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Generalized Kinetic Models in Applied Sciences

2003 Mathematics
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Release : 2003
Genre : Mathematics
Kind : eBook
Book Rating : 604/5 ( reviews)

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Book Synopsis Generalized Kinetic Models in Applied Sciences by : Luisa Arlotti

Download or read book Generalized Kinetic Models in Applied Sciences written by Luisa Arlotti. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with analytic problems related to some developments and generalizations of the Boltzmann equation toward the modeling and qualitative analysis of large systems that are of interest in applied sciences. These generalizations are documented in the various surveys edited by Bellomo and Pulvirenti with reference to models of granular media, traffic flow, mathematical biology, communication networks, and coagulation models. The first generalization dealt with refers to the averaged Boltzmann equation, which is obtained by suitable averaging of the distribution function of the field particles into the action domain of the test particle. This model is further developed to describe equations with dissipative collisions and a class of models that are of interest in mathematical biology. In this latter case the state of the particles is defined not only by a mechanical variable but also by a biological microscopic state.

Generalized Kinetic Models in Applied Sciences

2003 Electronic books
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Release : 2003
Genre : Electronic books
Kind : eBook
Book Rating : 045/5 ( reviews)

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Book Synopsis Generalized Kinetic Models in Applied Sciences by : Luisa Arlotti

Download or read book Generalized Kinetic Models in Applied Sciences written by Luisa Arlotti. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt:

Modeling in Applied Sciences

2013-11-11 Mathematics
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Release : 2013-11-11
Genre : Mathematics
Kind : eBook
Book Rating : 131/5 ( reviews)

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Book Synopsis Modeling in Applied Sciences by : Nicola Bellomo

Download or read book Modeling in Applied Sciences written by Nicola Bellomo. This book was released on 2013-11-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

From the Boltzmann Equation to Generalized Kinetic Models in Applied Sciences

1997
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Release : 1997
Genre :
Kind : eBook
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Book Synopsis From the Boltzmann Equation to Generalized Kinetic Models in Applied Sciences by : N. Bellomo

Download or read book From the Boltzmann Equation to Generalized Kinetic Models in Applied Sciences written by N. Bellomo. This book was released on 1997. Available in PDF, EPUB and Kindle. Book excerpt:

Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models

2000 Science
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Release : 2000
Genre : Science
Kind : eBook
Book Rating : 783/5 ( reviews)

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Book Synopsis Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models by : N. Bellomo

Download or read book Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models written by N. Bellomo. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions. 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.

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