Percolation theory using Python

• Main Author: Malthe-Sørenssen, Anders
• Format: eBook Book
• Language: English
• Published: Cham Springer 2024; Springer Nature; Springer International Publishing; Springer International Publishing AG
• Edition: 1
• Series: Lecture Notes in Physics
• Subjects: anomalous diffusion; Applied physics; Condensed matter physics (liquid state and solid state physics); critical phenomena in statistical physics; Cybernetics and systems theory; disordered systems; Engineering applications of electronic, magnetic, optical materials; fractal models; Geophysics; Information theory; Materials / States of matter; Materials science; Mathematical physics; Mathematics and Science; Mechanical engineering and materials; Percolation (Statistical physics); Physics; Python (Computer program language); random media textbook; Reference, Information and Interdisciplinary subjects; Research and information: general; scaling theory; Statistical physics; Technology, Engineering, Agriculture, Industrial processes
• ISBN: 3031598997; 9783031598999; 3031599004; 9783031599002
• DOI: 10.1007/978-3-031-59900-2

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.