Quantum Hydrodynamic Equation And Its Mathematical Theory

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Quantum Hydrodynamic Equation And Its Mathematical Theory

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Author : Boling Guo
language : en
Publisher: World Scientific
Release Date : 2023-06-21

Quantum Hydrodynamic Equation And Its Mathematical Theory written by Boling Guo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-21 with Mathematics categories.

Quantum hydrodynamics comes from superfluid, superconductivity, semiconductor and so on. Quantum hydrodynamic model describes Helium II superfluid, Bose-Einstein condensation in inert gas, dissipative perturbation of Hamilton-Jacobi system, amplitude and dissipative perturbation of Eikonal quantum wave and so on. Owing to the broad application of quantum hydrodynamic equations, the study of the quantum hydrodynamic equations has aroused the concern of more and more scholars. Based on the above facts, we collected and collated the data of quantum hydrodynamic equations, and studied the concerning mathematical problems.The main contents of this book are: the derivation and mathematical models of quantum hydrodynamic equations, global existence of weak solutions to the compressible quantum hydrodynamic equations, existence of finite energy weak solutions of inviscid quantum hydrodynamic equations, non-isentropic quantum Navier-Stokes equations with cold pressure, boundary problem of compressible quantum Euler-Poisson equations, asymptotic limit to the bipolar quantum hydrodynamic equations.

Quantum Dynamics With Trajectories

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Author : Robert E. Wyatt
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-05-20

Quantum Dynamics With Trajectories written by Robert E. Wyatt 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 2005-05-20 with Mathematics categories.

This is a rapidly developing field to which the author is a leading contributor New methods in quantum dynamics and computational techniques, with applications to interesting physical problems, are brought together in this book Useful to both students and researchers

From Kinetic Models To Hydrodynamics

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Author : Matteo Colangeli
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-25

From Kinetic Models To Hydrodynamics written by Matteo Colangeli 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 2013-03-25 with Science categories.

​​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.​

Partial Differential Equations And Spectral Theory

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Author : Michael Demuth
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-01

Partial Differential Equations And Spectral Theory written by Michael Demuth 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 2011-02-01 with Mathematics categories.

This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of current research, with original contributions from the authors. They are written in a clear expository style that makes them accessible to a broader audience. The articles contain a detailed introduction and discuss recent progress, provide additional motivation, and develop the necessary tools. Moreover, the authors share their views on future developments, hypotheses, and unsolved problems.

Hyperbolic Problems Theory Numerics And Applications

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Author : Eitan Tadmor
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Hyperbolic Problems Theory Numerics And Applications written by Eitan Tadmor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

The International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 'HYP2008', was held at the University of Maryland from June 9-13, 2008. This book, the first in a two-part volume, contains nineteen papers based on plenary and invited talks presented at the conference.

Unified Non Local Theory Of Transport Processes

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Author : Boris V. Alexeev
language : en
Publisher: Elsevier
Release Date : 2015-02-10

Unified Non Local Theory Of Transport Processes written by Boris V. Alexeev and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-10 with Science categories.

Unified Non-Local Theory of Transport Processess, 2nd Edition provides a new theory of transport processes in gases, plasmas and liquids. It is shown that the well-known Boltzmann equation, which is the basis of the classical kinetic theory, is incorrect in the definite sense. Additional terms need to be added leading to a dramatic change in transport theory. The result is a strict theory of turbulence and the possibility to calculate turbulent flows from the first principles of physics. - Fully revised and expanded edition, providing applications in quantum non-local hydrodynamics, quantum solitons in solid matter, and plasmas - Uses generalized Boltzmann kinetic theory as an highly effective tool for solving many physical problems beyond classical physics - Addresses dark matter and energy - Presents non-local physics in many related problems of hydrodynamics, gravity, black holes, nonlinear optics, and applied mathematics

Hyperbolic Problems Theory Numerics Applications

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Author : Thomas Y. Hou
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Hyperbolic Problems Theory Numerics Applications written by Thomas Y. Hou 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.

The International Conference on "Hyperbolic Problems: Theory, Numerics and Applications'' was held in CalTech on March 25-30, 2002. The conference was the ninth meeting in the bi-annual international series which became one of the highest quality and most successful conference series in Applied mathematics. This volume contains more than 90 contributions presented in this conference, including plenary presentations by A. Bressan, P. Degond, R. LeVeque, T.-P. Liu, B. Perthame, C.-W. Shu, B. Sjögreen and S. Ukai. Reflecting the objective of series, the contributions in this volume keep the traditional blend of theory, numerics and applications. The Hyp2002 meeting placed a particular emphasize on fundamental theory and numerical analysis, on multi-scale analysis, modeling and simulations, and on geophysical applications and free boundary problems arising from materials science and multi-component fluid dynamics. The volume should appeal to researchers, students and practitioners with general interest in time-dependent problems governed by hyperbolic equations.

Encyclopaedia Of Mathematics

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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Encyclopaedia Of Mathematics written by Michiel Hazewinkel 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 2013-12-01 with Mathematics categories.

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

High Dimensional Nonlinear Diffusion Stochastic Processes

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Author : Yevgeny Mamontov
language : en
Publisher: World Scientific
Release Date : 2001-01-19

High Dimensional Nonlinear Diffusion Stochastic Processes written by Yevgeny Mamontov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-19 with Mathematics categories.

This book is the first one devoted to high-dimensional (or large-scale) diffusion stochastic processes (DSPs) with nonlinear coefficients. These processes are closely associated with nonlinear Ito's stochastic ordinary differential equations (ISODEs) and with the space-discretized versions of nonlinear Ito's stochastic partial integro-differential equations. The latter models include Ito's stochastic partial differential equations (ISPDEs).The book presents the new analytical treatment which can serve as the basis of a combined, analytical-numerical approach to greater computational efficiency in engineering problems. A few examples discussed in the book include: the high-dimensional DSPs described with the ISODE systems for semiconductor circuits; the nonrandom model for stochastic resonance (and other noise-induced phenomena) in high-dimensional DSPs; the modification of the well-known stochastic-adaptive-interpolation method by means of bases of function spaces; ISPDEs as the tool to consistently model non-Markov phenomena; the ISPDE system for semiconductor devices; the corresponding classification of charge transport in macroscale, mesoscale and microscale semiconductor regions based on the wave-diffusion equation; the fully time-domain nonlinear-friction aware analytical model for the velocity covariance of particle of uniform fluid, simple or dispersed; the specific time-domain analytics for the long, non-exponential “tails” of the velocity in case of the hard-sphere fluid.These examples demonstrate not only the capabilities of the developed techniques but also emphasize the usefulness of the complex-system-related approaches to solve some problems which have not been solved with the traditional, statistical-physics methods yet. From this veiwpoint, the book can be regarded as a kind of complement to such books as “Introduction to the Physics of Complex Systems. The Mesoscopic Approach to Fluctuations, Nonlinearity and Self-Organization” by Serra, Andretta, Compiani and Zanarini, “Stochastic Dynamical Systems. Concepts, Numerical Methods, Data Analysis” and “Statistical Physics: An Advanced Approach with Applications” by Honerkamp which deal with physics of complex systems, some of the corresponding analysis methods and an innovative, stochastics-based vision of theoretical physics.To facilitate the reading by nonmathematicians, the introductory chapter outlines the basic notions and results of theory of Markov and diffusion stochastic processes without involving the measure-theoretical approach. This presentation is based on probability densities commonly used in engineering and applied sciences.

Encyclopaedia Of Mathematics Set

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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-02-28

Encyclopaedia Of Mathematics Set written by Michiel Hazewinkel 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 1994-02-28 with Mathematics categories.

The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.