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2079 results in Statistical Physics

Page 28 of 104

Fractional Diffusion Equations and Anomalous Diffusion
  • Luiz Roberto Evangelista, Ervin Kaminski Lenzi
  • Published online:
    17 January 2018
    Print publication:
    25 January 2018
  • Anomalous diffusion has been detected in a wide variety of scenarios, from fractal media, systems with memory, transport processes in porous media, to fluctuations of financial markets, tumour growth, and complex fluids. Providing a contemporary treatment of this process, this book examines the recent literature on anomalous diffusion and covers a rich class of problems in which surface effects are important, offering detailed mathematical tools of usual and fractional calculus for a wide audience of scientists and graduate students in physics, mathematics, chemistry and engineering. Including the basic mathematical tools needed to understand the rules for operating with the fractional derivatives and fractional differential equations, this self-contained text presents the possibility of using fractional diffusion equations with anomalous diffusion phenomena to propose powerful mathematical models for a large variety of fundamental and practical problems in a fast-growing field of research.

Probability on Graphs
  • Random Processes on Graphs and Lattices
  • 2nd edition
  • Geoffrey Grimmett
  • Published online:
    12 January 2018
    Print publication:
    25 January 2018
  • This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.

  • Preface

  • Yoshitsugu Oono, University of Illinois, Urbana-Champaign
  • Book:
    Perspectives on Statistical Thermodynamics
    Published online:
    24 November 2017
    Print publication:
    14 December 2017, pp xxi-xxii

  • Summary

    This book is for a motivated undergraduate student to learn elements of thermal physics on her own after a rudimentary introduction to the subject (at the highest, 200 level in the US). This is a book I wished I had when I was an undergraduate student, struggling to learn physics by myself (I was never taught what I am teaching now; I was a wet chemist). Thus, most intermediate formulas are explicitly given and all the problems are with detailed solutions except for extremely elementary ones (even they come with answers).

    Every student graduating from physics should know at least the existence of the topics covered in this book. This book can be used as a course textbook for a ‘second introduction’ to thermal physics or as a bridge between traditional thermal physics undergraduate and graduate courses. All the key elements of thermal physics are explained without demanding any prior experience of advanced physics as a second introduction, but we go far beyond the elementary introduction.

    I intended to write a thermal physics book that can connect rudimentary gas kinetics and Brownian motion to statistical thermodynamics. Traditionally, equilibrium statistical mechanics books do not tell the reader how to count atoms, even though atomism should be the key idea of the traditional exposition. I explain Einstein's Brownian motion theory before thermodynamics and statistical mechanics. The explanation of Brownian motion and Langevin equations naturally leads us to large deviation theory, one of the pillars of the modern probability theory. Thus, this book emphasizes three levels of descriptions of our world: microscopic, mesoscopic, and macroscopic. Accordingly, the law of large numbers and the large deviation principle are used as the mathematical backbone of thermal physics.

    Although this book does not hesitate to point out the key mathematical ideas that physicists should know, “back of the envelope” calculation and intuitive understanding are emphasized whenever possible (e.g., dimensional analysis is stressed). The required mathematics is restricted to a minimum throughout this book. Still, some minimal prerequisites are desirable to read this book. They are linear algebra, calculus, and (classical and quantum) mechanics (and perhaps a bit of electromagnetism). There is an appendix explaining (quantum) mechanics for the reader who may be learning quantum mechanics concurrently, but it is only a brief summary and should not be regarded as a substitute of an elementary mechanics course.

Page 28 of 104