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OverviewThis book provides the first rigorous derivation of mesoscopic and macroscopic equations from a deterministic system of microscopic equations. The microscopic equations are cast in the form of a deterministic (Newtonian) system of coupled nonlinear oscillators for N large particles and infinitely many small particles. The mesoscopic equations are stochastic ordinary differential equations (SODEs) and stochastic partial differential equatuions (SPDEs), and the macroscopic limit is described by a parabolic partial differential equation. A detailed analysis of the SODEs and (quasi-linear) SPDEs is presented. Semi-linear (parabolic) SPDEs are represented as first order stochastic transport equations driven by Stratonovich differentials. The time evolution of correlated Brownian motions is shown to be consistent with the depletion phenomena experimentally observed in colloids. A covariance analysis of the random processes and random fields as well as a review section of various approaches to SPDEs are also provided. An extensive appendix makes the book accessible to both scientists and graduate students who may not be specialized in stochastic analysis. Probabilists, mathematical and theoretical physicists as well as mathematical biologists and their graduate students will find this book useful. Peter Kotelenez is a professor of mathematics at Case Western Reserve University in Cleveland, Ohio. Full Product DetailsAuthor: Peter KotelenezPublisher: Springer Imprint: Springer ISBN: 9786611140533ISBN 10: 6611140530 Pages: 452 Publication Date: 01 January 2008 Audience: General/trade , General Format: Electronic book text Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsReviewsFrom the reviews: <p> This book treats the transition from microscopic to macroscopic equations for particle systems. a ] Peter Kotelenez a ] has written a monograph in which he rigorously constructs the theory of correlated Brownian motion in interacting particle systems. a ] Researchers working on interacting particle systems and probability theory will definitely find this book very useful. (J. Dubbeldam, Kwantitatieve Methoden, Issue R11, 2008) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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