Transfer-matrix Method (combinatorics)

	Transfer-matrix Method (combinatorics) Transfer-matrix method may refer to: * Transfer-matrix method (statistical mechanics), a mathematical technique used to write the partition function into a simpler form. * Transfer-matrix method (optics) The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic wave, electromagnetic or acoustic waves through a stratified medium; a stack of thin films. This is, for example, relevant for the ..., a method to analyze the propagation of electromagnetic or acoustic waves through a stratified medium. * Ray transfer matrix analysis in geometric optics, a mathematical method for performing ray tracing calculations. * Transfer-matrix method (combinatorics), a method for computing the total weight of all walks of a given length between a pair of vertices in a weighted graph.{{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Transfer-matrix Method (statistical Mechanics) In statistical mechanics, the transfer-matrix method is a mathematical technique which is used to write the partition function into a simpler form. It was introduced in 1941 by Hans Kramers and Gregory Wannier. In many one dimensional lattice models, the partition function is first written as an ''n''-fold summation over each possible microstate, and also contains an additional summation of each component's contribution to the energy of the system within each microstate. Overview Higher-dimensional models contain even more summations. For systems with more than a few particles, such expressions can quickly become too complex to work out directly, even by computer. Instead, the partition function can be rewritten in an equivalent way. The basic idea is to write the partition function in the form : \mathcal = \mathbf_0 \cdot \left\ \cdot \mathbf_ where v0 and v''N''+1 are vectors of dimension ''p'' and the ''p'' × ''p'' matrices W''k'' are the so-called transfer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Transfer-matrix Method (optics) The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic wave, electromagnetic or acoustic waves through a stratified medium; a stack of thin films. This is, for example, relevant for the design of anti-reflective coatings and dielectric mirrors. The Reflection (physics), reflection of light from a single interface between two medium (optics), media is described by the Fresnel equations. However, when there are multiple Wiktionary:interface, interfaces, such as in the figure, the reflections themselves are also partially transmitted and then partially reflected. Depending on the exact path length, these reflections can Interference (wave propagation), interfere destructively or constructively. The overall reflection of a layer structure is the sum of an infinite number of reflections. The transfer-matrix method is based on the fact that, according to Maxwell's equations, there are simple continuity conditions for the elec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Ray Transfer Matrix Analysis Ray transfer matrix analysis (also known as ABCD matrix analysis) is a mathematical form for performing ray tracing calculations in sufficiently simple problems which can be solved considering only paraxial rays. Each optical element (surface, interface, mirror, or beam travel) is described by a ray transfer matrix which operates on a vector describing an incoming light ray to calculate the outgoing ray. Multiplication of the successive matrices thus yields a concise ray transfer matrix describing the entire optical system. The same mathematics is also used in accelerator physics to track particles through the magnet installations of a particle accelerator, see electron optics. This technique, as described below, is derived using the '' paraxial approximation'', which requires that all ray directions (directions normal to the wavefronts) are at small angles relative to the optical axis of the system, such that the approximation remains valid. A small further implies that t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]