LEADER 05494nam 2200697Ia 450 001 9910457244703321 005 20200520144314.0 010 $a1-280-74716-1 010 $a9786610747160 010 $a0-08-046792-X 035 $a(CKB)1000000000357867 035 $a(EBL)283995 035 $a(OCoLC)476032412 035 $a(SSID)ssj0000188797 035 $a(PQKBManifestationID)11171974 035 $a(PQKBTitleCode)TC0000188797 035 $a(PQKBWorkID)10155427 035 $a(PQKB)11593595 035 $a(MiAaPQ)EBC283995 035 $a(PPN)144456427 035 $a(Au-PeEL)EBL283995 035 $a(CaPaEBR)ebr10158349 035 $a(CaONFJC)MIL74716 035 $a(EXLCZ)991000000000357867 100 $a20060619d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems$b[electronic resource] /$fIan Snook 210 $aBoston $cElsevier$d2006 215 $a1 online resource (321 p.) 300 $aDescription based upon print version of record. 311 $a0-444-52129-1 320 $aIncludes bibliographical references and index. 327 $aCover; 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 327 $a2.3 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 Expansion 327 $a3.2 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 Limit 327 $a5.1 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 Field 327 $a6.6 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; References 327 $aChapter 9. Theories Based on Distribution Functions, Master Equations and Stochastic Equations 330 $aThe 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 illustra 606 $aLangevin equations 606 $aBrownian movements 606 $aRandom dynamical systems 606 $aPhysics 608 $aElectronic books. 615 0$aLangevin equations. 615 0$aBrownian movements. 615 0$aRandom dynamical systems. 615 0$aPhysics. 676 $a530.14/4 700 $aSnook$b Ian$0866978 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910457244703321 996 $aThe Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems$91935160 997 $aUNINA