Statistical Mechanics

Part B: Time-Dependent Processes, Modern Theoretical Chemistry 6

Inhaltsangabe1. Molecular Dynamics Techniques for Hard-Core Systems.- 1. Introduction.- 2. Statistical-Mechanical Background.- 2.1. Canonical-Ensemble Averages.- 2.2. Molecular Dynamics Averages.- 2.3. Periodic Boundary Conditions.- 3. Approach to Equilibrium.- 4. Equilibrium Thermodynamic Functions.- 4.1. Dynamical Pressure.- 4.2. Virial Theorem.- 4.3. Relationship of Dynamical and Canonical-Ensemble Pressures.- 4.4. Pressure from Collision Rate.- 5. Equilibrium Time Correlation Functions.- 5.1. Time Correlation Functions for Self-Diffusion.- 5.2. Computational Procedures and Results for D(2) (t).- 6. Nonequilibrium Molecular Dynamics.- 6.1. Numerical Details.- 6.2. Analysis of Data.- 7. Accuracy of Molecular Dynamics Trajectory.- 7.1. Constants of Motion.- 7.2. Growth of Trajectory Error.- 8. Programming Techniques.- 8.1. Simple Molecular Dynamics Program.- 8.2. Time Table Method.- 8.3. Cell Table Method.- 8.4. Position Updating.- References.- 2. Molecular Dynamics Methods: Continuous Potentials.- 1. Introduction.- 2. Integration Procedures for the Equations of Motion.- 3. Time-Saving Techniques.- 4. Potential Functions for Anisotropic Molecules.- 5. The Calculation of Time Correlation Functions and Static Properties.- 6. Systems with Long-Range Forces.- 7. Brownian Molecular Dynamics.- 8. Conclusion.- References.- 3. The Kinetic Theory of Gases.- 1. Introduction.- 2. The Boltzmann Equation.- 2.1. Boltzmann’s Derivation.- 2.2. The H-Theorem and the Approach to Equilibrium.- 2.3. Solutions of the Boltzmann Equation.- 3. The Kinetic Theory of Dense Gases.- 3.1. Introduction.- 3.2. The Enskog Theory and Its Modifications.- 3.3. The Liouville Equation and the BBGKY Hierarchy Equations.- 3.4. The Cluster Expansion Method and the Generalized Boltzmann Equation.- 4. Time Correlation Functions.- 4.1. Basic Theory.- 4.2. Computer Results for the Velocity Autocorrelation Function.- 4.3. Applications of the Kinetic Theory of Gases to the Time Correlation Functions.- 5. Discussion.- 5.1. Problems Connected with the Boltzmann Equation.- 5.2. Problems Connected with the Kinetic Theory of Dense Gases.- References.- 4. Renormalized Kinetic Theory of Dense Fluids.- 1. Introduction.- 2. Phase Space Time Correlation Functions.- 3. The Memory Function Formulation.- 4. Symmetrized Two-Particle Correlations with Renormalized Interactions.- 4.1. Formal Solution for G.- 4.2. Properties of Renormalized Interactions.- 4.3. Mode-Coupling Approximations.- 5. The Boltzmann-Enskog Theory of Thermal Fluctuations.- 6. The Velocity Autocorrelation Function of a Dense Fluid.- 6.1. The Enskog Approximation.- 6.2. Effects of Recollisions.- 7. Summary and Discussions.- Appendix A.- Appendix B.- Appendix C. Reduction of the Memory Function in the Boltzmann-Enskog Approximation.- References.- 5. Projection Operator Techniques in the Theory of Fluctuations.- 1. Introduction.- 2. Liouville Space.- 3. Relaxation Equations.- 4. Symmetry Properties.- 5. Navier-Stokes Equations.- 6. Conclusions.- References.- 6. Principles of Mode-Mode Coupling Theory.- 1. Introduction.- 2. Writing Mode-Mode Equations.- 3. Solving Mode-Mode Equations.- 4. Examples.- 4.1. Mutual Diffusion in a Binary Critical Mixture.- 4.2. Self-Diffusion.- 4.3. Reorientation.- 5. Conclusion.- References.- 7. Global Analysis of Nonlinear Chemical Kinetics.- 1. Introduction.- 1.1. Structural Stability of Kinetic Equations.- 1.2. Critical Points and Dynamics in the Linear Regime.- 1.3. Graphical Analysis of Stability Criteria.- 2. An Index Theorem for Chemical Kinetics.- 2.1. Chemical Dynamics on Manifolds.- 2.2. Limitations of the Index Theorem.- 3. Flow Box Analysis in Chemical Kinetics.- 3.1. Classification of Flows in Kinetic Systems.- 3.2. Computation of State Transition Diagrams from the Nonlinear Equations.- 3.3. Critical Points and Qualitative Dynamics from State Transition Diagrams.- 4. Some Limit Cycle Oscillations in Nonlinear Kinetic Equations.- 4.1. The Hopf Bifurcation.- 4.2. Global Analysis of Limit Cyc