Theory and Applications of the Cluster Variation and Path Probability Methods

ISBN-13: 9781461380436 / Angielski / Miękka / 2011 / 435 str.

J. L. Mor N-L Pez; Jos M. S. Nchez

Opis

This volume is a compilation of papers presented at the International Workshop on the Theory and Applications of the Cluster Variation and Path Probability Methods, held in the city of San Juan, Teotihuacan, Mexico, during June 18-22, 1995. The presentations at the workshop provided a state of the art review of the fundamental aspects of the CVM and PPM and their application to a wide range of problems in statistical mechanics and alloy theory. The volume begins with several articles dealing with the study of the kinetics of ordering in Ising sytems and alloys using the PPM and other classical techniques. These articles are followed by the contribution of Professor Masuo Suzuki on the Coherent Anomaly Method which has added a new dimension to mean field theory, and the CVM in particular, in the study of critical phenomena. The remaining of the volume is dedicated to fundamental aspects and specific applications of the CVM in a wide range of subjects ranging from bulk and surface studies to new areas of inquiry such as the problem of image reconstruction. Since the inception by Prof. Ryoichi Kikuchi of the CVM in 1950 and of the PPM in 1966, the latter after a gestation period of approximately six years, the tech niques have found wide acceptance in the physics and materials science communities. Both methods are properly regarded as seminal contributions to equilibrium and non equilibrium statistical mechanics."

Spis treści

Problems in the Foundation of the Path Probability Method: Path Probability Function and Entropy Production (R. Kikuchi). Ising Model and Kinetic Mean Field Theories (F. Ducastelle). Kinetic Path and Fluctuation Calculated by the PPM (T. Mohri). Time Development of Fluctuations in the PPM (K. Wada). Universal Dynamic Response in Solid Electrolytes: Formalism of the Path Probability Method as Applied to Transport Properties (H. Sato). Cluster Variational Approach to Nonequilibrium Lattice Models (M. Katori). Coherent-Anomaly Method and Its Applications (M. Suzuki). Cluster Variation and Cluster Static (D. de Fontaine). The Cluster Variation Method, the Effective Field Method and the Method of Integral Equation on the Regular and Random Ising Model (S. Katsura). CVM, CCM, and QCVM (T. Morita). The Cluster Expansion Method (J.M. Sanchez). Lattice Models and Cluster Expansions for the Prediction of Oxide Phase Diagrams and Defect Arrangements (G. Ceder). Diffuse Scattering of Neutrons in Ni3V and Pt3V: Test of the Gamma Expansion Method Approximation in a Degenerate Case (R. Caudron). Cluster Variation Method Applications to Large Ising Aggregates (F. AguileraGranja). Thermodynamic Properties of Coherent Interphase Boundaries in fcc Substitutional Alloys (M. Asta). 8 additional articles. Index.