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Kelvin probe force microscope Therefore, KPFM can be performed simultaneously during AC topography measurements but not during contact topography measurements. | https://en.wikipedia.org/wiki?curid=2207911 |
Super black is a surface treatment developed at the National Physical Laboratory (NPL) in the United Kingdom. It absorbs approximately 99.6% of visible light at normal incidence, while conventional black paint absorbs about 97.5%. At other angles of incidence, super black is even more effective: at an angle of 45°, it ... | https://en.wikipedia.org/wiki?curid=2208748 |
Pentazole is an aromatic chemical molecule consisting of a five-membered ring with all nitrogen atoms, one of which is bonded to a hydrogen atom. It has a molecular formula HN. Although strictly speaking a homocyclic, inorganic compound, pentazole has historically been classed as the last in a series of heterocyclic az... | https://en.wikipedia.org/wiki?curid=2208859 |
Pentazole These results were initially challenged by some authors, but subsequent experiments involving the detailed analysis of the decomposition products, complemented by computational studies, bore out the initial conclusion. The pentazolide anion is not expected to last longer than a few seconds in aqueous solution... | https://en.wikipedia.org/wiki?curid=2208859 |
Inelastic mean free path The inelastic mean free path (IMFP) is an index of how far an electron on average travels through a solid before losing energy. If a monochromatic primary beam of electrons is incident on a solid surface, the majority of incident electrons lose their energy because they interact strongly with m... | https://en.wikipedia.org/wiki?curid=2209432 |
Einstein coefficients are mathematical quantities which are a measure of the probability of absorption or emission of light by an atom or molecule. The Einstein "A" coefficients are related to the rate of spontaneous emission of light, and the Einstein "B" coefficients are related to the absorption and stimulated emiss... | https://en.wikipedia.org/wiki?curid=2209688 |
Einstein coefficients A photon with an energy equal to the difference between the energy levels is released or absorbed in the process. The frequency at which the spectral line occurs is related to the photon energy by Bohr's frequency condition where denotes Planck's constant. An atomic spectral line refers to emissio... | https://en.wikipedia.org/wiki?curid=2209688 |
Einstein coefficients For thermodynamics and for the application of Kirchhoff's law, it is necessary that the total absorption be expressed as the algebraic sum of two components, described respectively by formula_11 and formula_12, which may be regarded as positive and negative absorption, which are, respectively, the... | https://en.wikipedia.org/wiki?curid=2209688 |
Einstein coefficients In strict thermodynamic equilibrium, the radiation field is said to be black-body radiation and is described by Planck's law. For local thermodynamic equilibrium, the radiation field does not have to be a black-body field, but the rate of interatomic collisions must vastly exceed the rates of abso... | https://en.wikipedia.org/wiki?curid=2209688 |
Einstein coefficients Einstein considered the case of isotropic radiation of frequency and spectral energy density . Hilborn has compared various formulations for derivations for the Einstein coefficients, by various authors. For example, Herzberg works with irradiance and wavenumber. Yariv works with energy per unit v... | https://en.wikipedia.org/wiki?curid=2209688 |
Einstein coefficients If formula_24 is the number density of atoms in state "i" , then the change in the number density of atoms in state 2 per unit time due to spontaneous emission will be The same process results in increasing of the population of the state 1: Stimulated emission (also known as induced emission) is t... | https://en.wikipedia.org/wiki?curid=2209688 |
Einstein coefficients The process is described by the Einstein coefficient formula_11 (m J s), which gives the probability per unit time per unit spectral radiance of the radiation field that an electron in state 1 with energy formula_23 will absorb a photon with an energy and jump to state 2 with energy formula_22. Th... | https://en.wikipedia.org/wiki?curid=2209688 |
Einstein coefficients Detailed balance (valid only at equilibrium) requires that the change in time of the number of atoms in level 1 due to the above three processes be zero: Along with detailed balancing, at temperature we may use our knowledge of the equilibrium energy distribution of the atoms, as stated in the Max... | https://en.wikipedia.org/wiki?curid=2209688 |
Einstein coefficients The oscillator strength formula_51 is defined by the following relation to the cross section formula_52 for absorption: where formula_54 is the electron charge, formula_55 is the electron mass, and formula_56 and formula_57 are normalized distribution functions in frequency and angular frequency r... | https://en.wikipedia.org/wiki?curid=2209688 |
Finite strain theory In continuum mechanics, the finite strain theory—also called large strain theory, or large deformation theory—deals with deformations in which strains and/or rotations are large enough to invalidate assumptions inherent in infinitesimal strain theory. In this case, the undeformed and deformed confi... | https://en.wikipedia.org/wiki?curid=2210759 |
Finite strain theory Using formula_5 in place of formula_3 and formula_7 in place of formula_4, both of which are vectors from the origin of the coordinate system to each respective point, we have the Lagrangian description of the displacement vector: Where formula_10 are the orthonormal unit vectors that define the ba... | https://en.wikipedia.org/wiki?curid=2210759 |
Finite strain theory Thus The relationship between formula_26 and formula_27 is then given by Knowing that then It is common to superimpose the coordinate systems for the deformed and undeformed configurations, which results in formula_31, and the direction cosines become Kronecker deltas, i.e. Thus in material (undefo... | https://en.wikipedia.org/wiki?curid=2210759 |
Finite strain theory differentiable function of formula_48 and time formula_49, which implies that cracks and voids do not open or close during the deformation. Thus we have, Consider a particle or material point formula_16 with position vector formula_52 in the undeformed configuration (Figure 2). After a displacement... | https://en.wikipedia.org/wiki?curid=2210759 |
Finite strain theory For an infinitesimal element formula_64, and assuming continuity on the displacement field, it is possible to use a Taylor series expansion around point formula_16, neglecting higher-order terms, to approximate the components of the relative displacement vector for the neighboring particle formula_... | https://en.wikipedia.org/wiki?curid=2210759 |
Finite strain theory To transform quantities that are defined with respect to areas in a deformed configuration to those relative to areas in a reference configuration, and vice versa, we use Nanson's relation, expressed as where formula_86 is an area of a region in the deformed configuration, formula_87 is the same ar... | https://en.wikipedia.org/wiki?curid=2210759 |
Finite strain theory This decomposition implies that the deformation of a line element formula_64 in the undeformed configuration onto formula_65 in the deformed configuration, i.e. formula_110, may be obtained either by first stretching the element by formula_111, i.e. formula_112, followed by a rotation formula_113, ... | https://en.wikipedia.org/wiki?curid=2210759 |
Finite strain theory In 1839, George Green introduced a deformation tensor known as the "right Cauchy–Green deformation tensor" or "Green's deformation tensor", defined as: Physically, the Cauchy–Green tensor gives us the square of local change in distances due to deformation, i.e. formula_130 Invariants of formula_131... | https://en.wikipedia.org/wiki?curid=2210759 |
Finite strain theory For incompressible materials, a slightly different set of invariants is used: Earlier in 1828, Augustin Louis Cauchy introduced a deformation tensor defined as the inverse of the left Cauchy–Green deformation tensor, formula_141. This tensor has also been called the Piola tensor and the Finger tens... | https://en.wikipedia.org/wiki?curid=2210759 |
Finite strain theory The undeformed length of the curve is given by After deformation, the length becomes Note that the right Cauchy–Green deformation tensor is defined as Hence, which indicates that changes in length are characterized by formula_170. The concept of "strain" is used to evaluate how much a given displac... | https://en.wikipedia.org/wiki?curid=2210759 |
Finite strain theory Many other different definitions of tensors formula_183 are admissible, provided that they all satisfy the conditions that: An example is the set of tensors which do not belong to the Seth–Hill class, but have the same 2nd-order approximation as the Seth–Hill measures at formula_191 for any value o... | https://en.wikipedia.org/wiki?curid=2210759 |
Finite strain theory 1 (reference?) The diagonal components formula_206 of the Lagrangian finite strain tensor are related to the normal strain, e.g. where formula_208 is the normal strain or engineering strain in the direction formula_209. The off-diagonal components formula_206 of the Lagrangian finite strain tensor ... | https://en.wikipedia.org/wiki?curid=2210759 |
Finite strain theory The tangent vector to the deformed coordinate grid line curve formula_217 at formula_218 is given by The three tangent vectors at formula_218 form a local basis. These vectors are related the reciprocal basis vectors by Let us define a second-order tensor field formula_222 (also called the metric t... | https://en.wikipedia.org/wiki?curid=2210759 |
Finite strain theory Therefore, The problem of compatibility in continuum mechanics involves the determination of allowable single-valued continuous fields on bodies. These allowable conditions leave the body without unphysical gaps or overlaps after a deformation. Most such conditions apply to simply-connected bodies.... | https://en.wikipedia.org/wiki?curid=2210759 |
Hot atom In physical chemistry, a hot atom is an atom that has a high kinetic or internal energy. When molecule AB adsorbs on a surface dissociatively, In case 2, B gains a high translational energy from the adsorption energy of A, and hot atom B is generated. For example, the hydrogen molecule, because of its light ma... | https://en.wikipedia.org/wiki?curid=2211117 |
Pentanitroaniline is an explosive organic compound. It is a relatively sensitive explosive (much more so than TNT) that can be used as a base charge for detonators, although it is uncommon in this application. can be reacted with ammonia in benzene, dichloromethane or another similar solvent to produce triaminotrinitro... | https://en.wikipedia.org/wiki?curid=2211236 |
Crystallographic defects in diamond Imperfections in the crystal lattice of diamond are common. Such crystallographic defects in diamond may be the result of lattice irregularities or extrinsic substitutional or interstitial impurities, introduced during or after the diamond growth. The defects affect the material prop... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond In diamond, only defects of the following symmetries have been observed thus far: tetrahedral (T), tetragonal (D), trigonal (D,C), rhombic (C), monoclinic (C, C, C) and triclinic (C or C). The defect symmetry allows predicting many optical properties. For example, one-phonon (infrare... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond Manganese and tungsten have been unambiguously detected in diamond, but they might originate from foreign inclusions. Detection of isolated iron in diamond has later been re-interpreted in terms of micro-particles of ruby produced during the diamond synthesis. Oxygen is believed to b... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond The four main nitrogen forms are as follows: The C center corresponds to electrically neutral single substitutional nitrogen atoms in the diamond lattice. These are easily seen in electron paramagnetic resonance spectra (in which they are confusingly called P1 centers). C centers imp... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond The latter has a characteristic IR absorption spectrum with a sharp peak at 1332 cm and broader and weaker peaks at 1115, 1046 and 950 cm. The A center is probably the most common defect in natural diamonds. It consists of a neutral nearest-neighbor pair of nitrogen atoms substitutin... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond Early assignment of the N9 absorption system to the B center have been disproven later. The B center has a characteristic IR absorption spectrum (see the infrared absorption picture above) with a sharp peak at 1332 cm and a broader feature at 1280 cm. The latter is routinely used to ... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond Boron is an acceptor in diamond: boron atoms have one less available electron than the carbon atoms; therefore, each boron atom substituting for a carbon atom creates an electron hole in the band gap that can accept an electron from the valence band. This allows red light absorption,... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond This important property of phosphorus in diamond favors electronic applications, such as UV light-emitting diodes (LEDs, at 235 nm). Hydrogen is one of the most technological important impurities in semiconductors, including diamond. Hydrogen-related defects are very different in nat... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond The microscopic structure of the corresponding defects is yet unknown and it is not even certain whether or not those defects originate in diamond or in foreign inclusions. Gray color in some diamonds from the Argyle mine in Australia is often associated with those hydrogen defects, ... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond Its production mechanism is generally accepted as follows: large nickel atom incorporates substitutionally, then expels a nearby carbon (creating a neighboring vacancy), and shifts in-between the two sites. Although the physical and chemical properties of cobalt and nickel are rather... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond It is believed (though no proof exists) that much silicon substitutes for carbon thus becoming invisible to most spectroscopic techniques because silicon and carbon atoms have the same configuration of the outer electronic shells. Germanium, tin and lead are normally absent in diamon... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond The easiest way to produce intrinsic defects in diamond is by displacing carbon atoms through irradiation with high-energy particles, such as alpha (helium), beta (electrons) or gamma particles, protons, neutrons, ions, etc. The irradiation can occur in the laboratory or in nature (s... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond When it meets other interstitials it aggregates into larger complexes of two and three split-interstitials, identified by electron paramagnetic resonance (R1 and O3 centers), optical absorption and photoluminescence. Most high-energy particles, beside displacing carbon atom from the ... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond Upon annealing of pure diamond at ~700 °C, vacancies migrate and form divacancies, characterized by optical absorption and electron paramagnetic resonance. Similar to single interstitials, divacancies do not produce photoluminescence. Divacancies, in turn, anneal out at ~900 °C creat... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond Their size ranges from nanometers to many micrometers, and large ones are easily observed in an optical microscope via their luminescence. For a long time, platelets were tentatively associated with large nitrogen complexes — nitrogen sinks produced as a result of nitrogen aggregatio... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond Such interaction usually occurs if a diamond containing extrinsic defects (impurities) is either plastically deformed or is irradiated and annealed. Most important is the interaction of vacancies and interstitials with nitrogen. Carbon interstitials react with substitutional nitrogen... | https://en.wikipedia.org/wiki?curid=2212557 |
Crystallographic defects in diamond The assumed mechanism is trapping of migrating vacancy by substitutional silicon resulting in the Si-V (semi-divacancy) configuration. A similar mechanism is expected for nickel, for which both substitutional and semi-divacancy configurations are reliably identified (see subsection "... | https://en.wikipedia.org/wiki?curid=2212557 |
Umklapp scattering In crystalline materials, (also U-process or Umklapp process) is a scattering process that results in a wave vector (usually written "k") which falls outside the first Brillouin zone. If a material is periodic, it has a Brillouin zone, and any point outside the first Brillouin zone can also be expres... | https://en.wikipedia.org/wiki?curid=2212817 |
Umklapp scattering With increasing phonon momentum and thus larger wave vectors "k" and "k", their sum might point outside the first Brillouin zone ("k<nowiki>'</nowiki>"). As shown in Figure 2, "k"-vectors outside the first Brillouin zone are physically equivalent to vectors inside it and can be mathematically transfo... | https://en.wikipedia.org/wiki?curid=2212817 |
Detailed balance The principle of detailed balance can be used in kinetic systems which are decomposed into elementary processes (collisions, or steps, or elementary reactions). It states that at equilibrium, each elementary process is in equilibrium with its reverse process. The principle of detailed balance was expli... | https://en.wikipedia.org/wiki?curid=2212867 |
Detailed balance The principle of detailed balance has been used in Markov chain Monte Carlo methods since their invention in 1953. In particular, in the Metropolis–Hastings algorithm and in its important particular case, Gibbs sampling, it is used as a simple and reliable condition to provide the desirable equilibrium... | https://en.wikipedia.org/wiki?curid=2212867 |
Detailed balance for Boltzmann's equation requires "PT"-invariance of collisions' dynamics, not just "T"-invariance. Indeed, after the time reversal the collision +A_\mathit{w} -> {A_\mathit{v'}}+A_\mathit{w'}</chem>,}} transforms into +A_\mathit{-w'} -> {A_\mathit{-v}}+A_\mathit{-w}</chem>.}} For the detailed balance ... | https://en.wikipedia.org/wiki?curid=2212867 |
Detailed balance equilibrium probability distribution) π such that where "P" is the Markov transition probability from state "i" to state "j", i.e. , and π and π are the equilibrium probabilities of being in states "i" and "j", respectively. When for all "i", this is equivalent to the joint probability matrix, being sy... | https://en.wikipedia.org/wiki?curid=2212867 |
Detailed balance For continuous systems with detailed balance, it may be possible to continuously transform the coordinates until the equilibrium distribution is uniform, with a transition kernel which then is symmetric. In the case of discrete states, it may be possible to achieve something similar by breaking the Mar... | https://en.wikipedia.org/wiki?curid=2212867 |
Detailed balance Lorentz stated that the principle of detailed balance is not applicable to collisions of polyatomic molecules. Boltzmann immediately invented a new, more general condition sufficient for entropy growth. Boltzmann's condition holds for all Markov processes, irrespective of time-reversibility. Later, ent... | https://en.wikipedia.org/wiki?curid=2212867 |
Detailed balance This matrix need not be square. The "stoichiometric vector" formula_17 is the "r"th row of formula_18 with coordinates formula_16. According to the "generalized mass action law", the reaction rate for an elementary reaction is where formula_21 is the activity (the "effective concentration") of formula_... | https://en.wikipedia.org/wiki?curid=2212867 |
Detailed balance In particular, for any cycle in the monomolecular (linear) reactions the product of the reaction rate constants in the clockwise direction is equal to the product of the reaction rate constants in the counterclockwise direction. The same condition is valid for the reversible Markov processes (it is equ... | https://en.wikipedia.org/wiki?curid=2212867 |
Detailed balance For this purpose, use the representation of the activity through the chemical potential: where "μ" is the chemical potential of the species under the conditions of interest, is the chemical potential of that species in the chosen standard state, "R" is the gas constant and "T" is the thermodynamic temp... | https://en.wikipedia.org/wiki?curid=2212867 |
Detailed balance Similar inequalities are valid for other classical conditions for the closed systems and the corresponding characteristic functions: for isothermal isobaric conditions the Gibbs free energy decreases, for the isochoric systems with the constant internal energy (isolated systems) the entropy increases a... | https://en.wikipedia.org/wiki?curid=2212867 |
Detailed balance In this case, the kinetic equations have the form: Let us use the notations formula_71, formula_72 for the input and the output vectors of the stoichiometric coefficients of the "r"th elementary reaction. Let formula_73 be the set of all these vectors formula_74. For each formula_75, let us define two ... | https://en.wikipedia.org/wiki?curid=2212867 |
Detailed balance For systems that obey the generalized mass action law the semi-detailed balance condition is sufficient for the dissipation inequality formula_86 (for the Helmholtz free energy under isothermal isochoric conditions and for the dissipation inequalities under other classical conditions for the correspond... | https://en.wikipedia.org/wiki?curid=2212867 |
Detailed balance Let us count the direct and reverse reaction in the kinetic equation separately: An auxiliary function formula_93 of one variable formula_94 is convenient for the representation of dissipation for the mass action law This function formula_93 may be considered as the sum of the reaction rates for "defor... | https://en.wikipedia.org/wiki?curid=2212867 |
Detailed balance For example, the irreversible cycle <chem>A1 -> A2 -> A3 -> A1</chem> cannot be obtained as such a limit but the reaction mechanism <chem>A1 -> A2 -> A3 <- A1</chem> can. Gorban–Yablonsky theorem. "A system of reactions with some irreversible reactions is a limit of systems with detailed balance when s... | https://en.wikipedia.org/wiki?curid=2212867 |
Anderson localization In condensed matter physics, (also known as strong localization) is the absence of diffusion of waves in a "disordered" medium. This phenomenon is named after the American physicist P. W. Anderson, who was the first to suggest that electron localization is possible in a lattice potential, provided... | https://en.wikipedia.org/wiki?curid=2213942 |
Anderson localization Anderson's analysis shows the following: The phenomenon of Anderson localization, particularly that of weak localization, finds its origin in the wave interference between multiple-scattering paths. In the strong scattering limit, the severe interferences can completely halt the waves inside the d... | https://en.wikipedia.org/wiki?curid=2213942 |
Anderson localization Most numerical approaches to the localization problem use the standard tight-binding Anderson Hamiltonian with onsite-potential disorder. Characteristics of the electronic eigenstates are then investigated by studies of participation numbers obtained by exact diagonalization, multifractal properti... | https://en.wikipedia.org/wiki?curid=2213942 |
Anderson localization Transverse of light has also been demonstrated in an optical fiber medium (Karbasi "et al.", 2012) and a biological medium (Choi "et al.", 2018), and has also been used to transport images through the fiber (Karbasi "et al.", 2014). It has also been observed by localization of a Bose–Einstein cond... | https://en.wikipedia.org/wiki?curid=2213942 |
Thouless energy The is a characteristic energy scale of diffusive disordered conductors. It was first introduced by the Scottish-American physicist David J. Thouless when studying Anderson localization, as a measure of the sensitivity of energy levels to a change in the boundary conditions of the system. Though being a... | https://en.wikipedia.org/wiki?curid=2213992 |
Stagnation temperature In thermodynamics and fluid mechanics, stagnation temperature is the temperature at a stagnation point in a fluid flow. At a stagnation point the speed of the fluid is zero and all of the kinetic energy has been converted to internal energy and is added to the local static enthalpy. In both compr... | https://en.wikipedia.org/wiki?curid=2215177 |
Stagnation temperature Performance testing of solar thermal collectors utilizes the term "stagnation temperature" to indicate the maximum achievable collector temperature with a stagnant fluid (no motion), an ambient temperature of 30C, and incident solar radiation of 1000W/m. The aforementioned figures are just arbitr... | https://en.wikipedia.org/wiki?curid=2215177 |
Stagnation point In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object. The Bernoulli equation shows that the static pressure is highest when th... | https://en.wikipedia.org/wiki?curid=2215288 |
Stagnation point The streamline at a stagnation point is perpendicular to the surface of the body. | https://en.wikipedia.org/wiki?curid=2215288 |
Nuclear reaction analysis (NRA) is a nuclear method of nuclear spectroscopy in materials science to obtain concentration vs. depth distributions for certain target chemical elements in a solid thin film. If irradiated with select projectile nuclei at kinetic energies "E", target solid thin-film chemical elements can un... | https://en.wikipedia.org/wiki?curid=2216044 |
Nuclear reaction analysis Rutherford backscattering (RBS) reactions are elastic (Q = 0), and the interaction (scattering) cross-section σ given by the famous formula derived by Lord Rutherford in 1911. But non-Rutherford cross-sections (so-called "EBS", elastic backscattering spectrometry) can also be resonant: for exa... | https://en.wikipedia.org/wiki?curid=2216044 |
Phosgene oxime Phosgene oxime, or CX, is an organic compound with the formula ClCNOH. It is a potent chemical weapon, specifically a nettle agent. The compound itself is a colorless solid, but impure samples are often yellowish liquids. It has a strong, disagreeable odor and a violently irritating vapor. can be prepare... | https://en.wikipedia.org/wiki?curid=2216518 |
Gallium(III) hydroxide Gallium hydroxide, Ga(OH) is formed as a gel following the addition of ammonia to Ga salts. It is also found in nature as the rare mineral söhngeite which is reported to contain octahedrally coordinated gallium atoms Gallium hydroxide is amphoteric. In strongly acidic conditions, the gallium ion,... | https://en.wikipedia.org/wiki?curid=2217326 |
Crystallographic restriction theorem The crystallographic restriction theorem in its basic form was based on the observation that the rotational symmetries of a crystal are usually limited to 2-fold, 3-fold, 4-fold, and 6-fold. However, quasicrystals can occur with other diffraction pattern symmetries, such as 5-fold; ... | https://en.wikipedia.org/wiki?curid=2218040 |
Crystallographic restriction theorem If a displacement exists between any two lattice points, then that same displacement is repeated everywhere in the lattice. So collect all the edge displacements to begin at a single lattice point. The edge vectors become radial vectors, and their 8-fold symmetry implies a regular o... | https://en.wikipedia.org/wiki?curid=2218040 |
Crystallographic restriction theorem And without the discrete lattice assumption, the above construction not only fails to reach a contradiction, but produces a (non-discrete) counterexample. Thus 5-fold rotational symmetry cannot be eliminated by an argument missing either of those assumptions. A Penrose tiling of the... | https://en.wikipedia.org/wiki?curid=2218040 |
Crystallographic restriction theorem In radians, the only allowed rotations consistent with lattice periodicity are given by 2π/"n", where "n" = 1, 2, 3, 4, 6. This corresponds to 1-, 2-, 3-, 4-, and 6-fold symmetry, respectively, and therefore excludes the possibility of 5-fold or greater than 6-fold symmetry. Conside... | https://en.wikipedia.org/wiki?curid=2218040 |
Crystallographic restriction theorem In the lattice basis, the rotation operation must map every lattice point into an integer number of lattice vectors, so the entries of the rotation matrix in the lattice basis — and hence the trace — are necessarily integers. Similar as in other proofs, this implies that the only al... | https://en.wikipedia.org/wiki?curid=2218040 |
Crystallographic restriction theorem The following 4D rotation matrix is the aforementioned eightfold symmetry of the hypercube (and the cross-polytope): Transforming this matrix to the new coordinates given by This third matrix then corresponds to a rotation both by 45° (in the first two dimensions) and by 135° (in th... | https://en.wikipedia.org/wiki?curid=2218040 |
Crystallographic restriction theorem Using the fundamental theorem of arithmetic, we can write any other positive integer uniquely as a product of prime powers, "m" = ∏ "p"; set ψ("m") = ∑ ψ("p"). This differs from the totient itself, because it is a sum instead of a product. The crystallographic restriction in general... | https://en.wikipedia.org/wiki?curid=2218040 |
Crystallographic restriction theorem The theorem also excludes "S", "S", "D", and "D" (see point groups in three dimensions), even though they have 4- and 6-fold rotational symmetry only. Rotational symmetry of any order about an axis is compatible with translational symmetry along that axis. The result in the table ab... | https://en.wikipedia.org/wiki?curid=2218040 |
Polymersome In biotechnology, polymersomes are a class of artificial vesicles, tiny hollow spheres that enclose a solution. Polymersomes are made using amphiphilic synthetic block copolymers to form the vesicle membrane, and have radii ranging from 50 nm to 5 µm or more. Most reported polymersomes contain an aqueous so... | https://en.wikipedia.org/wiki?curid=2218269 |
Polymersome The most frequently used are the linear diblock or triblock copolymers. In these cases, the block copolymer has one block that is hydrophobic; the other block or blocks are hydrophilic. Other morphologies used include comb copolymers, where the backbone block is hydrophilic and the comb branches are hydroph... | https://en.wikipedia.org/wiki?curid=2218269 |
Polymersome For in vivo applications, polymersomes are de facto limited to the use of FDA-approved polymers as most pharmaceutical firms are unlikely to develop novel polymers due to cost issues. Fortunately there are a number of such polymers available, with varying properties, including: "Hydrophilic blocks" "Hydroph... | https://en.wikipedia.org/wiki?curid=2218269 |
Sodium manganate is the inorganic compound with the formula NaMnO. This deep green solid is a rarely encountered analogue of the related salt KMnO. is rare because it cannot be readily prepared from the oxidation of manganese dioxide and sodium hydroxide. Instead this oxidation stops at the level of NaMnO, and this Mn(... | https://en.wikipedia.org/wiki?curid=2218718 |
Adatom An adatom is an atom that lies on a crystal surface, and can be thought of as the opposite of a surface vacancy. This term is used in surface chemistry and epitaxy, when describing single atoms lying on surfaces and surface roughness. The word is a portmanteau of "adsorbed atom". A single atom, a cluster of atom... | https://en.wikipedia.org/wiki?curid=2218753 |
Catherine wheel (firework) The Catherine wheel or pinwheel is a type of firework consisting either of a powder-filled spiral tube, or an angled rocket mounted with a pin through its center. When ignited, the energy of the fireworks not only create sparks and flame, but cause the wheel to quickly rotate, making the disp... | https://en.wikipedia.org/wiki?curid=2218995 |
Catherine wheel (firework) In the Philippines, Catherine wheel is also known as trompillo and according to Republic Act 7183, it is a legal firework. | https://en.wikipedia.org/wiki?curid=2218995 |
Calcium signaling is the use of calcium ions (Ca) to communicate and drive intracellular processes often as a step in signal transduction. Ca is important for cellular signalling, for once it enters the cytosol of the cytoplasm it exerts allosteric regulatory effects on many enzymes and proteins. Ca can act in signal t... | https://en.wikipedia.org/wiki?curid=2219538 |
Calcium signaling The mechanisms through which ICRAC occurs are currently still under investigation. Although Orai1 and STIM1, have been linked by several studies, for a proposed model of store-operated calcium influx. Recent studies have cited the phospholipase A2 beta, nicotinic acid adenine dinucleotide phosphate (N... | https://en.wikipedia.org/wiki?curid=2219538 |
Calcium signaling Once depolarized the sarcoplasmic reticulm (SR) releases Ca into the myoplasm where it will bind to a number of calcium sensitive buffers. The Ca in the myoplasm will diffuse to Ca regulator sites on the thin filaments. This leads to the actual contraction of the muscle. Contractions of smooth muscle ... | https://en.wikipedia.org/wiki?curid=2219538 |
Calcium signaling IP Ca release is caused by activation of the IP receptor on the SR. These influxes are often spontaneous and localized as seen in the colon and portal vein, but may lead to a global Ca wave as observed in many vascular tissues. In neurons, concomitant increases in cytosolic and mitochondrial Ca are im... | https://en.wikipedia.org/wiki?curid=2219538 |
Calcium signaling Ca influx during fertilization has been observed in many species as a trigger for development of the oocyte. These influxes may occur as a single increase in concentration as seen with fish and echinoderms, or may occur with the concentrations oscillating as observed in mammals. The triggers to these ... | https://en.wikipedia.org/wiki?curid=2219538 |
Selective catalytic reduction (SCR) is a means of converting nitrogen oxides, also referred to as with the aid of a catalyst into diatomic nitrogen (), and water (). A gaseous reductant, typically anhydrous ammonia, aqueous ammonia or urea, is added to a stream of flue or exhaust gas and is adsorbed onto a catalyst. Ca... | https://en.wikipedia.org/wiki?curid=2219841 |
Selective catalytic reduction Before entering the catalyst chamber the ammonia, or other reductant (such as urea), is injected and mixed with the gases. The chemical equation for a stoichiometric reaction using either anhydrous or aqueous ammonia for a selective catalytic reduction process is: With several secondary re... | https://en.wikipedia.org/wiki?curid=2219841 |
Selective catalytic reduction They also have a high catalysing potential to oxidize into , which can be extremely damaging due to its acidic properties. Zeolite catalysts have the potential to operate at substantially higher temperature than base metal catalysts; they can withstand prolonged operation at temperatures o... | https://en.wikipedia.org/wiki?curid=2219841 |
Selective catalytic reduction Anhydrous ammonia can be stored as a liquid at approximately 10 bar pressure in steel tanks. It is classified as an inhalation hazard, but it can be safely stored and handled if well-developed codes and standards are followed. Its advantage is that it needs no further conversion to operate... | https://en.wikipedia.org/wiki?curid=2219841 |
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