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Linear Kinetic Theory And Particle Transport In Stochastic Mixtures
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Book Synopsis Linear Kinetic Theory and Particle Transport in Stochastic Mixtures by : Gerald C. Pomraning
Download or read book Linear Kinetic Theory and Particle Transport in Stochastic Mixtures written by Gerald C. Pomraning and published by World Scientific. This book was released on 1991 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with neutral particle flow in a stochastic mixture consisting of two or more immiscible fluids. After giving an introduction to linear kinetic theory and particle transport in a nonstochastic setting, it discusses recent formulations for particle flow through a background material whose properties are only known in a statistical sense. The mixing descriptions considered are both Markovian and renewal statistics. Various models and exact results are presented for the ensemble average of the intensity in such stochastic mixtures. In the Markovian case, the underlying kinetic description is the integro-differential transport equation, whereas for renewal statistics the natural starting point is the purely integral formulation of transport theory.
Book Synopsis Linear Kinetic Theory and Particle Transport in Stochastic Mixtures by : Gerald C. Pomraning
Download or read book Linear Kinetic Theory and Particle Transport in Stochastic Mixtures written by Gerald C. Pomraning and published by . This book was released on 1997 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear Kinetic Theory and Particle Transport in Stochastic Mixtures by :
Download or read book Linear Kinetic Theory and Particle Transport in Stochastic Mixtures written by and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear Kinetic Theory and Particle Transport in Stochastic Mixtures. Progress Report, June 15, 1993--March 21, 1994 by :
Download or read book Linear Kinetic Theory and Particle Transport in Stochastic Mixtures. Progress Report, June 15, 1993--March 21, 1994 written by and published by . This book was released on 1994 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary goal in this research is to develop a comprehensive theory of linear transport/kinetic theory in a stochastic mixture of solids and immiscible fluids. The statistics considered correspond to N-state discrete random variables for the interaction coefficients and sources, with N denoting the number of components of the mixture. The mixing statistics studied are Markovian as well as more general statistics, such as renewal processes. A further goal of this work is to demonstrate the applicability of the formalism to real world engineering problems. This three year program was initiated June 15, 1993 and has been underway nine months. Many significant results have been obtained, both in the formalism development and in representative applications. These results are summarized by listing the archival publications resulting from this grant, including the abstracts taken directly from the papers.
Book Synopsis Linear Kinetic Theory and Particle Transport in Stochastic Mixtures. Third Year and Final Report, June 15, 1993--December 14, 1996 by :
Download or read book Linear Kinetic Theory and Particle Transport in Stochastic Mixtures. Third Year and Final Report, June 15, 1993--December 14, 1996 written by and published by . This book was released on 1997 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal in this research was to continue the development of a comprehensive theory of linear transport/kinetic theory in a stochastic mixture of solids and immiscible fluids. Such a theory should predict the ensemble average and higher moments, such as the variance, of the particle or energy density described by the underlying transport/kinetic equation. The statistics studied correspond to N-state discrete random variables for the interaction coefficients and sources, with N denoting the number of components in the mixture. The mixing statistics considered were Markovian as well as more general statistics. In the absence of time dependence and scattering, the theory is well developed and described exactly by the master (Liouville) equation for Markovian mixing, and by renewal equations for non-Markovian mixing. The intent of this research was to generalize these treatments to include both time dependence and scattering. A further goal of this research was to develop approximate, but simpler, models from any comprehensive theory. In particular, a specific goal was to formulate a renormalized transport/kinetic theory of the usual nonstochastic form, but with effective interaction coefficients and sources to account for the stochastic nature of the problem. In the three and one-half year period of research summarized in this final report, they have made substantial progress in the development of a comprehensive theory of kinetic processes in stochastic mixtures. This progress is summarized in 16 archival journal articles, 7 published proceedings papers, and 2 comprehensive review articles. In addition, 17 oral presentations were made describing these research results.
Book Synopsis Calculus Of Variations, Homogenization And Continuum Mechanics by : Guy Bouchitte
Download or read book Calculus Of Variations, Homogenization And Continuum Mechanics written by Guy Bouchitte and published by World Scientific. This book was released on 1994-06-28 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the workshop was to promote a better understanding of the connections between recent problems in Theoretical or Computational Mechanics (bounds in composites, phase transitions, microstructure of crystals, optimal design, nonlinear elasticity) and new mathematical tools in the Calculus of Variations (relaxation and Γ-convergence theory, Young and H-measures, compensated compactness and quasiconvexity).
Book Synopsis Lectures on Probability and Second Order Random Fields by : Diego Bricio Hern ndez
Download or read book Lectures on Probability and Second Order Random Fields written by Diego Bricio Hern ndez and published by World Scientific. This book was released on 1995 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book of lecture notes contains theoretical background material required for computer generation of random fields, which is of interest in various fields of applied mathematics.The necessary probabilistic background suitable for applied work in engineering as well as signal and image processing is also covered.The book is a valuable guide for higher level engineering students.
Book Synopsis Recent Advances in Elasticity, Viscoelasticity, and Inelasticity by : Tse-Chin Woo
Download or read book Recent Advances in Elasticity, Viscoelasticity, and Inelasticity written by Tse-Chin Woo and published by World Scientific. This book was released on 1995 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of papers dedicated to Prof T C Woo to mark his 70th birthday. The papers focus on recent advances in elasticity, viscoelasticity and inelasticity, which are related to Prof Woo's work. Prof Woo's recent work concentrates on the viscoelastic and viscoplastic response of metals and plastics when thermal effects are significant, and the papers here address open questions in these and related areas.
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 Generalized Kinetic Models in Applied Sciences by : Luisa Arlotti
Download or read book Generalized Kinetic Models in Applied Sciences written by Luisa Arlotti and published by World Scientific. This book was released on 2003 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with analytic problems related to some developments and generalizations of the Boltzmann equation toward the modeling and qualitative analysis of large systems that are of interest in applied sciences. These generalizations are documented in the various surveys edited by Bellomo and Pulvirenti with reference to models of granular media, traffic flow, mathematical biology, communication networks, and coagulation models. The first generalization dealt with refers to the averaged Boltzmann equation, which is obtained by suitable averaging of the distribution function of the field particles into the action domain of the test particle. This model is further developed to describe equations with dissipative collisions and a class of models that are of interest in mathematical biology. In this latter case the state of the particles is defined not only by a mechanical variable but also by a biological microscopic state.
Book Synopsis Theory of the Navier-Stokes Equations by : John Groves Heywood
Download or read book Theory of the Navier-Stokes Equations written by John Groves Heywood and published by World Scientific. This book was released on 1998 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects the articles presented at the Third International Conference on ?The Navier-Stokes Equations: Theory and Numerical Methods?, held in Oberwolfach, Germany. The articles are important contributions to a wide variety of topics in the Navier-Stokes theory: general boundary conditions, flow exterior to an obstacle, conical boundary points, the controllability of solutions, compressible flow, non-Newtonian flow, magneto-hydrodynamics, thermal convection, the interaction of fluids with elastic solids, the regularity of solutions, and Rothe's method of approximation.
Book Synopsis Microscopic Theory of Condensation in Gases and Plasma by : A. L. Itkin
Download or read book Microscopic Theory of Condensation in Gases and Plasma written by A. L. Itkin and published by World Scientific. This book was released on 1997 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes results on the creation of a new theory of condensation which has an impact on consideration of some microscopic effects left aside in the usual nucleation theories. In particular, the main idea of the authors' microscopic condensation theory is that it considers the violation of the equilibrium cluster distribution over the internal degrees of freedom due to co-occurring condensation and decay reactions of the clusters.
Book Synopsis Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models by : Nicola Bellomo
Download or read book Lecture Notes On The Mathematical Theory Of Generalized Boltzmann Models written by Nicola Bellomo and published by World Scientific. This book was released on 2000-01-11 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions.Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the book provides a unified presentation of this topic with direct reference to modelling, mathematical statement of problems, qualitative and computational analysis, and applications. Models reported and proposed in the book refer to several fields of natural, applied and technological sciences. In particular, the following classes of models are discussed: population dynamics and socio-economic behaviours, models of aggregation and fragmentation phenomena, models of biology and immunology, traffic flow models, models of mixtures and particles undergoing classic and dissipative interactions.
Book Synopsis Lecture Notes on the Mathematical Theory of the Boltzmann Equation by : N. Bellomo
Download or read book Lecture Notes on the Mathematical Theory of the Boltzmann Equation written by N. Bellomo and published by World Scientific. This book was released on 1995 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of four lectures on some mathematical aspects related to the nonlinear Boltzmann equation. The following topics are dealt with: derivation of kinetic equations, qualitative analysis of the initial value problem, singular perturbation analysis towards the hydrodynamic limit and computational methods towards the solution of problems in fluid dynamics.
Book Synopsis Nonlinear Evolution Equations: Kinetic Approach by : Niva B Maslova
Download or read book Nonlinear Evolution Equations: Kinetic Approach written by Niva B Maslova and published by World Scientific. This book was released on 1993-03-10 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the questions of the long-time behavior of solutions for evolution equations, connected with kinetic models in statistical physics. There is a wide variety of problems where such models are used to obtain reasonable physical as well as numerical results (Fluid Mechanics, Gas Dynamics, Plasma Physics, Nuclear Physics, Turbulence Theory etc.). The classical examples provide the nonlinear Boltzmann equation. Investigation of the long-time behavior of the solutions for the Boltzmann equation gives an approach to the nonlinear fluid dynamic equations. From the viewpoint of dynamical systems, the fluid dynamic equations arise in the theory as a tool to describe an attractor of the kinetic equation.
Book Synopsis Applications Of Pade' Approximation Theory In Fluid Dynamics by : Amilcare Pozzi
Download or read book Applications Of Pade' Approximation Theory In Fluid Dynamics written by Amilcare Pozzi and published by World Scientific. This book was released on 1994-03-07 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although Padé presented his fundamental paper at the end of the last century, the studies on Padé's approximants only became significant in the second part of this century.Padé procedure is related to the theory of continued fractions, and some convergence theorems can be expressed only in terms of continued fractions. Further, Padé approximants have some advantages of practical applicability with respect to the continued-fraction theory. Moreover, as Chisholm notes, a given power series determines a set of approximants which are usually unique, whereas there are many ways of writing an associated continued fraction.The principal advantage of Padé approximants with respect to the generating Taylor series is that they provide an extension beyond the interval of convergence of the series.Padé approximants can be applied in many parts of fluid-dynamics, both in steady and in nonsteady flows, both in incompressible and in compressible regimes.This book is divided into four parts. The first one deals with the properties of the Padé approximants that are useful for the applications and illustrates, with the aid of diagrams and tables, the effectiveness of this technique in the field of applied mathematics. The second part recalls the basic equations of fluid-dynamics (those associated with the names of Navier-Stokes, Euler and Prandtl) and gives a quick derivation of them from the general balance equation. The third shows eight examples of the application of Padé approximants to steady flows, also taking into account the influence of the coupling of heat conduction in the body along which a fluid flows with conduction and convection in the fluid itself. The fourth part considers two examples of the application of Padé approximants to unsteady flows.
Book Synopsis Thermomechanics Of Phase Transitions In Classical Field Theory by : Ingo Claben
Download or read book Thermomechanics Of Phase Transitions In Classical Field Theory written by Ingo Claben and published by World Scientific. This book was released on 1993-11-30 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The complex processes of state changes can be interpreted by resorting to Statistical Quantum Mechanics. However, it is well known that a phenomenological description of state changes can be obtained by using the classical continuum theory. This book supplies a panoramic picture of known and new mathematical models which are suitable to describe phase changes from a macroscopic view point. All these models are derived from the theory of continuous systems with a nonmaterial interface and allow to describe processes of solidification, melting, and vaporization. The nonlocal continuum theory of systems with a non material interface provides a more complex mathematical model in dealing with crystal growth either in a pure melt or in a mixture. A chapter is devoted to the analysis of phase changes in ferroelectric and ferromagnetic crystals.
