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Intrinsic Hyperpolarizability
Intrinsic hyperpolarizability in physics, mathematics and statistics, is a Scale invariance, scale invariant quantity that can be used to compare molecules of different sizes. The intrinsic hyperpolarizability is defined as the hyperpolarizability divided by the Kuzyk Limit. This quantity is scale invariant and thus is independent of the energy scale and number of electrons in a molecule that is being evaluated for its nonlinear optical response. Therefore, it can be used to compare molecules of different shapes and sizes. The Intrinsic Hyperpolarizability can be used as a figure of merit for comparing molecules for their usefulness in electro-optics applications. See also *Molecular mechanics *Molecular modelling *Quantum chemistry References Nonlinear optics {{optics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale Invariance
In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry. *In mathematics, scale invariance usually refers to an invariance of individual functions or curves. A closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilations. It is also possible for the probability distributions of random processes to display this kind of scale invariance or self-similarity. *In classical field theory, scale invariance most commonly applies to the invariance of a whole theory under dilatations. Such theories typically describe classical physical processes with no characteristic length scale. *In quantum field theory, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperpolarizability
The hyperpolarizability, a nonlinear-optical property of a molecule, is the second-order electric susceptibility per unit volume. The hyperpolarizability can be calculated using quantum chemical calculations developed in several software packages. See nonlinear optics. Definition and higher orders The linear electric polarizability \alpha in isotropic media is defined as the ratio of the induced dipole moment \mathbf of an atom to the electric field \mathbf that produces this dipole moment. Therefore the dipole moment is :\mathbf=\alpha \mathbf In an isotropic medium \mathbf is in the same direction as \mathbf, i.e. \alpha is a scalar. In an anisotropic medium \mathbf and \mathbf can be in different directions and the polarisability is now a tensor. The total density of induced polarization is the product of the number density of molecules multiplied by the dipole moment of each molecule, i.e. :\mathbf = \rho \mathbf = \rho \alpha \mathbf = \varepsilon_0 \chi \mathbf, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kuzyk Limit
The Kuzyk quantum gap is a discrepancy between the maximum value of the nonlinear-optical susceptibility allowed by quantum mechanics and the highest values actually observed in real molecules. The highest possible value (in theory) is known as the Kuzyk limit, after its discoverer Professor Mark G. Kuzyk of Washington State University. Background In 2000, Professor Mark G. Kuzyk of Washington State University calculated the fundamental limit of the nonlinear-optical susceptibility of molecules. The nonlinear susceptibility is a measure of how strongly light interacts with matter. As such, these results can be used to predict the maximum attainable efficiency of various types of optical devices. For example, Kuzyk's theory can be used to estimate how efficiently optical information can be manipulated in an optical fiber (based on the Kerr effect), which in turn is related to the amount of information that a fiber-optic system can handle. In effect, the speed limit of the inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale Invariant
In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry. *In mathematics, scale invariance usually refers to an invariance of individual functions or curves. A closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilations. It is also possible for the probability distributions of random processes to display this kind of scale invariance or self-similarity. *In classical field theory, scale invariance most commonly applies to the invariance of a whole theory under dilatations. Such theories typically describe classical physical processes with no characteristic length scale. *In quantum field theory, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Figure Of Merit
A figure of merit is a quantity used to characterize the performance of a device, system or method, relative to its alternatives. Examples *Clock rate of a CPU * Calories per serving *Contrast ratio of an LCD *Frequency response of a speaker * Fill factor of a solar cell *Resolution of the image sensor in a digital camera *Measure of the detection performance of a sonar system, defined as the propagation loss for which a 50% detection probability is achieved *Noise figure of a radio receiver *The thermoelectric figure of merit, ''zT'', a material constant proportional to the efficiency of a thermoelectric couple made with the material *The figure of merit of digital-to-analog converter, calculated as (power dissipation)/(2ENOB × effective bandwidth) /Hz*Luminous efficacy of lighting * Profit of a company *Residual noise remaining after compensation in an aeromagnetic survey *Battery life of a laptop computer [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electro-optics
Electro–optics is a branch of electrical engineering, electronic engineering, materials science, and material physics involving components, electronic devices such as lasers, laser diodes, LEDs, waveguides, etc. which operate by the propagation and interaction of light with various tailored materials. It is closely related to the branch of optics, involving application of generation of photons, called photonics. It is not only concerned with the "electro–optic effect", since it deals with the interaction between the electromagnetic (optical) and the electrical (electronic) states of materials. Electro-optical devices The electro-optic effect is a change in the optical properties of an optically active material due to interaction with light. This interaction usually results in a change in the birefringence, and not simply the refractive index of the medium. In a Kerr cell, the change in birefringence is proportional to the square of the optical electric field, and the mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Mechanics
Molecular mechanics uses classical mechanics to model molecular systems. The Born–Oppenheimer approximation is assumed valid and the potential energy of all systems is calculated as a function of the nuclear coordinates using force fields. Molecular mechanics can be used to study molecule systems ranging in size and complexity from small to large biological systems or material assemblies with many thousands to millions of atoms. All-atomistic molecular mechanics methods have the following properties: * Each atom is simulated as one particle * Each particle is assigned a radius (typically the van der Waals radius), polarizability, and a constant net charge (generally derived from quantum calculations and/or experiment) * Bonded interactions are treated as ''springs'' with an equilibrium distance equal to the experimental or calculated bond length Variants on this theme are possible. For example, many simulations have historically used a ''united-atom'' representation in which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Modelling
Molecular modelling encompasses all methods, theoretical and computational, used to model or mimic the behaviour of molecules. The methods are used in the fields of computational chemistry, drug design, computational biology and materials science to study molecular systems ranging from small chemical systems to large biological molecules and material assemblies. The simplest calculations can be performed by hand, but inevitably computers are required to perform molecular modelling of any reasonably sized system. The common feature of molecular modelling methods is the atomistic level description of the molecular systems. This may include treating atoms as the smallest individual unit (a molecular mechanics approach), or explicitly modelling protons and neutrons with its quarks, anti-quarks and gluons and electrons with its photons (a quantum chemistry approach). Molecular mechanics Molecular mechanics is one aspect of molecular modelling, as it involves the use of classical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
