April 17, 2021

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The Langevin and Generalised Langevin Approach to the Dynamics of Atomic, Polymeric and Colloidal Systems

The Langevin and Generalised Langevin Approach to the Dynamics of Atomic, Polymeric and Colloidal Systems
Author : Ian Snook
Publisher : Elsevier
Release Date : 2006-12-11
Category : Science
Total pages :320
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The Langevin and Generalised Langevin Approach To The Dynamics Of Atomic, Polymeric And Colloidal Systems is concerned with the description of aspects of the theory and use of so-called random processes to describe the properties of atomic, polymeric and colloidal systems in terms of the dynamics of the particles in the system. It provides derivations of the basic equations, the development of numerical schemes to solve them on computers and gives illustrations of application to typical systems. Extensive appendices are given to enable the reader to carry out computations to illustrate many of the points made in the main body of the book. * Starts from fundamental equations * Gives up-to-date illustration of the application of these techniques to typical systems of interest * Contains extensive appendices including derivations, equations to be used in practice and elementary computer codes

Nonequilibrium Molecular Dynamics

Nonequilibrium Molecular Dynamics
Author : Billy D. Todd,Peter J. Daivis
Publisher : Cambridge University Press
Release Date : 2017-03-16
Category : Science
Total pages :352
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Written by two specialists with over twenty-five years of experience in the field, this valuable text presents a wide range of topics within the growing field of nonequilibrium molecular dynamics (NEMD). It introduces theories which are fundamental to the field - namely, nonequilibrium statistical mechanics and nonequilibrium thermodynamics - and provides state-of-the-art algorithms and advice for designing reliable NEMD code, as well as examining applications for both atomic and molecular fluids. It discusses homogenous and inhomogenous flows and pays considerable attention to highly confined fluids, such as nanofluidics. In addition to statistical mechanics and thermodynamics, the book covers the themes of temperature and thermodynamic fluxes and their computation, the theory and algorithms for homogenous shear and elongational flows, response theory and its applications, heat and mass transport algorithms, applications in molecular rheology, highly confined fluids (nanofluidics), the phenomenon of slip and how to compute it from basic microscopic principles, and generalized hydrodynamics.

Microhydrodynamics, Brownian Motion, and Complex Fluids

Microhydrodynamics, Brownian Motion, and Complex Fluids
Author : Michael D. Graham
Publisher : Cambridge University Press
Release Date : 2018-09-13
Category : Mathematics
Total pages :280
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Provides a foundation for understanding complex fluids by integrating fluid dynamics, statistical physics, and polymer and colloid science.

Langevin And Fokker-planck Equations And Their Generalizations: Descriptions And Solutions

Langevin And Fokker-planck Equations And Their Generalizations: Descriptions And Solutions
Author : Kwok Sau Fa
Publisher : World Scientific
Release Date : 2018-03-06
Category : Science
Total pages :208
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This invaluable book provides a broad introduction to a rapidly growing area of nonequilibrium statistical physics. The first part of the book complements the classical book on the Langevin and Fokker–Planck equations (H. Risken, The Fokker–Planck Equation: Methods of Solution and Applications (Springer, 1996)). Some topics and methods of solutions are presented and discussed in details which are not described in Risken's book, such as the method of similarity solution, the method of characteristics, transformation of diffusion processes into the Wiener process in different prescriptions, harmonic noise and relativistic Brownian motion. Connection between the Langevin equation and Tsallis distribution is also discussed. Due to the growing interest in the research on the generalized Langevin equations, several of them are presented. They are described with some details. Recent research on the integro-differential Fokker–Planck equation derived from the continuous time random walk model shows that the topic has several aspects to be explored. This equation is worked analytically for the linear force and the generic waiting time probability distribution function. Moreover, generalized Klein-Kramers equations are also presented and discussed. They have the potential to be applied to natural systems, such as biological systems. Contents: Introduction Langevin and Fokker–Planck Equations Fokker–Planck Equation for One Variable and its Solution Fokker–Planck Equation for Several Variables Generalized Langevin Equations Continuous Time Random Walk Model Uncoupled Continuous Time Random Walk Model andits Solution Readership: Advanced undergraduate and graduate students in mathematical physics and statistical physics; biologists and chemists who are interested in nonequilibrium statistical physics. Keywords: Langevin Equation;Fokker-Planck Equation;Klein-Kramers Equation;Continuous Time Random Walk Model;Colored Noise;Tsallis Entropy;Population Growth Models;Wright Functions;Mittag-Leffler Function;Method of Similarity Solution;First Passage Time;Relativistic Brownian Motion;Fractional Derivatives;Integro-Differential Fokker-Planck EquationsReview: Key Features: This book complements Risken's book on the Langevin and Fokker-Planck equations. Some topics and methods of solutions are presented and discussed in details which are not described in Risken's book Several generalized Langevin equations are presented and discussed with some detail Integro-differential Fokker–Planck equation is derived from the uncoupled continuous time random walk model for generic waiting time probability distribution function which can be used to distinguish the differences for the initial and intermediate times with the same behavior in the long-time limit. Moreover, generalized Klein–Kramers equations are also described and discussed. To our knowledge these approaches are not found in other textbooks

Time Reversability, Computer Simulation, Algorithms, Chaos

Time Reversability, Computer Simulation, Algorithms, Chaos
Author : William Graham Hoover
Publisher : World Scientific
Release Date : 2012
Category : Mathematics
Total pages :401
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The book begins with a discussion, contrasting the idealized reversibility of basic physics against the pragmatic irreversibility of real life. Computer models, and simulation, are next discussed and illustrated. Simulations provide the means to assimilate concepts through worked-out examples. State-of-the-art analyses, from the point of view of dynamical systems, are applied to many-body examples from nonequilibrium molecular dynamics and to chaotic irreversible flows from finite-difference, finite-element, and particle-based continuum simulations. Two necessary concepts from dynamical-systems theory - fractals and Lyapunov instability - are fundamental to the approach. Undergraduate-level physics, calculus, and ordinary differential equations are sufficient background for a full appreciation of this book, which is intended for advanced undergraduates, graduates, and research workers.

American Book Publishing Record

American Book Publishing Record
Author : Anonim
Publisher : Unknown
Release Date : 2006
Category : American literature
Total pages :129
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The Langevin Equation

The Langevin Equation
Author : William Coffey,Yu. P. Kalmykov,J. T. Waldron
Publisher : World Scientific
Release Date : 2004
Category : Science
Total pages :704
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This volume is the second edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the Brownian motion in a potential, with emphasis on modern applications in the natural sciences, electrical engineering and so on. It has been substantially enlarged to cover in a succinct manner a number of new topics, such as anomalous diffusion, continuous time random walks, stochastic resonance etc, which are of major current interest in view of the large number of disparate physical systems exhibiting these phenomena. The book has been written in such a way that all the material should be accessible to an advanced undergraduate or beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of research papers or scattered review articles. Contents: Historical Background and Introductory Concepts; Langevin Equations and Methods of Solution; Brownian Motion of a Free Particle and a Harmonic Oscillator; Two-Dimensional Rotational Brownian Motion in N -Fold Cosine Potentials; Brownian Motion in a Tilted Cosine Potential: Application to the Josephson Tunnelling Junction; Translational Brownian Motion in a Double-Well Potential; Three-Dimensional Rotational Brownian Motion in an External Potential: Application to the Theory of Dielectric and Magnetic Relaxation; Rotational Brownian Motion in Axially Symmetric Potentials: Matrix Continued Fraction Solutions; Rotational Brownian Motion in Non-Axially Symmetric Potentials; Inertial Langevin Equations: Application to Orientational Relaxation in Liquids; Anomalous Diffusion. Readership: Advanced undergraduates, graduate students, academics and researchers in statistical physics, condensed matter physics and magnetism, the physics of fluids, theoretical chemistry and applied mathematics.

Polymer Translocation

Polymer Translocation
Author : M. Muthukumar
Publisher : CRC Press
Release Date : 2016-04-19
Category : Technology & Engineering
Total pages :372
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Polymer translocation occurs in many biological and biotechnological phenomena where electrically charged polymer molecules move through narrow spaces in crowded environments. Unraveling the rich phenomenology of polymer translocation requires a grasp of modern concepts of polymer physics and polyelectrolyte behavior. Polymer Translocation discusses universal features of polymer translocations and summarizes the key concepts of polyelectrolyte structures, electrolyte solutions, ionic flow, mobility of charged macromolecules, polymer capture by pores, and threading of macromolecules through pores. With approximately 150 illustrations and 850 equations, the book: Avoids heavy mathematics Uses examples to illustrate the richness of the phenomenon Introduces the entropic barrier idea behind polymer translocation Outlines conceptual components necessary for a molecular understanding of polymer translocation Provides mathematical formulas for the various quantities pertinent to polymer translocation The challenge in understanding the complex behavior of translocation of polyelectrolyte molecules arises from three long-range forces due to chain connectivity, electrostatic interactions, and hydrodynamic interactions. Polymer Translocation provides an overview of fundamentals, established experimental facts, and important concepts necessary to understand polymer translocation. Readers will gain detailed strategies for applying these concepts and formulas to the design of new experiments.

Nonlinear Fokker-Planck Equations

Nonlinear Fokker-Planck Equations
Author : T.D. Frank
Publisher : Springer Science & Business Media
Release Date : 2006-03-30
Category : Science
Total pages :408
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Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions. It emphasizes principles and notions of the theory (e.g. self-organization, stochastic feedback, free energy, and Markov processes), while also illustrating the wide applicability (e.g. collective behavior, multistability, front dynamics, and quantum particle distribution). The focus is on relaxation processes in homogeneous many-body systems describable by nonlinear Fokker-Planck equations. Also treated are Langevin equations and correlation functions. Since these phenomena are exhibited by a diverse spectrum of systems, examples and applications span the fields of physics, biology and neurophysics, mathematics, psychology, and biomechanics.

Introduction to Molecular-Microsimulation for Colloidal Dispersions

Introduction to Molecular-Microsimulation for Colloidal Dispersions
Author : A. Satoh
Publisher : Elsevier
Release Date : 2003-06-20
Category : Science
Total pages :364
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Introduction to Molecular-Microsimulation for Colloidal Dispersions provides an introduction to molecular-microsimulation methods for colloidal dispersions and is suitable for both self-study and reference. It provides the reader with a systematic understanding of the theoretical background to simulation methods, together with a wide range of practical skills for developing computational programs. Exercises are included at the end of each chapter to further assist the understanding of the subjects addressed. Provides the reader with the theoretical background to molecular-microsimulation methods Suitable for both self-study and reference Aids the reader in developing programs to meet their own requirements

Hierarchical Methods for Dynamics in Complex Molecular Systems

Hierarchical Methods for Dynamics in Complex Molecular Systems
Author : Johannes Grotendorst
Publisher : Forschungszentrum Jülich
Release Date : 2012
Category :
Total pages :540
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The British National Bibliography

The British National Bibliography
Author : Arthur James Wells
Publisher : Unknown
Release Date : 2006
Category : English literature
Total pages :129
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Strongly Coupled Plasma Physics

Strongly Coupled Plasma Physics
Author : S. Ichimaru
Publisher : Elsevier
Release Date : 2012-12-02
Category : Science
Total pages :732
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Charged particles in dense matter exhibit strong correlations due to the exchange and Coulomb interactions, and thus make a strongly coupled plasma. Examples in laboratory and astrophysical settings include solid and liquid metals, semiconductors, charged particles in lower dimensions such as those trapped in interfacial states of condensed matter or beams, dense multi-ionic systems such a superionic conductors and inertial-confinement-fusion plasmas . The aim of the conference was to elucidate the various physical processes involved in these dense materials. The subject areas covered include plasma physics, atomic and molecular physics, condensed matter physics and astrophysics.

The Fokker-Planck Equation

The Fokker-Planck Equation
Author : Hannes Risken
Publisher : Springer Science & Business Media
Release Date : 2012-12-06
Category : Science
Total pages :454
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One of the central problems synergetics is concerned with consists in the study of macroscopic qualitative changes of systems belonging to various disciplines such as physics, chemistry, or electrical engineering. When such transitions from one state to another take place, fluctuations, i.e., random processes, may play an im portant role. Over the past decades it has turned out that the Fokker-Planck equation pro vides a powerful tool with which the effects of fluctuations close to transition points can be adequately treated and that the approaches based on the Fokker Planck equation are superior to other approaches, e.g., based on Langevin equa tions. Quite generally, the Fokker-Planck equation plays an important role in problems which involve noise, e.g., in electrical circuits. For these reasons I am sure that this book will find a broad audience. It pro vides the reader with a sound basis for the study of the Fokker-Planck equation and gives an excellent survey of the methods of its solution. The author of this book, Hannes Risken, has made substantial contributions to the development and application of such methods, e.g., to laser physics, diffusion in periodic potentials, and other problems. Therefore this book is written by an experienced practitioner, who has had in mind explicit applications to important problems in the natural sciences and electrical engineering.

Polymer Solutions

Polymer Solutions
Author : Iwao Teraoka
Publisher : John Wiley & Sons
Release Date : 2004-04-07
Category : Science
Total pages :360
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Polymer Solutions: An Introduction to Physical Properties offers a fresh, inclusive approach to teaching the fundamentals of physical polymer science. Students, instructors, and professionals in polymer chemistry, analytical chemistry, organic chemistry, engineering, materials, and textiles will find Iwao Teraoka’s text at once accessible and highly detailed in its treatment of the properties of polymers in the solution phase. Teraoka’s purpose in writing Polymer Solutions is twofold: to familiarize the advanced undergraduate and beginning graduate student with basic concepts, theories, models, and experimental techniques for polymer solutions; and to provide a reference for researchers working in the area of polymer solutions as well as those in charge of chromatographic characterization of polymers. The author’s incorporation of recent advances in the instrumentation of size-exclusion chromatography, the method by which polymers are analyzed, renders the text particularly topical. Subjects discussed include: Real, ideal, Gaussian, semirigid, and branched polymer chains Polymer solutions and thermodynamics Static light scattering of a polymer solution Dynamic light scattering and diffusion of polymers Dynamics of dilute and semidilute polymer solutions Study questions at the end of each chapter not only provide students with the opportunity to test their understanding, but also introduce topics relevant to polymer solutions not included in the main text. With over 250 geometrical model diagrams, Polymer Solutions is a necessary reference for students and for scientists pursuing a broader understanding of polymers.