Download or read book Spectral Methods in Chemistry and Physics written by Bernard Shizgal and published by Springer. This book was released on 2015-01-07 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectral Methods written by Claudio Canuto and published by Springer Science & Business Media. This book was released on 2007-09-23 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.
Download or read book Implementing Spectral Methods for Partial Differential Equations written by David A. Kopriva and published by . This book was released on 2009-07-01 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectral Methods of Chemical Analysis written by V. Raj and published by LAP Lambert Academic Publishing. This book was released on 2011-09 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains all advanced spectroscopic methods which are very very essential to identification of a chemical compound. This book will be useful to Master degree students of chemistry, food science, biochemistry etc. The content of this book is designed in such a way that it will be well suited to graduates and post graduate courses of all science disciplines. To carryout the analysis and identification of a new compound.
Download or read book Spectral Methods written by Claudio Canuto and published by Springer. This book was released on 2011-09-07 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.
Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2001-12-03 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applications of Numerical Methods in Molecular Spectroscopy written by Peter Pelikan and published by CRC Press. This book was released on 1994-01-19 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Photothermal Spectroscopy Methods for Chemical Analysis written by Stephen E. Bialkowski and published by John Wiley & Sons. This book was released on 1996-01-12 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique guide to the application and theory of photothermalspectroscopy. This book debunks the myth that photothermal spectroscopy is toocomplicated for practical application to chemical analysis, anddemonstrates the advantages this technique has over conventionalspectroscopy in facilitating extremely sensitive measurements ofoptical absorption in homogeneous media. The book covers thesubject from the ground up, lists all practical considerationsneeded to obtain accurate results, and provides a working knowledgeof the various methods in use--including photo acoustics andphotopyroelectric techniques. Bringing together a wealth of information that has been scatteredthroughout the professional literature, Photothermal SpectroscopyMethods for Chemical Analysis covers methods and information thatshould be known to every analytical chemist, including: * Descriptions of photothermal spectroscopy using a consistentmathematical language * Helpful examples from the literature of analytical applicationsand current research * Illustrations of all important points, consistent equations, andnumerous original figures * A discussion of laser technology and how it is used to obtainaccurate results from extremely small samples of a few molecules * Everything spectroscopists need to know to construct their ownapparatus and use it to conduct successful experiments * Tips on how to interpret experimental results effectively whenusing nonlinear processes and in many other situations inphotothermal spectroscopy * Considerations for further study of heterogeneous sampleanalysis * Unified nomenclature of the patchwork of terms used byresearchers in analytical and physical chemistry, physics, andoptical engineering * Equations that are derived with the aid of a symbolic languageprocessor to ensure correct results Photothermal spectroscopy has seen major advances since the adventof laser technology twenty-five years ago. It is now possible,using a laser's coherent and powerful output, to obtain extremelysensitive measurements of optical absorption that exceed those ofmass spectroscopy by two or three times, and produce accurateresults from only a few molecules. Focusing on samples in homogeneous media, this book provides aunique guide--incorporating theory and application--to allavailable photothermal spectroscopy techniques for chemical andmaterial analysis. It uses a systematic approach in itscomprehensive treatment of the theory, and covers all the necessarybackground material, from laser optics to fluid dynamics. This accessible text describes the various processes used to detectthermal perturbation of a sample, ranging from optical excitationto nonlinear processes, and covers all optical principles necessaryto understand photothermal spectroscopy. When dealing withhydrodynamic equations that govern energy transfer in the samplematrix, it provides an original impulse-response approach. Inaddition, the book explains how to construct the apparatus oneneeds to conduct successful photothermal experiments, sincecommercial equipment is not available as in conventionalspectrophotometry. Throughout, this book draws on information from a wide range offields, including analytical spectroscopy, measurement physics,physical optics, and chemical dynamics. Providing clearexplanations at every turn, the author demonstrates a completeunderstanding of the theory and applications as a firm basis forthe correct interpretation of experimental results. For analytical chemists, as well as for students at the graduatelevel, Photothermal Spectroscopy Methods for Chemical Analysis isan unmatched resource that develops a consistent mathematical basisfor signal description, consolidates previous theories, andprovides invaluable insight into laser technology.
Download or read book Spectral Methods and Their Applications written by Benyu Guo and published by World Scientific. This book was released on 1998 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basic algorithms, the main theoretical results, and some applications of spectral methods. Particular attention is paid to the applications of spectral methods to nonlinear problems arising in fluid dynamics, quantum mechanics, weather prediction, heat conduction and other fields.The book consists of three parts. The first part deals with orthogonal approximations in Sobolev spaces and the stability and convergence of approximations for nonlinear problems, as the mathematical foundation of spectral methods. In the second part, various spectral methods are described, with some applications. It includes Fourier spectral method, Legendre spectral method, Chebyshev spectral method, spectral penalty method, spectral vanishing viscosity method, spectral approximation of isolated solutions, multi-dimensional spectral method, spectral method for high-order equations, spectral-domain decomposition method and spectral multigrid method. The third part is devoted to some recent developments of spectral methods, such as mixed spectral methods, combined spectral methods and spectral methods on the surface.
Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2013-06-05 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectral methods written by Claudio Canuto and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Methods for Uncertainty Quantification written by Olivier Le Maitre and published by Springer Science & Business Media. This book was released on 2010-03-11 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectrometry of Fuels written by R. A. Friedel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Learning with Fractional Orthogonal Kernel Classifiers in Support Vector Machines written by Jamal Amani Rad and published by Springer Nature. This book was released on 2023-03-18 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fractional Order Analysis written by Hemen Dutta and published by John Wiley & Sons. This book was released on 2020-08-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectral Methods in Fluid Dynamics written by C. Canuto and published by . This book was released on 1988 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Astrophysical Hydrodynamics written by Steven N. Shore and published by Academic Press. This book was released on 2012-12-02 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to astrophysical hydrodynamics for both astronomy and physics students. It provides a comprehensive and unified view of the general problems associated with fluids in a cosmic context, with a discussion of fluid dynamics and plasma physics. It is the only book on hydrodynamics that addresses the astrophysical context. Researchers and students will find this work to be an exceptional reference. Contents include chapters on irrotational and rotational flows, turbulence, magnetohydrodynamics, and instabilities.
