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Books in Nonlinear statistical and applied physics

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    • Nonlinear Topics in Ocean Physics

      • 1st Edition
      • Volume 109
      • July 4, 1991
      • A.R. Osborne
      • English
      • Paperback
        9 7 8 0 4 4 4 5 6 7 9 3 2
      • eBook
        9 7 8 0 4 4 4 5 9 7 8 2 3
      The main fields presented at this school were mesoscale and large scale flows, and nonlinear wave dynamics. The resulting proceedings present the latest developments in these fields.

    • Quantum Physics, Relativity, and Complex Spacetime

      • 1st Edition
      • Volume 163
      • December 11, 1990
      • G. Kaiser
      • English
      • eBook
        9 7 8 0 0 8 0 8 7 2 7 4 2
      A new synthesis of the principles of quantum mechanics and Relativity is proposed in the context of complex differential geometry. The positivity of the energy implies that wave functions and fields can be extended to complex spacetime, and it is shown that this complexification has a solid physical interpretation as an extended phase space. The extended fields can be said to be realistic wavelet transforms of the original fields. A new, algebraic theory of wavelets is developed.

    • Dissipative Structures and Weak Turbulence

      • 1st Edition
      • May 28, 1990
      • English
      • Hardback
        9 7 8 0 1 2 4 6 9 2 6 0 2
      • Paperback
        9 7 8 1 4 9 3 3 0 7 5 8 6
      • eBook
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      Dissipative Structure and Weak Turbulence provides an understanding of the emergence and evolution of structures in macroscopic systems. This book discusses the emergence of dissipative structures. Organized into 10 chapters, this book begins with an overview of the stability of a fluid layer with potentially unstable density stratification in the field of gravity. This text then explains the theoretical description of the dynamics of a given system at a formal level. Other chapters consider several examples of how such simplified models can be derived, complicating the picture progressively to account for other phenomena. This book discusses as well the theory and experiments on plain Rayleigh–Bénard convection by setting first the theoretical frame and deriving the analytical solution of the marginal stability problem. The final chapter deals with building a bridge between chaos as studied in weakly confined systems and more advanced turbulence in the most conventional sense. This book is a valuable resource for physicists.

    • Statistical Mechanics

      • 1st Edition
      • April 19, 1990
      • R. Kubo + 3 more
      • English
      • Paperback
        9 7 8 0 4 4 4 8 7 1 0 3 9
      • eBook
        9 7 8 0 0 8 0 5 7 1 0 2 7
      Statistical Mechanics provides a series of concise lectures on the fundamental theories of statistical mechanics, carefully chosen examples and a number of problems with complete solutions. Modern physics has opened the way for a thorough examination of infra-structure of nature and understanding of the properties of matter from an atomistic point of view. Statistical mechanics is an essential bridge between the laws of nature on a microscopic scale and the macroscopic behaviour of matter. A good training in statistical mechanics thus provides a basis for modern physics and is indispensable to any student in physics, chemistry, biophysics and engineering sciences who wishes to work in these rapidly developing scientific and technological fields. The collection of examples and problems is comprehensive. The problems are grouped in order of increasing difficulty.

    • 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.

    • Quantum Probability

      • 1st Edition
      • August 28, 1988
      • Stanley P. Gudder
      • English
      • Hardback
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      • Paperback
        9 7 8 1 4 9 3 3 0 0 5 6 3
      • 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
      • Paperback
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      • eBook
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      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
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      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.

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Relativity and gravitation

Statistical physics and thermodynamics

Ultrasonics