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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)
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
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
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
(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
microscope Scattering Scattering-matrix method Scattering (optics) Scattering channel Scattering cross-section Scattering from rough surfaces Scattering length
Index_of_physics_articles_(S)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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
Technique in computational electromagnetism
incorporated. It cannot be used for scattering analysis. Being a Fourier-space method, Gibbs phenomenon affects the method's accuracy. This is particularly
Plane_wave_expansion_method
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
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
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
Multi-photon microscopy technique
techniques in CRS microscopy are stimulated Raman scattering (SRS) and coherent anti-Stokes Raman scattering (CARS). SRS and CARS were theoretically predicted
Coherent Raman scattering microscopy
Coherent_Raman_scattering_microscopy
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
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
Statistical property
matrices B and C are heteroscedastic. In matrix B, the variance is time-varying, increasing steadily across time; in matrix C, the variance depends on the value
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
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
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
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
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
Pictorial representation of the behavior of subatomic particles
between scattering and correlation functions is the LSZ-theorem: The scattering amplitude for n particles to go to m particles in a scattering event is
Feynman_diagram
Correlation of a signal with a time-shifted copy of itself, as a function of shift
autocorrelation matrix is a Hermitian matrix for complex random vectors and a symmetric matrix for real random vectors. The autocorrelation matrix is a positive
Autocorrelation
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 interaction in quantum physics
1)-dimensional matrix. The fine electronic structure can be directly detected by many different spectroscopic methods, including the inelastic neutron scattering (INS)
Spin–orbit_interaction
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
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
spectroscopic methods. Spectroscopic implementations include elastic light scattering and light scattering spectroscopy. Light scattering spectroscopy
Diagnostic_microbiology
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
in the late 1970s and early 1980s concerning the quantum inverse scattering method. The name Yangian was introduced by Vladimir Drinfeld in 1985 in honor
Yangian
SCATTERING MATRIX-METHOD
SCATTERING MATRIX-METHOD
Female
Welsh
Welsh form of Old French Caterine, CATRIN means "pure."
Male
English
Anglicized form of Irish Gaelic MainchÃn, MANNIX means "little monk."
Female
English
French form of Latin Maria, MARIE means "obstinacy, rebelliousness" or "their rebellion."
Male
Italian
Italian form of Hebrew Mattithyah, MATTIA means "gift of God."
Biblical
scattering the battle
Male
English
Pet form of English Matthew, MATTIE means "gift of God." Compare with feminine Mattie.
Girl/Female
Biblical
Scattering the battle.
Female
Finnish
Finnish form of Greek Maria, MAARIA means "obstinacy, rebelliousness" or "their rebellion."Â
Female
Finnish
Pet form of Finnish Katariina, KATRI means "pure."
Male
French
 French form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Male
French
French and German form of Greek Mattathias, MATHIS means "gift of God."
Male
English
Pet form of English Martin, MARTIE means "of/like Mars."
Male
Hungarian
Czech and Hungarian form of Greek Patrikios, PATRIK means "patrician, of noble descent."
Girl/Female
Arabic, Australian, Basque, French, Latin
Lady; Feminine of Martin; Warlike
Female
German
Pet form of German Katarine, KATRIN means "pure."
Girl/Female
Maori
The Maori form of April.
Female
English
Pet form of English Matilda, MATTIE means "mighty in battle." Compare with masculine Mattie.
Male
English
 English form of Roman Latin Martinus, MARTIN means "of/like Mars." Compare with another form of Martin.
Female
Finnish
Finnish form of Greek Margarites, MAARIT means "pearl."
Female
English
English form of Latin Viatrix, BEATRIX means "voyager (through life)."
SCATTERING MATRIX-METHOD
SCATTERING MATRIX-METHOD
Girl/Female
Indian
Flower
Girl/Female
Hindu, Indian
Shining
Girl/Female
Indian
Love; Beautiful
Girl/Female
Tamil
Darling girl
Girl/Female
English
Abbreviation of Patricia: noble.
Girl/Female
Hindu, Indian, Marathi, Oriya
Beautiful
Girl/Female
Muslim
Beautiful Angel, Night
Girl/Female
Hindu, Indian, Marathi
Fame
Girl/Female
Hindu
Fixed zodiac without precession
Boy/Male
Australian, Vietnamese
Scenery; Environment; Something that Spreads out Limitlessly; Supports Life; Is Colorful with Trees; Grass; Flowers and Fruit
SCATTERING MATRIX-METHOD
SCATTERING MATRIX-METHOD
SCATTERING MATRIX-METHOD
SCATTERING MATRIX-METHOD
SCATTERING MATRIX-METHOD
p. pr. & vb. n.
of Scatter
pl.
of Maori
a.
Of or pertaining to the meter as a standard of measurement; of or pertaining to the decimal system of measurement of which a meter is the unit; as, the metric system; a metric measurement.
n.
The act of scattering or spreading.
n.
See Matrix.
a.
Of or pertaining to the Maoris or to their language.
a.
Flattering; sycophantic.
n.
A mold; a matrix.
a.
Going or falling in various directions; not united or aggregated; divided among many; as, scattering votes.
pl.
of Matrix
adv.
In a scattering manner; dispersedly.
a.
That flatters (in the various senses of the verb); as, a flattering speech.
n.
Act of strewing about; something scattered.
v. t.
To spirt in a scattering manner.
n.
Blattering.
a.
Flattering; deceitful.
adv.
With clattering.
n.
Superficial knowledge; a smattering.
n.
The act of sprinkling or scattering.