Continuum Percolation
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Continuum Percolation
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Author : Ronald Meester
language : en
Publisher: Cambridge University Press
Release Date : 2008-05-15
Continuum Percolation written by Ronald Meester and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-15 with Mathematics categories.
Many phenomena in physics, chemistry, and biology can be modeled by spatial random processes. One such process is continuum percolation, which is used when the phenomenon being modeled is made up of individual events that overlap e.g., individual raindrops that eventually make the ground evenly wet. This is a systematic, rigorous account of continuum percolation. The authors treat two models, the Boolean model and the random connection model, in detail, and they discuss related continuum models. Meester and Roy explain all important techniques and methods and apply them to obtain results on the existence of phase transitions, equality and continuity of critical densities, compressions, rarefaction, and other aspects of continuum models.
Fractures And Fracture Networks
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Author : P.M. Adler
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Fractures And Fracture Networks written by P.M. Adler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
Both the beauty and interest of fractures and fracture networks are easy to grasp, since they are abundant in nature. An example is the road from Digne to Nice in the south of France, with an impressive number and variety of such structures: the road for the most part, goes through narrow valleys with fast running streams penetrating the rock faces; erosion is favored by the Mediterranean climate, so that rocks are barely covered by meager vegetation. In this inhospitable and sterile landscape, the visitor can im mediately discover innumerable fractures in great masses which have been distorted by slow, yet powerful movements. This phenomenon can be seen for about 100 kilometers; all kinds of shapes and combinations are repre sented and can be observed either in the mountain itself or in the man-made cliffs and excavations, resulting from improvements made to the road. In the same region, close to the Turini Pass, a real large scale hydrody namic experiment is taking place -a source which is situated on the flank on the mountain, has been equiped with a tap; if the tap is open, water flows through the tap only, but when it is closed, then the side of the mountain releases water in a matter of seconds. Other outlets are also influenced by this tap, such as a water basin situated a few hundred meters away.
Fractals In Petroleum Geology And Earth Processes
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Author : C.C. Barton
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fractals In Petroleum Geology And Earth Processes written by C.C. Barton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
In this unique volume, renowned experts discuss the applications of fractals in petroleum research-offering an excellent introduction to the subject. Contributions cover a broad spectrum of applications from petroleum exploration to production. Papers also illustrate how fractal geometry can quantify the spatial heterogeneity of different aspects of geology and how this information can be used to improve exploration and production results.
Random Heterogeneous Materials
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Author : Salvatore Torquato
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Random Heterogeneous Materials written by Salvatore Torquato and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
This accessible text presents a unified approach of treating the microstructure and effective properties of heterogeneous media. Part I deals with the quantitative characterization of the microstructure of heterogeneous via theoretical methods; Part II treats a wide variety of effective properties of heterogeneous materials and how they are linked to the microstructure, accomplished by using rigorous methods.
The Physics Of Amorphous Solids
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Author : Richard Zallen
language : en
Publisher: John Wiley & Sons
Release Date : 2008-07-11
The Physics Of Amorphous Solids written by Richard Zallen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-11 with Science categories.
An in-depth study of non-crystalline solids in which the arrangement of the atoms do not have long-range order. Describes the way amorphous solids are formed, the phenomenology of the liquid-to-glass and glass- to-liquid transition, and the technological applications. Emphasizes modern approaches such as scaling, localization, and percolation. Includes extensive treatment of structural aspects of amorphous solids, ranging from metallic glasses, to chalcogenides, to organic polymers. Incorporates illustrations for the clarification of physics concepts.
Network Models For Data Science
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Author : Alan Julian Izenman
language : en
Publisher: Cambridge University Press
Release Date : 2023-01-05
Network Models For Data Science written by Alan Julian Izenman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-05 with Mathematics categories.
This text on the theory and applications of network science is aimed at beginning graduate students in statistics, data science, computer science, machine learning, and mathematics, as well as advanced students in business, computational biology, physics, social science, and engineering working with large, complex relational data sets. It provides an exciting array of analysis tools, including probability models, graph theory, and computational algorithms, exposing students to ways of thinking about types of data that are different from typical statistical data. Concepts are demonstrated in the context of real applications, such as relationships between financial institutions, between genes or proteins, between neurons in the brain, and between terrorist groups. Methods and models described in detail include random graph models, percolation processes, methods for sampling from huge networks, network partitioning, and community detection. In addition to static networks the book introduces dynamic networks such as epidemics, where time is an important component.
Mathematics Of Random Media
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Author : Werner E. Kohler
language : en
Publisher: American Mathematical Soc.
Release Date :
Mathematics Of Random Media written by Werner E. Kohler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In recent years, there has been remarkable growth in the mathematics of random media. The field has deep scientific and technological roots, as well as purely mathematical ones in the theory of stochastic processes. This collection of papers by leading researchers provides an overview of this rapidly developing field. The papers were presented at the 1989 AMS-SIAM Summer Seminar in Applied Mathematics, held at Virginia Polytechnic Institute and State University in Blacksburg, Virginia. In addition to new results on stochastic differential equations and Markov processes, fields whose elegant mathematical techniques are of continuing value in application areas, the conference was organized around four themes: Systems of interacting particles are normally viewed in connection with the fundamental problems of statistical mechanics, but have also been used to model diverse phenomena such as computer architectures and the spread of biological populations. Powerful mathematical techniques have been developed for their analysis, and a number of important systems are now well understood. Random perturbations of dynamical systems have also been used extensively as models in physics, chemistry, biology, and engineering. Among the recent unifying mathematical developments is the theory of large deviations, which enables the accurate calculation of the probabilities of rare events. For these problems, approaches based on effective but formal perturbation techniques parallel rigorous mathematical approaches from probability theory and partial differential equations. The book includes representative papers from forefront research of both types. Effective medium theory, otherwise known as the mathematical theory of homogenization, consists of techniques for predicting the macroscopic properties of materials from an understanding of their microstructures. For example, this theory is fundamental in the science of composites, where it is used for theoretical determination of electrical and mechanical properties. Furthermore, the inverse problem is potentially of great technological importance in the design of composite materials which have been optimized for some specific use. Mathematical theories of the propagation of waves in random media have been used to understand phenomena as diverse as the twinkling of stars, the corruption of data in geophysical exploration, and the quantum mechanics of disordered solids. Especially effective methods now exist for waves in randomly stratified, one-dimensional media. A unifying theme is the mathematical phenomenon of localization, which occurs when a wave propogating into a random medium is attenuated exponentially with propagation distance, with the attenuation caused solely by the mechanism of random multiple scattering. Because of the wide applicability of this field of research, this book would appeal to mathematicians, scientists, and engineers in a wide variety of areas, including probabilistic methods, the theory of disordered materials, systems of interacting particles, the design of materials, and dynamical systems driven by noise. In addition, graduate students and others will find this book useful as an overview of current research in random media.
Applications Of Percolation Theory
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Author : Muhammad Sahimi
language : en
Publisher: Springer Nature
Release Date : 2023-03-18
Applications Of Percolation Theory written by Muhammad Sahimi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-18 with Science categories.
The first edition of this book was published in 1994. Since then considerable progress has been made in both theoretical developments of percolation theory, and in its applications. The 2nd edition of this book is a response to such developments. Not only have all of the chapters of the 1st edition been completely rewritten, reorganized, and updated all the way to 2022, but also 8 new chapters have been added that describe extensive new applications, including biological materials, networks and graphs, directed percolation, earthquakes, geochemical processes, and large-scale real world problems, from spread of technology to ad-hoc mobile networks.
Probability And Statistics
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Author : Cain Mckay
language : en
Publisher: Scientific e-Resources
Release Date : 2019-01-30
Probability And Statistics written by Cain Mckay and has been published by Scientific e-Resources this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-30 with categories.
Fractals In Natural Science
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Author : M Matsushita
language : en
Publisher: World Scientific
Release Date : 1994-10-26
Fractals In Natural Science written by M Matsushita and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-26 with Science categories.
During the last couple of years, fractals have been shown to represent the common aspects of many complex processes occurring in an unusually diverse range of fields including biology, chemistry, earth sciences, physics and technology. Using fractal geometry as a language, it has become possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iteractive functions, colloidal aggregation, biological pattern formation and inhomogenous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality.This volume contains a selection of high quality papers that discuss the latest developments in the research of fractals. It is divided into 5 sections and contains altogether 64 papers. Each paper is written by a well known author or authors in the field. Beginning each section is a short introduction, written by a prominent author, which gives a brief overview of the topics discussed in the respective sections.