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 Equation -- 2.3 The Generalised Langevin Equation in Terms of the Velocity -- 2.4 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 Expansion -- 3.2 Spectra -- 3.3 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 Limit -- 5.1 A Dilute Suspension - One Large Particle in a Background.

5.2 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 Field -- 6.6 Boundary Conditions in Simulations -- 6.7 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 -- References -- Chapter 9. Theories Based on Distribution Functions, Master Equations and Stochastic Equations -- 9.1 Fokker-Planck Equation -- 9.2 The Diffusive Limit and the Smoluchowski Equation -- 9.3 Quantum Monte Carlo Method -- 9.4 Master Equations -- 9.5 Conclusions -- References -- Chapter 10. An Overview -- Appendix A: Expressions for Equilibrium Properties, Transport Coefficients and Scattering Functions -- A.1 Equilibrium Properties -- A.2 Expressions for Linear Transport Coefficients -- A.3 Scattering Functions -- References -- Appendix B: Some Basic Results About Operators -- Appendix C: Proofs Required for the GLE for a Selected Particle -- Appendix D: The Langevin Equation from the Mori-Zwanzig Approach -- Appendix E: The Friction Coefficient and Friction Factor.

Appendix F: Mori Coefficients for a Two-Component System -- F.1 Basics -- F.2 Short Time Expansions -- F.3 Relative Initial Behaviour of c(t) -- Appendix G: Time-Reversal Symmetry of Non-Equilibrium Correlation Functions -- References -- Appendix H: Some Proofs Needed for the Albers, Deutch and Oppenheim Treatment -- Appendix I: A Proof Needed for the Deutch and Oppenheim Treatment -- Appendix J: The Calculation of the Bulk Properties of Colloids and Polymers -- J.1 Equilibrium Properties -- J.2 Static Structure -- J.3 Time Correlation Functions -- References -- Appendix K: Monte Carlo Methods -- K.1 Metropolis Monte Carlo Technique -- K.2 An MC Routine -- References -- Appendix L: The Generation of Random Numbers -- L.1 Generation of Random Deviates for BD Simulations -- References -- Appendix M: Hydrodynamic Interaction Tensors -- M.1 The Oseen Tensor for Two Bodies -- M.2 The Rotne-Prager Tensor for Two Bodies -- M.3 The Series Result of Jones and Burfield for Two Bodies -- M.4 Mazur and van Saarloos Results for Three Bodies -- M.5 Results of Lubrication Theory -- M.6 The Rotne-Prager Tensor in Periodic Boundary Conditions -- References -- Appendix N: Calculation of Hydrodynamic Interaction Tensors -- References -- Appendix O: Some Fortran Programs -- Index.