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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.

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Genre : Mathematics
Author : Geoffrey R. Grimmett
Publisher : Springer Science & Business Media
Release : 2013-03-09
File : 447 Pages
ISBN-13 : 9783662039816

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

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Genre : Mathematics
Author : Bela Bollobás
Publisher : Cambridge University Press
Release : 2006-09-21
File : 323 Pages
ISBN-13 : 9780521872324

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This work dealing with percolation theory clustering, criticallity, diffusion, fractals and phase transitions takes a broad approach to the subject, covering basic theory and also specialized fields like disordered systems and renormalization groups.

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Genre : Science
Author : Dietrich Stauffer
Publisher : CRC Press
Release : 1994-07-18
File : 192 Pages
ISBN-13 : 9781420074796

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This monograph presents, for the first time, a unified and comprehensive introduction to some of the basic transport properties of porous media, such as electrical and hydraulic conductivity, air permeability and diffusion. The approach is based on critical path analysis and the scaling of transport properties, which are individually described as functions of saturation. At the same time, the book supplies a tutorial on percolation theory for hydrologists, providing them with the tools for solving actual problems. In turn, a separate chapter serves to introduce physicists to some of the language and complications of groundwater hydrology necessary for successful modeling. The end-of-chapter problems often indicate open questions, which young researchers entering the field can readily start working on. This significantly revised and expanded third edition includes in particular two new chapters: one on advanced fractal-based models, and one devoted to the discussion of various open issues such as the role of diffusion vs. advection, preferential flow vs. critical path, universal vs. non-universal exponents for conduction, and last but not least, the overall influence of the experimental apparatus in data collection and theory validation. "The book is suitable for advanced graduate courses, with selected problems and questions appearing at the end of each chapter. [...] I think the book is an important work that will guide soil scientists, hydrologists, and physicists to gain a better qualitative and quantitative understanding of multitransport properties of soils." (Marcel G. Schaap, Soil Science Society of America Journal, May-June, 2006)

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Genre : Science
Author : Allen Hunt
Publisher : Springer
Release : 2014-02-04
File : 447 Pages
ISBN-13 : 9783319037714

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This lecture notes in physics volume mainly focuses on the semi classical and qu- tum aspects of percolation and breakdown in disordered, composite or granular s- tems. The main reason for this undertaking has been the fact that, of late, there have been a lot of (theoretical) work on quantum percolation, but there is not even a (single) published review on the topic (and, of course, no book). Also, there are many theoretical and experimental studies on the nonlinear current-voltage characteristics both away from, as well as one approaches, an electrical breakdown in composite materials. Some of the results are quite intriguing and may broadly be explained utilising a semi classical (if not, fully quantum mechanical) tunnelling between - cron or nano-sized metallic islands dispersed separated by thin insulating layers, or in other words, between the dangling ends of small percolation clusters. There have also been several (theoretical) studies of Zener breakdown in Mott or Anderson in- lators. Again, there is no review available, connecting them in any coherent fashion. A compendium volume connecting these experimental and theoretical studies should be unique and very timely, and hence this volume. The book is organised as follows. For completeness, we have started with a short and concise introduction on classical percolation. In the ?rst chapter, D. Stauffer reviews the scaling theory of classical percolation emphasizing (biased) diffusion, without any quantum effects. The next chapter by A. K.

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Genre : Science
Author : Asok K. Sen
Publisher : Springer Science & Business Media
Release : 2009-03-20
File : 326 Pages
ISBN-13 : 9783540854272

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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.

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Genre : Mathematics
Author : M Sahini
Publisher : CRC Press
Release : 2003-07-13
File : 276 Pages
ISBN-13 : 9780203221532

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Genre :
Author :
Publisher : DIANE Publishing
Release :
File : Pages
ISBN-13 : 9781428917361

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This thesis is devoted to the study of the Bohman-Frieze-Wormald percolation model, which exhibits a discontinuous transition at the critical threshold, while the phase transitions in random networks are originally considered to be robust continuous phase transitions. The underlying mechanism that leads to the discontinuous transition in this model is carefully analyzed and many interesting critical behaviors, including multiple giant components, multiple phase transitions, and unstable giant components are revealed. These findings should also be valuable with regard to applications in other disciplines such as physics, chemistry and biology.

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Genre : Mathematics
Author : Wei Chen
Publisher : Springer
Release : 2014-07-15
File : 63 Pages
ISBN-13 : 9783662437391

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Percolation theory deals with clustering, criticality, diffusion, fractals, phase transitions and disordered systems. It provides a quantitative model for understanding these phenomena, and therefore a theoretical and statistical background to many physical and natural sciences. This book explains the basic theory for the graduate while also reaching into the specialized fields of disordered systems and renormalization groups. Much of the book deals with systems lying close to the critical point phase transition point, where the subject is at its most interesting and sensitive. This text is ideal for those who deal with systems which exhibit critical points and phase transition behavior.

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Genre : Science
Author : A. Aharony
Publisher : Taylor & Francis
Release : 2003-07-13
File : 192 Pages
ISBN-13 : 9781135747831

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Genre : Agriculture
Author : Clarence Sheldon Slater
Publisher :
Release : 1931
File : 24 Pages
ISBN-13 : UIUC:30112101919402

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