Many phenomena in physics, chemistry, and biology can be modelled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modelled is made up of individual events that overlap, for example, the way individual raindrops eventually make the ground evenly wet. This is a systematic rigorous account of continuum percolation. Two models, the Boolean model and the random connection model, are treated in detail, and related continuum models are discussed. All important techniques and methods are explained and applied to obtain results on the existence of phase transitions, equality and continuity of critical densities, compressions, rarefaction, and other aspects of continuum models. This self-contained treatment, assuming only familiarity with measure theory and basic probability theory, will appeal to students and researchers in probability and stochastic geometry.

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.

In this unique volume, renowned experts discuss the applications of fractals in petroleum research-offering an excellent introduction to the subject. Contributions cover a broad spectrum of applications from petroleum exploration to production. Papers also illustrate how fractal geometry can quantify the spatial heterogeneity of different aspects of geology and how this information can be used to improve exploration and production results.

Both the beauty and interest of fractures and fracture networks are easy to grasp, since they are abundant in nature. An example is the road from Digne to Nice in the south of France, with an impressive number and variety of such structures: the road for the most part, goes through narrow valleys with fast running streams penetrating the rock faces; erosion is favored by the Mediterranean climate, so that rocks are barely covered by meager vegetation. In this inhospitable and sterile landscape, the visitor can im mediately discover innumerable fractures in great masses which have been distorted by slow, yet powerful movements. This phenomenon can be seen for about 100 kilometers; all kinds of shapes and combinations are repre sented and can be observed either in the mountain itself or in the man-made cliffs and excavations, resulting from improvements made to the road. In the same region, close to the Turini Pass, a real large scale hydrody namic experiment is taking place -a source which is situated on the flank on the mountain, has been equiped with a tap; if the tap is open, water flows through the tap only, but when it is closed, then the side of the mountain releases water in a matter of seconds. Other outlets are also influenced by this tap, such as a water basin situated a few hundred meters away.

An in-depth study of non-crystalline solids in which the arrangement of the atoms do not have long-range order. Describes the way amorphous solids are formed, the phenomenology of the liquid-to-glass and glass- to-liquid transition, and the technological applications. Emphasizes modern approaches such as scaling, localization, and percolation. Includes extensive treatment of structural aspects of amorphous solids, ranging from metallic glasses, to chalcogenides, to organic polymers. Incorporates illustrations for the clarification of physics concepts.

In this standard reference of the field, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible displacements in porous media and fractured rock are considered. Two different approaches are discussed and contrasted with each other. The first approach is based on the classical equations of flow and transport, called 'continuum models'. The second approach is based on modern methods of statistical physics of disordered media; that is, on 'discrete models', which have become increasingly popular over the past 15 years. The book is unique in its scope, since (1) there is currently no book that compares the two approaches, and covers all important aspects of porous media problems; and (2) includes discussion of fractured rocks, which so far has been treated as a separate subject. Portions of the book would be suitable for an advanced undergraduate course. The book will be ideal for graduate courses on the subject, and can be used by chemical, petroleum, civil, environmental engineers, and geologists, as well as physicists, applied physicist and allied scientists that deal with various porous media problems.

This book, first published in 2006, is an account of percolation theory and its ramifications.