Modeling And Computational Methods For Kinetic Equations
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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. New applications in traffic flow engineering, granular media modeling, and polymer and phase transition physics have resulted in new numerical algorithms which depart from traditional stochastic Monte--Carlo methods. 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 theoretical or applied works. The book is divided into two parts. Part I is devoted to the most fundamental kinetic model: the Boltzmann equation of rarefied gas dynamics. Additionally, widely used numerical methods for the discretization of the Boltzmann equation are reviewed: the Monte--Carlo method, spectral methods, and finite-difference methods. Part II considers specific applications: plasma kinetic modeling using the Landau--Fokker--Planck equations, traffic flow modeling, granular media modeling, quantum kinetic modeling, and coagulation-fragmentation problems. "Modeling and Computational Methods of Kinetic Equations" will be accessible to readers working in different communities where kinetic theory is important: graduate students, researchers and practitioners in mathematical physics, applied mathematics, and various branches of engineering. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.
Modeling And Computational Methods For Kinetic Equations
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Author : Pierre Degond
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-04-07
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 2004-04-07 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. New applications in traffic flow engineering, granular media modeling, and polymer and phase transition physics have resulted in new numerical algorithms which depart from traditional stochastic Monte--Carlo methods. 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 theoretical or applied works. The book is divided into two parts. Part I is devoted to the most fundamental kinetic model: the Boltzmann equation of rarefied gas dynamics. Additionally, widely used numerical methods for the discretization of the Boltzmann equation are reviewed: the Monte--Carlo method, spectral methods, and finite-difference methods. Part II considers specific applications: plasma kinetic modeling using the Landau--Fokker--Planck equations, traffic flow modeling, granular media modeling, quantum kinetic modeling, and coagulation-fragmentation problems. "Modeling and Computational Methods of Kinetic Equations" will be accessible to readers working in different communities where kinetic theory is important: graduate students, researchers and practitioners in mathematical physics, applied mathematics, and various branches of engineering. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.
Modeling Approaches And Computational Methods For Particle Laden Turbulent Flows
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Author : Shankar Subramaniam
language : en
Publisher: Academic Press
Release Date : 2022-10-20
Modeling Approaches And Computational Methods For Particle Laden Turbulent Flows written by Shankar Subramaniam and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-20 with Technology & Engineering categories.
Modelling Approaches and Computational Methods for Particle-laden Turbulent Flows introduces the principal phenomena observed in applications where turbulence in particle-laden flow is encountered while also analyzing the main methods for analyzing numerically. The book takes a practical approach, providing advice on how to select and apply the correct model or tool by drawing on the latest research. Sections provide scales of particle-laden turbulence and the principal analytical frameworks and computational approaches used to simulate particles in turbulent flow. Each chapter opens with a section on fundamental concepts and theory before describing the applications of the modelling approach or numerical method. Featuring explanations of key concepts, definitions, and fundamental physics and equations, as well as recent research advances and detailed simulation methods, this book is the ideal starting point for students new to this subject, as well as an essential reference for experienced researchers. - Provides a comprehensive introduction to the phenomena of particle laden turbulent flow - Explains a wide range of numerical methods, including Eulerian-Eulerian, Eulerian-Lagrange, and volume-filtered computation - Describes a wide range of innovative applications of these models
Landau Equation Boltzmann Type Equations Discrete Models And Numerical Methods
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Author : Alexander V. Bobylev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-09-23
Landau Equation Boltzmann Type Equations Discrete Models And Numerical Methods written by Alexander V. Bobylev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-23 with Mathematics categories.
This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The second volume covers discrete velocity models of the Boltzmann equation, results on the Landau equation, and numerical (deterministic and stochastic) methods for the solution of kinetic equations.
Computational Methods For Estimating The Kinetic Parameters Of Biological Systems
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Author : Quentin Vanhaelen
language : en
Publisher: Humana
Release Date : 2022-12-24
Computational Methods For Estimating The Kinetic Parameters Of Biological Systems written by Quentin Vanhaelen and has been published by Humana this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-24 with Science categories.
This detailed book provides an overview of various classes of computational techniques, including machine learning techniques, commonly used for evaluating kinetic parameters of biological systems. Focusing on three distinct situations, the volume covers the prediction of the kinetics of enzymatic reactions, the prediction of the kinetics of protein-protein or protein-ligand interactions (binding rates, dissociation rates, binding affinities), and the prediction of relatively large set of kinetic rates of reactions usually found in quantitative models of large biological networks. Written for the highly successful Methods in Molecular Biology series, chapters include the kind of expert implementation advice that leads to successful results. Authoritative and practical, Computational Methods for Estimating the Kinetic Parameters of Biological Systems will be of great interest for researchers working through the challenge of identifying the best type of algorithm and who would like to use or develop a computational method for the estimation of kinetic parameters.
Computational Methods For Process Simulation
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Author : W. Fred Ramirez
language : en
Publisher: Butterworth-Heinemann
Release Date : 1997-11-20
Computational Methods For Process Simulation written by W. Fred Ramirez and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-20 with Science categories.
Process Modelling and simulation have proved to be extremely successful engineering tools for the design and optimisation of physical, chemical and biochemical processes. The use of simulation has expanded rapidly over the last two decades because of the availability of large high-speed computers and indeed has become even more widespread with the rise of the desk-top PC resources now available to nearly every engineer and student. In the chemical industry large, realistic non-linear problems are routinely solved with the aid of computer simulation. This has a number of benefits, including easy assessment of the economic desirability of a project, convenient investigation of the effects of changes to system variables, and finally the introduction of mathematical rigour into the design process and inherent assumptions that may not have been there before. Computational Methods for Process Simulation develops the methods needed for the simulation of real processes to be found in the process industries. It also stresses the engineering fundamentals used in developing process models. Steady state and dynamic systems are considered, for both spatially lumped and spatially distributed problems. It develops analytical and numerical computational techniques for algebraic, ordinary and partial differential equations, and makes use of computer software routines that are widely available. Dedicated software examples are available via the internet. - Written for a compulsory course element in the US - Includes examples using software used in academia and industry - Software available via the Internet
Modeling And Computational Methods For Multi Scale Quantum Dynamics And Kinetic Equations
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Author :
language : en
Publisher:
Release Date : 2013
Modeling And Computational Methods For Multi Scale Quantum Dynamics And Kinetic Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
This dissertation consists of two parts: quantum transitions (Part 1) and hydrodynamic limits of kinetic equations (Part 2). In both parts, we investigate the inner mathematical connections between equations for different physics at different scales, and use these connections to design efficient computational methods for multi-scale problems. Despite its numerous applications in chemistry and physics, the mathematics of quantum transition is not well understood. Using the Wigner transformation, we derive semi-classical models in phase space for two problems: the dynamics of electrons in crystals near band- crossing points; surface hopping of quantum molecules when the Born-Oppenheimer approximation breaks down. In both cases, particles may jump between states with comparable energies. Our models can capture the transition rates for such processes. We provide analytic analysis of and numerical methods for our models, demonstrated by explicit examples. The second part is to construct numerical methods for kinetic equation that are efficient in the hydrodynamic regime. Asymptotically, the kinetic equations reduce to fluid dynamics described by the Euler or Navier-Stokes equations in the fluid regime. Numerically the Boltzmann equation is still hard to handle in the hydrodynamic regime due to the stiff collision term. We review the theoretical work that links the two sets of equations, and present our asymptotic-preserving numerical solvers for the Boltzmann equation that naturally capture the asymptotic limits in the hydrodynamic regime. We also extend our methods to the case of multi-species systems.
Modeling Of Atmospheric Chemistry
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Author : Guy P. Brasseur
language : en
Publisher: Cambridge University Press
Release Date : 2017-06-19
Modeling Of Atmospheric Chemistry written by Guy P. Brasseur and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-19 with Nature categories.
This book presents the fundamental principles, mathematical methods and applications of atmospheric chemistry models for graduate students and researchers.
Continuum Mechanics Applied Mathematics And Scientific Computing Godunov S Legacy
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Author : Gennadii V. Demidenko
language : en
Publisher: Springer Nature
Release Date : 2020-04-03
Continuum Mechanics Applied Mathematics And Scientific Computing Godunov S Legacy written by Gennadii V. Demidenko and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-03 with Science categories.
This book is a liber amicorum to Professor Sergei Konstantinovich Godunov and gathers contributions by renowned scientists in honor of his 90th birthday. The contributions address those fields that Professor Godunov is most famous for: differential and difference equations, partial differential equations, equations of mathematical physics, mathematical modeling, difference schemes, advanced computational methods for hyperbolic equations, computational methods for linear algebra, and mathematical problems in continuum mechanics.
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.