Stochastic Numerics For The Boltzmann Equation

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Stochastic Numerics For The Boltzmann Equation

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Author : Sergej Rjasanow
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-04

Stochastic Numerics For The Boltzmann Equation written by Sergej Rjasanow 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 2005-11-04 with Mathematics categories.

Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes as a unifying framework. The second goal is a systematic treatment of an extension of DSMC, called stochastic weighted particle method. This method includes several new features, which are introduced for the purpose of variance reduction (rare event simulation). Rigorous convergence results as well as detailed numerical studies are presented.

Stochastic Numerical Methods

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Author : Raúl Toral
language : en
Publisher: John Wiley & Sons
Release Date : 2014-06-26

Stochastic Numerical Methods written by Raúl Toral and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-26 with Science categories.

Stochastic Numerical Methods introduces at Master level the numerical methods that use probability or stochastic concepts to analyze random processes. The book aims at being rather general and is addressed at students of natural sciences (Physics, Chemistry, Mathematics, Biology, etc.) and Engineering, but also social sciences (Economy, Sociology, etc.) where some of the techniques have been used recently to numerically simulate different agent-based models. Examples included in the book range from phase-transitions and critical phenomena, including details of data analysis (extraction of critical exponents, finite-size effects, etc.), to population dynamics, interfacial growth, chemical reactions, etc. Program listings are integrated in the discussion of numerical algorithms to facilitate their understanding. From the contents: Review of Probability Concepts Monte Carlo Integration Generation of Uniform and Non-uniform Random Numbers: Non-correlated Values Dynamical Methods Applications to Statistical Mechanics Introduction to Stochastic Processes Numerical Simulation of Ordinary and Partial Stochastic Differential Equations Introduction to Master Equations Numerical Simulations of Master Equations Hybrid Monte Carlo Generation of n-Dimensional Correlated Gaussian Variables Collective Algorithms for Spin Systems Histogram Extrapolation Multicanonical Simulations

Advances In Numerical Methods For Hyperbolic Balance Laws And Related Problems

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Author : Giacomo Albi
language : en
Publisher: Springer Nature
Release Date : 2023-06-02

Advances In Numerical Methods For Hyperbolic Balance Laws And Related Problems written by Giacomo Albi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-02 with Mathematics categories.

A broad range of phenomena in science and technology can be described by non-linear partial differential equations characterized by systems of conservation laws with source terms. Well known examples are hyperbolic systems with source terms, kinetic equations, and convection-reaction-diffusion equations. This book collects research advances in numerical methods for hyperbolic balance laws and kinetic equations together with related modelling aspects. All the contributions are based on the talks of the speakers of the Young Researchers’ Conference “Numerical Aspects of Hyperbolic Balance Laws and Related Problems”, hosted at the University of Verona, Italy, in December 2021.

Entropy Methods For The Boltzmann Equation

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Author :
language : en
Publisher: Springer Science & Business Media
Release Date : 2007

Entropy Methods For The Boltzmann Equation written by 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 2007 with categories.

Computational Methods In Transport Verification And Validation

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Author : Frank Graziani
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-09

Computational Methods In Transport Verification And Validation written by Frank Graziani 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 2008-08-09 with Science categories.

The focus of this book deals with a cross cutting issue affecting all transport disciplines, whether it be photon, neutron, charged particle or neutrino transport. That is, verification and validation. In this book, we learn what the astrophysicist, atmospheric scientist, mathematician or nuclear engineer do to assess the accuracy of their code. What convergence studies, what error analysis, what problems do each field use to ascertain the accuracy of their transport simulations.

Uncertainty Quantification For Hyperbolic And Kinetic Equations

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Author : Shi Jin
language : en
Publisher: Springer
Release Date : 2018-03-20

Uncertainty Quantification For Hyperbolic And Kinetic Equations written by Shi Jin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-20 with Mathematics categories.

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.

Computational Fluid And Solid Mechanics 2003

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Author : K.J Bathe
language : en
Publisher: Elsevier
Release Date : 2003-06-02

Computational Fluid And Solid Mechanics 2003 written by K.J Bathe and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-02 with Technology & Engineering categories.

Bringing together the world's leading researchers and practitioners of computational mechanics, these new volumes meet and build on the eight key challenges for research and development in computational mechanics.Researchers have recently identified eight critical research tasks facing the field of computational mechanics. These tasks have come about because it appears possible to reach a new level of mathematical modelling and numerical solution that will lead to a much deeper understanding of nature and to great improvements in engineering design.The eight tasks are: - The automatic solution of mathematical models - Effective numerical schemes for fluid flows - The development of an effective mesh-free numerical solution method - The development of numerical procedures for multiphysics problems - The development of numerical procedures for multiscale problems - The modelling of uncertainties - The analysis of complete life cycles of systems - Education - teaching sound engineering and scientific judgement Readers of Computational Fluid and Solid Mechanics 2003 will be able to apply the combined experience of many of the world's leading researchers to their own research needs. Those in academic environments will gain a better insight into the needs and constraints of the industries they are involved with; those in industry will gain a competitive advantage by gaining insight into the cutting edge research being carried out by colleagues in academia. Features - Bridges the gap between academic researchers and practitioners in industry - Outlines the eight main challenges facing Research and Design in Computational mechanics and offers new insights into the shifting the research agenda - Provides a vision of how strong, basic and exciting education at university can be harmonized with life-long learning to obtain maximum value from the new powerful tools of analysis

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.

Interacting Multiagent Systems

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Author : Lorenzo Pareschi
language : en
Publisher: Oxford University Press, USA
Release Date : 2014

Interacting Multiagent Systems written by Lorenzo Pareschi and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Business & Economics categories.

Mathematical modelling of systems constituted by many agents using kinetic theory is a new tool that has proved effective in predicting the emergence of collective behaviours and self-organization. This idea has been applied by the authors to various problems which range from sociology to economics and life sciences.

Nonequilibrium Processes In The Planetary And Cometary Atmospheres Theory And Applications

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Author : Mikhail Ya. Marov
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-30

Nonequilibrium Processes In The Planetary And Cometary Atmospheres Theory And Applications written by Mikhail Ya. Marov 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 2001-11-30 with Science categories.

This book reviews the approach to the kinetic simulation of nonequilib rium processes in the planetary atmospheres which the authors developed and dealt with since the 1970s. The results of this study, which are focused on the nonequilibrium collisional processes in the atmospheres of planets and comets, are thoroughly reviewed and discussed. Many specific problems of atmospheric modeling, involving numerical evaluation of aeronomic pro cesses, are addressed and compared with the available experimental data. The kinetic approach proved to be especially effective to model the in teraction of the incident shortwave solar radiation with the rarefied gas of planetary upper atmospheres. It involves various processes of photolysis, en ergetic electron impacts, and accompanying numerous chemical reactions, as well as processes occurring in the intermediate ("transition") zones of planetary and cometary gas envelopes. The underlying mathematical treat ment is based on the stochastic approach for the solution of the Boltzmann type equation and implies the development of the efficient algorithms for its computer simulation. Some results of this study were previously summa rized in the monograph issued in Russian (Marov et al. , 1990) and later in the review paper published in Space Science Reviews (Marov et al. , 1996). The basic principles of stochastic simulation were first developed in the field of rarefied gas dynamics and were successfully applied to the solution of some engineering problems of aerodynamics and heat transfer.