Percolation Theory Using Python / by Anders Malthe-Sørenssen.

Format:

Book

Author/Creator:

Malthe-Sørenssen, Anders.

Series:

Lecture Notes in Physics, 1616-6361 ; 1029

Language:

English

Subjects (All):

Statistical physics.

Condensed matter.

System theory.

Porous materials.

Mathematical physics.

Computer simulation.

Geophysics.

Statistical Physics.

Phase Transition and Critical Phenomena.

Complex Systems.

Porous Materials.

Computational Physics and Simulations.

Local Subjects:

Statistical Physics.

Phase Transition and Critical Phenomena.

Complex Systems.

Porous Materials.

Computational Physics and Simulations.

Geophysics.

Physical Description:

1 online resource (221 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2024.

Summary:

This course-based open access textbook delves into percolation theory, examining the physical properties of random media—materials characterized by varying sizes of holes and pores. The focus is on both the mathematical foundations and the computational and statistical methods used in this field. Designed as a practical introduction, the book places particular emphasis on providing a comprehensive set of computational tools necessary for studying percolation theory. Readers will learn how to generate, analyze, and comprehend data and models, with detailed theoretical discussions complemented by accessible computer codes. The book's structure ensures a complete exploration of worked examples, encompassing theory, modeling, implementation, analysis, and the resulting connections between theory and analysis. Beginning with a simplified model system—a model porous medium—whose mathematical theory is well-established, the book subsequently applies the same framework to realistic random systems. Key topics covered include one- and infinite-dimensional percolation, clusters, scaling theory, diffusion in disordered media, and dynamic processes. Aimed at graduate students and researchers, this textbook serves as a foundational resource for understanding essential concepts in modern statistical physics, such as disorder, scaling, and fractal geometry.

Contents:

Introduction to Percolation

One-dimensional Percolation

Infinite-dimensional Percolation

Finite-dimensional Percolation

Geometry of Clusters

Finite Size Scaling

Renormalization

Subset Geometry

Flow in Disordered Media

Elastic Properties of Disordered Media

Diffusion in Disordered Media

Dynamic Processes in Disordered Media

References

Index.

ISBN:

9783031599002