Complex Media and Percolation Theory
Published on 24. August 2021
Book
Hardback
XX, 439 pages
978-1-0716-1456-3 (ISBN)
Description
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.
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.
More details
Series
Edition
1st ed. 2021
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Illustrations
77 s/w Abbildungen, 75 farbige Abbildungen
XX, 439 p. 152 illus., 75 illus. in color.
Dimensions
Height: 260 mm
Width: 183 mm
Thickness: 29 mm
Weight
1159 gr
ISBN-13
978-1-0716-1456-3 (9781071614563)
DOI
10.1007/978-1-0716-1457-0
Schweitzer Classification
Other editions
Additional editions
Muhammad Sahimi | Allen G. Hunt
Complex Media and Percolation Theory
Book
10/2021
Springer
€822.50
The article will not be published
Persons
Muhammad Sahimi
is professor of chemical engineering and materials science, and the NIOC chair in petroleum engineering at the University of Southern California in Los Angeles. He has been involved for over 40 years in the development of the applications of percolation theory to various fields, particularly in porous media, and heterogeneous materials.
Allen Hunt is appointed jointly in Physics and the Earth & Environmental Sciences Departments at Wright State University. He is author or editor of 5 books with 200 publications. His interests are currently in problems of environmental science with strong physics component, typically referenced to transport in disordered systems as addressed in percolation theory. An example is the ability to forecast the fate of precipitation falling on the continents, whether evapotranspiration or run-off (called the water balance). His teaching has been recognized by the Latter-DaySaints Student Association while teaching in a community college and, at Wright State, by election to Who's Who Among American Teachers.
Allen Hunt is appointed jointly in Physics and the Earth & Environmental Sciences Departments at Wright State University. He is author or editor of 5 books with 200 publications. His interests are currently in problems of environmental science with strong physics component, typically referenced to transport in disordered systems as addressed in percolation theory. An example is the ability to forecast the fate of precipitation falling on the continents, whether evapotranspiration or run-off (called the water balance). His teaching has been recognized by the Latter-DaySaints Student Association while teaching in a community college and, at Wright State, by election to Who's Who Among American Teachers.
Content
Bootstrap Percolation.- Conduction and Diffusion in Percolating Systems.- Continuum Percolation.- Correlated Percolation.- Elastic Percolation Networks.- Invasion Percolation.- Networks, Flexibility and Mobility in.- Percolation in Complex Networks, and Faults and Fractures in Rock.- Percolation, Introduction to.- Lattices, Efficient Simulation of Large.- Percolation Phase Transition.- Percolation and Polymer Morphology and Rheology.- Percolation in Porous Media.- Percolation Thresholds, Exact.- Properties, Fractals, and the Renormalization Group Approach to Percolation.