Percolation

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Author: Geoffrey R. Grimmett

Publisher: Springer Science & Business Media

ISBN: 3662039818

Category: Mathematics

Page: 447

View: 1598

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.

Percolation

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Author: Bela Bollobás,Oliver Riordan

Publisher: Cambridge University Press

ISBN: 0521872324

Category: Mathematics

Page: 323

View: 5008

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

Applications Of Percolation Theory

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Author: M Sahini,M Sahimi

Publisher: CRC Press

ISBN: 148227244X

Category: Mathematics

Page: 276

View: 3640

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.

Introduction To Percolation Theory

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Author: Dietrich Stauffer,Ammon Aharony

Publisher: CRC Press

ISBN: 1420074792

Category: Science

Page: 192

View: 8691

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.

Percolation Theory for Flow in Porous Media

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Author: Allen Hunt,Robert Ewing,Behzad Ghanbarian

Publisher: Springer

ISBN: 3319037714

Category: Science

Page: 447

View: 4313

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)

Quantum and Semi-classical Percolation and Breakdown in Disordered Solids

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Author: Asok K. Sen,Kamal K. Bardhan,Bikas K. Chakrabarti

Publisher: Springer Science & Business Media

ISBN: 3540854274

Category: Science

Page: 326

View: 3788

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.

Explosive Percolation in Random Networks

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Author: Wei Chen

Publisher: Springer

ISBN: 3662437392

Category: Mathematics

Page: 63

View: 5409

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.

Noise Sensitivity of Boolean Functions and Percolation

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Author: Christophe Garban,Jeffrey E. Steif

Publisher: Cambridge University Press

ISBN: 1316123898

Category: Mathematics

Page: N.A

View: 3884

This is a graduate-level introduction to the theory of Boolean functions, an exciting area lying on the border of probability theory, discrete mathematics, analysis, and theoretical computer science. Certain functions are highly sensitive to noise; this can be seen via Fourier analysis on the hypercube. The key model analyzed in depth is critical percolation on the hexagonal lattice. For this model, the critical exponents, previously determined using the now-famous Schramm–Loewner evolution, appear here in the study of sensitivity behavior. Even for this relatively simple model, beyond the Fourier-analytic set-up, there are three crucially important but distinct approaches: hypercontractivity of operators, connections to randomized algorithms, and viewing the spectrum as a random Cantor set. This book assumes a basic background in probability theory and integration theory. Each chapter ends with exercises, some straightforward, some challenging.

Continuum Percolation

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Author: Ronald Meester,Rahul Roy

Publisher: Cambridge University Press

ISBN: 052147504X

Category: Mathematics

Page: 238

View: 9588

A unified treatment of a spatial random process that can be used to model many natural phenomena.

Percolation theory and ergodic theory of infinite particle systems

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Author: Harry Kesten

Publisher: Springer Verlag

ISBN: 9780387965376

Category: Business & Economics

Page: 323

View: 5784

This is the eighth volume (out of a projected ten) with papers which appeared during the "Stochastic Equations and Their Applications" year (1985-1986) at the Institute for Mathematics and its Applications at the University of Minnesota. This volume, which is directed towards researchers in applied mathematics, engineering, and physics, contains contributions by: M. Aizeman, R. Holley, M. Bramson, D. Griffeath, D.C. Brydges, J.T. Chayes, L. Chayes, J.T. Cox, R. Durrett, R.H. Schonmann, S. Goldstein, L. Gray, J.W. Halley, R. Holley, H. Kesten, T.M. Leggett, C.M. Newman, H.E. Stanley, D. Stauffer, and J.C. Wierman.

The Wulff Crystal in Ising and Percolation Models

Ecole d'Eté de Probabilités de Saint-Flour XXXIV - 2004

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Author: Raphaël Cerf

Publisher: Springer Science & Business Media

ISBN: 3540309888

Category: Mathematics

Page: 264

View: 3867

This volume is a synopsis of recent works aiming at a mathematically rigorous justification of the phase coexistence phenomenon, starting from a microscopic model. It is intended to be self-contained. Those proofs that can be found only in research papers have been included, whereas results for which the proofs can be found in classical textbooks are only quoted.

Groundwater Recharge from Run-off, Infiltration and Percolation

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Author: K.-P. Seiler,J.R. Gat

Publisher: Springer Science & Business Media

ISBN: 1402053053

Category: Science

Page: 248

View: 7917

To face the threats to the water supply and to maintain sustainable water management policies, detailed knowledge is needed on the surface-to-subsurface transformation link in the water cycle. Recharge flux is covered in this book as well as many other groundwater issues, including a comparison of the traditional and modern approaches to determine groundwater recharge. The authors also explain in detail the fate of groundwater recharge in the subsurface by hydraulic and geologic means, in order to stimulate adapted groundwater-management strategies.

Percolation

Of Poems

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Author: Amisha Mehta

Publisher: Notion Press

ISBN: 1945579161

Category: Poetry

Page: 68

View: 1076

Short, precise and crisp… that’s the way poetry is supposed to be served to its readers. In this fast–paced, multitasking world, I believe poetry is the quickest way to convey thoughts beautifully to readers. Writing poetry is an art where you are not just telling a story in a few words, but the words have to follow a certain pattern and are chosen in such a fashion that the emotion embedded in the poem remains intact. Every page of this book is a new poem with a new story. It will give you a glimpse of the world that we all are a part of. Each poem unfolds a part of the author on paper. It is the language of her soul. Happy reading!

Percolation Theory In Reservoir Engineering

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Author: King Peter,Masihi Mohsen

Publisher: World Scientific

ISBN: 1786345250

Category: Technology & Engineering

Page: 384

View: 7721

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

Fractals in Petroleum Geology and Earth Processes

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Author: C.C. Barton,P.R. La Pointe

Publisher: Springer Science & Business Media

ISBN: 9780306448683

Category: Mathematics

Page: 317

View: 3303

Statistics of natural resources and the law of pareto. The fractal size and spatial distribution of hydrocarbon accumulations: implications for resourse assessment and exploration strategy. Estimation of Undicovered hydrocarbon potential through fractal geometry. Fractals and the pareto distribution applied to petroleum accumulation size distributions. Fractal and multifractal models and methods and stratigraphy. On the scale indenpendent shape of prograding stratigraphic units: applications to sequence stratigraphy. New models require new data: fractal and multifractal measures of gravel bedload. Erosional development of the epithopian plateau of northeast Africa from fractal analysis of topography. Hierarchical cascades and single fracture: percolation and seismic detection. Fractals paterns in porous media flow: modeling of laboratory experiments. Diffusion-limited aggregation in the earth sciences. Creating reservoir simulations with fractasl characteristics. Vertical versus Horizontal well log variability and application to fractal reservoir modeling. Fractals and exploration geophysics: seismic deconvolution and geophysical inverse problems.

Percolation Theory for Mathematicians

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Author: Kesten

Publisher: Springer Science & Business Media

ISBN: 1489927301

Category: Mathematics

Page: 423

View: 964

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.