Statistical Mechanics And Fractals
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| Author | : Rainer Klages |
| Publisher | : World Scientific |
| Total Pages | : 458 |
| Release | : 2007 |
| Genre | : Science |
| ISBN | : 9812565078 |
A valuable introduction for newcomers as well as an important reference and source of inspiration for established researchers, this book provides an up-to-date summary of central topics in the field of nonequilibrium statistical mechanics and dynamical systems theory.Understanding macroscopic properties of matter starting from microscopic chaos in the equations of motion of single atoms or molecules is a key problem in nonequilibrium statistical mechanics. Of particular interest both for theory and applications are transport processes such as diffusion, reaction, conduction and viscosity.Recent advances towards a deterministic theory of nonequilibrium statistical physics are summarized: Both Hamiltonian dynamical systems under nonequilibrium boundary conditions and non-Hamiltonian modelings of nonequilibrium steady states by using thermal reservoirs are considered. The surprising new results include transport coefficients that are fractal functions of control parameters, fundamental relations between transport coefficients and chaos quantities, and an understanding of nonequilibrium entropy production in terms of fractal measures and attractors.The theory is particularly useful for the description of many-particle systems with properties in-between conventional thermodynamics and nonlinear science, as they are frequently encountered on nanoscales.
| Author | : Tsuneyoshi Nakayama |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 216 |
| Release | : 2013-06-29 |
| Genre | : Science |
| ISBN | : 3662051931 |
Concisely and clearly written by two foremost scientists, this book provides a self-contained introduction to the basic concepts of fractals and demonstrates their use in a range of topics. The authors’ unified description of different dynamic problems makes the book extremely accessible.
| Author | : Dietrich Stauffer |
| Publisher | : Springer |
| Total Pages | : 233 |
| Release | : 2013-11-11 |
| Genre | : Science |
| ISBN | : 3642867804 |
From Newton to Mandelbrot takes the student on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, and, the most modern and exciting of all, the physics of fractals. The treatment is confined to the essentials of each area, and short computer programs, numerous problems, and beautiful color illustrations round off this unusual textbook. Ideally suited for a one-year course in theoretical physics it will also prove useful in preparing and revising for exams. This edition is corrected and includes a new appendix on elementary particle physics, answers to all short questions, and a diskette where a selection of executable programs exploring the fractal concept can be found.
| Author | : Alberto Carpinteri |
| Publisher | : Springer |
| Total Pages | : 352 |
| Release | : 2014-05-04 |
| Genre | : Technology & Engineering |
| ISBN | : 3709126649 |
The book is characterized by the illustration of cases of fractal, self-similar and multi-scale structures taken from the mechanics of solid and porous materials, which have a technical interest. In addition, an accessible and self-consistent treatment of the mathematical technique of fractional calculus is provided, avoiding useless complications.
| Author | : Bruce West |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 355 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 0387217460 |
This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The discussion emphasizes physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. The book gives general strategies for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of heat transport in heterogeneous materials.
| Author | : James Sethna |
| Publisher | : OUP Oxford |
| Total Pages | : 374 |
| Release | : 2006-04-07 |
| Genre | : Science |
| ISBN | : 0191566217 |
In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics - a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.
| Author | : Chin-Kun Hu |
| Publisher | : World Scientific |
| Total Pages | : 424 |
| Release | : 1988 |
| Genre | : Science |
| ISBN | : 9789971507145 |
| Author | : J. R. Dorfman |
| Publisher | : Cambridge University Press |
| Total Pages | : 303 |
| Release | : 1999-08-28 |
| Genre | : Science |
| ISBN | : 0521655897 |
Introduction to applications and techniques in non-equilibrium statistical mechanics of chaotic dynamics.
| Author | : Didier Sornette |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 445 |
| Release | : 2013-04-17 |
| Genre | : Science |
| ISBN | : 366204174X |
A modern up-to-date introduction for readers outside statistical physics. It puts emphasis on a clear understanding of concepts and methods and provides the tools that can be of immediate use in applications.
| Author | : David Carfi |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 384 |
| Release | : 2013-10-24 |
| Genre | : Mathematics |
| ISBN | : 0821891480 |
This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.
