Lecture Notes On The Discretization Of The Boltzmann Equation
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Lecture Notes On The Discretization Of The Boltzmann Equation
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Author : Nicola Bellomo
language : en
Publisher: World Scientific
Release Date : 2003
Lecture Notes On The Discretization Of The Boltzmann Equation 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 2003 with Science categories.
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 Schrrer). Readership: Higher level postgraduates in applied mathematics.
Lecture Notes On The Discretization Of The Boltzmann Equation
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Author : Nicola Bellomo
language : en
Publisher: World Scientific
Release Date : 2003-01-24
Lecture Notes On The Discretization Of The Boltzmann Equation 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 2003-01-24 with Mathematics categories.
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.
A Quest Towards A Mathematical Theory Of Living Systems
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Author : Nicola Bellomo
language : en
Publisher: Birkhäuser
Release Date : 2017-07-13
A Quest Towards A Mathematical Theory Of Living Systems written by Nicola Bellomo and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-13 with Mathematics categories.
This monograph aims to lay the groundwork for the design of a unified mathematical approach to the modeling and analysis of large, complex systems composed of interacting living things. Drawing on twenty years of research in various scientific fields, it explores how mathematical kinetic theory and evolutionary game theory can be used to understand the complex interplay between mathematical sciences and the dynamics of living systems. The authors hope this will contribute to the development of new tools and strategies, if not a new mathematical theory. The first chapter discusses the main features of living systems and outlines a strategy for their modeling. The following chapters then explore some of the methods needed to potentially achieve this in practice. Chapter Two provides a brief introduction to the mathematical kinetic theory of classical particles, with special emphasis on the Boltzmann equation; the Enskog equation, mean field models, and Monte Carlo methods are also briefly covered. Chapter Three uses concepts from evolutionary game theory to derive mathematical structures that are able to capture the complexity features of interactions within living systems. The book then shifts to exploring the relevant applications of these methods that can potentially be used to derive specific, usable models. The modeling of social systems in various contexts is the subject of Chapter Five, and an overview of modeling crowd dynamics is given in Chapter Six, demonstrating how this approach can be used to model the dynamics of multicellular systems. The final chapter considers some additional applications before presenting an overview of open problems. The authors then offer their own speculations on the conceptual paths that may lead to a mathematical theory of living systems hoping to motivate future research activity in the field. A truly unique contribution to the existing literature, A Quest Toward a Mathematical Theory of Living Systems is an important book that will no doubt have a significant influence on the future directions of the field. It will be of interest to mathematical biologists, systems biologists, biophysicists, and other researchers working on understanding the complexities of living systems.
Continuum Thermodynamics
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Author : Wilmanski
language : en
Publisher: World Scientific
Release Date : 2008
Continuum Thermodynamics written by Wilmanski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
This book is a unique presentation of thermodynamic methods of construction of continuous models. It is based on a uniform approach following from the entropy inequality and using Lagrange multipliers as auxiliary quantities in its evaluation. It covers a wide range of models — ideal gases, thermoviscoelastic fluids, thermoelastic and thermoviscoelastic solids, plastic polycrystals, miscible and immiscible mixtures, and many others. The structure of phenomenological thermodynamics is justified by a systematic derivation from the Liouville equation, through the BBGKY-hierarchy-derived Boltzmann equation, to an extended thermodynamics. In order to simplify the reading, an extensive introduction to classical continuum mechanics and thermostatics is included. As a complementary volume to Part II, which will contain applications and examples, and to Part III, which will cover numerical methods, only a few simple examples are presented in this first Part. One exception is an extensive example of a linear poroelastic material because it will not appear in future Parts.The book is the first presentation of continuum thermodynamics in which foundations of continuum mechanics, microscopic foundations and transition to extended thermodynamics, applications of extended thermodynamics beyond ideal gases, and thermodynamic foundations of various material theories are exposed in a uniform and rational way. The book may serve both as a support for advanced courses as well as a desk reference.
Continuum Thermodynamics Part I Foundations
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Author : Krzysztof Wilmanski
language : en
Publisher: World Scientific
Release Date : 2008-11-25
Continuum Thermodynamics Part I Foundations written by Krzysztof Wilmanski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-25 with Science categories.
This book is a unique presentation of thermodynamic methods of construction of continuous models. It is based on a uniform approach following from the entropy inequality and using Lagrange multipliers as auxiliary quantities in its evaluation. It covers a wide range of models — ideal gases, thermoviscoelastic fluids, thermoelastic and thermoviscoelastic solids, plastic polycrystals, miscible and immiscible mixtures, and many others. The structure of phenomenological thermodynamics is justified by a systematic derivation from the Liouville equation, through the BBGKY-hierarchy-derived Boltzmann equation, to an extended thermodynamics. In order to simplify the reading, an extensive introduction to classical continuum mechanics and thermostatics is included. As a complementary volume to Part II, which will contain applications and examples, and to Part III, which will cover numerical methods, only a few simple examples are presented in this first Part. One exception is an extensive example of a linear poroelastic material because it will not appear in future Parts.The book is the first presentation of continuum thermodynamics in which foundations of continuum mechanics, microscopic foundations and transition to extended thermodynamics, applications of extended thermodynamics beyond ideal gases, and thermodynamic foundations of various material theories are exposed in a uniform and rational way. The book may serve both as a support for advanced courses as well as a desk reference.
Continuum Thermodynamics Part I
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Author : Krzysztof Wilmanski
language : en
Publisher: World Scientific
Release Date : 2008
Continuum Thermodynamics Part I written by Krzysztof Wilmanski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
This book is a unique presentation of thermodynamic methods of construction of continuous models. It is based on a uniform approach following from the entropy inequality and using Lagrange multipliers as auxiliary quantities in its evaluation. It covers a wide range of models OCo ideal gases, thermoviscoelastic fluids, thermoelastic and thermoviscoelastic solids, plastic polycrystals, miscible and immiscible mixtures, and many others. The structure of phenomenological thermodynamics is justified by a systematic derivation from the Liouville equation, through the BBGKY-hierarchy-derived Boltzmann equation, to an extended thermodynamics. In order to simplify the reading, an extensive introduction to classical continuum mechanics and thermostatics is included. As a complementary volume to Part II, which will contain applications and examples, and to Part III, which will cover numerical methods, only a few simple examples are presented in this first Part. One exception is an extensive example of a linear poroelastic material because it will not appear in future Parts. The book is the first presentation of continuum thermodynamics in which foundations of continuum mechanics, microscopic foundations and transition to extended thermodynamics, applications of extended thermodynamics beyond ideal gases, and thermodynamic foundations of various material theories are exposed in a uniform and rational way. The book may serve both as a support for advanced courses as well as a desk reference.
Motor Vehicle Dynamics Modelling And Simulation
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Author : Giancarlo Genta
language : en
Publisher: World Scientific
Release Date : 1997-04-19
Motor Vehicle Dynamics Modelling And Simulation written by Giancarlo Genta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-04-19 with Technology & Engineering categories.
The book starts with an historical overview of road vehicles. The first part deals with the forces exchanged between the vehicle and the road and the vehicle and the air with the aim of supplying the physical facts and the relevant mathematical models about the forces which dominate the dynamics of the vehicle.The second part deals with the dynamic behaviour of the vehicle in normal driving conditions with some extensions towards conditions encountered in high-speed racing driving.
Dissipative Phase Transitions
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Author : Pierluigi Colli
language : en
Publisher: World Scientific
Release Date : 2006-03-06
Dissipative Phase Transitions written by Pierluigi Colli and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-06 with Mathematics categories.
Phase transition phenomena arise in a variety of relevant real world situations, such as melting and freezing in a solid-liquid system, evaporation, solid-solid phase transitions in shape memory alloys, combustion, crystal growth, damage in elastic materials, glass formation, phase transitions in polymers, and plasticity.The practical interest of such phenomenology is evident and has deeply influenced the technological development of our society, stimulating intense mathematical research in this area.This book analyzes and approximates some models and related partial differential equation problems that involve phase transitions in different contexts and include dissipation effects.
Advanced Mathematical Computational Tools In Metrology Vii
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Author : P. Ciarlini
language : en
Publisher: World Scientific
Release Date : 2006
Advanced Mathematical Computational Tools In Metrology Vii written by P. Ciarlini and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This volume collects the refereed contributions based on the presentations made at the Seventh Workshop on Advanced Mathematical and Computational Tools in Metrology, a forum for metrologists, mathematicians and software engineers that will encourage a more effective synthesis of skills, capabilities and resources. The volume contains articles by world renowned metrologists and mathematicians involved in measurement science and, together with the six previous volumes in this series, constitutes an authoritative source of the mathematical, statistical and software tools necessary in modern metrology. Sample Chapter(s). Chapter 1: Modelling Measurement Processes in Complex Systems with Partial Differential Equations: From Heat Conduction to the Heart (537 KB). Contents: Modeling Measurement Processes in Complex Systems with Partial Differential Equations: From Heat Conduction to the Heart (M Bnr et al.); Mereotopological Approach for Measurement Software (E Benoit & R Dapoigny); Data Evaluation of Key Comparisons Involving Several Artefacts (M G Cox et al.); Box-Cox Transformations and Robust Control Charts in SPC (M I Gomes & F O Figueiredo); Multisensor Data Fusion and Its Application to Decision Making (P S Giruo et al.); Generic System Design for Measurement Databases OCo Applied to Calibrations in Vacuum Metrology, Bio-Signals and a Template System (H Gross et al.); Evaluation of Repeated Measurements from the Viewpoint of Conventional and Bayesian Statistics (I Lira & W WAger); Detection of Outliers in Interlaboratory Testing (C Perruchet); On Appropriate Methods for the Validation of Metrological Software (D Richter et al.); Data Analysis OCo A Dialogue with the Data (D S Sivia); Validation of Soft Sensors in Monitoring Ambient Parameters (P Ciarlini et al.); Evaluation of Standard Uncertainties in Nested Structures (E Filipe); Measurement System Analysis and Statistical Process Control (A B Forbes); Monte Carlo Study on Logical and Statistical Correlation (B Siebert et al.); Some Problems Concerning the Estimate of the Degree of Equivalence in MRA Key Comparisons and of Its Uncertainty (F Pavese); Preparing for a European Research Area Network in Metrology: Where are We Now? (M Khne et al.); and other papers. Readership: Researchers, graduate students, academics and professionals in metrology."
Applied And Industrial Mathematics In Italy Proceedings Of The 7th Conference
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Author : Mario Primicerio
language : en
Publisher: World Scientific
Release Date : 2005-06-14
Applied And Industrial Mathematics In Italy Proceedings Of The 7th Conference written by Mario Primicerio and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-14 with Mathematics categories.
Industrial mathematics is evolving into an important branch of mathematics. Mathematicians, in Italy in particular, 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. In this respect, 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.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