The first edition of this book was published in 1994. Since then considerable progress has been made in both theoretical developments of percolation theory, and in its applications. The 2nd edition of this book is a response to such developments. Not only have all of the chapters of the 1st edition been completely rewritten, reorganized, and updated all the way to 2022, but also 8 new chapters have been added that describe extensive new applications, including biological materials, networks and graphs, directed percolation, earthquakes, geochemical processes, and large-scale real world problems, from spread of technology to ad-hoc mobile networks.

Over the past two decades percolation theory has been used to explain and model a wide variety of phenomena that are of industrial and scientific importance. Examples include characterization of porous materials and reservoir rocks, fracture patterns and earthquakes in rocks, calculation of effective transport properties of porous media permeability, conductivity, diffusivity, etc., groundwater flow, polymerization and gelation, biological evolution, galactic formation in the universe, spread of knowledge, and many others. Most of such applications have resulted in qualitative as well as quantitative predictions for the system of interest. This book attempts to describe in simple terms some of these applications, outline the results obtained so far, and provide further references for future reading.

Percolation theory describes the effects of the connectivity of microscopic or small-scale elements of a complex medium to its macroscopic or large-scale properties. It also describes the conditions under which there may be a continuously connected path of local elements across the medium. The point at which the path is formed is called the percolation threshold. Percolation theory also predicts that many macroscopic properties of complex media follow universal power laws near the percolation threshold that are independent of many microscopic features of such media. There are many applications of percolation theory across the natural sciences, from porous materials, to composite solids, complex networks, and biological systems. This book presents the essential elements of percolation theory, covers the problem of calculating the exponents that characterize the power laws that the percolation quantities follow near the percolation threshold, provides a clear description of the geometry of percolation clusters of the connected paths, and addresses several variations of percolation theory. In particular, bootstrap percolation, explosive percolation, and invasion percolation are featured, which expand the range of natural systems to which percolation may be applicable. In addition, coverage includes several important applications of percolation theory to a range of phenomena, ranging from electrical conductivity, thermopower, the Hall effect, and photoconductivity of disordered semiconductors, to flow, transport and reaction in porous media, geochemistry, biology, and ecology.

Percolation theory provides a mathematical framework for the study of random physical processes such as flow through disordered porous media. It spans applications in the physical sciences and beyond natural phenomena. Double in size, this second edition provides an up-to-date account of these applications. After reviewing the theory, the book covers a range of applications and variations. Well known in the field, the author presents examples in phase transitions, semiconductors, geology, astrophysics, network modeling, and the social sciences.

This book aims to develop the ideas from fundamentals of percolation theory to practical reservoir engineering applications. Through a focus on field scale applications of percolation concepts to reservoir engineering problems, it offers an approximation method to determine many important reservoir parameters, such as effective permeability and reservoir connectivity and the physical analysis of some reservoir engineering properties. Starring with the concept of percolation theory, it then develops into methods to simple geological systems like sand-bodies and fractures. The accuracy and efficiency of the percolation concept for these is explained and further extended to more complex realistic models.Percolation Theory in Reservoir Engineering primarily focuses on larger reservoir scale flow and demonstrates methods that can be used to estimate large scale properties and their uncertainty, crucial for major development and investment decisions in hydrocarbon recovery.

Percolation theory is the study of an idealized random medium in two or more dimensions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. Much new material appears in this second edition including dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications.

This IMA Volume in ~athematics and its Applications PERCOLATION THEORY AND ERGODIC THEORY OF INFINITE PARTICLE SYSTEMS represents the proceedings of a workshop which was an integral part of the 19R4-85 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS We are grateful to the Scientific Committee: naniel Stroock (Chairman) Wendell Fleming Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaoo for planning and implementing an exciting and stimulating year-long program. We especially thank the Workshop Organizing Committee, Harry Kesten (Chairman), Richard Holley, and Thomas Liggett for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinherger PREFACE Percolation theory and interacting particle systems both have seen an explosive growth in the last decade. These suhfields of probability theory are closely related to statistical mechanics and many of the publications on these suhjects (especially on the former) appear in physics journals, wit~ a great variahility in the level of rigour. There is a certain similarity and overlap hetween the methods used in these two areas and, not surprisingly, they tend to attract the same probabilists. It seemed a good idea to organize a workshop on "Percolation Theory and Ergodic Theory of Infinite Particle Systems" in the framework of the special probahility year at the Institute for Mathematics and its Applications in 1985-86. Such a workshop, dealing largely with rigorous results, was indeed held in February 1986.