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Generalized Kinetic Models In Applied Sciences
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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 and published by World Scientific. This book was released on 2003 with total page 224 pages. 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.
Book Synopsis Modeling in Applied Sciences by : Nicola Bellomo
Download or read book Modeling in Applied Sciences written by Nicola Bellomo and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 429 pages. 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.
Book Synopsis Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models by : Nicola Bellomo
Download or read book Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models written by Nicola Bellomo and published by World Scientific. This book was released on 2000-01-11 with total page 355 pages. 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.
Book Synopsis High-dimensional Nonlinear Diffusion Stochastic Processes by : Yevgeny Mamontov
Download or read book High-dimensional Nonlinear Diffusion Stochastic Processes written by Yevgeny Mamontov and published by World Scientific. This book was released on 2001 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Mathematical Models of the Cell and Cell Associated Objects by : Viktor V. Ivanov
Download or read book Mathematical Models of the Cell and Cell Associated Objects written by Viktor V. Ivanov and published by Elsevier. This book was released on 2006-05-10 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Methods of Small Parameter in Mathematical Biology by : Jacek Banasiak
Download or read book Methods of Small Parameter in Mathematical Biology written by Jacek Banasiak and published by Springer Science & Business. This book was released on 2014-04-19 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents new tools for modeling multiscale biological processes. Natural processes are usually driven by mechanisms widely differing from each other in the time or space scale at which they operate and thus should be described by appropriate multiscale models. However, looking at all such scales simultaneously is often infeasible, costly, and provides information that is redundant for a particular application. Hence, there has been a growing interest in providing a more focused description of multiscale processes by aggregating variables in a way that is relevant to the purpose at hand and preserves the salient features of the dynamics. Many ad hoc methods have been devised, and the aim of this book is to present a systematic way of deriving the so-called limit equations for such aggregated variables and ensuring that the coefficients of these equations encapsulate the relevant information from the discarded levels of description. Since any approximation is only valid if an estimate of the incurred error is available, the tools the authors describe allow for proving that the solutions to the original multiscale family of equations converge to the solution of the limit equation if the relevant parameter converges to its critical value. The chapters are arranged according to the mathematical complexity of the analysis, from systems of ordinary linear differential equations, through nonlinear ordinary differential equations, to linear and nonlinear partial differential equations. Many chapters begin with a survey of mathematical techniques needed for the analysis. All problems discussed in this book belong to the class of singularly perturbed problems; that is, problems in which the structure of the limit equation is significantly different from that of the multiscale model. Such problems appear in all areas of science and can be attacked using many techniques. Methods of Small Parameter in Mathematical Biology will appeal to senior undergraduate and graduate students in applied and biomathematics, as well as researchers specializing in differential equations and asymptotic analysis.
Book Synopsis Modeling Complex Living Systems by : N. Bellomo
Download or read book Modeling Complex Living Systems written by N. Bellomo and published by Springer Science & Business Media. This book was released on 2008 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops different mathematical methods and tools to model living systems. This book presents material that can be used in such real-world applications as immunology, transportation engineering, and economics. It is of interest to those involved in modeling complex social systems and living matter in general.
Book Synopsis Selected Topics in Cancer Modeling by : Nicola Bellomo
Download or read book Selected Topics in Cancer Modeling written by Nicola Bellomo and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of selected chapters offers a comprehensive overview of state-of-the-art mathematical methods and tools for modeling and analyzing cancer phenomena. Topics covered include stochastic evolutionary models of cancer initiation and progression, tumor cords and their response to anticancer agents, and immune competition in tumor progression and prevention. The complexity of modeling living matter requires the development of new mathematical methods and ideas. This volume, written by first-rate researchers in the field of mathematical biology, is one of the first steps in that direction.
Book Synopsis Applied and Industrial Mathematics in Italy II by : Vincenzo Cutello
Download or read book Applied and Industrial Mathematics in Italy II written by Vincenzo Cutello and published by World Scientific. This book was released on 2007 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: Industrial mathematics is evolving into an important branch of mathematics. Mathematicians, in particular in Italy, are becoming increasingly aware of this new trend and are engaged in bridging the gap between highly specialized mathematical research and the emerging demand for innovation from industry. The contributions in this volume provide both R&D workers in industry with a general view of existing skills, and academics with state-of-the-art applications of mathematics to real-world problems, which may also be incorporated in advanced courses.
Book Synopsis Wavelet and Wave Analysis as Applied to Materials with Micro Or Nanostructure by : Carlo Cattani
Download or read book Wavelet and Wave Analysis as Applied to Materials with Micro Or Nanostructure written by Carlo Cattani and published by World Scientific. This book was released on 2007 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This seminal book unites three different areas of modern science: the micromechanics and nanomechanics of composite materials; wavelet analysis as applied to physical problems; and the propagation of a new type of solitary wave in composite materials, nonlinear waves. Each of the three areas is described in a simple and understandable form, focusing on the many perspectives of the links among the three.All of the techniques and procedures are described here in the clearest and most open form, enabling the reader to quickly learn and use them when faced with the new and more advanced problems that are proposed in this book. By combining these new scientific concepts into a unitary model and enlightening readers on this pioneering field of research, readers will hopefully be inspired to explore the more advanced aspects of this promising scientific direction. The application of wavelet analysis to nanomaterials and waves in nanocomposites can be very appealing to both specialists working on theoretical developments in wavelets as well as specialists applying these methods and experiments in the mechanics of materials.
Book Synopsis Mathematical Methods for the Natural and Engineering Sciences by : Ronald E. Mickens
Download or read book Mathematical Methods for the Natural and Engineering Sciences written by Ronald E. Mickens and published by World Scientific. This book was released on 2004 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a variety of methods required for the analysis and solution of equations which arise in the modeling of phenomena from the natural and engineering sciences. It can be used productively by both undergraduate and graduate students, as well as others who need to learn and understand these techniques. A detailed discussion is also presented for several topics that are usually not included in standard textbooks at this level: qualitative methods for differential equations, dimensionalization and scaling, elements of asymptotics, difference equations, and various perturbation methods. Each chapter contains a large number of worked examples and provides references to the appropriate literature.
Book Synopsis Advanced Mathematical And Computational Tools In Metrology Vi by : Patrizia Ciarlini
Download or read book Advanced Mathematical And Computational Tools In Metrology Vi written by Patrizia Ciarlini and published by World Scientific. This book was released on 2004-07-09 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects refereed contributions based on the presentations made at the Sixth Workshop on Advanced Mathematical and Computational Tools in Metrology, held at the Istituto di Metrologia “G. Colonnetti” (IMGC), Torino, Italy, in September 2003. It provides a forum for metrologists, mathematicians and software engineers that will encourage a more effective synthesis of skills, capabilities and resources, and promotes collaboration in the context of EU programmes, EUROMET and EA projects, and MRA requirements. It contains articles by an important, worldwide group of metrologists and mathematicians involved in measurement science and, together with the five previous volumes in this series, constitutes an authoritative source for the mathematical, statistical and software tools necessary to modern metrology.The proceedings have been selected for coverage in:Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)CC Proceedings — Engineering & Physical Sciences
Book Synopsis Complex Systems and Society by : Nicola Bellomo
Download or read book Complex Systems and Society written by Nicola Bellomo and published by Springer Science & Business Media. This book was released on 2013-05-24 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work aims to foster the interdisciplinary dialogue between mathematicians and socio-economic scientists. Interaction among scholars and practitioners traditionally coming from different research areas is necessary more than ever in order to better understand many real-world problems we face today. On the one hand, mathematicians need economists and social scientists to better address the methodologies they design in a more realistic way; on the other hand, economists and social scientists need to be aware of sound mathematical modelling tools in order to understand and, ultimately, solve the complex problems they encounter in their research. With this goal in mind, this work is designed to take into account a multidisciplinary approach that will encourage the transfer of knowledge, ideas, and methodology from one discipline to the other. In particular, the work has three main themes: Demystifying and unravelling complex systems; Introducing models of individual behaviours in the social and economic sciences; Modelling socio-economic sciences as complex living systems. Specific tools examined in the work include a recently developed modelling approach using stochastic game theory within the framework of statistical mechanics and progressing up to modeling Darwinian evolution. Special attention is also devoted to social network theory as a fundamental instrument for the understanding of socio-economic systems.
Book Synopsis Active Particles, Volume 1 by : Nicola Bellomo
Download or read book Active Particles, Volume 1 written by Nicola Bellomo and published by Birkhäuser. This book was released on 2017-04-06 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects ten surveys on the modeling, simulation, and applications of active particles using methods ranging from mathematical kinetic theory to nonequilibrium statistical mechanics. The contributing authors are leading experts working in this challenging field, and each of their chapters provides a review of the most recent results in their areas and looks ahead to future research directions. The approaches to studying active matter are presented here from many different perspectives, such as individual-based models, evolutionary games, Brownian motion, and continuum theories, as well as various combinations of these. Applications covered include biological network formation and network theory; opinion formation and social systems; control theory of sparse systems; theory and applications of mean field games; population learning; dynamics of flocking systems; vehicular traffic flow; and stochastic particles and mean field approximation. Mathematicians and other members of the scientific community interested in active matter and its many applications will find this volume to be a timely, authoritative, and valuable resource.
Book Synopsis Fundamentals of Enzyme Kinetics by : Athel Cornish-Bowden
Download or read book Fundamentals of Enzyme Kinetics written by Athel Cornish-Bowden and published by Elsevier. This book was released on 2014-05-20 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Enzyme Kinetics details the rate of reactions catalyzed by different enzymes and the effects of varying the conditions on them. The book includes the basic principles of chemical kinetics, especially the order of a reaction and its rate constraints. The text also gives an introduction to enzyme kinetics - the idea of an enzyme-substrate complex; the Michaelis-Menten equation; the steady state treatment; and the validity of its assumption. Practical considerations, the derivation of steady-state rate equations, inhibitors and activators, and two-substrate reactions are also explained. Problems after the end of each chapter have also been added, as well as their solutions at the end of the book, to test the readers' learning. The text is highly recommended for undergraduate students in biochemistry who wish to study about enzymes or focus completely on enzymology, as most of the mathematics used in this book, which have been explained in detail to remove most barriers of understanding, is elementary.
Book Synopsis Modelling Mathematical Methods and Scientific Computation by : Nicola Bellomo
Download or read book Modelling Mathematical Methods and Scientific Computation written by Nicola Bellomo and published by CRC Press. This book was released on 1994-12-22 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addressed to engineers, scientists, and applied mathematicians, this book explores the fundamental aspects of mathematical modelling in applied sciences and related mathematical and computational methods. After providing the general framework needed for mathematical modelling-definitions, classifications, general modelling procedures, and validation methods-the authors deal with the analysis of discrete models. This includes modelling methods and related mathematical methods. The analysis of models is defined in terms of ordinary differential equations. The analysis of continuous models, particularly models defined in terms of partial differential equations, follows. The authors then examine inverse type problems and stochastic modelling. Three appendices provide a concise guide to functional analysis, approximation theory, and probability, and a diskette included with the book includes ten scientific programs to introduce the reader to scientific computation at a practical level.
Book Synopsis Computational Methods for Kinetic Models of Magnetically Confined Plasmas by : J. Killeen
Download or read book Computational Methods for Kinetic Models of Magnetically Confined Plasmas written by J. Killeen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because magnetically confined plasmas are generally not found in a state of thermodynamic equilibrium, they have been studied extensively with methods of applied kinetic theory. In closed magnetic field line confinement devices such as the tokamak, non-Maxwellian distortions usually occur as a result of auxiliary heating and transport. In magnetic mirror configurations even the intended steady state plasma is far from local thermodynamic equilibrium because of losses along open magnetic field lines. In both of these major fusion devices, kinetic models based on the Boltzmann equation with Fokker-Planck collision terms have been successful in representing plasma behavior. The heating of plasmas by energetic neutral beams or microwaves, the production and thermalization of a-particles in thermonuclear reactor plasmas, the study of runaway electrons in tokamaks, and the performance of two-energy compo nent fusion reactors are some examples of processes in which the solution of kinetic equations is appropriate and, moreover, generally necessary for an understanding of the plasma dynamics. Ultimately, the problem is to solve a nonlinear partial differential equation for the distribution function of each charged plasma species in terms of six phase space variables and time. The dimensionality of the problem may be reduced through imposing certain symmetry conditions. For example, fewer spatial dimensions are needed if either the magnetic field is taken to be uniform or the magnetic field inhomogeneity enters principally through its variation along the direction of the field.
