Statistical Physics and Spatial Statistics

by Mecke, Klaus R.; Stoyan, Dietrich

• ISBN13: 9783540677505
• ISBN10: 354067750X
• Format: Hardcover
• Copyright: 2000-09-01
• Publisher: Springer Verlag

Summary

Modern physics is confronted with a large variety of complex spatial patterns. Although both spatial statisticians and statistical physicists study random geometrical structures, there has been only little interaction between the two up to now because of different traditions and languages. This volume aims to change this situation by presenting in a clear way fundamental concepts of spatial statistics which are of great potential value for condensed matter physics and materials sciences in general, and for porous media, percolation and Gibbs processes in particular. Geometric aspects, in particular ideas of stochastic and integral geometry, play a central role throughout. With nonspecialist researchers and graduate students also in mind, prominent physicists give an excellent introduction here to modern ideas of statistical physics pertinent to this exciting field of research.

Table of Contents

Part I Spatial Statistics and Point Processes
Basic Ideas of Spatial Statistics	3	(19)
Dietrich Stoyan
Stationary Models in Stochastic Geometry - Palm Distributions as Distributions of Typical Elements. An Approach Without Limits	22	(14)
Werner Nagel
Statistical Analysis of Large-Scale Structure in the Universe	36	(36)
Martin Kerscher
Dynamics of Structure Formation in Thin Liquid Films: A Special Spatial Analysis	72	(23)
Karin Jacobs
Ralf Seemann
Klaus Mecke
Part II Integral Geometry and Morphology of Patterns
Mixed Measures and Inhomogeneous Boolean Models	95	(16)
Wolfgang Weil
Additivity, Convexity, and Beyond: Applications of Minkowski Functionals in Statistical Physics	111	(74)
Klaus R. Mecke
Considerations About the Estimation of the Size Distribution in Wicksell's Corpuscle Problem	185	(18)
Joachim Ohser
Konrad Sandau
Local Porosity Theory and Stochastic Reconstruction for Porous Media	203	(39)
Rudolf Hilfer
Stochastic Models as Tools for the Analysis of Decomposition and Crystallisation Phenomena in Solids	242	(25)
Helmut Hermann
Part III Phase Transitions and Simulations of Hard Particles
Phase Transition and Percolation in Gibbsian Particle Models	267	(28)
Hans-Otto Georgii
Fun with Hard Spheres	295	(37)
Hartmut Lowen
Finite Packings and Parametric Density	332	(17)
Jorg M. Wills
A Primer on Perfect Simulation	349	(30)
Elke Thonnes
Grand Canonical Simulations of Hard-Disk Systems by Simulated Tempering	379	(15)
Gunter Doge
Dynamic Triangulations for Granular Media Simulations	394	(17)
Jean-Albert Ferrez
Thomas M. Liebling
Didier Muller
Index	411