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Author: Matteo Colangeli
Publisher: Springer Science & Business Media
ISBN: 1461463068
Category : Science
Languages : en
Pages : 102
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Book Description
From Kinetic Models to Hydrodynamics serves as an introduction to the asymptotic methods necessary to obtain hydrodynamic equations from a fundamental description using kinetic theory models and the Boltzmann equation. The work is a survey of an active research area, which aims to bridge time and length scales from the particle-like description inherent in Boltzmann equation theory to a fully established “continuum” approach typical of macroscopic laws of physics.The author sheds light on a new method—using invariant manifolds—which addresses a functional equation for the nonequilibrium single-particle distribution function. This method allows one to find exact and thermodynamically consistent expressions for: hydrodynamic modes; transport coefficient expressions for hydrodynamic modes; and transport coefficients of a fluid beyond the traditional hydrodynamic limit. The invariant manifold method paves the way to establish a needed bridge between Boltzmann equation theory and a particle-based theory of hydrodynamics. Finally, the author explores the ambitious and longstanding task of obtaining hydrodynamic constitutive equations from their kinetic counterparts. The work is intended for specialists in kinetic theory—or more generally statistical mechanics—and will provide a bridge between a physical and mathematical approach to solve real-world problems.
Author: Matteo Colangeli
Publisher: Springer Science & Business Media
ISBN: 1461463068
Category : Science
Languages : en
Pages : 102
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Book Description
From Kinetic Models to Hydrodynamics serves as an introduction to the asymptotic methods necessary to obtain hydrodynamic equations from a fundamental description using kinetic theory models and the Boltzmann equation. The work is a survey of an active research area, which aims to bridge time and length scales from the particle-like description inherent in Boltzmann equation theory to a fully established “continuum” approach typical of macroscopic laws of physics.The author sheds light on a new method—using invariant manifolds—which addresses a functional equation for the nonequilibrium single-particle distribution function. This method allows one to find exact and thermodynamically consistent expressions for: hydrodynamic modes; transport coefficient expressions for hydrodynamic modes; and transport coefficients of a fluid beyond the traditional hydrodynamic limit. The invariant manifold method paves the way to establish a needed bridge between Boltzmann equation theory and a particle-based theory of hydrodynamics. Finally, the author explores the ambitious and longstanding task of obtaining hydrodynamic constitutive equations from their kinetic counterparts. The work is intended for specialists in kinetic theory—or more generally statistical mechanics—and will provide a bridge between a physical and mathematical approach to solve real-world problems.
Author: Giovanni Naldi
Publisher: Springer Science & Business Media
ISBN: 0817649468
Category : Mathematics
Languages : en
Pages : 437
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Book Description
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.
Author: Matteo Colangeli
Publisher:
ISBN: 9781461463078
Category :
Languages : en
Pages : 110
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Book Description
Author: Alexander V. Bobylev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110550172
Category : Mathematics
Languages : en
Pages : 344
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Book Description
This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The first volume covers many-particle dynamics, Maxwell models of the Boltzmann equation (including their exact and self-similar solutions), and hydrodynamic limits beyond the Navier-Stokes level.
Author: Alexander N. Gorban
Publisher: Springer Science & Business Media
ISBN: 9783540226840
Category : Science
Languages : en
Pages : 524
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Book Description
By bringing together various ideas and methods for extracting the slow manifolds, the authors show that it is possible to establish a more macroscopic description in nonequilibrium systems. The book treats slowness as stability. A unifying geometrical viewpoint of the thermodynamics of slow and fast motion enables the development of reduction techniques, both analytical and numerical. Examples considered in the book range from the Boltzmann kinetic equation and hydrodynamics to the Fokker-Planck equations of polymer dynamics and models of chemical kinetics describing oxidation reactions. Special chapters are devoted to model reduction in classical statistical dynamics, natural selection, and exact solutions for slow hydrodynamic manifolds. The book will be a major reference source for both theoretical and applied model reduction. Intended primarily as a postgraduate-level text in nonequilibrium kinetics and model reduction, it will also be valuable to PhD students and researchers in applied mathematics, physics and various fields of engineering.
Author: Alexander V. Bobylev
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110550989
Category : Mathematics
Languages : en
Pages : 260
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Book Description
This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The first volume covers many-particle dynamics, Maxwell models of the Boltzmann equation (including their exact and self-similar solutions), and hydrodynamic limits beyond the Navier-Stokes level.
Author: G. Hancock
Publisher: Elsevier
ISBN: 0080527345
Category : Science
Languages : en
Pages : 737
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Book Description
Volume 37 is concerned with the use and role of modelling in chemical kinetics and seeks to show the interplay of theory or simulation with experiment in a diversity of physico-chemical areas in which kinetics measurements provide significant physical insight. Areas of application covered within the volume include electro- and interfacial chemistry, physiology, biochemistry, solid state chemistry and chemical engineering. A leading contributor to this general area has been Professor W. John Albery, FRS, to whom the contributors and editors dedicate this book.
Author: James L. Martin
Publisher: CRC Press
ISBN: 1351439871
Category : Technology & Engineering
Languages : en
Pages : 820
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Book Description
Hydrodynamics and Transport for Water Quality Modeling presents a complete overview of current methods used to describe or predict transport in aquatic systems, with special emphasis on water quality modeling. The book features detailed descriptions of each method, supported by sample applications and case studies drawn from the authors' years of experience in the field. Each chapter examines a variety of modeling approaches, from simple to complex. This unique text/reference offers a wealth of information previously unavailable from a single source. The book begins with an overview of basic principles, and an introduction to the measurement and analysis of flow. The following section focuses on rivers and streams, including model complexity and data requirements, methods for estimating mixing, hydrologic routing methods, and unsteady flow modeling. The third section considers lakes and reservoirs, and discusses stratification and temperature modeling, mixing methods, reservoir routing and water balances, and dynamic modeling using one-, two-, and three-dimensional models. The book concludes with a section on estuaries, containing topics such as origins and classification, tides, mixing methods, tidally averaged estuary models, and dynamic modeling. Over 250 figures support the text. This is a valuable guide for students and practicing modelers who do not have extensive backgrounds in fluid dynamics.
Author: Edmilson Costa Teixeira
Publisher: CRC Press
ISBN: 1351023055
Category : Technology & Engineering
Languages : en
Pages : 119
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Book Description
Water and wastewater treatment normally take place in a series of continuous flow units, each designed to perform a step of the intended purification process - typically involving coagulation or flocculation, sedimentation or filtration, and disinfection. The flow pattern governs the residence/contact time, turbulence levels, collisions and shear to which different fluid portions are subjected in their passage through the unit. The efficiency of a given unit depends as much on the relevant physical, chemical or biological reaction as on the flow pattern taking place inside. This combined effect of flow features on process efficiency is often overlooked in teaching the design of water and wastewater treatment units, and so it is not uncommon to find treatment units in operating in a cost-ineffective way, causing health and environmental problems. This book introduces engineering students to concepts and practical measures associated with the rational design of treatment units, leading to more realistic and potentially optimal solutions for new units as well as for retrofitting existing units. Key basic concepts and suitable analytical tools are described, illustrated and worked through using practical examples. Engineering undergraduates and graduates should benefit from the book while undertaking standalone modules on the topic and/or supplementary classes of existing courses on unit treatment processes. The book may also be useful for technical and engineering staff involved in designing and/or retrofitting units for better cost-effectiveness and footprint reduction of the water and wastewater treatment sector.
Author: Anna DeMasi
Publisher: Springer
ISBN: 3540466363
Category : Mathematics
Languages : en
Pages : 204
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Book Description
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.
