Regular and Chaotic Motions in Dynamic Systems, A. S. Wightman

Автор: Hoover William Graham, Hoover Carol Griswold
Название: Simulation and Control of Chaotic Nonequilibrium Systems: With a Foreword by Julien Clinton Sprott
ISBN: 9814656828 ISBN-13(EAN): 9789814656825
Издательство: World Scientific Publishing
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Описание: This book aims to provide a lively working knowledge of the thermodynamic control of microscopic simulations, while summarizing the historical development of the subject, along with some personal reminiscences.

Автор: Weiss
Название: Reflected Brownian Motions in the KPZ Universality Class
ISBN: 3319494988 ISBN-13(EAN): 9783319494982
Издательство: Springer
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Описание: This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the n-th Brownian motion is reflected from the Brownian motion with label n-1. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, because of the singular interaction, many universal properties can be established with rigor. They depend on the choice of initial conditions. Discussion addresses packed and periodic initial conditions (Chapter 5), stationary initial conditions (Chapter 6), and mixtures thereof (Chapter 7). The suitably scaled spatial process will be proven to converge to an Airy process in the long time limit. A chapter on determinantal random fields and another one on Airy processes are added to have the notes self-contained. These notes serve as an introduction to the KPZ universality class, illustrating the main concepts by means of a single model only. The notes will be of interest to readers from interacting diffusion processes and non-equilibrium statistical mechanics.