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Percolation Theory Using Python
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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.
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Keywords
- anomalous diffusion
- critical phenomena in statistical physics
- disordered systems
- fractal models
- random media textbook
- scaling theory
- thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general::GPF Information theory::GPFC Cybernetics and systems theory
- thema EDItEUR::P Mathematics and Science::PH Physics::PHF Materials / States of matter::PHFC Condensed matter physics (liquid state and solid state physics)
- thema EDItEUR::P Mathematics and Science::PH Physics::PHS Statistical physics
- thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics
- thema EDItEUR::P Mathematics and Science::PH Physics::PHV Applied physics::PHVG Geophysics
Links
DOI: 10.1007/978-3-031-59900-2web: https://link.springer.com/book/10.1007/978-3-031-59900-2
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