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Author: Nicola Bellomo
Publisher: World Scientific
ISBN: 9814494259
Category : Mathematics
Languages : en
Pages : 356
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Book Description
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.
Author: Nicola Bellomo
Publisher: World Scientific
ISBN: 9814494259
Category : Mathematics
Languages : en
Pages : 356
Get Book
Book Description
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.
Author: N. Bellomo
Publisher: World Scientific
ISBN: 9789810240783
Category : Science
Languages : en
Pages : 360
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Book Description
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.
Author: N. Bellomo
Publisher: World Scientific
ISBN: 9789810221669
Category : Science
Languages : en
Pages : 276
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Book Description
This is a collection of four lectures on some mathematical aspects related to the nonlinear Boltzmann equation. The following topics are dealt with: derivation of kinetic equations, qualitative analysis of the initial value problem, singular perturbation analysis towards the hydrodynamic limit and computational methods towards the solution of problems in fluid dynamics.
Author: Luisa Arlotti
Publisher: World Scientific Publishing Company
ISBN: 9813106174
Category : Science
Languages : en
Pages : 220
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Book Description
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.
Author: Nicola Bellomo
Publisher: World Scientific
ISBN: 9814487066
Category : Mathematics
Languages : en
Pages : 316
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Book Description
This book presents contributions on the following topics: discretization methods in the velocity and space, analysis of the conservation properties, asymptotic convergence to the continuous equation when the number of velocities tends to infinity, and application of discrete models. It consists of ten chapters. Each chapter is written by applied mathematicians who have been active in the field, and whose scientific contributions are well recognized by the scientific community. 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
Author: Luisa Arlotti
Publisher: World Scientific
ISBN: 9789812385604
Category : Mathematics
Languages : en
Pages : 224
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Book Description
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.
Author: N. Bellomo
Publisher: World Scientific
ISBN: 9812382259
Category : Science
Languages : en
Pages : 317
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Book Description
This book presents contributions on the following topics: discretization methods in the velocity and space, analysis of the conservation properties, asymptotic convergence to the continuous equation when the number of velocities tends to infinity, and application of discrete models. It consists of ten chapters. Each chapter is written by applied mathematicians who have been active in the field, and whose scientific contributions are well recognized by the scientific community.
Author: Yevgeny Mamontov
Publisher: World Scientific
ISBN: 9789812810540
Category : Mathematics
Languages : en
Pages : 332
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Book Description
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
Author: P Ciarlini
Publisher: World Scientific
ISBN: 9814482412
Category : Computers
Languages : en
Pages : 368
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Book Description
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 Contents:Processing the Coherent Anomalies on Digitalized Surfaces in Wavelet Domain (P Ciarlini & M L Lo Cascio)Least Squares Adjustment in the Presence of Discrepant Data (M G Cox et al.)Some Differences between the Applied Statistical Approach for Measurement Uncertainty Theory and the Traditional Approach in Metrology and Testing (C Perruchet)Compound-Modelling of Metrological Data Series (F Pavese)Validation of Calibration Methods — A Practical Approach (E Filipe)A Hybrid Method for (ℓ1 Approximation (D Lei & J C Mason)A New Off-Line Gain Stabilisation Method Applied to Alpha-Particle Spectrometry (S Pommé & G Sibbens)Development of Software for ANOVA that Can Generate Expressions of Variance Expectations (H Tanaka et al.)Short Course on Uncertainty Evaluation (M G Cox)Software Requirements in Legal Metrology: Short Course Held Adjacent to the Conference (D Richter)and other articles Readership: Researchers, graduate students, academics, professionals and industrialists in metrology. Keywords:Metrology;Measurement Science;Statistics;Software ToolsKey Features:Promotes effective mathematical and computational tools in metrologyClarifies the modelling, statistical and computational requirements in metrologyAssists young researchers in metrology and related fieldsAddresses industrial requirements
Author: Carlo Cattani
Publisher: World Scientific
ISBN: 9812707840
Category : Science
Languages : en
Pages : 473
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Book Description
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.
