Contents:From the Boltzmann Equation to Discretized Kinetic Models (N Bellomo & R Gatignol)Discrete Velocity Models for Gas Mixtures (C Cercignani)Discrete Velocity Models with Multiple Collisions (R Gatignol)Discretization of the Boltzmann Equation and the Semicontinuous Model (L Preziosi & L Rondoni)Semi-continuous Extended Kinetic Theory (W Koller)Steady Kinetic Boundary Value Problems (H Babovsky et al.)Computational Methods and Fast Algorithms for the Boltzmann Equation (L Pareschi)Discrete Velocity Models and Dynamical Systems (A Bobylev & N Bernhoff)Numerical Method for the Compton Scattering Operator (C Buet & S Cordier)Discrete Models of the Boltzmann Equation in Quantum Optics and Arbitrary Partition of the Velocity Space (F Schürrer)
Readership: Higher level postgraduates in applied mathematics.
Keywords:Boltzmann Equation;Discrete Velocity Models;Evolution of a System of Equal Particles;Discretization Methods;Asymptotic Convergence;Initial/Boundary ConditionsReviews:“This book is a collection of high quality and very interesting articles dedicated to Henri Cabannes, one of the pioneers and prime movers of discrete kinetic theory, on the occasion of his 80th birthday … This is a really nice collection of articles and will be a very useful reference for some time to come.”Mathematical Reviews
“This is a really nice collection of articles and will be a very useful reference for some time to come.”Zentralblatt MATH
Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the book provides a unified presentation of this topic with direct reference to modelling, mathematical statement of problems, qualitative and computational analysis, and applications. Models reported and proposed in the book refer to several fields of natural, applied and technological sciences. In particular, the following classes of models are discussed: population dynamics and socio-economic behaviours, models of aggregation and fragmentation phenomena, models of biology and immunology, traffic flow models, models of mixtures and particles undergoing classic and dissipative interactions.
Contents:Generalized Kinetic ModelsMathematical Background: Measure, Integration, TopologyModels of Population Dynamics with Stochastic InteractionsGeneralized Kinetic Models for Coagulation and FragmentationKinetic Cellular Models in the Immune System CompetitionKinetic Models for the Evolution of Antigens Generalized ShapeThe Boltzmann ModelGeneralized Kinetic Models for Traffic FlowDissipative Kinetic Models for Disparate MixturesResearch Perspectives
Readership: Researchers and postgraduate students in applied mathematics and mathematical physics.
Keywords:Antigenes Evolution;Boltzmann Equation;Cellular Interactions;Coagulation Models;Immune System;Kinetic Equations;Integro-Differential Equations;Mixtures of Clusters;Non-Linearity;Population Dynamics;Stochastic InteractionsReviews:
“… the book offers a simple and painless introduction to many applications of kinetic theory.”Mathematical Reviews
“… the authors give a unified presentation of the whole, large and highly general class of models among which the Boltzmann equation can be regarded as a particular, however relevant, example … mathematical problems related to the analysis of these models are often an interesting and challenging task for applied mathematics.”Mathematics Abstracts