Synopses & Reviews
Modeling complex biological, chemical, and physical systems, in the context of spatially heterogeneous mediums, is a challenging task for scientists and engineers using traditional methods of analysis. Modeling in Applied Sciences is a comprehensive survey of modeling large systems using kinetic equations, and in particular the Boltzmann equation and its generalizations. An interdisciplinary group of leading authorities carefully develop the foundations of kinetic models and discuss the connections and interactions between model theories, qualitative and computational analysis and real-world applications. This book provides a thoroughly accessible and lucid overview of the different aspects, models, computations, and methodology for the kinetic-theory modeling process. Topics and Features: * Integrated modeling perspective utilized in all chapters * Fluid dynamics of reacting gases * Self-contained introduction to kinetic models * Becker-Doring equations * Nonlinear kinetic models with chemical reactions * Kinetic traffic-flow models * Models of granular media * Large communication networks * Thorough discussion of numerical simulations of Boltzmann equation This new book is an essential resource for all scientists and engineers who use large-scale computations for studying the dynamics of complex systems of fluids and particles. Professionals, researchers, and postgraduates will find the book a modern and authoritative guide to the topic.
Review
"...The contributions and the references listed at the end of each chapter seem to give an excellent overview of current research." --Ceramics "This book is a resource for all scientists and engineers who use large-scale computations for studying the dynamics of complex systems of fluids and particles. Professionals, researchers and post-graduates will find the book a modern guide to the topic." --Simulation News Europe
Synopsis
Modeling complex biological, chemical and physical systems in the context of spatially heterogeneous media is a challenging task and of interest to scientists and engineers. This book provides a comprehensive and authoritative presentation of current methods and applications for Boltzmann models (i.e., nonlinear kinetic theory) and computational methods. Selected applications address topics in complex fluid flows, geophysical problems, communications, and biochemical processes.
Table of Contents
Preface
Generalized Kinetic Models in Applied Science / N. Bellomo and M. Pulvirenti
Rapid Granular Flows: Kinetics and Hydrodynamics / I. Goldhirsch
Collective Behavior of One-Dimensional Granular Media / D. Benedetto, E. Caglioti, and M. Pulvirenti
Notes on Mathematical Problems on the Dynamics of Dispersed Particles Interacting through a Fluid / P.E. Jabin and B. Perthame
The Becker-Döring Equations / M. Slemrod
Nonlinear Kinetic Models with Chemical Reactions / C.P. Grünfeld
Development of Boltzmann Models in Mathematical Biology / N. Bellomo and S. Stöcker
Kinetic Traffic Flow Models / A. Klar and R. Wegener
Kinetic Limits for Large Communication Networks / C. Grahm
Numerical Simulation of the Boltzmann Equation by Particle Methods / J. Struckmaier