Spectral Methods In Chemistry And Physics

Author : Bernard Shizgal
Publisher : Springer
Page : 431 pages
File Size : 46,9 Mb
Release : 2015-01-07
Category : Science
ISBN : 9789401794541

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Spectral Methods in Chemistry and Physics by Bernard Shizgal Pdf

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.

Author : George Rawitscher,Victo dos Santos Filho,Thiago Carvalho Peixoto
Publisher : Springer
Page : 221 pages
File Size : 47,8 Mb
Release : 2018-10-24
Category : Science
ISBN : 9783319427034

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An Introductory Guide to Computational Methods for the Solution of Physics Problems by George Rawitscher,Victo dos Santos Filho,Thiago Carvalho Peixoto Pdf

This monograph presents fundamental aspects of modern spectral and other computational methods, which are not generally taught in traditional courses. It emphasizes concepts as errors, convergence, stability, order and efficiency applied to the solution of physical problems. The spectral methods consist in expanding the function to be calculated into a set of appropriate basis functions (generally orthogonal polynomials) and the respective expansion coefficients are obtained via collocation equations. The main advantage of these methods is that they simultaneously take into account all available information, rather only the information available at a limited number of mesh points. They require more complicated matrix equations than those obtained in finite difference methods. However, the elegance, speed, and accuracy of the spectral methods more than compensates for any such drawbacks. During the course of the monograph, the authors examine the usually rapid convergence of the spectral expansions and the improved accuracy that results when nonequispaced support points are used, in contrast to the equispaced points used in finite difference methods. In particular, they demonstrate the enhanced accuracy obtained in the solutionof integral equations. The monograph includes an informative introduction to old and new computational methods with numerous practical examples, while at the same time pointing out the errors that each of the available algorithms introduces into the specific solution. It is a valuable resource for undergraduate students as an introduction to the field and for graduate students wishing to compare the available computational methods. In addition, the work develops the criteria required for students to select the most suitable method to solve the particular scientific problem that they are confronting.

Author : David A. Kopriva
Publisher : Unknown
Page : 350 pages
File Size : 48,9 Mb
Release : 2009-07-01
Category : Science
ISBN : 3540927417

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Implementing Spectral Methods for Partial Differential Equations by David A. Kopriva Pdf

This book presents a systematic development of the fundamental algorithms needed to write spectral methods codes to solve basic problems of mathematical physics: Steady potentials, transport, and wave propagation. It shows that only a few fundamental algorithms for interpolation, differentiation and the FFT form the building blocks of any spectral code, even for problems in complex geometries. The algorithms approximate problems in 1D and 2D to show the flexibility of spectral methods, and to make the transition from exploratory to application codes as straightforward as possible. The book serves as a textbook for graduate students and as a starting point for applications scientists.

Author : John P. Boyd
Publisher : Courier Corporation
Page : 690 pages
File Size : 41,8 Mb
Release : 2013-06-05
Category : Mathematics
ISBN : 9780486141923

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Chebyshev and Fourier Spectral Methods by John P. Boyd Pdf

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.

Author : Hemen Dutta,Ahmet Ocak Akdemir,Abdon Atangana
Publisher : John Wiley & Sons
Page : 336 pages
File Size : 54,9 Mb
Release : 2020-08-06
Category : Mathematics
ISBN : 9781119654230

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Fractional Order Analysis by Hemen Dutta,Ahmet Ocak Akdemir,Abdon Atangana Pdf

A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.

Author : Jamal Amani Rad,Kourosh Parand,Snehashish Chakraverty
Publisher : Springer Nature
Page : 312 pages
File Size : 51,5 Mb
Release : 2023-03-18
Category : Mathematics
ISBN : 9789811965531

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Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines by Jamal Amani Rad,Kourosh Parand,Snehashish Chakraverty Pdf

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.

Author : Olivier Le Maitre,Omar M Knio
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 43,7 Mb
Release : 2010-03-11
Category : Science
ISBN : 9789048135202

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Spectral Methods for Uncertainty Quantification by Olivier Le Maitre,Omar M Knio Pdf

This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.

Author : Anonim
Publisher : Unknown
Page : 806 pages
File Size : 50,6 Mb
Release : 1992
Category : Power resources
ISBN : MSU:31293010869489

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Energy Research Abstracts by Anonim Pdf

Author : John P. Boyd
Publisher : Courier Corporation
Page : 690 pages
File Size : 50,7 Mb
Release : 2001-12-03
Category : Mathematics
ISBN : 9780486411835

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Chebyshev and Fourier Spectral Methods by John P. Boyd Pdf

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.

Author : S. Haykin
Publisher : Unknown
Page : 284 pages
File Size : 49,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 366230922X

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Nonlinear Methods of Spectral Analysis by S. Haykin Pdf

Author : Peter Pelikan,Michal Ceppan,Marek Liska
Publisher : CRC Press
Page : 368 pages
File Size : 47,6 Mb
Release : 2020-11-25
Category : Science
ISBN : 9781000098945

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Applications of Numerical Methods in Molecular Spectroscopy by Peter Pelikan,Michal Ceppan,Marek Liska Pdf

Applications of Numerical Methods in Molecular Spectroscopy provides a mathematical background, theoretical perspective, and review of spectral data processing methods. The book discusses methods of complex spectral profile separation into bands, factor analysis methods, methods of quantitative analysis in molecular spectroscopy and reflectance spectroscopy, and new data processing methods. Mathematical methods in special areas of molecular spectroscopy, such as color science, electron spin resonance, and nuclear magnetic resonance spectroscopies are also covered. The book will benefit researchers and postgraduate students in fields of chemistry, physics, and biology.

Author : I D Iliev,Eugeni Khristov,Kiril Petrov Kirchev
Publisher : CRC Press
Page : 412 pages
File Size : 46,7 Mb
Release : 1994-11-21
Category : Mathematics
ISBN : 058223963X

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Spectral Methods in Soliton Equations by I D Iliev,Eugeni Khristov,Kiril Petrov Kirchev Pdf

Soliton theory as a method for solving some classes of nonlinear evolution equations (soliton equations) is one of the most actively developing topics in mathematical physics. This book presents some spectral theory methods for the investigation of soliton equations ad the inverse scattering problems related to these equations. The authors give the theory of expansions for the Sturm-Liouville operator and the Dirac operator. On this basis, the spectral theory of recursion operators generating Korteweg-de Vries type equations is presented and the Ablowitz-Kaup-Newell-Segur scheme, through which the inverse scattering method could be understood as a Fourier-type transformation, is considered. Following these ideas, the authors investigate some of the questions related to inverse spectral problems, i.e. uniqueness theorems, construction of explicit solutions and approximative methods for solving inverse scattering problems. A rigorous investigation of the stability of soliton solutions including solitary waves for equations which do not allow integration within inverse scattering method is also presented.

Author : R. A. Friedel
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781468481211

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Spectrometry of Fuels by R. A. Friedel Pdf

Fuels represent an important aspect of world economy. The study of the chemical properties and compositions of fuels is necessary to provide a better understanding of their reactions, and, possibly, to promote their improved commercial utilization. Spectrometry comprises a valuable group of tools and techniques for the study of fuels and their derivatives. Some of the undesirable by-products from fuels-specifically, pollutants-provide the spectroscopist with an additional vast area for the application of his tools. The fight against pollution of all kinds has spawned one of our most rapidly growing industries. It thus seems pertinent to devote a book to the spectrometric investiga tion of fuels and related materials. This book is intended to be of interest to people concerned with fuels, with related chemicals, with applications of the newest spectral methods, or with organic and physical chemistry. The pur pose of the book is threefold: (l) To give details of 23 new researches using modern spectral methods on fuels and related materials, (2) to give the reader some feeling for these modern techniques and their applications, and (3) to provide him with indications of material for further reading. The book is not intended to cover details of specific analyses of fuels or of fuel deriva tives such as gasoline, lubricating oil, coal gas, etc. ; considerable space in other books and in journals has been devoted to these subjects.

Author : Mohammad Taeibi Rahni,Mohsen Karbaschi,Reinhard Miller
Publisher : CRC Press
Page : 538 pages
File Size : 43,6 Mb
Release : 2015-11-11
Category : Science
ISBN : 9781498722094

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Computational Methods for Complex Liquid-Fluid Interfaces by Mohammad Taeibi Rahni,Mohsen Karbaschi,Reinhard Miller Pdf

Computational Methods for Complex Liquid-Fluid Interfaces highlights key computational challenges involved in the two-way coupling of complex liquid-fluid interfaces. The book covers a variety of cutting-edge experimental and computational techniques ranging from macro- to meso- and microscale approaches (including pivotal applications). As examples, the text: defines the most important interfacial quantities and their experimental investigations, providing theoretical background and detailed solutions, describes vital techniques used in interfacial flow problems, such as modern meshless numerical methods and conventional computational fluid dynamics methods, and discusses the technicalities of correctly using the computational methods developed for interfacial flows, as well as the simulation of interesting interfacial flow physics. Edited and authored by leading scientists and researchers, Computational Methods for Complex Liquid-Fluid Interfaces offers an authoritative and state-of-the-art overview of computational methodologies and simulation techniques for the quantification of interfacial quantities.

Author : Anonim
Publisher : Unknown
Page : 430 pages
File Size : 51,8 Mb
Release : 2000
Category : Liquid crystals
ISBN : UOM:39015050121600

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Liquid Crystals: Chemistry, Physics, and Applications by Anonim Pdf