Statistical Mechanics and Random Walks: Principles, Processes and Applications


Abram Skogseid (Editor)
Vicente Fasano (Editor)

Series: Mathematics Research Developments, Physics Research and Technology
BISAC: MAT029040

In this book, the authors gather and present topical research in the study of statistical mechanics and random walk principles and applications. Topics discussed in this compilation include the application of stochastic approaches to modelling suspension flow in porous media; subordinated Gaussian processes; random walk models in biophysical science; non-equilibrium dynamics and diffusion processes; global random walk algorithm for diffusion processes and application of random walks for the analysis of graphs, musical composition and language phylogeny. (Imprint: Nova)

Table of Contents


Table of Contents


Chapter 1 – Application of Stochastic Approaches to Modelling Suspension Flow in Porous Media pp. 1-38
Authors / Editors: (Alexander A. Shapiro, Hao Yuan, CERE, Center for Energy Resources Engineering, Department of Chemical and Biochemical Engineering, Technical University of Denmark, Lyngby, Denmark)
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Chapter 2 – Unusual Brownian Motion pp. 39-64
Authors / Editors: (Jana Tothova, Vladimir Lisy, Department of Physics, Technical University of Kosice, Slovak Republic)

Chapter 3 – Anomalous Diffusion of Particles in Edge Plasma Turbulence in Tokamaks and Random and Lévy Walk Distributions pp. 65-90
Authors / Editors: (L. Krlin, R. Paprok, J. Seidl, R. Panek, J. Stockel, Association EURATOM/IPP, CR, Institute of Plasma Physics AS CR, Prague, Czech Republic, and others)

Chapter 4 – Subordinated Gaussian Processes, the Log-Return Principles pp. 91-116
Authors / Editors: (Stergios B. Fotopoulos, Yuxing Luo, Washington State University, Washington, USA)

Chapter 5 – Random Walk Models in Biophysical Sciences: Particle Transport in the Human Respiratory Tract pp. 117-134
Authors / Editors: (Robert Sturm, Brunnleitenweg, Elsbethen, Salzburg, Austria)

Chapter 6 – Nonlinear Generalization of Fluctuation-Dissipation Theorem for Levy Flights Diffusion and its Scaling pp. 135-152
Authors / Editors: (V.E. Arkhincheev, Buryat Science Center of SB Russian Academy of Sciences, Ulan-Ude, Russia)

Chapter 7 – Scaling and Correlation of Time Recurrence in Fracture Systems pp. 153-164
Authors / Editors: (G. Niccolini, A. Schiavi, A. Carpinteri, G. Lacidogna, Istituto Nazionale di Ricerca Metrologica, Turin, Italy, and others)

Chapter 8 – On an Integral Related to Two-Dimensional Random Walk pp. 165-170
Authors / Editors: (Zhaohui Qin, Mechanical Engineering Department, Iowa State University, Ames, Iowa, USA)

Chapter 9 – Non-Equilibrium Dynamics and Diffusion Processes pp. 171-232
Authors / Editors: (Z. Chvoj, Institute of Physics, AS CR, Prague, Czech Republic)

Chapter 10 – Hierarchies of Quantum Evolution Equations and Dynamics of Many Particle Correlations pp. 233-288
Authors / Editors: (V. I. Gerasimenko, Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine)

Chapter 11 – Recent Results on Branching Random Walks pp. 289-340
Authors / Editors: (D. Bertacchi, F. Zucca, Universit`a di Milano–Bicocca, Dipartimento di Matematica e Applicazioni, Milano, Italy, and others)

Chapter 12 – Global Random Walk Algorithm for Diffusion Processes pp. 341-388
Authors / Editors: (Nicolae Suciu, Cặlin Vamos, Mathematics Department, Friedrich-Alexander University Erlangen, Nuremberg, Germany, and others)

Chapter 13 – Asymptotics for Random Walks in the Quarter Plane with Queueing Applications pp. 389-420
Authors / Editors: (Fabrice Guillemin, Alain Simonian, Orange Labs, Lannion, France)

Chapter 14 – Random Walk in a Finite Directed Graph Subject to a Synchronizing Road Coloring pp. 421-432
Authors / Editors: (Kouji Yano, Kenji Yasutomi, Department of Mathematics, Graduate School of Science, Kyoto University, Japan, and others)
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Chapter 15 – Solving Partial Differential Equations Via Random Walks: A Review pp. 433-442
Authors / Editors: (Chi-Ok Hwang, School of General Studies, GIST College, Gwangju Institute of Science and Technology, Gwangju, South Korea)

Chapter 16 – Applications of Random Walks for the Analysis of Graphs, Musical Compositions, and Language Phylogeny pp. 443-508
Authors / Editors: (Dimitri Volchenkov, Cognitive Interaction Technology, Center of Excellence, Bielefeld University, Germany)

Chapter 17 – The Stock Size and the Predicitability of Returns pp. 509-544
Authors / Editors: (Alexandre Semenov, Andrei Semenov, Department of Economics, York University, Toronto, Ontario, Canada)

Chapter 18 – A Random Walk Model Related to the Clustering of Membrane Receptors pp. 545-580
Authors / Editors: (Aimé Lachal, Université de Lyon, CNRS, INSA, Lyon, France, and others)
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Chapter 19 – The Random Flight and the Persistent Random Walk pp. 581-612
Authors / Editors: (Ricardo García-Pelayo, ETS de Ingeniería Aeronáutica, Universidad Politécnica de Madrid, Madrid, Spain)
Free Download Available

Chapter 20 – Transport on Lattices with Random Traps: Diffusion, Relaxation and Fluctuations pp. 613-640
Authors / Editors: (Kirill A. Pronin, Institute of Biochemical Physics, Russian Academy of Sciences, Moscow, Russia)



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