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Books in Nonlinear statistical and applied physics

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301-310 of 331 results in All results

Electron Tunneling in Chemistry

  • 1st Edition
  • Volume 30
  • October 17, 1989
  • R.F. Khairutdinov + 2 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 6 8 2 4 - 0
In Volume 30, an attempt is made to consider comprehensively both theoretical and experimental data that have been obtained to date on electron tunneling reactions involving chemical compounds of various classes, and to discuss the role played by these reactions in different areas of chemistry. The discussion of the above problem is preceded by a review of data on tunneling phenomena in nuclear physics, atomic physics, solid-state physics, as well as on the tunneling effects in chemistry that go beyond the framework of the main subject of this monograph. This review is included to acquaint the reader with the role of tunneling phenomena in physics and chemistry as a whole, to show how diversified the kingdom of tunneling phenomena is, and to see more distinctly the similarities and the differences between electron tunneling in chemical reactions and other tunnel phenomena.

Vibration Measurement and Analysis

  • 1st Edition
  • April 5, 1989
  • J. D. Smith
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 6 1 6 3 - 1
Vibration Measurement and Analysis presents the different approaches of vibration measurement and analysis techniques. The book begins with a discussion of the reasons for conducting vibration measurements. Subsequent chapters cover topics on general measurement requirements, transducers and the measurement of sound, and signal conditioning and recording. Analysis methods and frequency analysis, techniques of correlation and averaging, and automation of vibration testing are discussed as well. Mechanical engineers will find the book very useful.

Quantum Probability

  • 1st Edition
  • August 28, 1988
  • Stanley P. Gudder
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 1 8 4 8 - 8
Quantum probability is a subtle blend of quantum mechanics and classical probability theory. Its important ideas can be traced to the pioneering work of Richard Feynman in his path integral formalism.Only recently have the concept and ideas of quantum probability been presented in a rigorous axiomatic framework, and this book provides a coherent and comprehensive exposition of this approach. It gives a unified treatment of operational statistics, generalized measure theory and the path integral formalism that can only be found in scattered research articles.The first two chapters survey the necessary background in quantum mechanics and probability theory and therefore the book is fairly self-contained, assuming only an elementary knowledge of linear operators in Hilbert space.

Mathematical Physics

  • 1st Edition
  • Volume 152
  • June 1, 1988
  • R. Carroll
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 2 6 3 - 6
An introduction to the important areas of mathematical physics, this volume starts with basic ideas and proceeds (sometimes rapidly) to a more sophisticated level, often to the context of current research.All of the necessary functional analysis and differential geometry is included, along with basic calculus of variations and partial differential equations (linear and nonlinear). An introduction to classical and quantum mechanics is given with topics in Feynman integrals, gauge fields, geometric quantization, attractors for PDE, Ginzburg-Landau Equations in superconductivity, Navier-Stokes equations, soliton theory, inverse problems and ill-posed problems, scattering theory, convex analysis, variational inequalities, nonlinear semigroups, etc. Contents: 1. Classical Ideas and Problems. Introduction. Some Preliminary Variational Ideas. Various Differential Equations and Their Origins. Linear Second Order PDE. Further Topics in the Calculus of Variations. Spectral Theory for Ordinary Differential Operators, Transmutation, and Inverse Problems. Introduction to Classical Mechanics. Introduction to Quantum Mechanics. Weak Problems in PDE. Some Nonlinear PDE. Ill-Posed Problems and Regularization. 2. Scattering Theory and Solitons. Introduction. Scattering Theory I (Operator Theory). Scattering Theory II (3-D). Scattering Theory III (A Medley of Themes). Scattering Theory IV (Spectral Methods in 3-D). Systems and Half Line Problems. Relations between Potentials and Spectral Data. Introduction to Soliton Theory. Solitons via AKNS Systems. Soliton Theory (Hamiltonian Structure). Some Topics in Integrable Systems. 3. Some Nonlinear Analysis: Some Geometric Formalism. Introduction. Nonlinear Analysis. Monotone Operators. Topological Methods. Convex Analysis. Nonlinear Semigroups and Monotone Sets. Variational Inequalities. Quantum Field Theory. Gauge Fields (Physics). Gauge Fields (Mathematics) and Geometric Quantization. Appendices: Introduction to Linear Functional Analysis. Selected Topics in Functional Analysis. Introduction to Differential Geometry. References. Index.

Problems in Distributions and Partial Differential Equations

  • 1st Edition
  • Volume 143
  • April 1, 1988
  • C. Zuily
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 2 5 4 - 4
The aim of this book is to provide a comprehensive introduction to the theory of distributions, by the use of solved problems. Although written for mathematicians, it can also be used by a wider audience, including engineers and physicists.The first six chapters deal with the classical theory, with special emphasis on the concrete aspects. The reader will find many examples of distributions and learn how to work with them. At the beginning of each chapter the relevant theoretical material is briefly recalled. The last chapter is a short introduction to a very wide and important field in analysis which can be considered as the most natural application of distributions, namely the theory of partial differential equations. It includes exercises on the classical differential operators and on fundamental solutions, hypoellipticity, analytic hypoellipticity, Sobolev spaces, local solvability, the Cauchy problem, etc.

Synergetics and Dynamic Instabilities

  • 1st Edition
  • January 1, 1988
  • G. Caglioti + 2 more
  • English
  • eBook
    9 7 8 - 0 - 4 4 4 - 6 0 0 9 2 - 9
This collection of papers presented at the Enrico Fermi School considers the subject of synergetics as a firmly established field of interdisciplinary research, ranging from physics, chemistry and biology, to subjects like economy and sociology. These proceedings focus on the natural sciences.

Difference Schemes

  • 1st Edition
  • Volume 19
  • May 1, 1987
  • S.K. Godunov + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 5 4 0 - 8
Much applied and theoretical research in natural sciences leads to boundary-value problems stated in terms of differential equations. When solving these problems with computers, the differential problems are replaced approximately by difference schemes.This book is an introduction to the theory of difference schemes, and was written as a textbook for university mathematics and physics departments and for technical universities. Some sections of the book will be of interest to computations specialists.While stressing a mathematically rigorous treatment of model problems, the book also demonstrates the relation between theory and computer experiments, using difference schemes created for practical computations.

Solitons and Instantons

  • 1st Edition
  • Volume 15
  • April 1, 1987
  • R. Rajaraman
  • English
  • Paperback
    9 7 8 - 0 - 4 4 4 - 8 7 0 4 7 - 6
This book offers an elementary and unified introduction to the non-perturbative results obtained in relativistic quantum field theory based on classical soliton and instanton solutions. Such solutions are derived for a variety of models and classified by topological indices. The methods are then developed for quantizing solitons to obtain quantum particles. Vacuum tunneling, &ugr;-vacua and the dilute-instanton-gas approximation are described in detail. Other instanton effects related to quark-quark forces, confinement, the U(1) problem and Borel summability are also discussed. The emphasis is on presenting the basic ideas in a simple pedagogical way. Technical tools like functional methods, Grassman integrals, homotopy classification, collective co-ordinates etc. are developed ab initio.The presentation of this work is kept at a fairly simple level and ideas are developed through illustrative examples. Techniques not covered in older field theory textbooks, such as functional integral methods, are presented in some detail to the necessary extent. These techniques are important in their own right. Although the book is mainly addressed to particle physicists and quantum field theorists, several portions will be of relevance to other branches of physics, particularly statistical mechanics. These include three chapters devoted to deriving classical soliton and instanton solutions and one on collective co-ordinates, as well as sections devoted to general techniques.

Obstacle Problems in Mathematical Physics

  • 1st Edition
  • Volume 134
  • March 1, 1987
  • J.-F. Rodrigues
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 2 4 5 - 2
The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics.The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitation problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.

Solitons

  • 1st Edition
  • Volume 17
  • December 1, 1986
  • S.E. Trullinger + 2 more
  • English
  • eBook
    9 7 8 - 0 - 4 4 4 - 5 9 8 2 9 - 5
In the twenty years since Zabusky and Kruskal coined the term ``soliton'', this concept changed the outlook on certain types of nonlinear phenomena and found its way into all branches of physics. The present volume deals with a great variety of applications of the new concept in condensed-matter physics, which is particularly reached in experimentally observable occurrences. The presentation is not centred around the mathematical aspects; the emphasis is on the physical nature of the nonlinear phenomena occurring in particular situations.With its emphasis on concrete, mostly experimentally verifiable cases, ``Solitons'' constitutes a very readable and instructive introduction to the subject as well as an up-to-date account of current developments in a field of research reaching maturity.

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