Download or read book Numerical Grid Methods and Their Application to Schr dinger s Equation written by C. Cerjan and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of numerical grid methods to solve the Schrodinger equation has rapidly evolved in the past decade.The early attempts to demonstrate the computational viability of grid methods have been largely superseded by applications to specific problems and deeper research into more sophisticated quadrature schemes. Underpinning this research, of course, is the belief that the generic nature of grid methods can enjoy a symbiotic development with advances in computer technology, harnessing this technology in an effective manner. The contributions to this proceedings demonstrate these points in full: several appli cations displayed creative use and extension of existing grid methodology; other research concentrated on the development of new quadrature schemes or mixed numerical meth ods. The research represented ranges from highly specific spectral simulations of van der Waals complexs to general schemes for reactive scattering. The novelty of grid methods in Density Functional Theory calculations should also be highlighted since it represents an alternative to standard basis set expansion techniques and might offer distinct advantages to the standard techniques. A deliberate attempt was made to present research material with more motivational and background discussion than is typical of research publications. It is hoped that these contributed proceedings will be useful to students and researchers outside the field to have a rapid and complete introduction to many of the exciting uses of grid methodology in atomic and molecular physics. Special thanks are due to the NATO Science Committee for its generous support of the activities of this workshop.
Download or read book Modern Methods For Multidimensional Dynamics Computations In Chemistry written by Donald L Thompson and published by World Scientific. This book was released on 1998-04-15 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume describes many of the key practical theoretical techniques that have been developed to treat chemical dynamics problems in many-atom systems. It contains thorough treatments of fundamental theory and prescriptions for performing computations. The selection of methods, ranging from gas phase bimolecular reactions to complex processes in condensed phases, reflects the breadth of the field.The book is an excellent reference for proven and accepted methods as well as for theoretical approaches that are still being developed. It is appropriate for graduate students and other “novices” who wish to begin working in chemical dynamics as well as active researchers who wish to acquire a wider knowledge of the field.
Download or read book Dynamics of Molecules and Chemical Reactions written by Robert Wyatt and published by CRC Press. This book was released on 1996-06-27 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers both molecular and reaction dynamics. The work presents important theroetical and computational approaches to the study of energy transfer within and between molecules, discussing the application of these approaches to problems of experimental interest. It also describes time-dependent and time-independent methods, variational and perturbative techniques, iterative and direct approaches, and methods based upon the use of physical grids of finite sets of basic function.
Download or read book Models And Methods For Quantum Condensation And Fluids written by Weizhu Bao and published by World Scientific. This book was released on 2023-01-04 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Institute for Mathematical Sciences at the National University of Singapore hosted a thematic program on Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications from September 2019 to March 2020. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers. This invaluable volume collects six expanded lecture notes with self-contained tutorials. The coverage includes mathematical models and numerical methods for multidimensional solitons in linear and nonlinear potentials; Bose-Einstein condensation (BEC) with dipole-dipole interaction, higher order interaction and spin-orbit coupling; classical and quantum turbulence; and molecular dynamics process based on the first-principle in quantum chemistry.This volume serves to inspire graduate students and researchers who will embark into original research work in these fields.
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 Applications of Quantum Dynamics in Chemistry written by Fabien Gatti and published by Springer. This book was released on 2017-09-05 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains the usage and application of Molecular Quantum Dynamics, the methodology where both the electrons and the nuclei in a molecule are treated with quantum mechanical calculations. This volume of Lecture Notes in Chemistry addresses graduate students and postdocs in the field of theoretical chemistry, as well as postgraduate students, researchers and teachers from neighboring fields, such as quantum physics, biochemistry, biophysics, or anyone else who is interested in this rising method in theoretical chemistry, and who wants to gain experience in the opportunities it can offer. It can also be useful for teachers interested in illustrative examples of time-dependent quantum mechanics as animations of realistic wave packets have been designed to assist in visualization. Assuming a basic knowledge about quantum mechanics, the authors link their explanations to recent experimental investigations where Molecular Quantum Dynamics proved successful and necessary for the understanding of the experimental results. Examples including reactive scattering, photochemistry, tunneling, femto- and attosecond chemistry and spectroscopy, cold chemistry or crossed-beam experiments illustrate the power of the method. The book restricts complicated formalism to the necessary and in a self-contained and clearly explained way, offering the reader an introduction to, and instructions for, practical exercises. Continuative explanation and math are optionally supplemented for the interested reader. The reader learns how to apply example simulations with the MCTDH program package (Multi Configuration Time Dependent Hartree calculations). Readers can thus obtain the tools to run their own simulations and apply them to their problems. Selected scripts and program code from the examples are made available as supplementary material. This book bridges the gap between the existing textbooks on fundamental theoretical chemistry and research monographs focusing on sophisticated applications. It is a must-read for everyone who wants to gain a sound understanding of Molecular Quantum Dynamics simulations and to obtain basic experience in running their own simulations.
Download or read book Research Methodology and Strategy written by Patrick X. W. Zou and published by John Wiley & Sons. This book was released on 2024-01-16 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides comprehensive coverage of the entire research process, ideal for advanced students and professionals Research Methodology and Strategy: Theory and Practice is designed to help advanced students understand the research process and equip them with the skills required to successfully execute their projects. In-depth chapters describe the general research processes, different research paradigms and their application domains, the role of criticism, and more. Written by authors with decades of research experience, this authoritative textbook addresses the skills needed by all active researchers, including mixed method research design and development, data- and technology-driven research methodologies, writing and publishing research outcomes, strengthening research-practice nexus and strategies for improving research impact and citations. Provides a solid understanding of interdisciplinary research and analytical methods Offers clear guidance on the application of data-driven and technology-enabled research methods Covers qualitative, quantitative and mixed methods research methodologies Discusses different case study research methods and practices Describes methods drawn from business, management, economics, and social sciences research Provides strategies for thesis and journal article writing and publishing Provides theoretical frameworks and examples for research-practice nexus and improving research impacts Research Methodology and Strategy: Theory and Practice is an invaluable textbook for senior undergraduate, masters, and PhD research students, academic and scientific researchers, and industry professionals who perform research in the course of their work.
Download or read book Advances in Chemical Physics Volume 163 written by K. Birgitta Whaley and published by John Wiley & Sons. This book was released on 2018-05-08 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Advances in Chemical Physics series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. • This is the only series of volumes available that presents the cutting edge of research in chemical physics • Includes 10 contributions from leading experts in this field of research • Contains a representative cross-section of research in chemical reaction dynamics and state of the art quantum description of intramolecular and intermolecular dynamics • Structured with an editorial framework that makes the book an excellent supplement to an advanced graduate class in physical chemistry, chemical physics, or molecular physics
Download or read book Molecular Quantum Dynamics written by Fabien Gatti and published by Springer Science & Business Media. This book was released on 2014-04-09 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on current applications of molecular quantum dynamics. Examples from all main subjects in the field, presented by the internationally renowned experts, illustrate the importance of the domain. Recent success in helping to understand experimental observations in fields like heterogeneous catalysis, photochemistry, reactive scattering, optical spectroscopy, or femto- and attosecond chemistry and spectroscopy underline that nuclear quantum mechanical effects affect many areas of chemical and physical research. In contrast to standard quantum chemistry calculations, where the nuclei are treated classically, molecular quantum dynamics can cover quantum mechanical effects in their motion. Many examples, ranging from fundamental to applied problems, are known today that are impacted by nuclear quantum mechanical effects, including phenomena like tunneling, zero point energy effects, or non-adiabatic transitions. Being important to correctly understand many observations in chemical, organic and biological systems, or for the understanding of molecular spectroscopy, the range of applications covered in this book comprises broad areas of science: from astrophysics and the physics and chemistry of the atmosphere, over elementary processes in chemistry, to biological processes (such as the first steps of photosynthesis or vision). Nevertheless, many researchers refrain from entering this domain. The book "Molecular Quantum Dynamics" offers them an accessible introduction. Although the calculation of large systems still presents a challenge - despite the considerable power of modern computers - new strategies have been developed to extend the studies to systems of increasing size. Such strategies are presented after a brief overview of the historical background. Strong emphasis is put on an educational presentation of the fundamental concepts, so that the reader can inform himself about the most important concepts, like eigenstates, wave packets, quantum mechanical resonances, entanglement, etc. The chosen examples highlight that high-level experiments and theory need to work closely together. This book thus is a must-read both for researchers working experimentally or theoretically in the concerned fields, and generally for anyone interested in the exciting world of molecular quantum dynamics.
Download or read book Computational Science and Its Applications ICCSA 2004 written by Antonio Laganà and published by Springer. This book was released on 2004-04-29 with total page 1081 pages. Available in PDF, EPUB and Kindle. Book excerpt: The natural mission of Computational Science is to tackle all sorts of human problems and to work out intelligent automata aimed at alleviating the b- den of working out suitable tools for solving complex problems. For this reason ComputationalScience,thoughoriginatingfromtheneedtosolvethemostch- lenging problems in science and engineering (computational science is the key player in the ?ght to gain fundamental advances in astronomy, biology, che- stry, environmental science, physics and several other scienti?c and engineering disciplines) is increasingly turning its attention to all ?elds of human activity. In all activities, in fact, intensive computation, information handling, kn- ledge synthesis, the use of ad-hoc devices, etc. increasingly need to be exploited and coordinated regardless of the location of both the users and the (various and heterogeneous) computing platforms. As a result the key to understanding the explosive growth of this discipline lies in two adjectives that more and more appropriately refer to Computational Science and its applications: interoperable and ubiquitous. Numerous examples of ubiquitous and interoperable tools and applicationsaregiveninthepresentfourLNCSvolumescontainingthecontri- tions delivered at the 2004 International Conference on Computational Science and its Applications (ICCSA 2004) held in Assisi, Italy, May 14–17, 2004.
Download or read book Applied Bohmian Mechanics written by Xavier Oriols Pladevall and published by CRC Press. This book was released on 2019-05-24 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most textbooks explain quantum mechanics as a story where each step follows naturally from the one preceding it. However, the development of quantum mechanics was exactly the opposite. It was a zigzag route, full of personal disputes where scientists were forced to abandon well-established classical concepts and to explore new and imaginative pathways. Some of the explored routes were successful in providing new mathematical formalisms capable of predicting experiments at the atomic scale. However, even such successful routes were painful enough, so that relevant scientists like Albert Einstein and Erwin Schrödinger decided not to support them. In this book, the authors demonstrate the huge practical utility of another of these routes in explaining quantum phenomena in many different research fields. Bohmian mechanics, the formulation of the quantum theory pioneered by Louis de Broglie and David Bohm, offers an alternative mathematical formulation of quantum phenomena in terms of quantum trajectories. Novel computational tools to explore physical scenarios that are currently computationally inaccessible, such as many-particle solutions of the Schrödinger equation, can be developed from it.
Download or read book Theory of Chemical Reaction Dynamics written by Antonio Laganà and published by Springer Science & Business Media. This book was released on 2006-03-28 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Research Workshop, held in Balatonföldvár, Hungary, 8-12 June 2003
Download or read book Advances in Chemical Physics Volume 100 written by Ilya Prigogine and published by John Wiley & Sons. This book was released on 2009-09-09 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics.
Download or read book Multi Grid Methods and Applications written by Wolfgang Hackbusch and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to multi-grid algorithms as well as a comprehensive convergence analysis. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.). The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other problems. Readers with a practical interest in multi-grid methods will benefit from this book as well as readers with a more theoretical interest.
Download or read book The Role of Degenerate States in Chemistry Volume 124 written by Michael Baer and published by John Wiley & Sons. This book was released on 2002-08-22 with total page 837 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited by Nobel Prize-winner Ilya Prigogine and renowned authority Stuart A. Rice, the Advances in Chemical Physics series provides a forum for critical, authoritative evaluations in every area of the discipline. In a format that encourages the expression of individual points of view, experts in the field present comprehensive analyses of subjects of interest. This stand-alone, special topics volume, edited by Gert D. Billing of the University of Copenhagen and Michael Baer of the Soreq Nuclear Research Center in Yavne, Israel, reports recent advances on the role of degenerate states in chemistry. Volume 124 collects innovative papers on "Complex States of Simple Molecular Systems," "Electron Nuclear Dynamics," "Conical Intersections and the Spin-Orbit Interaction," and many more related topics. Advances in Chemical Physics remains the premier venue for presentations of new findings in its field.
Download or read book Molecular Dynamics written by Perla Balbuena and published by Elsevier. This book was released on 1999-04-22 with total page 971 pages. Available in PDF, EPUB and Kindle. Book excerpt: The latest developments in quantum and classical molecular dynamics, related techniques, and their applications to several fields of science and engineering. Molecular simulations include a broad range of methodologies such as Monte Carlo, Brownian dynamics, lattice dynamics, and molecular dynamics (MD). Features of this book: • Presents advances in methodologies, introduces quantum methods and lists new techniques for classical MD • Deals with complex systems: biomolecules, aqueous solutions, ice and clathrates, liquid crystals, polymers • Provides chemical reactions, interfaces, catalysis, surface phenomena and solids Although the book is not formally divided into methods and applications, the chapters are arranged starting with those that discuss new algorithms, methods and techniques, followed by several important applications.
Download or read book Grid Generation Methods written by Vladimir D. Liseikin and published by Springer. This book was released on 2018-05-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an introduction to methods of grid generation technology in scientific computing. Special attention is given to methods developed by the author for the treatment of singularly-perturbed equations, e.g. in modeling high Reynolds number flows. Functionals of conformality, orthogonality, energy and alignment are discussed.
