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  • Reference work
  • © 2021

Complex Media and Percolation Theory

  • Presents the essential elements of percolation theory

  • Provides a clear description of the geometry of percolation clusters of the connected paths

  • Details important applications to a range of phenomena

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  • ISBN: 978-1-0716-1457-0
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Table of contents (20 entries)

  1. Front Matter

    Pages i-xx
  2. Percolation Phase Transition

    • Muhammad Sahimi
    Pages 1-9
  3. Introduction to Percolation

    • Muhammad Sahimi
    Pages 11-14
  4. Exact Percolation Thresholds

    • John C. Wierman
    Pages 15-24
  5. Scaling Theory of Percolation Clusters

    • Dietrich Stauffer, Muhammad Sahimi
    Pages 49-60
  6. Correlated Percolation

    • Antonio Coniglio, Annalisa Fierro
    Pages 61-88
  7. Bootstrap Percolation

    • Paolo De Gregorio, Aonghus Lawlor, Kenneth A. Dawson
    Pages 149-173
  8. Invasion Percolation

    • Mark Knackstedt, Lincoln Paterson
    Pages 175-190
  9. Conduction and Diffusion in Percolating Systems

    • Barry D. Hughes
    Pages 191-235
  10. Percolation in Porous Media

    • Peter King, Mohsen Masihi
    Pages 237-254
  11. Percolation, Faults and Fractures in Rock

    • Pierre M. Adler, Jean-François Thovert, Valeri V. Mourzenko
    Pages 255-271
  12. Elastic Percolation Networks

    • Phillip M. Duxbury
    Pages 343-364
  13. Networks, Flexibility and Mobility in

    • Michael F. Thorpe
    Pages 365-377
  14. Percolation and Polymer Morphology and Rheology

    • Muhammad Sahimi
    Pages 379-404
  15. Explosive Percolation Processes

    • Raissa M. D’Souza
    Pages 405-418

About this book

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.

Keywords

  • bootstrap percolation
  • diffusion in percolating systems
  • continuum percolation
  • elastic percolation networks
  • percolation lattice simulation
  • phase transition percolation
  • porous media

Editors and Affiliations

  • Department of Physics, Wright State University, Dayton, USA

    Muhammad Sahimi, Allen G. Hunt

About the editors

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-Day Saints Student Association while teaching in a community college and, at Wright State, by election to Who's Who Among American Teachers.  

 


Bibliographic Information

Buying options

eBook USD 349.99
Price excludes VAT (USA)
  • ISBN: 978-1-0716-1457-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 399.99
Price excludes VAT (USA)