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The last decade has been marked by a rapid growth in statistical mechanics, especially in connection with the physics and chemistry of the fluid state. Our understanding in these areas has been considerably advanced and enriched by the discovery of new techniques and the sharpening of old techniques, ranging all the way from computer simulation to mode-mode coupling theories. Statistical mechanics brings together under one roof a broad spectrum of mathematical techniques. The aim of these volumes is to provide a didactic treatment of those techniques that are most useful for the study of problems of current interest to theoretical chemists. The emphasis throughout is on the techniques themselves and not on reviewing the enormous literature in statistical mechanics. Each author was charged with the following task. Given N pages, (a) pose the problem, (b) present those aspects of the particular technique that clearly illustrate its internal workings, (c) apply the technique to the solution of several illustrative examples, and (d) write the chapter so that it will enable the reader to approach key citations to the literature intelligently. These volumes are designed for graduate students and research workers in statistical mechanics. Nevertheless, because of the range of techniques and their general utility, they should be useful in other areas as well.
Table des matières
of Volume 5.- 1. Cluster Methods in Equilibrium Statistical Mechanics of Fluids.- 1. Introduction.- 2. Graph-Theoretic Definitions.- 3. Partition Function, Pair Correlation Function, and Their Graphical Representation.- 4. Topological Reduction.- 5. General Philosophy of the Renormalization Method.- 6. Applications of Cluster Theory.- 7. Concluding Remarks.- References.- 2. Fluids with Long-Range Forces: Toward a Simple Analytic Theory.- 1. Introduction.- 2. Some General Features of the Fluids under Consideration.- 3. Large ?-Small ? Interpolation; Padé Approximants.- 4. Large r-Small r Interpolation; The Mean Spherical Approximation.- 5. Beyond the MSA.- 6. Summary of Results.- References.- 3. Electrolyte Solutions at Equilibrium.- 1. Introduction.- 2. Models for Ionic Solutions.- 3. Measurable Properties of Solutions at Equilibrium.- 4. McMillan-Mayer Theory.- 5. Thermodynamic Aspects of the McMillan-Mayer Theory.- 6. Cluster Expansions.- 7. Integral Equations.- References.- 4. A Guide to Monte Carlo for Statistical Mechanics: 1. Highways.- 1. Introduction.- 2. The Monte Carlo Method.- 3. Some Practical Details.- 4. Boundary Conditions.- 5. Conclusion.- Appendix A: Random Number Generators.- Appendix B: Ewald Potential Technique.- References.- 5. A Guide to Monte Carlo for Statistical Mechanics: 2. Byways.- 1. Introduction.- 2. Estimations of Free Energy and Entropy.- 3. Quantum Mechanical Calculations.- 4. Microscopic Studies.- 5. Conclusion.- References.- 6. Nucleation Theory.- 1. Introduction.- 2. Mathematical Formalism.- 3. Homogeneous Gas Phase Nucleation.- 4. Condensation of Water on Ions.- 5. Void Nucleation in Nuclear Reactor Materials.- References.- Author Index.
