Percolation

Author: Bela Bollobás,Oliver Riordan

Publisher: Cambridge University Press

ISBN: 0521872324

Category: Mathematics

Page: 323

View: 6428

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

Author: M Sahini,M Sahimi

Publisher: CRC Press

ISBN: 0203221532

Category: Mathematics

Page: 276

View: 5388

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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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Introduction To Percolation Theory

Author: Dietrich Stauffer,Ammon Aharony

Publisher: CRC Press

ISBN: 1420074792

Category: Science

Page: 192

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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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Percolation

Author: Geoffrey R. Grimmett

Publisher: Springer Science & Business Media

ISBN: 3662039818

Category: Mathematics

Page: 447

View: 454

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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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Percolation Theory for Flow in Porous Media

Author: Allen Hunt,Robert Ewing,Behzad Ghanbarian

Publisher: Springer

ISBN: 3319037714

Category: Science

Page: 447

View: 9405

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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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Percolation

Of Poems

Author: Amisha Mehta

Publisher: Notion Press

ISBN: 1945579161

Category: Poetry

Page: 68

View: 442

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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!
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Quantum and Semi-classical Percolation and Breakdown in Disordered Solids

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

Publisher: Springer Science & Business Media

ISBN: 3540854274

Category: Science

Page: 326

View: 8856

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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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Explosive Percolation in Random Networks

Author: Wei Chen

Publisher: Springer

ISBN: 3662437392

Category: Mathematics

Page: 63

View: 1417

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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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