Adiabatic T matrix theory for three dimensional reactive scattering: Application to the (H, H2) system

1983 ◽  
Vol 78 (7) ◽  
pp. 4523-4532 ◽  
Author(s):  
J. C. Sun ◽  
B. H. Choi ◽  
R. T. Poe ◽  
K. T. Tang
Keyword(s):  
Matrix Theory ◽  
Three Dimensional ◽  
Reactive Scattering ◽  
T Matrix

scholarly journals Symmetric Boundary Condition for Laplacian on Net of Regular Hexagons

2017 ◽  
Vol 9 (3) ◽  
pp. 46
Author(s):  
Daniel Lee
Keyword(s):  
Boundary Condition ◽  
Matrix Theory ◽  
Three Dimensional ◽  
Cardiac Tissues ◽  
Energy Product ◽  
Symmetric Boundary Condition ◽  
Almost All ◽  
Wave Phenomena ◽  
Dimensional Cell ◽  
Theory Series

Hexagonal grid methods are found useful in many research works, including numerical modeling in spherical coordinates, in atmospheric and ocean models, and simulation of electrical wave phenomena in cardiac tissues. Almost all of these used standard Laplacian and mostly on one configuration of regular hexagons. In this work, discrete symmetric boundary condition and energy product for anisotropic Laplacian are investigated firstly on general net of regular hexagons, and then generalized to its most extent in two- or three-dimensional cell-center finite difference applications up to the usage of symmetric stencil in central differences. For analysis of Laplacian related applications, this provides with an approach in addition to the M-matrix theory, series method, functional interpolations and Fourier vectors.

UNIFIED VARIATIONAL PRINCIPLES FOR THE VON NEUMANN, MASTER AND BOLTZMANN-BLOCH EQUATIONS AND THE T-MATRIX

1995 ◽  
Vol 09 (10) ◽  
pp. 1227-1242
Author(s):  
MASUMI HATTORI ◽  
HUZIO NAKANO
Keyword(s):  
Density Matrix ◽  
Variational Principles ◽  
Matrix Theory ◽  
Bloch Equation ◽  
Irreversible Processes ◽  
Collision Term ◽  
Maximum Condition ◽  
Von Neumann ◽  
Maximum Problem ◽  
T Matrix

The variational principle of irreversible processes, which was previously presented for the von Neumann equation as a stationarity problem and then converted into a maximum problem by contracting the density matrix perturbatively, is reinvestigated w.r.t. the contraction of the density matrix. The present contraction relies on the T-matrix theory of scattering, where no perturbational consideration enters. By taking the electron transport in solids as a typical example, the contraction is performed in two steps: the even component of the density matrix as to time reversal is eliminated first and then the off-diagonal elements in the scheme of diagonalizing the unperturbed Hamiltonian. The maximum problem thus obtained is for the diagonal elements of the odd component of the density matrix. The maximum condition gives the master equation, which is reduced to the Boltzmann-Bloch equation in the scheme of one-body picture. It is noticeable in this equation that the collision term is given in terms of the T-matrix in scattering theory.

The Transition Matrix Formalism for the Scattering of an Alluvium on an Elastic Half-Space

2007 ◽  
Author(s):  
Wen-I Liao ◽  
Tsung-Jen Teng ◽  
Shiang-Jung Wang
Keyword(s):  
Half Space ◽  
Transition Matrix ◽  
Plane Waves ◽  
Three Dimensional ◽  
Scattering Matrix ◽  
Elastic Half Space ◽  
Basis Functions ◽  
Matrix Formalism ◽  
T Matrix ◽  
Singular Wave

This paper develops the transition matrix formalism for scattering from an three-dimensional alluvium on an elastic half-space. Betti’s third identity is employed to establish orthogonality conditions among basis functions that are Lamb’s singular wave functions. The total displacements and associated tractions exterior and interior to the surface are expanded in a Rayleigh series. The boundary conditions are applied and the T-matrix is derived. A linear transformation is utilized to construct a set of orthogonal basis functions. The transformed T-matrix is related to the scattering matrix and it is shown that the scattering matrix is symmetric and unitary and that the T-matrix is symmetric. Typical numerical results obtained by incident plane waves for verification are presented.

Quantum dynamics with real wave packets, including application to three-dimensional (J=0)D+H2→HD+H reactive scattering

1998 ◽  
Vol 108 (3) ◽  
pp. 950-962 ◽  
Author(s):  
Stephen K. Gray ◽  
Gabriel G. Balint-Kurti
Keyword(s):  
Quantum Dynamics ◽  
Wave Packets ◽  
Three Dimensional ◽  
Reactive Scattering

Light scattering by anisotropic spherical particles: Rayleigh-Gans approximation versus T-matrix theory

2002 ◽  
Author(s):  
Alexei D. Kiselev ◽  
A. A. Panyukov ◽  
Victor Y. Reshetnyak ◽  
Timothy J. Sluckin
Keyword(s):  
Light Scattering ◽  
Matrix Theory ◽  
Spherical Particles ◽  
T Matrix

Three-dimensional quantum mechanical studies of D+H2→HD+H reactive scattering. II

1975 ◽  
Vol 63 (7) ◽  
pp. 2854 ◽  
Author(s):  
B. H. Choi ◽  
K. T. Tang
Keyword(s):  
Three Dimensional ◽  
Quantum Mechanical ◽  
Reactive Scattering ◽  
Mechanical Studies
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