . This causes the net force on electrons in outer shells to be significantly smaller in magnitude; therefore, these electrons are not as strongly bonded to the nucleus as electrons closer to the nucleus. This phenomenon is often referred to as the orbital penetration effect. The shielding theory also contributes to the explanation of why valence-shell electrons are more easily removed from the atom.
Additionally, there is also a shielding effect that occurs between sublevels within the same principal energy level. An electron in the s-sublevel is capable of shielding electrons in the p-sublevel of the same principal energy level.
The size of the shielding effect is difficult to calculate precisely due to effects from quantum mechanics . As an approximation, we can estimate the effective nuclear charge on each electron by the following:
Where Z is the number of protons in the nucleus and σ {\displaystyle \sigma \,} is the average number of electrons between the nucleus and the electron in question. σ {\displaystyle \sigma \,} can be found by using quantum chemistry and the Schrödinger equation , or by using Slater's empirical formulas .
In Rutherford backscattering spectroscopy , the correction due to electron screening modifies the Coulomb repulsion between the incident ion and the target nucleus at large distances. It is the repulsion effect caused by the inner electron on the outer electron. | https://en.wikipedia.org/wiki/Shielding_effect |
Shielding gases are inert or semi- inert gases that are commonly used in several welding processes, most notably gas metal arc welding and gas tungsten arc welding (GMAW and GTAW, more popularly known as MIG (Metal Inert Gas) and TIG (Tungsten Inert Gas), respectively). Their purpose is to protect the weld area from oxygen and water vapour . Depending on the materials being welded, these atmospheric gases can reduce the quality of the weld or make the welding more difficult. Other arc welding processes use alternative methods of protecting the weld from the atmosphere as well – shielded metal arc welding , for example, uses an electrode covered in a flux that produces carbon dioxide when consumed, a semi-inert gas that is an acceptable shielding gas for welding steel.
Improper choice of a welding gas can lead to a porous and weak weld, or to excessive spatter; the latter, while not affecting the weld itself, causes loss of productivity due to the labor needed to remove the scattered drops.
If used carelessly, shielding gasses can displace oxygen, causing hypoxia and potentially death. [ 1 ] [ 2 ]
Shielding gases fall into two categories—inert or semi-inert. Only two of the noble gases , helium and argon , are cost effective enough to be used in welding. These inert gases are used in gas tungsten arc welding , and also in gas metal arc welding for the welding of non-ferrous metals . Semi-inert shielding gases, or active shield gases, include carbon dioxide , oxygen , nitrogen , and hydrogen . These active gases are used with GMAW on ferrous metals . Most of these gases, in large quantities, would damage the weld, but when used in small, controlled quantities, can improve weld characteristics.
The important properties of shielding gases are their thermal conductivity and heat transfer properties, their density relative to air, and the ease with which they undergo ionization. Gases heavier than air (e.g. argon) blanket the weld and require lower flow rates than gases lighter than air (e.g. helium). Heat transfer is important for heating the weld around the arc. Ionizability influences how easy the arc starts, and how high voltage is required. Shielding gases can be used pure, or as a blend of two or three gases. [ 3 ] [ 4 ] In laser welding, the shielding gas has an additional role, preventing formation of a cloud of plasma above the weld, absorbing significant fraction of the laser energy. This is important for CO 2 lasers; Nd:YAG lasers show lower tendency to form such plasma. Helium plays this role best due to its high ionization potential; the gas can absorb high amount of energy before becoming ionized.
Argon is the most common shielding gas, widely used as the base for the more specialized gas mixes. [ 5 ]
Carbon dioxide is the least expensive shielding gas, providing deep penetration, however it negatively affects the stability of the arc and enhances the molten metal's tendency to create droplets (spatter). [ 6 ] Carbon dioxide in concentration of 1-2% is commonly used in the mix with argon to reduce the surface tension of the molten metal. Another common blend is 25% carbon dioxide and 75% argon for GMAW. [ 7 ]
Helium is lighter than air; larger flow rates are required. It is an inert gas, not reacting with the molten metals. Its thermal conductivity is high. It is not easy to ionize, requiring higher voltage to start the arc. Due to higher ionization potential it produces hotter arc at higher voltage, provides wide deep bead; this is an advantage for aluminium, magnesium, and copper alloys. Other gases are often added. Blends of helium with addition of 5–10% of argon and 2–5% of carbon dioxide ("tri-mix") can be used for welding of stainless steel. Used also for aluminium and other non-ferrous metals, especially for thicker welds. In comparison with argon, helium provides more energy-rich but less stable arc. Helium and carbon dioxide were the first shielding gases used, since the beginning of World War 2. Helium is used as a shield gas in laser welding for carbon dioxide lasers . [ 8 ] Helium is more expensive than argon and requires higher flow rates, so despite its advantages it may not be a cost-effective choice for higher-volume production. [ 9 ] Pure helium is not used for steel, as it causes an erratic arc and encourages spatter.
Oxygen is used in small amounts as an addition to other gases; typically as 2–5% addition to argon. It enhances arc stability and reduces the surface tension of the molten metal, increasing wetting of the solid metal. It is used for spray transfer welding of mild carbon steels , low alloy and stainless steels . Its presence increases the amount of slag. Argon-oxygen ( Ar-O 2 ) blends are often being replaced with argon-carbon dioxide ones. Argon-carbon dioxide-oxygen blends are also used. Oxygen causes oxidation of the weld, so it is not suitable for welding aluminium, magnesium, copper, and some exotic metals. Increased oxygen makes the shielding gas oxidize the electrode, which can lead to porosity in the deposit if the electrode does not contain sufficient deoxidizers . Excessive oxygen, especially when used in application for which it is not prescribed, can lead to brittleness in the heat affected zone. Argon-oxygen blends with 1–2% oxygen are used for austenitic stainless steel where argon-CO 2 can not be used due to required low content of carbon in the weld; the weld has a tough oxide coating and may require cleaning.
Hydrogen is used for welding of nickel and some stainless steels, especially thicker pieces. It improves the molten metal fluidity, and enhances cleanness of the surface. It is added to argon in amounts typically under 10%. It can be added to argon-carbon dioxide blends to counteract the oxidizing effects of carbon dioxide. Its addition narrows the arc and increases the arc temperature, leading to better weld penetration. In higher concentrations (up to 25% hydrogen), it may be used for welding conductive materials such as copper. However, it should not be used on steel, aluminum or magnesium because it can cause porosity and hydrogen embrittlement ; its application is usually limited only to some stainless steels.
Nitric oxide addition serves to reduce production of ozone . It can also stabilize the arc when welding aluminium and high-alloyed stainless steel.
Other gases can be used for special applications, pure or as blend additives; e.g. sulfur hexafluoride or dichlorodifluoromethane . [ 10 ]
Sulfur hexafluoride can be added to shield gas for aluminium welding to bind hydrogen in the weld area to reduce weld porosity. [ 11 ]
Dichlorodifluoromethane with argon can be used for protective atmosphere for melting of aluminium-lithium alloys. [ 12 ] It reduces the content of hydrogen in the aluminium weld, preventing the associated porosity. This gas, however, is being used less because it has a strong ozone depletion potential .
The applications of shielding gases are limited primarily by the cost of the gas, the cost of the equipment, and by the location of the welding. Some shielding gases, like argon, are expensive, limiting its use. The equipment used for the delivery of the gas is also an added cost, and as a result, processes like shielded metal arc welding, which require less expensive equipment, might be preferred in certain situations. Finally, because atmospheric movements can cause the dispersion of the shielding gas around the weld, welding processes that require shielding gases are often only done indoors, where the environment is stable and atmospheric gases can be effectively prevented from entering the weld area.
The desirable rate of gas flow depends primarily on weld geometry, speed, current, the type of gas, and the metal transfer mode being utilized. Welding flat surfaces requires higher flow than welding grooved materials, since the gas is dispersed more quickly. Faster welding speeds, in general, mean that more gas needs to be supplied to provide adequate coverage. Additionally, higher current requires greater flow, and generally, more helium is required to provide adequate coverage than argon. Perhaps most importantly, the four primary variations of GMAW have differing shielding gas flow requirements—for the small weld pools of the short circuiting and pulsed spray modes, about 10 L /min (20 ft 3 / h ) is generally suitable, while for globular transfer, around 15 L/min (30 ft 3 /h) is preferred. The spray transfer variation normally requires more because of its higher heat input and thus larger weld pool; along the lines of 20–25 L/min (40–50 ft 3 /h). [ 16 ] | https://en.wikipedia.org/wiki/Shielding_gas |
The Shields formula is a formula for the stability calculation of granular material ( sand , gravel ) in running water.
The stability of granular material in flow can be determined by the Shields formula or the Izbash formula . The first is more suitable for fine grain material (such as sand and gravel ), while the Izbash formula is more suitable for larger stone. The Shields formula was developed by Albert F. Shields (1908-1974). In fact, the Shields method determines whether or not the soil material will move. The Shields parameter thus determines whether or not there is a beginning of movement. [ 1 ] [ 2 ]
Movement of (loose grained) soil material occurs when the shear pressure exerted by the water on the soil is greater than the resistance the soil provides. This dimensionless ratio (the Shields parameter ) was first described by Albert Shields and reads:
where:
The shear stress that works on the bottom (with a normal uniform flow along a slope) is:
where:
It is important to realise that τ {\displaystyle \tau } is the shear stress exerted by the flow (i.e. a property of the flow) and τ c {\displaystyle \tau _{c}} is the shear stress at which the grains move (i.e. a property of the grains).
The shear stress velocity is often used instead of the shear stress:
The shear stress velocity has the dimension of a velocity (m/s), but is actually a representation of the shear stress. So the shear stress velocity can never be measured with a velocity meter.
By using the shear stress velocity, the Shields parameter can also be written as:
where:
Shields found that the parameter Ψ c ∗ {\displaystyle \Psi _{c*}} is a function of u ∗ c d ν {\displaystyle {\frac {u_{*c}d}{\nu }}} , in which ν {\displaystyle \nu } is the kinematic viscosity . This parameter is also called the granular reynolds number :
Shields has performed tests with grains of different densities, and the found value of Ψ c ∗ {\displaystyle \Psi _{c*}} plotted as a function of R e ∗ {\displaystyle Re_{*}} . This led to the above graph. [ 1 ]
Van Rijn found that instead of the granular reynolds number a dimensionless grain size could be used: [ 3 ]
Because usually the values of Δ , g , ν {\displaystyle \Delta ,g,\nu } are quite constant, the true grain size can also be set on the horizontal axis (see right figure b). This means that the value of Ψ c ∗ {\displaystyle \Psi _{c*}} is only a function of the grain diameter and can be read directly.
.
From this follows that for grains greater than 5 mm the Shields parameter gets a constant value of 0,055.
The gradient of a river ( I ) can be determined by Chézy formula :
in which C {\displaystyle C} = the coefficiënt of Chézy ( m 1/2 / s ); This is often in the order 50 ( m 1/2 / s ). For a flat bed (i.e. without ripples) C can be approximated with:
By introducing this into the stability formula, a critical grain size formula is found at a given flow rate:
In this form, the stability relationship is usually called the "Shields formula".
The line of Shields (and of Van Rijn) in the graph is the separation between "movement" and "no movement". Shields has defined as "movement" that almost all grains move on the bottom. This is a useful definition for defining the beginning of sand transport by flow. However, if one wants to protect a bed from erosion, the requirement is that grains should hardly move. To make this operational, Breusers defined 7 phases of movement in 1969: [ 5 ]
These phases are shown in the figure below:
In practice, this means that for bed protections (where the grain is always larger than 5mm), a design value of Ψ=0.03 must be used.
Question: At what speed of flow does sand of 0.2cm move at a water depth of 1m?
Question: What stone size is needed to defend this soil against a current of 2 m/s?
The Shields approach is based on a uniform, permanent flow with a turbulence generated by the bed roughness (i.e. no additional turbulence by a for example a propeller current). In the case of a rough bed in shallow water, and in case of unusual turbulence, the Izbash's formula is therefore more recommended. [ 6 ] | https://en.wikipedia.org/wiki/Shields_formula |
The Shields parameter , also called the Shields criterion or Shields number , is a nondimensional number used to calculate the initiation of motion of sediment in a fluid flow . It is a dimensionalization of a shear stress , and is typically denoted ψ {\displaystyle \psi } or θ {\displaystyle \theta } . This parameter has been developed by Albert F. Shields , and is called later Shields parameter. The Shields parameter is the main parameter of the Shields formula . The Shields parameter is given by:
where:
The critical shear stress and also the critical Shields number ( τ ∗ {\displaystyle \tau _{\ast }} and θ ∗ {\displaystyle \theta _{\ast }} ) describe the conditions when the sediment starts moving. Note that the shear stress is a property of the current, while the critical shear stress is a property of the sediment.
By multiplying the top and bottom of the Shields parameter by D 2 , you can see that it is proportional to the ratio of fluid force on the particle to the weight of the particle.
This sedimentology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Shields_parameter |
A shift register lookup table , also shift register LUT or SRL , refers to a component in digital circuitry . It is essentially a shift register of variable length. The length of SRL is set by driving address pins high or low and can be changed dynamically, if necessary. [ 1 ]
The SRL component is used in FPGA devices.
The SRL can be used as a programmable delay element.
[ 2 ]
This electronics-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Shift_register_lookup_table |
In mathematics , the (exponential) shift theorem is a theorem about polynomial differential operators ( D -operators) and exponential functions . It permits one to eliminate, in certain cases, the exponential from under the D -operators.
The theorem states that, if P ( D ) is a polynomial of the D -operator, then, for any sufficiently differentiable function y ,
To prove the result, proceed by induction . Note that only the special case
needs to be proved, since the general result then follows by linearity of D -operators.
The result is clearly true for n = 1 since
Now suppose the result true for n = k , that is,
Then,
This completes the proof.
The shift theorem can be applied equally well to inverse operators:
There is a similar version of the shift theorem for Laplace transforms ( t < a {\displaystyle t<a} ):
The exponential shift theorem can be used to speed the calculation of higher derivatives of functions that is given by the product of an exponential and another function. For instance, if f ( x ) = sin ( x ) e x {\displaystyle f(x)=\sin(x)e^{x}} , one has that
D 3 f = D 3 ( e x sin ( x ) ) = e x ( D + 1 ) 3 sin ( x ) = e x ( D 3 + 3 D 2 + 3 D + 1 ) sin ( x ) = e x ( − cos ( x ) − 3 sin ( x ) + 3 cos ( x ) + sin ( x ) ) {\displaystyle {\begin{aligned}D^{3}f&=D^{3}(e^{x}\sin(x))=e^{x}(D+1)^{3}\sin(x)\\&=e^{x}\left(D^{3}+3D^{2}+3D+1\right)\sin(x)\\&=e^{x}\left(-\cos(x)-3\sin(x)+3\cos(x)+\sin(x)\right)\end{aligned}}}
Another application of the exponential shift theorem is to solve linear differential equations whose characteristic polynomial has repeated roots. [ 1 ] | https://en.wikipedia.org/wiki/Shift_theorem |
The net electrostatic force acting on a charged particle with index i {\displaystyle i} contained within a collection of particles is given as:
F ( r ) = ∑ j ≠ i F ( r ) r ^ ; F ( r ) = q i q j 4 π ε 0 r 2 {\displaystyle \mathbf {F} (\mathbf {r} )=\sum _{j\neq i}F(r)\mathbf {\hat {r}} \,\,\,;\,\,F(r)={\frac {q_{i}q_{j}}{4\pi \varepsilon _{0}r^{2}}}}
where r {\displaystyle \mathbf {r} } is the spatial coordinate, j {\displaystyle j} is a particle index, r {\displaystyle r} is the separation distance between particles i {\displaystyle i} and j {\displaystyle j} , r ^ {\displaystyle \mathbf {\hat {r}} } is the unit vector from particle j {\displaystyle j} to particle i {\displaystyle i} , F ( r ) {\displaystyle F(r)} is the force magnitude, and q i {\displaystyle q_{i}} and q j {\displaystyle q_{j}} are the charges of particles i {\displaystyle i} and j {\displaystyle j} , respectively. With the electrostatic force being proportional to r − 2 {\displaystyle r^{-2}} , individual particle-particle interactions are long-range in nature, presenting a challenging computational problem in the simulation of particulate systems. To determine the net forces acting on particles, the Ewald or Lekner summation methods are generally employed. One alternative and usually computationally faster technique based on the notion that interactions over large distances ( e.g. > 1 nm) are insignificant to the net forces acting in certain systems is the method of spherical truncation. [ 1 ] The equations for basic truncation are:
F C U T ( r ) = { q i q j 4 π ε 0 r 2 for r ≤ r c 0 for r > r c . {\displaystyle \displaystyle F_{CUT}(r)={\begin{cases}{\frac {q_{i}q_{j}}{4\pi \varepsilon _{0}r^{2}}}&{\text{for }}r\leq r_{c}\\0&{\text{for }}r>r_{c}.\end{cases}}}
where r c {\displaystyle r_{c}} is the cutoff distance. Simply applying this cutoff method introduces a discontinuity in the force at r c {\displaystyle r_{c}} that results in particles experiencing sudden impulses when other particles cross the boundary of their respective interaction spheres. In the particular case of electrostatic forces, as the force magnitude is large at the boundary, this unphysical feature can compromise simulation accuracy. A way to correct this problem is to shift the force to zero at r c {\displaystyle r_{c}} , thus removing the discontinuity. [ 2 ] This can be accomplished with a variety of functions, but the most simple/computationally efficient approach is to simply subtract the value of the electrostatic force magnitude at the cutoff distance as such:
F S F ( r ) = { q i q j 4 π ε 0 r 2 − q i q j 4 π ε 0 r c 2 for r ≤ r c 0 for r > r c . {\displaystyle \displaystyle F_{SF}(r)={\begin{cases}{\frac {q_{i}q_{j}}{4\pi \varepsilon _{0}r^{2}}}-{\frac {q_{i}q_{j}}{4\pi \varepsilon _{0}r_{c}^{2}}}&{\text{for }}r\leq r_{c}\\0&{\text{for }}r>r_{c}.\end{cases}}}
As mentioned before, the shifted force (SF) method is generally suited for systems that do not have net electrostatic interactions that are long-range in nature. This is the case for condensed systems that show electric-field screening effects. Note that anisotropic systems ( e.g. interfaces ) may not be accurately simulated with the SF method, [ 3 ] although an adaption of the SF method for interfaces has been recently suggested. [ 4 ] Additionally, note that certain system properties (e.g. energy -dependent observables ) will be more greatly influenced by the use of the SF method than others. It is not safe to assume, without reasonable argument, that the SF method can be used to accurately determine a certain property for a given system. If the accuracy of the SF method need be tested, this may be done by testing for convergence ( i.e. showing that simulation results do not significantly change with increasing cutoff) or by comparing with results obtained through other electrostatics techniques (such as Ewald) that are known to perform well. [ 5 ] As a rough rule of thumb, results obtained with the SF method tend to be sufficiently accurate when the cutoff is at least five times larger than the distance of the near neighbor interactions.
With the SF method, a discontinuity is still present in the derivative of the force, and it may be preferable for ionic liquids to further alter the force equation as to remove that discontinuity. [ 6 ] | https://en.wikipedia.org/wiki/Shifted_force_method |
The shifting balance theory is a theory of evolution proposed in 1932 by Sewall Wright , suggesting that adaptive evolution may proceed most quickly when a population divides into subpopulations with restricted gene flow . The name of the theory is borrowed from Wright's metaphor of fitness landscapes ( evolutionary landscapes ), attempting to explain how a population may move across an adaptive valley to a higher adaptive peak . According to the theory, this movement occurs in three steps:
Although shifting balance theory has been influential in evolutionary biology , inspiring the theories of quantum evolution and punctuated equilibrium , [ 1 ] little empirical evidence exists to support the shifting balance process as an important factor in evolution. [ 2 ] | https://en.wikipedia.org/wiki/Shifting_balance_theory |
Shiga toxins are a family of related toxins with two major groups, Stx1 and Stx2, expressed by genes considered to be part of the genome of lambdoid prophages . [ 1 ] The toxins are named after Kiyoshi Shiga , who first described the bacterial origin of dysentery caused by Shigella dysenteriae . [ 2 ] Shiga-like toxin ( SLT ) is a historical term for similar or identical toxins produced by Escherichia coli . [ 3 ] The most common sources for Shiga toxin are the bacteria S. dysenteriae and some serotypes of Escherichia coli (shigatoxigenic or STEC), which include serotypes O157:H7 , and O104:H4 . [ 4 ] [ 5 ]
Microbiologists use many terms to describe Shiga toxin and differentiate more than one unique form. Many of these terms are used interchangeably .
The toxin is named after Kiyoshi Shiga , who discovered S. dysenteriae in 1897. [ 2 ] In 1977, researchers in Ottawa, Ontario discovered the Shiga toxin normally produced by Shigella dysenteriae in a line of E. coli . [ 12 ] The E. coli version of the toxin was named "verotoxin" because of its ability to kill Vero cells ( African green monkey kidney cells) in culture. Shortly after, the verotoxin was referred to as Shiga-like toxin because of its similarities to Shiga toxin.
It has been suggested by some researchers that the gene coding for Shiga-like toxin comes from a toxin-converting lambdoid bacteriophage , such as H-19B or 933W, inserted into the bacteria's chromosome via transduction . [ 13 ] Phylogenetic studies of the diversity of E. coli suggest that it may have been relatively easy for Shiga toxin to transduce into certain strains of E. coli , because Shigella is itself a subgenus of Escherichia ; in fact, some strains traditionally considered E. coli (including those that produce this toxin) in fact belong to this lineage. Being closer relatives of Shigella dysenteriae than of the typical E. coli , it is not at all unusual that toxins similar to that of S. dysenteriae are produced by these strains. As microbiology advances, the historical variation in nomenclature (which arose because of gradually advancing science in multiple places) is increasingly giving way to recognizing all of these molecules as "versions of the same toxin" rather than "different toxins". [ 14 ] : 2–3
The toxin requires highly specific receptors on the cells' surface in order to attach and enter the cell ; species such as cattle , swine , and deer which do not carry these receptors may harbor toxigenic bacteria without any ill effect, shedding them in their feces , from where they may be spread to humans. [ 15 ]
Symptoms of Shiga toxin ingestion include abdominal pain as well as watery diarrhea. Severe life-threatening cases are characterized by hemorrhagic colitis (HC). [ 16 ]
The toxin is associated with hemolytic-uremic syndrome . In contrast, Shigella species may also produce shigella enterotoxins , which are the cause of dysentery .
The toxin is effective against small blood vessels, such as found in the digestive tract , the kidney , and lungs , but not against large vessels such as the arteries or major veins . A specific target for the toxin appears to be the vascular endothelium of the glomerulus . This is the filtering structure that is a key to the function of the kidney. Destroying these structures leads to kidney failure and the development of the often deadly and frequently debilitating hemolytic uremic syndrome. Food poisoning with Shiga toxin often also has effects on the lungs and the nervous system .
The B subunits of the toxin bind to a component of the cell membrane known as glycolipid globotriaosylceramide (Gb3). Binding of the subunit B to Gb3 causes induction of narrow tubular membrane invaginations, which drives formation of inward membrane tubules for toxin-receptor complex [ 17 ] uptake into the cell. These tubules are essential for uptake into the host cell. [ 18 ] The Shiga toxin (a non-pore forming toxin) is transferred to the cytosol via Golgi network and endoplasmic reticulum (ER). From the Golgi toxin is trafficked to the ER. It is then processed through cleavage by a furin -like protease to separate the A1 subunit. Some toxin-receptor complexes reportedly bypass these steps and are transported to the nucleus rather than the cytosol, with unknown effects. [ 17 ]
Shiga toxins act to inhibit protein synthesis within target cells by a mechanism similar to that of the infamous plant toxin ricin . [ 19 ] [ 20 ] After entering a cell via a macropinosome , [ 21 ] the payload (A subunit) cleaves a specific adenine nucleobase from the 28S RNA of the 60S subunit of the ribosome , thereby halting protein synthesis. [ 22 ] As they mainly act on the lining of the blood vessels , the vascular endothelium, a breakdown of the lining and hemorrhage eventually occurs. [ clarification needed ] The first response is commonly a bloody diarrhea. This is because Shiga toxin is usually taken in with contaminated food or water . [ citation needed ]
The bacterial Shiga toxin can be used for targeted therapy of gastric cancer, because this tumor entity expresses the receptor of the Shiga toxin. For this purpose an unspecific chemotherapeutical is conjugated to the B-subunit to make it specific. In this way only the tumor cells, but not healthy cells, are destroyed during therapy. [ 23 ]
The toxin has two subunits—designated A ( mol. wt. 32000 Da) and B (mol. wt. 7700 Da)—and is one of the AB 5 toxins . The B subunit is a pentamer that binds to specific glycolipids on the host cell, specifically globotriaosylceramide (Gb3). [ 24 ] [ 25 ] Following this, the A subunit is internalised and cleaved into two parts. The A1 component then binds to the ribosome, disrupting protein synthesis. Stx-2 has been found to be about 400 times more toxic (as quantified by LD 50 in mice) than Stx-1.
Gb3 is, for unknown reasons, present in greater amounts in renal epithelial tissues, to which the renal toxicity of Shiga toxin may be attributed. Gb3 is also found in central nervous system neurons and endothelium, which may lead to neurotoxicity . [ 26 ] Stx-2 is also known to increase the expression of its receptor GB3 and cause neuronal dysfunctions. [ 27 ] | https://en.wikipedia.org/wiki/Shiga_toxin |
Shiina esterification is an organic chemical reaction that synthesizes carboxylic esters from nearly equal amounts of carboxylic acids and alcohols by using aromatic carboxylic acid anhydrides as dehydration condensation agents. In 1994, Prof. Isamu Shiina ( Tokyo University of Science , Japan) reported an acidic coupling method using Lewis acid , [ 1 ] [ 2 ] and, in 2002, a basic esterification using nucleophilic catalyst. [ 3 ] [ 4 ]
The successive addition of carboxylic acids and alcohols into a system containing aromatic carboxylic acid anhydride and catalyst produces corresponding carboxylic esters through the process shown in the following figure. In acidic Shiina esterification, Lewis acid catalysts are used, while nucleophilic catalysts are used for Shiina esterification under basic conditions.
In the acidic reaction, 4-trifluoromethylbenzoic anhydride (TFBA) is mainly used as a dehydration condensation agent. First, the Lewis acid catalyst activates the TFBA, and then a carboxyl group in carboxylic acid reacts with the activated TFBA to produce mixed anhydride (MA) once. Then, a carbonyl group derived from the carboxylic acid in MA is selectively activated and is attacked by a hydroxyl group in the alcohol through intermolecular nucleophilic substitution. Simultaneously, residual aromatic carboxylic acid salt, which is derived from the MA, acts as a deprotonation agent, causing the esterification to progress and produce the desired carboxylic ester. To balance the reaction, each TFBA accepts the atoms of one water molecule from its starting materials, i.e., the carboxylic acid and alcohol, and then changes itself into two molecules of 4-trifluoromethylbenzoic acid at the end of the reaction. Since the Lewis acid catalyst is reproduced at the end of the reaction, only a small proportion of catalyst is needed relative to the starting material to drive the reaction forward.
In the basic reaction, 2-methyl-6-nitrobenzoic anhydride ( MNBA ) is primarily used as a dehydration condensation agent. [ 5 ] First, the nucleophilic catalyst acts on the MNBA to produce activated acyl carboxylate. The reaction of carboxyl group in the carboxylic acid with the activated acyl carboxylate produces the corresponding MA, in the same manner as in the acidic reaction. Then, the nucleophilic catalyst acts selectively on a carbonyl group derived from the carboxylic acid in MA to again produce activated acyl carboxylate. The hydroxyl group in the alcohol attacks its host molecule through intermolecular nucleophilic substitution, and at the same time, carboxylate anion, derived from 2-methyl-6-nitrobenzoic acid, acts as a deprotonation agent, promoting the progression of the esterification and producing the desired carboxylic ester. To balance the reaction, each MNBA accepts the atoms of one water molecule from its starting materials, changing itself into two molecules of the amine salt of 2-methyl-6-nitrobenzoic acid, and thus, terminating the reaction. Because the nucleophilic catalyst is reproduced at the end of the reaction, only small stoichiometric quantities are required.
All of the processes of Shiina esterification consist of reversible reactions, with the exception of the last nucleophilic substitution step with alcohol. Therefore, the aromatic carboxylic acid anhydride and the mixed anhydride (MA) coexist in the system. Furthermore, aliphatic carboxylic acid anhydride produced via disproportionation of the MA is simultaneously present in the system; thus, it is directly used as a mixture without being separated. Owing to activation by Lewis acid catalysts or nucleophilic catalysts, the mixture of these three components begins to react with alcohol; in addition to the targeted aliphatic carboxylic acid esters, aromatic carboxylic acid esters are likely to be formed as by-products.
However, by using 4-trifluoromethylbenzoic anhydride (TFBA) as the aromatic carboxylic acid anhydride under acidic conditions and 2-methyl-6-nitrobenzoic anhydride (MNBA) as the aromatic carboxylic acid anhydride under basic conditions, practically no aromatic carboxylic acid esters are obtained as by-products. (The chemoselectivity is 200:1 or higher.)
Aromatic carboxylic acid anhydrides are used as dehydration condensation agents not only for the intermolecular coupling of carboxylic acids with alcohols but also for the intramolecular cyclization of hydroxycarboxylic acids ( Shiina macrolactonization ). Both of these intermolecular and intramolecular reactions are used for the artificial synthesis of various natural products and pharmacologically active compounds, [ 6 ] [ 7 ] as the reaction of a carboxylic acid with an amine produces an amide or a peptide. [ 8 ]
In acidic reactions, Lewis acid catalysts, such as metal triflates, exhibit high activities, while in basic reactions, 4-dimethylaminopyridine ( DMAP ), 4-dimethylaminopyridine N-oxide (DMAPO), and 4-pyrrolidinopyridine (PPY) are employed.
In the Shiina esterification performed under basic conditions, asymmetric synthesis is realized using chiral nucleophilic catalysts. First, in the presence of a chiral nucleophilic catalyst, by the action of an appropriate carboxylic acid anhydride on a racemic aliphatic carboxylic acid, the corresponding MA is produced, resulting in the kinetic resolution of the racemic aliphatic carboxylic acid after having been subjected to reaction with achiral alcohol. [ 9 ] Using this method, optically active carboxylic acids and optically active carboxylic acid esters can be obtained. It is also possible to realize the kinetic resolution of racemic alcohols by modifying the compositions of the reactants, i.e., by forming MA through reactions between achiral carboxylic acid and the appropriate carboxylic acid anhydride; then, by activating the racemic alcohols using the MA, optically active alcohols and optically active carboxylic acid esters can be obtained. [ 10 ] | https://en.wikipedia.org/wiki/Shiina_esterification |
Shiina macrolactonization (or Shiina lactonization ) is an organic chemical reaction that synthesizes cyclic compounds by using aromatic carboxylic acid anhydrides as dehydration condensation agents. In 1994, Prof. Isamu Shiina ( Tokyo University of Science , Japan) reported an acidic cyclization method using Lewis acid catalyst , [ 1 ] [ 2 ] and, in 2002, a basic cyclization using nucleophilic catalyst . [ 3 ] [ 4 ]
The slow addition of hydroxycarboxylic acids (seco acids) into a system containing aromatic carboxylic acid anhydride and catalyst produces corresponding lactones (cyclic esters ) through the process shown in the following figure. In acidic Shiina macrolactonization, Lewis acid catalysts are used, while nucleophilic catalysts are used for Shiina macrolactonization under basic conditions.
In the acidic reaction, 4-trifluoromethylbenzoic anhydride (TFBA) is mainly used as a dehydration condensation agent. First, the Lewis acid catalyst activates the TFBA, and then a carboxyl group in seco acid reacts with the activated TFBA to produce mixed anhydride (MA) once. Then, a carbonyl group derived from the seco acid in MA is selectively activated and is attacked by a hydroxyl group in the seco acid through intramolecular nucleophilic substitution. Simultaneously, residual aromatic carboxylic acid salt, which is derived from the MA, acts as a deprotonation agent, causing the cyclization to progress and produce the desired lactone . To balance the reaction, each TFBA accepts the atoms of one water molecule from its starting material, i.e., the hydroxycarboxylic acid, and then changes itself into two molecules of 4-trifluoromethylbenzoic acid at the end of the reaction. Since the Lewis acid catalyst is reproduced at the end of the reaction, only a small proportion of catalyst is needed relative to the starting material to drive the reaction forward.
In the basic reaction, 2-methyl-6-nitrobenzoic anhydride ( MNBA ) is primarily used as a dehydration condensation agent. [ 5 ] First, the nucleophilic catalyst acts on the MNBA to produce activated acyl carboxylate. The reaction of carboxyl group in the seco acid with the activated acyl carboxylate produces the corresponding MA, in the same manner as in the acidic reaction. Then, the nucleophilic catalyst acts selectively on a carbonyl group derived from the seco acid in MA to again produce activated acyl carboxylate. The hydroxyl group in the seco acid attacks its host molecule through intramolecular nucleophilic substitution, and at the same time, carboxylate anion, derived from 2-methyl-6-nitrobenzoic acid, acts as a deprotonation agent, promoting the progression of the cyclization and producing the desired lactone. To balance the reaction, each MNBA accepts the atoms of one water molecule from its starting material, changing itself into two molecules of the amine salt of 2-methyl-6-nitrobenzoic acid, and thus, terminating the reaction. Because the nucleophilic catalyst is reproduced at the end of the reaction, only small stoichiometric quantities are required.
All of the processes of Shiina macrolactonization consist of reversible reactions , with the exception of the last cyclization step. At the first stage of the reaction, mixed anhydride (MA) is produced quickly under mild conditions; at the second stage, a faster cyclization of the MA prevents an increase in MA concentration. To maximize this concentration gradient effect, the starting material, i.e., hydroxycarboxylic acid (seco acid), is fed slowly into the system with a syringe driver . When seco acid is added into the system little by little using a syringe driver, all of the reactant is quickly converted into MA; then, the MA is immediately consumed by the cyclization reaction. As just described, MA concentration is kept low throughout the Shiina macrolactonization reaction. Therefore, the monomer production rate is very high.
Aromatic carboxylic acid anhydrides are used as dehydration condensation agents not only for the intramolecular reaction of hydroxycarboxylic acids but also for the intermolecular reaction of carboxylic acids with alcohols ( Shiina esterification ). Both of these intramolecular and intermolecular reactions are used for the artificial synthesis of various natural products and pharmacologically active compounds , [ 6 ] [ 7 ] as the reaction of a carboxylic acid with an amine produces an amide or a peptide . [ 8 ]
In acidic reactions, Lewis acid catalysts, such as metal triflates, exhibit high activities, while in basic reactions, 4-dimethylaminopyridine ( DMAP ), 4-dimethylaminopyridine N-oxide (DMAPO), and 4-pyrrolidinopyridine (PPY) are employed. | https://en.wikipedia.org/wiki/Shiina_macrolactonization |
Shikimic acid , more commonly known as its anionic form shikimate , is a cyclohexene , a cyclitol and a cyclohexanecarboxylic acid . It is an important biochemical metabolite in plants and microorganisms. Its name comes from the Japanese flower shikimi ( シキミ , the Japanese star anise , Illicium anisatum ), from which it was first isolated in 1885 by Johan Fredrik Eykman . [ 1 ] The elucidation of its structure was made nearly 50 years later. [ 2 ]
Phosphoenolpyruvate and erythrose-4-phosphate condense to form 3-deoxy- D -arabinoheptulosonate-7-phosphate (DAHP), in a reaction catalyzed by the enzyme DAHP synthase . DAHP is then transformed to 3-dehydroquinate (DHQ), in a reaction catalyzed by DHQ synthase . Although this reaction requires nicotinamide adenine dinucleotide (NAD) as a cofactor, the enzymic mechanism regenerates it, resulting in the net use of no NAD.
DHQ is dehydrated to 3-dehydroshikimic acid by the enzyme 3-dehydroquinate dehydratase , which is reduced to shikimic acid by the enzyme shikimate dehydrogenase , which uses nicotinamide adenine dinucleotide phosphate (NADPH) as a cofactor.
The shikimate pathway, named after shikimic acid as important intermediate, is a seven-step metabolic route used by bacteria , fungi , algae , parasites, and plants for the biosynthesis of aromatic amino acids ( phenylalanine , tyrosine , and tryptophan ). This pathway is not found in animals; therefore, phenylalanine and tryptophan are essential nutrients and must be obtained from the animal's diet. Tyrosine is not essential, as it can be synthesized from phenylalanine, except for individuals unable to hydroxylate phenylalanine to tyrosine .
Phenylalanine and tyrosine are the precursors used in the phenylpropanoids biosynthesis . The phenylpropanoids are then used to produce the flavonoids , coumarins , tannins and lignin . The first enzyme involved is phenylalanine ammonia-lyase (PAL) that converts L - phenylalanine to trans - cinnamic acid and ammonia .
Gallic acid is formed from 3-dehydroshikimate by the action of the enzyme shikimate dehydrogenase to produce 3,5-didehydroshikimate . This latter compound spontaneously rearranges to gallic acid. [ 3 ]
Shikimic acid is a precursor for:
Mycosporine-like amino acids are small secondary metabolites produced by organisms that live in environments with high volumes of sunlight, usually marine environments.
In the pharmaceutical industry, shikimic acid from the Chinese star anise ( Illicium verum ) is used as a base material for production of oseltamivir ( Tamiflu ). Although shikimic acid is present in most autotrophic organisms, it is a biosynthetic intermediate and in general found in very low concentrations. The low isolation yield of shikimic acid from the Chinese star anise is blamed for the 2005 shortage of oseltamivir. Shikimic acid can also be extracted from the seeds of the sweetgum ( Liquidambar styraciflua ) fruit, [ 2 ] which is abundant in North America, in yields of around 1.5%. For example, 4 kg (8.8 lb) of sweetgum seeds is needed for fourteen packages of Tamiflu. By comparison, star anise has been reported to yield 3% to 7% shikimic acid. Biosynthetic pathways in E. coli have recently been enhanced to allow the organism to accumulate enough material to be used commercially. [ 4 ] [ 5 ] [ 6 ] A 2010 study released by the University of Maine showed that shikimic acid can also be readily harvested from the needles of several species of pine tree. [ 7 ]
Protecting groups are more commonly used in small-scale laboratory work and initial development than in industrial production processes because their use adds additional steps and material costs to the process. However, the availability of a cheap chiral building block can overcome these additional costs, for example, shikimic acid for oseltamivir .
Aminoshikimic acid is also an alternative to shikimic acid as a starting material for the synthesis of oseltamivir.
Shikimate can be used to synthesise (6 S )-6-fluoroshikimic acid , [ 8 ] an antibiotic which inhibits the aromatic biosynthetic pathway. [ 9 ] More specifically, glyphosate inhibits the enzyme 5-enolpyruvylshikimate-3-phosphate synthase (EPSPS). "Roundup Ready" genetically modified crops overcome that inhibition. [ 10 ]
It occurs in tree fern fronds, a specialty called fiddlehead (furled fronds of a young tree fern in the order Cyatheales , harvested for use as a vegetable). These fronds are edible, but can be roasted to remove shikimic acid. [ 11 ]
Shikimic acid is also the glycoside part of some hydrolysable tannins . The acid is highly soluble in water and insoluble in nonpolar solvents, and this is why shikimic acid is active only against Gram-positive bacteria , due to outer cell membrane impermeability of Gram-negatives . [ 12 ] | https://en.wikipedia.org/wiki/Shikimic_acid |
The Shilov system is a classic example of catalytic C-H bond activation and oxidation which preferentially activates stronger C-H bonds over weaker C-H bonds for an overall partial oxidation. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] [ 8 ]
The Shilov system was discovered by Alexander E. Shilov in 1969-1972 while investigating H/D exchange between isotopologues of CH 4 and H 2 O catalyzed simple transition metal coordination complexes . The Shilov cycle is the partial oxidation of a hydrocarbon to an alcohol or alcohol precursor (RCl) catalyzed by Pt II Cl 2 in an aqueous solution with [Pt IV Cl 6 ] 2− acting as the ultimate oxidant. The cycle consists of three major steps, the electrophilic activation of the C-H bond, oxidation of the complex, and the nucleophilic oxidation of the alkane substrate. An equivalent transformation is performed industrially by steam reforming methane to syngas then reducing the carbon monoxide to methanol . The transformation can also performed biologically by methane monooxygenase .
Overall Transformation
RH + H 2 O + [PtCl 6 ] 2− → ROH + 2H + + PtCl 2 + 4Cl −
The initial and rate limiting step involving the electrophilic activation of RH 2 C-H by a Pt II center to produce a Pt II -CH 2 R species and a proton. The mechanism of this activation is debated. One possibility is the oxidative addition of a sigma coordinated C-H bond followed by the reductive removal of the proton. Another is a sigma-bond metathesis involving the formation of the M-C bond and a H-Cl or H-O bond. Regardless it is this step that kinetically imparts the chemoselectivity to the overall transformation. Stronger, more electron-rich bonds are activated preferentially over weaker, more electron-poor bonds of species that have already been partially oxidized. This avoids a problem that plagues many partial oxidation processes, namely, the over-oxidation of substrate to thermodynamic sinks such as H 2 O and CO 2 .
In the next step the Pt II -CH 2 R complex is oxidized by [Pt IV Cl 6 ] 2− to a Pt IV -CH 2 R complex. There have been multiple studies to find a replacement oxidant that is less expensive than [Pt IV Cl 6 ] 2− or a method to regenerate [Pt IV Cl 6 ] 2− . It would be most advantageous to develop an electron train which would use oxygen as the ultimate oxidant. It is important that the oxidant preferentially oxidizes the Pt II -CH 2 R species over the initial Pt II species since Pt IV complexes will not electrophilically activate a C-H bond of the alkane (although Pt IV complexes electrophilically substitute hydrogens in aromatics - see refs. [1] and [2] ). Such premature oxidation shuts down the catalysis.
Finally the Pt IV -CH 2 R undergoes nucleophilic attack by OH − or Cl − with the departure of Pt II complex to regenerate the catalyst. | https://en.wikipedia.org/wiki/Shilov_system |
Shilshila Acharya is a Nepalese environmental scientist who led successful campaigns to increase Nepal's plastic recycling. She has reduced her country's use of plastic bags and she has recovered refuse abandoned by visiting mountaineers. In 2024 she joined the BBC's list of 100 inspiring women .
Acharya was born in Baglung . She surprised her family after she won a valuable Bachelor of Medicine, Bachelor of Surgery scholarship that would establish her as a surgeon. She persuaded her family that she would prefer to study environmental science even though the finances made little sense. She would need to pay for her tuition at Kathmandu University as there was no scholarship for environmental science. After graduating she went to Norway to study this time with scholarship supported by Nepal's and Norway's government. She studied biodiversity and environmental science [ 1 ] at Tribhuvan University and the University of Bergen and she gained a master's degree. [ 2 ]
One of her early campaigns was to suggest the a Nepalese highway should have trees planted beside it. [ 3 ]
In 2014, she joined the Himalayan Climate Initiative as it began a move to reduce the use of plastic bags in Nepal [ 3 ] although this was not the initial idea. Her group wanted to reduce the number of girls who were trafficked abroad. Her group joined a partnership with Bhat-Bhateni Supermarket , a large supermarket chain, [ 3 ] to encourage the use of cloth bags instead of disposable plastic bags. The cloth bags were very popular. People bought them, but they didn't use them. The group needed to find a new way to influence people. [ 4 ] Their new campaign's slogan was "No Thanks, I Carry My Own Bag" and this changed behaviour. It led the Nepalese government to ban the use of plastic bags in Kathmandu. [ 5 ]
In 2018 the World Wildlife Fund in Nepal celebrated its 25th anniversary and they decided to reconstitute their Conservation awards. Acharya received one of the awards, given to individuals, because of her work as the CEO of the Himalayan Climate Initiative. [ 6 ]
In 2019 she was involved in a campaign to reduce the large amount of refuse left in the Himalayas by visiting mountaineers. Her campaign resulted in nearly 120 tonnes of rubbish being removed. [ 5 ]
In 2024 she was chosen to join the BBC's list of 100 inspiring women. [ 7 ] | https://en.wikipedia.org/wiki/Shilshila_Acharya |
A shim is a device used to adjust the homogeneity of a magnetic field . Shims received their name from the purely mechanical shims used to adjust position and parallelity of the pole faces of an electromagnet. Coils used to adjust the homogeneity of a magnetic field by changing the current flowing through it were called "electrical current shims" [ 1 ] because of their similar function.
In NMR and MRI , shimming is used prior to the operation of the magnet to eliminate inhomogeneities in its field.
Initially, the magnetic field inside an NMR spectrometer or MRI scanner will be far from homogeneous compared with an "ideal" field of the device. This is a result of production tolerances and of the magnetic field of the environment. Iron constructions in walls and floor of the examination room become magnetized and disturb the field of the scanner. The probe and the sample or the patient become slightly magnetized when brought into the strong magnetic field and create additional inhomogeneous fields. The process of correcting for these inhomogeneities is called shimming the magnet, shimming the probe or shimming the sample, depending on the assumed source of the remaining inhomogeneity.
Field homogeneity of the order of 1 ppm over a volume of several liters is needed in an MRI scanner. High-resolution NMR spectroscopy demands field homogeneity better than 1 ppb within a volume of a few milliliters. [ 2 ]
There are two types of shimming: active and passive.
Active shimming uses coils with adjustable current.
Passive shimming involves pieces of steel with good magnetic qualities. The steel pieces are placed near the permanent or superconducting magnet. They become magnetized and produce their own magnetic field.
In both cases, the additional magnetic fields (produced by coils or steel) add to the overall magnetic field of the superconducting magnet in such a way as to increase the homogeneity of the total field.
There are different ways to define inhomogeneity of a magnetic field in the center of the MR spectrometer. Currently, for medical MR scanners, the industry standard is to measure volume root mean square (VRMS) values of the field for the different (mostly concentric) volumes in the middle of the scanner.
http://web.mit.edu/8.13/www/pdf_files/shimming.pdf | https://en.wikipedia.org/wiki/Shim_(magnetism) |
In thermodynamics , the Shimansky equation describes the temperature dependence of the heat of vaporization (also known as the enthalpy of vaporization or the heat of evaporation ): [ 1 ]
where:
This equation was obtained in 1955 by Yu. I. Shimansky, at first empirically , and later derived theoretically. The Shimansky equation does not contain any arbitrary constants , since the value of T C can be determined experimentally and L 0 can be calculated if L has been measured experimentally for at least one given value of temperature T . The Shimansky equation describes quite well the heat of vaporization for a wide variety of liquids . For chemical compounds that belong to the same class (e.g. alcohols ) the value of L 0 T C {\displaystyle {\tfrac {L_{0}}{T_{C}}}} ratio remains constant. For each such class of liquids, the Shimansky equation can be re-written in a form of
where A = L 0 T C = const . {\displaystyle A={\tfrac {L_{0}}{T_{C}}}={\text{const}}.} The latter formula is a mathematical expression of structural similarity of liquids. The value of T C plays a role of the parameter for a group of curves of temperature dependence of L .
This thermodynamics -related article is a stub . You can help Wikipedia by expanding it .
This molecular physics –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Shimansky_equation |
Shimshon Avraham Amitsur (born Kaplan ; Hebrew : שמשון אברהם עמיצור ; August 26, 1921 – September 5, 1994) was an Israeli mathematician . He is best known for his work in ring theory , in particular PI rings , an area of abstract algebra .
Amitsur was born in Jerusalem and studied at the Hebrew University under the supervision of Jacob Levitzki . His studies were repeatedly interrupted, first by World War II and then by the 1948 Arab–Israeli War . He received his M.Sc. degree in 1946, and his Ph.D. in 1950. Later, for his joint work with Levitzki, he received the first Israel Prize in Exact Sciences . He worked at the Hebrew University until his retirement in 1989. Amitsur was a visiting scholar at the Institute for Advanced Study from 1952 to 1954. [ 1 ] He was an Invited Speaker at the ICM in 1970 in Nice. [ 2 ] He was a member of the Israel Academy of Sciences , where he was the Head for Experimental Science Section. He was one of the founding editors of the Israel Journal of Mathematics , and the mathematical editor of the Hebrew Encyclopedia . Amitsur received a number of awards, including the honorary doctorate from Ben-Gurion University in 1990. His students included Avinoam Mann, Amitai Regev , Eliyahu Rips and Aner Shalev .
Amitsur and Jacob Levitzki were each awarded the Israel Prize in exact sciences , in 1953, its inaugural year. [ 3 ] | https://en.wikipedia.org/wiki/Shimshon_Amitsur |
In mathematics , Shimura's reciprocity law , introduced by Shimura ( 1971 ), describes the action of ideles of imaginary quadratic fields on the values of modular functions at singular moduli . It forms a part of the Kronecker Jugendtraum , explicit class field theory for such fields. There are also higher-dimensional generalizations.
This number theory -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Shimura's_reciprocity_law |
Shingling was a stage in the production of bar iron or steel , in the finery and puddling processes. As with many ironmaking terms, this is derived from the French - cinglage .
The product of the finery was a bloom or loop (from old Frankish luppa or lopp , meaning a shapeless mass); that of the puddling furnace was a puddled ball. In each case, this needed to be consolidated by hammering it into a more regular shape. This was done manually with heavy hammers; later by a waterwheel or steam powered hammers, leading to modern power hammers . The result was an oblong-shaped iron product similar in appearance to shingles used on roofs. In the finery, this was part of the work of the finer; during puddling, it was done by a special workman called the shingler. The iron (or steel) then had to be further shaped (drawn out) under the hammer or rolled in a rolling mill to produce a bar. In more recent times, the process was carried out using mechanical jaws to squeeze the puddled ball into shape. | https://en.wikipedia.org/wiki/Shingling |
The Shinnar–Le Roux (SLR) algorithm [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] is a mathematical tool for generating frequency-selective radio frequency (RF) pulses in magnetic resonance imaging (MRI) . Frequency selective pulses are used in MRI to isolate a slice through the subject for excitation, inversion and saturation. [ 1 ]
Given a desired magnetization profile, determining the RF pulse that produces it is generally nonlinear, due to the non-linearity of the Bloch equations . At low tip angles, the RF excitation waveform can be approximated by the inverse Fourier Transform of the desired frequency profile, using the excitation kspace analysis. [ 8 ] [ 9 ] The small tip angle approximation continues to hold well for tip angles on the order of 90 degree. [ 8 ] However, for tip angles greater than 90 degree, a different approach must be used. [ 1 ]
A direct solution to the pulse design problem was independently proposed by Shinnar [ 2 ] [ 3 ] [ 4 ] [ 5 ] and Le Roux [ 6 ] based on a discrete approximation to the spin domain version of the Bloch equations.
The SLR algorithm simplifies the solution of the Bloch equations to the design of two polynomials, which can be solved using well-known digital filter design algorithms. [ 1 ]
Where N is the number of bins, or hard pulse divisions that you wish to approximate with, and φ(t) is the phase of the B 1 (t) waveform at a given time t .
The mapping of the RF pulse into two complex polynomials will be denoted as the Forward SLR Transform. Given two polynomials [ A N ( z ) , B N ( z ) ] {\displaystyle [A_{N}(z),B_{N}(z)]} the SLR transform can be inverted to calculate the RF pulse that produces these polynomials. The order of the polynomials [ A N ( z ) , B N ( z ) ] {\displaystyle [A_{N}(z),B_{N}(z)]} is N − 1 {\displaystyle N-1} . A minimum phase A N ( z ) {\displaystyle A_{N}(z)} results in a minimum energy RF pulse. | https://en.wikipedia.org/wiki/Shinnar–Le_Roux_algorithm |
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