Generalized Kinetic Models In Applied Sciences
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Generalized Kinetic Models In Applied Sciences
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Author : Luisa Arlotti
language : en
Publisher:
Release Date : 2003
Generalized Kinetic Models In Applied Sciences written by Luisa Arlotti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Electronic books categories.
Generalized Kinetic Models In Applied Sciences
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Author : Luisa Arlotti
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-08-12
Generalized Kinetic Models In Applied Sciences written by Luisa Arlotti and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-12 with Science categories.
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 above literature motivates applied mathematicians to study the Cauchy problem and to develop an asymptotic analysis for models regarded as developments of the Boltzmann equation. This book aims to initiate the research plan by the analyzing afore mentioned analysis problems. 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. The book is essentially devoted to analytic aspects and deals with the analysis of the Cauchy problem and with the development of an asymptotic theory to obtain the macroscopic description from the mesoscopic one.
Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models
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Author : N. Bellomo
language : en
Publisher: World Scientific
Release Date : 2000
Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models written by N. Bellomo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Science categories.
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.
Generalized Kinetic Models In Applied Sciences
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Author : Luisa Arlotti
language : en
Publisher: World Scientific
Release Date : 2003
Generalized Kinetic Models In Applied Sciences written by Luisa Arlotti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
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.
Modeling In Applied Sciences
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Author : Nicola Bellomo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Modeling In Applied Sciences written by Nicola Bellomo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
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.
Modeling In Applied Sciences
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Author : N. Bellomo
language : en
Publisher:
Release Date : 2000
Modeling In Applied Sciences written by N. Bellomo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematical models categories.
Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models
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Author : Nicola Bellomo
language : en
Publisher: World Scientific
Release Date : 2000-01-11
Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models written by Nicola Bellomo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-11 with Mathematics categories.
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.
High Dimensional Nonlinear Diffusion Stochastic Processes
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Author : Yevgeny Mamontov
language : en
Publisher: World Scientific
Release Date : 2001
High Dimensional Nonlinear Diffusion Stochastic Processes written by Yevgeny Mamontov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Annotation This book is one of the first few devoted to high-dimensional diffusion stochastic processes with nonlinear coefficients. These processes are closely associated with large systems of Ito's stochastic differential equations and with discretized-in-the-parameter versions of Ito's stochastic differential equations that are nonlocally dependent on the parameter. The latter models include Ito's stochastic integro-differential, partial differential and partial integro-differential equations.The book presents the new analytical treatment which can serve as the basis of a combined, analytical -- numerical approach to greater computational efficiency. Some examples of the modelling of noise in semiconductor devices are provided
Modeling And Computational Methods For Kinetic Equations
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Author : Pierre Degond
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Modeling And Computational Methods For Kinetic Equations written by Pierre Degond and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the fundamentals of the theory. Emphasizing modeling techniques and numerical methods, the book provides a unified treatment of kinetic equations not found in more focused works. Specific applications presented include plasma kinetic models, traffic flow models, granular media models, and coagulation-fragmentation problems. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.
Mathematical Models Of The Cell And Cell Associated Objects
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Author : Viktor V. Ivanov
language : en
Publisher: Elsevier
Release Date : 2006-05-10
Mathematical Models Of The Cell And Cell Associated Objects written by Viktor V. Ivanov and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-10 with Mathematics categories.
This book gives the reader a survey of hundreds results in the field of the cell and cell associated objects modeling. Applications to modeling in the areas of AIDS, cancers and life longevity are investigated in this book. Introduces and proves fundamental properties of evolutionary systems on optimal distribution of their various resources on their internal and external functions Gives detailed analysis of applications to modeling AIDS, cancers, and life longevity Introducing and grounding the respective numerical algorithms and software Detailed analysis of hundreds of scientific works in the field of mathematical modeling of the cell and cell associated objects