05482nam 2200709Ia 450 991082304740332120240410133129.01-280-74716-197866107471600-08-046792-X(CKB)1000000000357867(EBL)283995(OCoLC)476032412(SSID)ssj0000188797(PQKBManifestationID)11171974(PQKBTitleCode)TC0000188797(PQKBWorkID)10155427(PQKB)11593595(Au-PeEL)EBL283995(CaPaEBR)ebr10158349(CaONFJC)MIL74716(MiAaPQ)EBC283995(PPN)144456427(EXLCZ)99100000000035786720060619d2006 uy 0engur|n|---|||||txtccrThe Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems /Ian Snook1st ed.Boston Elsevier20061 online resource (321 p.)Description based upon print version of record.0-444-52129-1 Includes bibliographical references and index.Cover; The Langevin and Generalised Langevin Approach to the Dynamics of Atomic, Polymeric and Colloidal Systems; Copyright page; Contents; Preface; Notation; A. Potential Energy Functions; B. Symbols Used; C. Operations; Chapter 1. Background, Mechanics and Statistical Mechanics; 1.1 Background; 1.2 The Mechanical Description of a System of Particles; 1.3 Summary; 1.4. Conclusions; References; Chapter 2. The Equation of Motion for a Typical Particle at Equilibrium:The Mori-Zwanzig Approach; 2.1 The Projection Operator; 2.2 The Generalised Langevin Equation2.3 The Generalised Langevin Equation in Terms of the Velocity2.4 Equation of Motion for the Velocity Autocorrelation Function; 2.5 The Langevin Equation Derived from the Mori Approach: The Brownian Limit; 2.6 Generalisation to any Set of Dynamical Variables; 2.7 Memory Functions Derivation of Expressions for Linear Transport Coefficients; 2.8 Correlation Function Expression for the Coefficient of Newtonian Viscosity; 2.9 Summary; 2.10 Conclusions; References; Chapter 3. Approximate Methods to Calculate Correlation Functions and Mori-Zwanzig Memory Functions; 3.1 Taylor Series Expansion3.2 Spectra3.3 Mori ́s Continued Fraction Method; 3.4 Use of Information Theory; 3.5 Perturbation Theories; 3.6 Mode Coupling Theory; 3.7 Macroscopic Hydrodynamic Theory; 3.8 Memory Functions Calculated by the Molecular-Dynamics Method; 3.9 Conclusions; References; Chapter 4. The Generalised Langevin Equation in Non-Equilibrium; 4.1 Derivation of Generalised Langevin Equation in Non-Equilibrium; 4.2 Langevin Equation for a Single Brownian Particle in a Shearing Fluid; 4.3 Conclusions; References; Chapter 5. The Langevin Equation and the Brownian Limit5.1 A Dilute Suspension - One Large Particle in a Background5.2 Many-Body Langevin Equation; 5.3 Generalisation to Non-Equilibrium; 5.4 The Fokker-Planck Equation and the Diffusive Limit; 5.5 Approach to the Brownian Limit and Limitations; 5.6 Summary; 5.7 Conclusions; References; Chapter 6. Langevin and Generalised Langevin Dynamics; 6.1 Extensions of the GLE to Collections of Particles; 6.2 Numerical Solution of the Langevin Equation; 6.3 Higher-Order BD Schemes for the Langevin Equation; 6.4 Generalised Langevin Equation; 6.5 Systems in an External Field6.6 Boundary Conditions in Simulations6.7 Conclusions; References; Chapter 7. Brownian Dynamics; 7.1 Fundamentals; 7.2 Calculation of Hydrodynamic Interactions; 7.3 Alternative Approaches to Treat Hydrodynamic Interactions; 7.4 Brownian Dynamics Algorithms; 7.5 Brownian Dynamics in a Shear Field; 7.6 Limitations of the BD Method; 7.7 Alternatives to BD Simulations; 7.8 Conclusions; References; Chapter 8. Polymer Dynamics; 8.1 Toxvaerd Approach; 8.2 Direct Use of Brownian Dynamics; 8.3 Rigid Systems; 8.4 Conclusions; ReferencesChapter 9. Theories Based on Distribution Functions, Master Equations and Stochastic EquationsThe 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 illustraLangevin equationsBrownian movementsRandom dynamical systemsPhysicsLangevin equations.Brownian movements.Random dynamical systems.Physics.530.14/4530.144Snook Ian1675978MiAaPQMiAaPQMiAaPQBOOK9910823047403321The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems4041833UNINA