This book is a systematic introduction to a new and exciting field of patterns in granular matter. Granular materials are collections of discrete macroscopic solid grains with a typical size large enough that thermal fluctuations are negligible. Despite this seeming simplicity, properties of granular materials are different from conventional solids, liquids and gases due to the dissipative and highly nonlinear nature of forces among grains. The last decade has seen an explosion of interest to nonequilibrium phenomena in granular matter among physicists, both on the experimental and theoretical side. Among these phenomena, one of the most interesting is the ability of granular matter upon mechanical excitation to form highly ordered patterns such as ripples, avalanches, or bands of segregated materials. This book presents a comprehensive review of experiments and novel theoretical concepts needed to understand the mechanisms of pattern formation in granular materials. This book is
written for mature physicists interested in this new rapidly developing field, as well as young researchers and graduate students entering this field. We hope that both experimentalists and theorists already working in the field will find it useful.

About the Author:
Igor Aranson is a staff scientist at the Material Science Division, Argonne National Laboratory, Illinois. Dr. Aranson is a Fellow of American Physical Society, and he is a recipient of Alexander von Humboldt, Wolfson, and Guastello Fellowships. He obtained his Ph.D. in Physics and Mathematics from the Institute of Applied Physics, Academy of Science, Gorky, Russia, for studies of spatio-temporal chaos in non-equilibrium systems. Since then Dr. Aranson worked on a broad variety of topics, from the theory of superconductivity to soft condensed matter, granular physics, and more recently, biophysics. He published more than 140 papers in leading scientific journals, including two influential reviews in the Reviews of Modern Physics, and several book chapters. Dr. Aranson conducts experimental and theoretical studies of pattern formation in granular and biological systems.

Lev Tsimring is a Research Scientist at the University of California, San Diego. He holds a Ph.D. in Physics and Mathematics from the Moscow Institute of Oceanology for his early work in nonlinear theory of internal and surface gravity waves. After that Dr. Tsimring has done pioneering research and published more than a hundred papers in various areas of nonlinear dynamics, pattern formation, nonlinear time series analysis, and, most recently, granular and biological physics.