Spectral Methods in Chemistry and Physics

Applications to Kinetic Theory and Quantum Mechanics

Nonfiction, Science & Nature, Science, Chemistry, Physical & Theoretical, Physics, Mathematical Physics
Cover of the book Spectral Methods in Chemistry and Physics by Bernard Shizgal, Springer Netherlands
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Bernard Shizgal ISBN: 9789401794541
Publisher: Springer Netherlands Publication: January 7, 2015
Imprint: Springer Language: English
Author: Bernard Shizgal
ISBN: 9789401794541
Publisher: Springer Netherlands
Publication: January 7, 2015
Imprint: Springer
Language: English

This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of interest and to a wide audience. While spectral methods are generally based on Fourier Series or Chebychev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in the book. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, in elastic scattering theory and other applications. The subject matter includes the calculation of transport coefficients in gases and other gas dynamical problems based on spectral and pseudospectral solutions of the Boltzmann equation. Radiative transfer in astrophysics and atmospheric science, and applications to space physics are discussed.  The relaxation of initial non-equilibrium distributions to equilibrium for several different systems is studied with the Boltzmann and Fokker-Planck equations.
The eigenvalue spectra of the linear operators in the Boltzmann, Fokker-Planck and Schrödinger equations are studied with spectral and pseudospectral methods based on non-classical orthogonal polynomials.
The numerical methods referred to as the Discrete Ordinate Method, Differential Quadrature, the Quadrature Discretization Method, the Discrete Variable Representation, the Lagrange Mesh Method, and others are discussed and compared.
MATLAB codes are provided for most of the numerical results reported in the book - see Link under 'Additional Information' on the the right-hand column.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of interest and to a wide audience. While spectral methods are generally based on Fourier Series or Chebychev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in the book. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, in elastic scattering theory and other applications. The subject matter includes the calculation of transport coefficients in gases and other gas dynamical problems based on spectral and pseudospectral solutions of the Boltzmann equation. Radiative transfer in astrophysics and atmospheric science, and applications to space physics are discussed.  The relaxation of initial non-equilibrium distributions to equilibrium for several different systems is studied with the Boltzmann and Fokker-Planck equations.
The eigenvalue spectra of the linear operators in the Boltzmann, Fokker-Planck and Schrödinger equations are studied with spectral and pseudospectral methods based on non-classical orthogonal polynomials.
The numerical methods referred to as the Discrete Ordinate Method, Differential Quadrature, the Quadrature Discretization Method, the Discrete Variable Representation, the Lagrange Mesh Method, and others are discussed and compared.
MATLAB codes are provided for most of the numerical results reported in the book - see Link under 'Additional Information' on the the right-hand column.

More books from Springer Netherlands

Cover of the book Reason and World by Bernard Shizgal
Cover of the book Developmental Education for Young Children by Bernard Shizgal
Cover of the book Membrane Technology: Applications to Industrial Wastewater Treatment by Bernard Shizgal
Cover of the book Applied Computational Genomics by Bernard Shizgal
Cover of the book A Theodicy of Hell by Bernard Shizgal
Cover of the book On the Death of the Pilgrim: The Postcolonial Hermeneutics of Jarava Lal Mehta by Bernard Shizgal
Cover of the book Computer Aided Seismic and Fire Retrofitting Analysis of Existing High Rise Reinforced Concrete Buildings by Bernard Shizgal
Cover of the book Liberalism by Bernard Shizgal
Cover of the book The Dependence Phenomenon by Bernard Shizgal
Cover of the book Sulfur Metabolism in Plants by Bernard Shizgal
Cover of the book Accounting for the Public Interest by Bernard Shizgal
Cover of the book The Second Empire and the Press by Bernard Shizgal
Cover of the book The Arterial System in Hypertension by Bernard Shizgal
Cover of the book The Nature of General Family Practice by Bernard Shizgal
Cover of the book Coral Reefs of the Gulf by Bernard Shizgal
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy