Spectral Methods In Chemistry And Physics

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Spectral Methods In Chemistry And Physics

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Author : Bernard Shizgal
language : en
Publisher: Springer
Release Date : 2015-01-07

Spectral Methods In Chemistry And Physics written by Bernard Shizgal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-07 with Science categories.

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.

Chebyshev And Fourier Spectral Methods

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Author : John P. Boyd
language : en
Publisher: Courier Corporation
Release Date : 2013-06-05

Chebyshev And Fourier Spectral Methods written by John P. Boyd and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Mathematics categories.

Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.

Learning With Fractional Orthogonal Kernel Classifiers In Support Vector Machines

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Author : Jamal Amani Rad
language : en
Publisher: Springer Nature
Release Date : 2023-03-18

Learning With Fractional Orthogonal Kernel Classifiers In Support Vector Machines written by Jamal Amani Rad and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-18 with Mathematics categories.

This book contains select chapters on support vector algorithms from different perspectives, including mathematical background, properties of various kernel functions, and several applications. The main focus of this book is on orthogonal kernel functions, and the properties of the classical kernel functions—Chebyshev, Legendre, Gegenbauer, and Jacobi—are reviewed in some chapters. Moreover, the fractional form of these kernel functions is introduced in the same chapters, and for ease of use for these kernel functions, a tutorial on a Python package named ORSVM is presented. The book also exhibits a variety of applications for support vector algorithms, and in addition to the classification, these algorithms along with the introduced kernel functions are utilized for solving ordinary, partial, integro, and fractional differential equations. On the other hand, nowadays, the real-time and big data applications of support vector algorithms are growing. Consequently, the Compute Unified Device Architecture (CUDA) parallelizing the procedure of support vector algorithms based on orthogonal kernel functions is presented. The book sheds light on how to use support vector algorithms based on orthogonal kernel functions in different situations and gives a significant perspective to all machine learning and scientific machine learning researchers all around the world to utilize fractional orthogonal kernel functions in their pattern recognition or scientific computing problems.

Chemistry At The Frontier With Physics And Computer Science

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Author : Sergio Rampino
language : en
Publisher: Elsevier
Release Date : 2022-05-16

Chemistry At The Frontier With Physics And Computer Science written by Sergio Rampino and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-16 with Science categories.

Chemistry at the Frontier with Physics and Computer Science: Theory and Computation shows how chemical concepts relate to their physical counterparts and can be effectively explored via computational tools. It provides a holistic overview of the intersection of these fields and offers practical examples on how to solve a chemical problem from a theoretical and computational perspective, going from theory to models, methods and implementation. Sections cover both sides of the Born-Oppenheimer approximation (nuclear dynamics and electronic structure), chemical reactions, chemical bonding, and cover theory to practice on three related physical problems (wavepacket dynamics, Hartree-Fock equations and electron-cloud redistribution). Drawing on the interdisciplinary knowledge of its expert author, this book provides a contemporary guide to theoretical and computational chemistry for all those working in chemical physics, physical chemistry and related fields. - Combines a 'big picture' overview of chemistry as it relates to physics and computer science, including detailed guidance on tackling chemistry problems from both theoretical and computational perspectives - Treats nuclear dynamics and electronic structure on the same footing in discussions of the Born-Oppenheimer approximation - Includes examples of scientific programming in modern Fortran for problems related to the modeling of chemical reaction dynamics and the analysis of chemical bonding

Energy Research Abstracts

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Author :
language : en
Publisher:
Release Date : 1992

Energy Research Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Power resources categories.

Computing Methods In Applied Sciences And Engineering

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Author : R. Glowinski
language : en
Publisher: SIAM
Release Date : 1990-01-01

Computing Methods In Applied Sciences And Engineering written by R. Glowinski and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Science categories.

"Proceedings of the Ninth International Conference on Computing Methods in Applied Sciences and Engineering, Paris, France, January 29-February 2, 1990"--T.p. verso.

Stochastic Processes Multiscale Modeling And Numerical Methods For Computational Cellular Biology

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Author : David Holcman
language : en
Publisher: Springer
Release Date : 2017-10-04

Stochastic Processes Multiscale Modeling And Numerical Methods For Computational Cellular Biology written by David Holcman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-04 with Mathematics categories.

This book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of stochastic reaction-diffusion models, while in the latter, one can describe the processes by adopting the framework of Markov jump processes and stochastic differential equations. Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology will appeal to graduate students and researchers in the fields of applied mathematics, biophysics, and cellular biology.

Nuclear Science Abstracts

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Author :
language : en
Publisher:
Release Date : 1973

Nuclear Science Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Nuclear energy categories.

Scientific And Technical Aerospace Reports

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Author :
language : en
Publisher:
Release Date : 1995

Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Aeronautics categories.

Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Computational Methods For Physicists

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Author : Simon Sirca
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-17

Computational Methods For Physicists written by Simon Sirca and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-17 with Science categories.

This book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues as well as to the ways to optimize program execution speeds. Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a weekly basis in a one- or two-semester course. In these end-of-chapter problems the physics background is pronounced, and the main text preceding them is intended as an introduction or as a later reference. Less stress is given to the explanation of individual algorithms. It is tried to induce in the reader an own independent thinking and a certain amount of scepticism and scrutiny instead of blindly following readily available commercial tools.