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| Author | : Geoffrey R. Grimmett |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 459 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662039818 |
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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.
| Author | : Dietrich Stauffer |
| Publisher | : CRC Press |
| Total Pages | : 192 |
| Release | : 2018-12-10 |
| Genre | : Science |
| ISBN | : 1482272377 |
Download Introduction To Percolation Theory Book in PDF, ePub and Kindle
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.
| Author | : Bela Bollobás |
| Publisher | : Cambridge University Press |
| Total Pages | : 334 |
| Release | : 2006-09-21 |
| Genre | : Mathematics |
| ISBN | : 0521872324 |
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This book, first published in 2006, is an account of percolation theory and its ramifications.
| Author | : Dietrich Stauffer |
| Publisher | : CRC Press |
| Total Pages | : 205 |
| Release | : 1994-07-18 |
| Genre | : Science |
| ISBN | : 1420074792 |
Download Introduction To Percolation Theory Book in PDF, ePub and Kindle
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.
| Author | : Kesten |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 432 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 1489927301 |
Download Percolation Theory for Mathematicians Book in PDF, ePub and Kindle
Quite apart from the fact that percolation theory had its orlgln in an honest applied problem (see Hammersley and Welsh (1980)), it is a source of fascinating problems of the best kind a mathematician can wish for: problems which are easy to state with a minimum of preparation, but whose solutions are (apparently) difficult and require new methods. At the same time many of the problems are of interest to or proposed by statistical physicists and not dreamt up merely to demons~te ingenuity. Progress in the field has been slow. Relatively few results have been established rigorously, despite the rapidly growing literature with variations and extensions of the basic model, conjectures, plausibility arguments and results of simulations. It is my aim to treat here some basic results with rigorous proofs. This is in the first place a research monograph, but there are few prerequisites; one term of any standard graduate course in probability should be more than enough. Much of the material is quite recent or new, and many of the proofs are still clumsy. Especially the attempt to give proofs valid for as many graphs as possible led to more complications than expected. I hope that the Applications and Examples provide justifi cation for going to this level of generality.
| Author | : A. Aharony |
| Publisher | : Taylor & Francis |
| Total Pages | : 205 |
| Release | : 2003-07-13 |
| Genre | : Science |
| ISBN | : 1135747830 |
Download Introduction To Percolation Theory Book in PDF, ePub and Kindle
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.
| Author | : Allen Hunt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 334 |
| Release | : 2009-05-05 |
| Genre | : Science |
| ISBN | : 3540897895 |
Download Percolation Theory for Flow in Porous Media Book in PDF, ePub and Kindle
Why would we wish to start a 2nd edition of “Percolation theory for ?ow in porous media” only two years after the ?rst one was ?nished? There are essentially three reasons: 1) Reviews in the soil physics community have pointed out that the introductory material on percolation theory could have been more accessible. Our additional experience in teaching this material led us to believe that we could improve this aspect of the book. In the context of rewriting the ?rst chapter, however, we also expanded the discussion of Bethe lattices and their relevance for “classical” - ponents of percolation theory, thus giving more of a basis for the discussion of the relevance of hyperscaling. This addition, though it will not tend to make the book more accessible to hydrologists, was useful in making it a more complete reference, and these sections have been marked as being possible to omit in a ?rst reading. It also forced a division of the ?rst chapter into two. We hope that physicists without a background in percolation theory will now also ?nd the - troductory material somewhat more satisfactory. 2) We have done considerable further work on problems of electrical conductivity, thermal conductivity, and electromechanical coupling.
| Author | : M Sahini |
| Publisher | : CRC Press |
| Total Pages | : 289 |
| Release | : 2003-07-13 |
| Genre | : Mathematics |
| ISBN | : 0203221532 |
Download Applications Of Percolation Theory Book in PDF, ePub and Kindle
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.
| Author | : Ronald Meester |
| Publisher | : Cambridge University Press |
| Total Pages | : 252 |
| Release | : 1996-06-13 |
| Genre | : Mathematics |
| ISBN | : 131658254X |
Download Continuum Percolation Book in PDF, ePub and Kindle
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.
| Author | : King Peter |
| Publisher | : World Scientific |
| Total Pages | : 384 |
| Release | : 2018-09-14 |
| Genre | : Technology & Engineering |
| ISBN | : 1786345250 |
Download Percolation Theory In Reservoir Engineering Book in PDF, ePub and Kindle
This book aims to develop the ideas from fundamentals of percolation theory to practical reservoir engineering applications. Through a focus on field scale applications of percolation concepts to reservoir engineering problems, it offers an approximation method to determine many important reservoir parameters, such as effective permeability and reservoir connectivity and the physical analysis of some reservoir engineering properties. Starring with the concept of percolation theory, it then develops into methods to simple geological systems like sand-bodies and fractures. The accuracy and efficiency of the percolation concept for these is explained and further extended to more complex realistic models.Percolation Theory in Reservoir Engineering primarily focuses on larger reservoir scale flow and demonstrates methods that can be used to estimate large scale properties and their uncertainty, crucial for major development and investment decisions in hydrocarbon recovery. remove
