327-5103-00L Nonequilibrium Statistical Mechanics
Semester | Spring Semester 2014 |
Lecturers | H. C. Öttinger |
Periodicity | yearly recurring course |
Language of instruction | English |
Abstract | Foundations of nonequilbrium statistical mechanics based on a unified approach, including projection-operator method, linear response theory, fluctuation-dissipation theorem, kinetic theory of gases, Boltzmann's equation, Chapman-Enskog Method, Grad's Moment Expansion, kinetic theory of polymeric liquids, simulation techniques (Monte Carlo, Brownian dynamics, molecular dynamics) |
Objective | To provide, illustrate, and practice the thermodynamic recipes for bridging length and time scales in nonequilibrium systems, including an overview of the roles of various simulation techniques |
Content | 1. Projection-Operator Method: Notation of Classical Mechanics, Ensembles, Projection Operators, Atomistic Expressions, Exact Time-Evolution Equation, Markovian Approximation, Linear Response Theory, Probability Density Approach, Fluctuation-Dissipation Theorem, Relationship Between Coarse-Grained Levels, Quantum Systems 2. Kinetic Theory of Gases: Elementary Kinetic Theory, Mean Free Path, Transport Coefficients, Boltzmann's Equation, Differential Cross Section for Collisions, Projection-Operator Approach, Chapman-Enskog Method, Grad's Moment Expansion, Thirteen-Moment Expansion, Structured Moment Method 3. Simulations: Simulation Philosophy, Understanding Through Simplicity, Overview over Simulation Techniques, Monte Carlo Simulations, Markov Chains, Detailed Balance, Brownian Dynamics, Stochastic Differential Equations, Dilute Polymer Solutions, Molecular Dynamics, Expressions for the Friction Matrix, Verlet-Type Integrators, Rarefied Len¬nard-Jones Gas, Entangled Polymer Melts |
Lecture notes | The course is based on the book "Beyond Equilibrium Thermodynamics" |
Literature | 1. H. C. Öttinger, Beyond Equilibrium Thermodynamics (Wiley, New York, 2005) 2. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer-Verlag, Berlin 1985) |
Prerequisites / Notice | This course is part of the area of specialization Materials Modeling and Simulation of the master degree program in Materials Science. The course relies on the previous course Nonequilibrium Systems offered in the fall semester or on the corresponding chapters of the book "Beyond Equilibrium Thermodynamics". |