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electromagnetics, the scattering-matrix method (SMM) is a numerical method used to solve Maxwell's equations, related to the transfer-matrix method. SMM can, for
Scattering-matrix_method
Technique for computing light scattering by nonspherical particles
The transition matrix method (T-matrix method or TMM) is a computational technique of light scattering by nonspherical particles originally formulated
T-matrix_method
Mathematical method used in optics and acoustics
The transfer-matrix method is a method used in optics and acoustics to analyze the propagation of electromagnetic or acoustic waves through a stratified
Transfer-matrix method (optics)
Transfer-matrix_method_(optics)
Method used to solve integrable many-body quantum systems
Lax matrix features heavily and scattering data is used to construct solutions to the original system. While the classical inverse scattering method is
Quantum inverse scattering method
Quantum_inverse_scattering_method
Topics referred to by the same term
frequencies Maxwell (microarchitecture), a GPU microarchitecture Scattering-matrix method, to solve Maxwell's equations Storage modification machine, a type
SMM
Numerical analysis technique
Eigenmode expansion Beam propagation method Finite-difference frequency-domain Finite element method Scattering-matrix method Discrete dipole approximation J
Finite-difference time-domain method
Finite-difference_time-domain_method
Numerical technique
Multipole Method for Electromagnetic Scattering Computation,” IEEE Transactions on Antennas and Propagation 40, 634–641. "The Fast Multipole Method". Archived
Fast_multipole_method
problem of nuclear reactions is to relate the values of the scattering or collision matrix elements (which in principle can be obtained from measurements)
R-matrix
is a method for the simulation of the elastic scattering of an electron beam with matter, including all multiple scattering effects. The method is reviewed
Multislice
Method of computing electromagnetic fields
solution of 2-dimensional scattering problems using a transmission-line matrix", with Peter B. Johns in 1971. The TLM method is based on Huygens' model
Transmission-line matrix method
Transmission-line_matrix_method
Binary operation
widely adopted in computational methods for scattering matrices. Given two scattering matrices from different linear scatterers, the Redheffer star product
Redheffer_star_product
Matrix decomposition
in coherent electromagnetic scattering theory, the linear transformation A represents the action performed by the scattering object, and the eigenvectors
Eigendecomposition of a matrix
Eigendecomposition_of_a_matrix
Mechanism of light transport
skin, the broadest scattering is in red, then green, and blue has very little scattering.[citation needed] A major benefit of this method is its independence
Subsurface_scattering
Matrix-valued random variable
random matrix. For larger atoms, the distribution of the energy eigenvalues of the Hamiltonian could be computed in order to approximate scattering cross
Random_matrix
Range of physical processes in physics
physics the quantum interaction and scattering of fundamental particles is described by the Scattering Matrix or S-Matrix, introduced and developed by John
Scattering
Matrix representing the effect of scattering on a physical system
the S-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering process
S-matrix
Process by which dust, particulates, etc. scatter light
electromagnetic scattering by spheres Codes for electromagnetic scattering by cylinders Discrete dipole approximation codes Finite-difference time-domain method Scattering
Light_scattering_by_particles
Values which describe behavior of a linear electric circuit
Scattering parameters or S-parameters are the elements of a scattering matrix or S-matrix which describe the steady state response of linear electrical
Scattering_parameters
Form of radar used to create images of landscapes
covariance matrix. The method is based on simple physical scattering mechanisms (surface scattering, double-bounce scattering, and volume scattering). The
Synthetic-aperture_radar
Scattering of light by tiny particles in a colloidal suspension
scattering by particles in a colloid such as a very fine suspension (a sol). Also known as Tyndall scattering, it is similar to Rayleigh scattering,
Tyndall_effect
Scattering of an electromagnetic plane wave by a sphere
Lorenz–Mie solution, the Lorenz–Mie–Debye solution or Mie scattering) describes the scattering of an electromagnetic plane wave by a homogeneous sphere
Mie_scattering
Concepts from linear algebra
iterative method to compute eigenvalues and eigenvectors, among several other possibilities. Most numeric methods that compute the eigenvalues of a matrix also
Eigenvalues_and_eigenvectors
R-Matrix codes are a set of software routines used to calculate the effects of collision of electrons with atoms and molecules. The R-matrix method is
UK_Molecular_R-matrix_Codes
Branch of physics
finite element methods); matrix products (when using transfer matrix methods); calculating numerical integrals (when using the method of moments); using
Computational electromagnetics
Computational_electromagnetics
Theory for waves passing through multiple obstacles
waves traveling through porous media, light scattering from water droplets in a cloud, or x-rays scattering from a crystal. A more recent application is
Multiple_scattering_theory
Array of numbers
particles with specific and distinct masses. Another matrix serves as a key tool for describing the scattering experiments that form the cornerstone of experimental
Matrix_(mathematics)
Numerical solution method of computational electromagnetics
frequency-domain finite-difference methods, the title seems to mostly describe the method as applied to scattering problems. The method shares many similarities
Finite-difference frequency-domain method
Finite-difference_frequency-domain_method
American mathematician and physicist (1928–2012)
computation of wave scattering in electromagnetics, optics and acoustics. He has introduced the extended boundary condition and T-matrix methods, widely used
Peter_C._Waterman
Category of proteins
single-molecule experiment, wide-angle X-ray scattering, small-angle X-ray scattering, wide-angle X-ray scattering (WAXS), Nuclear magnetic resonance (NMR)
Dark_proteome
Precursor physical model to string theory and quantum chromodynamics
antiparticle scattering are the analytic continuation of particle scattering amplitudes. Dispersion relations: the values of the S-matrix can be calculated
S-matrix_theory
Numerical method in computational electromagnetics
addition to its use in electrical engineering, the method of moments has been applied to light scattering and plasmonic problems. An inhomogeneous integral
Method of moments (electromagnetics)
Method_of_moments_(electromagnetics)
American atmospheric scientist (1959–2020)
He is best known for his contributions to the T-matrix method for the computation of light scattering by complex particles and clusters, and atmospheric
Michael_I._Mishchenko
calculation of scattering from direction s ′ {\displaystyle \mathbf {s'} } to direction s {\displaystyle \mathbf {s} } . In the discrete ordinates method, the full
Discrete_ordinates_method
Computational electrodynamics technique
powerful method. As can be seen from the mathematical formulation, the algorithm is inherently bi-directional. It uses the scattering matrix (S-matrix) technique
Eigenmode_expansion
Plot using the dispersal of scattered dots to show the relationship between variables
Xk, the scatter plot matrix shows all the pairwise scatter plots of the variables on a single view with multiple scatterplots in a matrix format. For
Scatter_plot
microscope Scattering Scattering-matrix method Scattering (optics) Scattering channel Scattering cross-section Scattering from rough surfaces Scattering length
Index_of_physics_articles_(S)
Optical filter
Radomes Using the Method of Moments Tsao, Chich-Hsing; Mittra, Raj (1982), "A Spectral Iteration Approach for Analyzing Scattering from Frequency Selective
Frequency_selective_surface
Semi-analytic method of computational electromagnetism
Fourier modal method (FMM), is a semi-analytical method in computational electromagnetics that is most typically applied to solve scattering from periodic
Rigorous coupled-wave analysis
Rigorous_coupled-wave_analysis
Experiment in quantum physics
electron, the electron detection essentially occurs at their scattering site. Thus the scattering volume must be situated within the electron counter. The
Bothe–Geiger coincidence experiment
Bothe–Geiger_coincidence_experiment
Matrices satisfying a differential equation
{\displaystyle \psi } in the scattering region, compute L ( t ) {\displaystyle L(t)} and/or u ( t , x ) . {\displaystyle u(t,x).} If the Lax matrix additionally depends
Lax_pair
Mathematical tool in quantum physics
In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed
Density_matrix
In quantum mechanics, and in particular in scattering theory, the Feshbach–Fano method, named after Herman Feshbach and Ugo Fano, separates (partitions)
Feshbach–Fano_partitioning
System for describing optical polarization
Mueller calculus is a matrix method for manipulating Stokes vectors, which represent the polarization of light. It was developed in 1943 by Hans Mueller
Mueller_calculus
extinction matrix, a → {\displaystyle {\vec {a}}} is the absorption vector, B is the Planck function and Z is the scattering phase matrix. All the coefficient
Vector_radiative_transfer
(KKR) method is used to calculate the electronic band structure of periodic solids. In the derivation of the method using multiple scattering theory
Korringa–Kohn–Rostoker_method
Measure of covariance of components of a random vector
covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the
Covariance_matrix
Probabilistic problem-solving algorithm
Hessian matrix of the negative log-likelihood function that may be averaged to form an estimate of the Fisher information matrix. Monte Carlo methods are
Monte_Carlo_method
Quantum scattering theory T-matrix method Green's operator R.G. Newton, Scattering Theory of Waves and Particles Newton, Roger G. (2002). Scattering Theory
Schwinger variational principle
Schwinger_variational_principle
Statistical distance measure
and covariance matrix can be quite sensitive to outliers, therefore other approaches for calculating the multivariate location and scatter of data are also
Mahalanobis_distance
Spectroscopic technique
identified. Raman spectroscopy relies upon inelastic scattering of photons, known as Raman scattering. A source of monochromatic light, usually from a laser
Raman_spectroscopy
Photographic image processing tecnhique
covariance matrix method". Photogrammetric Engineering and Remote Sensing. 47: 1469–1476. Potter, J. F. (1984). "The channel correlation method for estimating
Atmospheric_correction
Formulation of quantum mechanics
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually
Matrix_mechanics
Ukrainian-American theoretical and computational physicist
data, photoionization, and electron scattering. A problem arose, because spurious solutions affected the R-matrix that joins the outer and inner regions
Oleg_Zatsarinny
Method for computing radiation
numerical method for computing the scattering and absorption of electromagnetic radiation by particles of arbitrary shape and composition. The method represents
Discrete_dipole_approximation
Deviation of electrons from their original trajectories
electron scattering occurs and the beam passes straight through. Single scattering: when an electron is scattered just once. Plural scattering: when electron(s)
Electron_scattering
Theory in particle physics
S-matrix for infinitely many particle types. The Regge hypothesis would determine the spectrum, crossing and analyticity would determine the scattering
Bootstrap_model
reason why the S matrix which maps the in states onto the out states must be unitary. The scattering channel are also called scattering asymptotes. The
Scattering_channel
Analytical method
process of measuring the loss of intensity of transmitted light due to the scattering effect of particles suspended in it. Light is passed through a filter
Turbidimetry
Software packages using DDA
calculation of standard scattering quantities. Computational electromagnetics Mie theory Finite-difference time-domain method Method of moments (electromagnetics)
Discrete dipole approximation codes
Discrete_dipole_approximation_codes
Method for finding the exact solution of certain quantum mechanics models
function can be represented entirely in terms of two-body scattering states. The overall scattering matrix equals the ordered product of these pairwise matrices
Bethe_ansatz
Method for structure analysis of biological materials
Biological small-angle scattering is a small-angle scattering method for structure analysis of biological materials. Small-angle scattering is used to study
Biological small-angle scattering
Biological_small-angle_scattering
the Matrix elements are commonly found by Fourier expanding the Hamiltonian H', as in the case of Impurity scattering or acoustic phonon scattering. In
Monte Carlo methods for electron transport
Monte_Carlo_methods_for_electron_transport
make a unitary S-matrix. But without extra assumptions on the high-energy behavior, unitarity is not enough to determine the scattering, and the proposal
History_of_string_theory
Indian academic
formulated the quantum scattering theory in two dimensions using Lippmann–Schwinger equations and the asymptotic wave function for scattering. From 2002 to 2009
Sadhan_Kumar_Adhikari
participated in the scattering process. Physical concepts of two-body elastic scattering are the basis of several nuclear methods for elemental material
Elastic_recoil_detection
The method of continued fractions is a method developed specifically for solution of integral equations of quantum scattering theory like Lippmann–Schwinger
Method_of_continued_fractions
Matrices similar to diagonal matrices
linear algebra, a square matrix A {\displaystyle A} is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there exists
Diagonalizable_matrix
Equation used in quantum scattering problems
particle collisions – or, more precisely, scattering – in quantum mechanics. It may be used in scattering of molecules, atoms, neutrons, photons or any
Lippmann–Schwinger_equation
Infinite sequence of differential equations
linear phase evolutions on the same scattering data. Thus the inverse scattering transform provides a common solution method for all flows of the hierarchy
Korteweg–De_Vries_hierarchy
Codes for electromagnetic scattering by spheres - this article list codes for electromagnetic scattering by a homogeneous sphere, layered sphere, and cluster
Codes for electromagnetic scattering by spheres
Codes_for_electromagnetic_scattering_by_spheres
Process of calculating the causal factors that produced a set of observations
of the inverse scattering problem especially by Gelfand and Levitan in the Soviet Union. They proposed an analytic constructive method for determining
Inverse_problem
the scattering matrix, ϕ ( s ) {\displaystyle \phi (s)} . The order of the zero equals the order of the corresponding pole of the scattering matrix. The
Selberg_zeta_function
Method of depicting site stratigraphy
The Harris matrix is a tool used to depict the temporal succession of archaeological contexts and thus the sequence of depositions and surfaces on a 'dry
Harris_matrix
Periodicity computation method
least-squares method is well explained in (Strutz, 2017). A data vector Φ is represented as a weighted sum of sinusoidal basis functions, tabulated in a matrix A
Least-squares spectral analysis
Least-squares_spectral_analysis
Scientific journal
in optics and spectroscopy, including light scattering, radiative heat transfer and computational methods. Its founding editor-in-chief was Stanford S
Journal of Quantitative Spectroscopy and Radiative Transfer
Journal_of_Quantitative_Spectroscopy_and_Radiative_Transfer
Generalized version of classical Green's function
G^{*}=G+GpG^{*}\qquad \qquad (13)} The MSGF method consists of solving Eq. (13) for G* by using the matrix partitioning technique or double Fourier transform
Multiscale_Green's_function
Mathematical problems related to differential equations
inverse scattering. Riemann–Hilbert problems have applications to several related classes of problems. A. Integrable models The inverse scattering or inverse
Riemann–Hilbert_problem
Method for estimating the unknown parameters in a linear regression model
multicollinearity in the predictors. For standard least squares estimation methods, the design matrix X must have full column rank p: Pr [ rank ( X ) = p ] = 1. {\displaystyle
Ordinary_least_squares
Process of reducing the number of random variables under consideration
covariance (and sometimes the correlation) matrix of the data is constructed and the eigenvectors on this matrix are computed. The eigenvectors that correspond
Dimensionality_reduction
Microwave remote sensing specialist
coherency matrix in real space based on the greatest value of degree of polarization (DOP) commonly termed as adaptive general four-component scattering power
Avik_Bhattacharya
Boston Consulting Group business analysis method
The growth–share matrix (also known as the product portfolio matrix, Boston Box, BCG-matrix, Boston matrix, Boston Consulting Group portfolio analysis
Growth–share_matrix
Assumption that motions of nuclei and electrons can be separated
Hilbert space in the given region in configuration space. To study the scattering process taking place on the two lowest surfaces, one extracts from the
Born–Oppenheimer approximation
Born–Oppenheimer_approximation
Theorem in physics
general law of wave scattering theory, which relates the zero-angle scattering amplitude to the total cross section of the scatterer. It is usually written
Optical_theorem
analysis: Sparse matrix Band matrix Bidiagonal matrix Tridiagonal matrix Pentadiagonal matrix Skyline matrix Circulant matrix Triangular matrix Diagonally dominant
List of numerical analysis topics
List_of_numerical_analysis_topics
Statistics concept
_{m}x_{i}^{m}+\varepsilon _{i}\ (i=1,2,\dots ,n)} can be expressed in matrix form in terms of a design matrix X {\displaystyle \mathbf {X} } , a response vector y →
Polynomial_regression
Chemical-analysis technique
couples a light scattering instrument, most commonly multi-angle light scattering (MALS) or another form of static light scattering (SLS), but possibly
Size-exclusion_chromatography
Imaging technique based on fluorescence
This technique also has the advantage of minimizing the effect of photon scattering in thick layers of sample. Being dependent on the micro-environment, lifetime
Fluorescence-lifetime imaging microscopy
Fluorescence-lifetime_imaging_microscopy
Belgian mathematician (1921–1999)
Belevitch first introduced the important idea of the scattering matrix (called repartition matrix by Belevitch). This work was reproduced in part in a
Vitold_Belevitch
Statistical method
components or factors to retain. By this method, components are maintained as long as the variance in the correlation matrix represents systematic variance, as
Factor_analysis
Relativistic quantum mechanical wave equation
various scattering processes. In particular, the Klein–Nishina formula, looking at photon-electron scattering, was also derived in 1928. Mott scattering, the
Dirac_equation
Display that uses the light-modulating properties of liquid crystals
Nester and J. Tults demonstrated the concept in 1968 with an 18x2 matrix dynamic scattering mode (DSM) LCD that used standard discrete MOSFETs. On December
Liquid-crystal_display
Laboratory technique
motion, gravitational settling of the particle and light scattering (Rayleigh and Mie scattering) of the particles. The particle size can have considerable
Particle_size_analysis
Method of data analysis
advanced matrix-free methods, such as the Lanczos algorithm or the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method. Subsequent
Principal_component_analysis
Mathematical model of waves on a shallow water surface
scattering method (ISM). In fact, Clifford Gardner, John M. Greene, Martin Kruskal and Robert Miura developed the classical inverse scattering method
Korteweg–De_Vries_equation
thus completely integrable. The Lax pair is a 3x3 matrix pair, to which the inverse scattering method can be applied, using techniques by Fokas. The class
Three-wave_equation
Approximation method in statistics
In regression analysis, least squares is a method to determine the best-fit model by minimizing the sum of the squared residuals—the differences between
Least_squares
Electric circuit with two pairs of terminals
impedance. Admittance parameters Impedance parameters Scattering parameters Transfer-matrix method (optics) for reflection/transmission calculation of light
Two-port_network
American mathematician (born 1940)
inverse scattering problem is proved. Exact inversion of low-frequency scattering data is given in the book. A powerful method, Property C method, based
Alexander_Ramm
approaches to calculations of light scattering by particles. Ray tracing techniques can be applied to study light scattering by spherical and non-spherical
Atmospheric optics ray-tracing codes
Atmospheric_optics_ray-tracing_codes
Method of estimating the parameters of a statistical model, given observations
triangular matrix and Γ T {\displaystyle \Gamma ^{\mathsf {T}}} is its transpose. In practice, restrictions are usually imposed using the method of Lagrange
Maximum_likelihood_estimation
SCATTERING MATRIX-METHOD
SCATTERING MATRIX-METHOD
SCATTERING MATRIX-METHOD
SCATTERING MATRIX-METHOD
SCATTERING MATRIX-METHOD
SCATTERING MATRIX-METHOD
SCATTERING MATRIX-METHOD
SCATTERING MATRIX-METHOD
SCATTERING MATRIX-METHOD