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Coupling Of Kinetic Equations And Their Hydrodynamic Limits
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Book Synopsis Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences by : Giovanni Naldi
Download or read book Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences written by Giovanni Naldi and published by Springer Science & Business Media. This book was released on 2010-08-12 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior. The topics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful reference text for applied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems.
Book Synopsis Modeling and Computational Methods for Kinetic Equations by : Pierre Degond
Download or read book Modeling and Computational Methods for Kinetic Equations written by Pierre Degond and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. 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 works. Specific applications presented include plasma kinetic models, traffic flow models, granular media models, and coagulation-fragmentation problems. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications.
Download or read book ESAIM. written by and published by . This book was released on 1999 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Methods in Transport by : Frank Graziani
Download or read book Computational Methods in Transport written by Frank Graziani and published by Springer Science & Business Media. This book was released on 2006-02-17 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thereexistawiderangeofapplicationswhereasigni?cantfractionofthe- mentum and energy present in a physical problem is carried by the transport of particles. Depending on the speci?capplication, the particles involved may be photons, neutrons, neutrinos, or charged particles. Regardless of which phenomena is being described, at the heart of each application is the fact that a Boltzmann like transport equation has to be solved. The complexity, and hence expense, involved in solving the transport problem can be understood by realizing that the general solution to the 3D Boltzmann transport equation is in fact really seven dimensional: 3 spatial coordinates, 2 angles, 1 time, and 1 for speed or energy. Low-order appro- mations to the transport equation are frequently used due in part to physical justi?cation but many in cases, simply because a solution to the full tra- port problem is too computationally expensive. An example is the di?usion equation, which e?ectively drops the two angles in phase space by assuming that a linear representation in angle is adequate. Another approximation is the grey approximation, which drops the energy variable by averaging over it. If the grey approximation is applied to the di?usion equation, the expense of solving what amounts to the simplest possible description of transport is roughly equal to the cost of implicit computational ?uid dynamics. It is clear therefore, that for those application areas needing some form of transport, fast, accurate and robust transport algorithms can lead to an increase in overall code performance and a decrease in time to solution.
Book Synopsis Mathematical Methods for Hydrodynamic Limits by : Anna DeMasi
Download or read book Mathematical Methods for Hydrodynamic Limits written by Anna DeMasi and published by Springer. This book was released on 2006-11-14 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a variety of fields as physics, biology, population dynamics, economics, ... The purpose of the book is to make theseand other mathematical methods accessible to readers with a limited background in probability and physics by examining in detail a few models where the techniques emerge clearly, while extra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy of equations for the truncated correlation functions, the v-functions, are presented and applied to prove the validity of macroscopic equations forstochastic particle systems which are perturbations of the independent and of the symmetric simple exclusion processes. Entropy inequalities are discussed in the frame of the Guo-Papanicolaou-Varadhan technique and of theKipnis-Olla-Varadhan super exponential estimates, with reference to zero-range models. Discrete velocity Boltzmann equations, reaction diffusion equations and non linear parabolic equations are considered, as limits of particles models. Phase separation phenomena are discussed in the context of Glauber+Kawasaki evolutions and reaction diffusion equations. Although the emphasis is onthe mathematical aspects, the physical motivations are explained through theanalysis of the single models, without attempting, however to survey the entire subject of hydrodynamical limits.
Book Synopsis Uncertainty Quantification for Hyperbolic and Kinetic Equations by : Shi Jin
Download or read book Uncertainty Quantification for Hyperbolic and Kinetic Equations written by Shi Jin and published by Springer. This book was released on 2018-03-20 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Discrete and Continuous Dynamical Systems by :
Download or read book Discrete and Continuous Dynamical Systems written by and published by . This book was released on 2002 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Active Particles, Volume 2 by : Nicola Bellomo
Download or read book Active Particles, Volume 2 written by Nicola Bellomo and published by Springer Nature. This book was released on 2019-08-22 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume compiles eight recent surveys that present state-of-the-art results in the field of active matter at different scales, modeled by agent-based, kinetic, and hydrodynamic descriptions. Following the previously published volume, these chapters were written by leading experts in the field and accurately reflect the diversity of subject matter in theory and applications. Several mathematical tools are employed throughout the volume, including analysis of nonlinear PDEs, network theory, mean field approximations, control theory, and flocking analysis. The book also covers a wide range of applications, including: Biological network formation Social systems Control theory of sparse systems Dynamics of swarming and flocking systems Stochastic particles and mean field approximations 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 Molecular Hydrodynamics by : Jean Pierre Boon
Download or read book Molecular Hydrodynamics written by Jean Pierre Boon and published by Courier Corporation. This book was released on 1991-01-01 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate level introduction to the theory and applications of time correlation functions and the molecular theory of fluid dynamics. "Quite well organized . . . the literature coverage is impressive." — Physics Today. 110 illustrations.
Book Synopsis Theory of Simple Liquids by : Jean-Pierre Hansen
Download or read book Theory of Simple Liquids written by Jean-Pierre Hansen and published by Elsevier. This book was released on 1990-09-24 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive and up-to-date treatment of the theory of "simple" liquids. The new second edition has been rearranged and considerably expanded to give a balanced account both of basic theory and of the advances of the past decade. It presents the main ideas of modern liquid state theory in a way that is both pedagogical and self-contained. The book should be accessible to graduate students and research workers, both experimentalists and theorists, who have a good background in elementary mechanics. - Compares theoretical deductions with experimental results - Molecular dynamics - Monte Carlo computations - Covers ionic, metallic, and molecular liquids
Book Synopsis Rarefied Gas Dynamics by : J. Leith Potter
Download or read book Rarefied Gas Dynamics written by J. Leith Potter and published by . This book was released on 1977 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Excitations in a Bose-condensed Liquid by : Allan Griffin
Download or read book Excitations in a Bose-condensed Liquid written by Allan Griffin and published by Cambridge University Press. This book was released on 1993-08-19 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gives an up-to-date, systematic account of the microscopic theory of Bose-condensed fluids developed since the late 1950s. In contrast to the usual phenomenological discussions of superfluid 4He, the present treatment is built on the pivotal role of the Bose broken symmetry and a Bose condensate. The many-body formalism is developed, with emphasis on the one- and two-particle Green's functions and their relation to the density response function. These are all coupled together by the Bose broken symmetry, which provides the basis for understanding the elementary excitations and response functions in the hydrodynamic and collisionless regions. It also explains the difference between excitations in the superfluid and normal phases. Chapter 4 gives the first critical assessment of the experimental evidence for a Bose condensate in liquid 4He, based on high-momentum neutron scattering data.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1960 with total page 1006 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hypocoercivity written by Cdric Villani and published by American Mathematical Soc.. This book was released on 2009-10-08 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir attempts at a systematic study of convergence to stationary state for certain classes of degenerate diffusive equations, taking the general form ${\frac{\partial f}{\partial t}}+ L f =0$. The question is whether and how one can overcome the degeneracy by exploiting commutators.
Book Synopsis Progress in Astronautics and Aeronautics by :
Download or read book Progress in Astronautics and Aeronautics written by and published by . This book was released on 1977 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Understanding the Origin of Matter by : David Blaschke
Download or read book Understanding the Origin of Matter written by David Blaschke and published by Springer Nature. This book was released on 2022-09-14 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims at providing a solid basis for the education of the next generation of researchers in hot, dense QCD (Quantum ChromoDynamics) matter. This is a rapidly growing field at the interface of the smallest, i.e. subnuclear physics, and the largest scales, namely astrophysics and cosmology. The extensive lectures presented here are based on the material used at the training school of the European COST action THOR (Theory of hot matter in relativistic heavy-ion collisions). The book is divided in three parts covering ultrarelativistic heavy-ion collisions, several aspects related to QCD, and simulations of QCD and heavy-ion collisions. The scientific tools and methods discussed provide graduate students with the necessary skills to understand the structure of matter under extreme conditions of high densities, temperatures, and strong fields in the collapse of massive stars or a few microseconds after the big bang. In addition to the theory, the set of lectures presents hands-on material that includes an introduction to simulation programs for heavy-ion collisions, equations of state, and transport properties.
