Book Description
Percolation theory was initiated some fifty years ago as a mathematical framework for the study of random physical processes such as flow through a disordered porous medium. It has proved to be a remarkably rich theory, with applications beyond natural phenomena to topics such as network modelling. The aims of this book are twofold. First to present classical results in a way that is accessible to non-specialists. Second, to describe, for the first time in a book, recent results of Smirnov in conformal invariance, and outline the proof that the critical probability for random Voronoi percolation in the plane is 1/2. Throughout, the presentation is streamlined, with elegant and straightforward proofs requiring minimal background in probability and graph theory. Numerous examples illustrate the important concepts and enrich the arguments. All-in-all, it will be an essential purchase for mathematicians, physicists, electrical engineers and computer scientists working in this exciting area.
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Water Flow In Soils, Second Edition (Books in Soils, Plants, and the Environment)
Tsuyoshi Miyazaki
Manufacturer: CRC
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ASIN: 0824753259 |
Book Description
The new edition of a bestseller, Water Flows in Soils bridges the fields of soil physics-where descriptions of water flow tend to be microscopic- and hydrology - where they tend to be macroscopic. This work conveys the fundamental concepts of water flow in soils with clear and essentially nonmathematical explanations. The author elegantly elucidates the basic and advanced principles of water movement in soils. More than 750 figures, tables, and equations provide a concrete image of the water flow phenomena in soils. Tightly focused and packed with examples, the book is a practical resource for graduate students of agriculture and environmental engineering, and researchers in soil physics.
Book Description
Percolation theory deals with clustering, criticality, diffusion, fractals, phase transitions and disordered systems. It provides a quantitative model for understanding these phenomena, and therefore provides a theoretical, statistical background to many physical and natural science disciplines. This book explains the basic theory for the graduate while also reaching into the specialized fields of disordered systems and renormalization groups. Readers are expected to be able to handle some fundamental mathematical procedures, such as integration and differentiation of single variable functions, probability and statistics. Computer programming experience in Fortran is also useful. While percolation is treated as a fundamentally physical concept, its relevance to various natural and living systems is addressed. 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 book should be of value to all those who deal with systems which exhibit critical points and phase transition behavior.
Customer Reviews:
Classic book.......2006-08-03
This is a classic book on percolation theory, which has excellent intuitive derivations. It gives a good introduction to the subject and also includes more advanced topics. It is ideal for graduate students and should be on every statistical mechanician's desk.
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Percolation Theory for Flow in Porous Media (Lecture Notes in Physics)
Allen Hunt
Manufacturer: Springer
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Dynamics of Fluids in Porous Media (Dover Books on Physics and Chemistry)
ASIN: 3540261109 |
Book Description
The present 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 treatment 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 introduces physicists to some of the language and complications of groundwater hydrology necessary for succesful modelling.
Book Description
The random-cluster model has emerged in recent years as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. This systematic study includes accounts of the subcritical and supercritical phases, together with clear statements of important open problems. There is an extensive treatment of the first-order (discontinuous) phase transition, as well as a chapter devoted to applications of the random-cluster method to other models of statistical physics.
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Environmental Impact of Land Use in Rural Regions: Development, Validation and Application of Model Tools for Management and Polity Analysis (Series on Environmental Science and Management, Vol 1)
Peter E. Rijtema ,
Piet Groenendijk , and
Joop G. Kroes
Manufacturer: World Scientific Publishing Company
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ASIN: 1860940412 |
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Percolation (Grundlehren der mathematischen Wissenschaften)
Geoffrey Grimmett
Manufacturer: Springer
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Percolation
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Introduction To Percolation Theory
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Enumerative Combinatorics, Volume 1
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LaTeX: A Document Preparation System (2nd Edition) (Addison-Wesley Series on Tools and Techniques for Computer T)
ASIN: 3540649026 |
Book Description
Percolation theory is the study of an idealized random medium in two or more dimensions. The mathematical theory is mature, and continues to give rise to problems of special beauty and difficulty. Percolation is pivotal for studying more complex physical systems exhibiting phase transitions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. The book is intended for graduate students and researchers in probability and mathematical physics. Almost no specialist knowledge is assumed. 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.
Customer Reviews:
Excellent.......2000-04-26
The latest edition of Dr Grimmett's Percolation is surely the best book on the subject. He presents topics as clearly as possible without neglecting the technical details. His writing style is very readable, making much of this book accessible even to those who don't have all the necessary background in mathematics to understand all the proofs. Anyone looking for an easy introduction to the topic would be better off with Stauffer's book. But to gain any moderate understanding of this fascinating subject, and the methods and results of current research, this is the only book to have.
Percolation.......2000-04-05
Grimmett's book, Percolation, is excellent.
Percolation theory began in the 50's; its mathematics is now quite mature, but the theory has recently acquired new techniques because many of the questions initially raised by percolation theory are still unanswered.
Percolation technology is now a cornerstone of the theory of disordered systems, and the methods of this book are now being extended into dynamical systems theory and the life sciences. This book covers the mathematics of percolation theory, presenting the shortest rigorous proofs of the main facts. Many problems in percolation theory are beautiful, but some of the apparent simplicity of the subject is deceiving, because the subject is quite deep. Grimmett cuts through many of the difficulties presenting the important concepts clearly and sucinctly.
The author restricts himself- for accessibility to the maximum readership-to bond percolation on a cubic lattice. Grimmett presents the core material at a graduate level for folks conversant with elementary probability theory and real analysis. Having some knowledge of ergodic theory, graph theory, and some mathematical physics helps, however. There is litle discussion of continuous, mixed, inhomogenous, long range, first passage or oriented percolation.
Beginning with existance of Psubc for the edge probability p we arrive at an infinite open cluster followed by discusssion of the basic techniques of the FKC, BK inequalities and Russo's formula. Grimmett then discusses open clusters per vertex and subcritical percolation, beginning with the Aizeman-Barsky and Menshikov methods for identifying the critical point, followed by a systematic study of the subcritical phase. He then discusses supercritical percolation, including 2 dimensional percolation, continuum percolation and random processes. The author gives a full list of references.
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Hydrodynamic Limits and Related Topics (Fields Institute Communications)
Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Hardcover
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ASIN: 0821819933 |
Book Description
This book presents the lecture notes and articles from the workshop on hydrodynamic limits held at The Fields Institute (Toronto). The first part of the book contains the notes from the mini-course given by Professor S. R. S. Varadhan. The second part contains research articles reviewing the diverse progress in the study of hydrodynamic limits and related areas. This book offers a comprehensive introduction to the theory and its techniques, including entropy and relative entropy methods, large deviation estimates, and techniques in nongradient systems. This book, especially the lectures of Part I, could be used as a text for an advanced graduate course in hydrodynamic limits and interacting particle systems.
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Applications Of Percolation Theory
M Sahimi
Manufacturer: CRC
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Introduction To Percolation Theory
ASIN: 0748400761 |
Book Description
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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The Bronte Sisters/Wuthering Heights/Jane Eyre/Agnes Grey (Great Classic Library)
Emily Bronte ,
Charlotte Bronte , and
Anne Bronte
Manufacturer: Longmeadow Pr
ProductGroup: Book
Binding: Paperback
Bronte, Anne
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ASIN: 0681007796 |
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- Physics for Scientists and Engineers, Vol. 1 (Third Edition)
- Physics for Scientists and Engineers, Volume II
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- Physics: Principles with Applications (6th Edition)
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Percolation (Grundlehren der mathematischen Wissenschaften)
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