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.

  Inhalt

  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