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Author : Daniel ben-Avraham,Shlomo Havlin
Publisher : Cambridge University Press
Page : 334 pages
File Size : 46,6 Mb
Release : 2000-11-02
Category : Mathematics
ISBN : 9780521622783
This book describes diffusion and transport in disordered media such as fractals and random resistor networks.
Author : Armin Bunde,Shlomo Havlin
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642848681
Fractals and disordered systems have recently become the focus of intense interest in research. This book discusses in great detail the effects of disorder on mesoscopic scales (fractures, aggregates, colloids, surfaces and interfaces, glasses and polymers) and presents tools to describe them in mathematical language. A substantial part is devoted to the development of scaling theories based on fractal concepts. In ten chapters written by leading experts in the field, the reader is introduced to basic concepts and techniques in disordered systems and is led to the forefront of current research. This second edition has been substantially revised and updates the literature in this important field.
Author : Fereydoon Family
Publisher : World Scientific
Page : 364 pages
File Size : 43,7 Mb
Release : 2002
Category : Technology & Engineering
ISBN : 9810248385
Investigation of the fractal and scaling properties of disordered systems has recently become a focus of great interest in research. Disordered or amorphous materials, like glasses, polymers, gels, colloids, ceramic superconductors and random alloys or magnets, do not have a homogeneous microscopic structure. The microscopic environment varies randomly from site to site in the system and this randomness adds to the complexity and the richness of the properties of these materials. A particularly challenging aspect of random systems is their dynamical behavior. Relaxation in disordered systems generally follows an unusual time-dependent trajectory. Applications of scaling and fractal concepts in disordered systems have become a broad area of interdisciplinary research, involving studies of the physics, chemistry, mathematics, biology and engineering aspects of random systems. This book is intended for specialists as well as graduate and postdoctoral students working in condensed-matter or statistical physics. It provides state-of-the-art information on the latest developments in this important and timely topic. The book is divided into three parts: Part I deals with critical phenomena, Part II is devoted to discussion of slow dynamics and Part III involves the application of scaling concepts to random systems. The effects of disorder at the mesoscopic scale as well as the latest results on the dynamical properties of disordered systems are presented. In particular, recent developments in static and dynamic scaling theories and applications of fractal concepts to disordered systems are discussed.
Author : Armin Bunde,Shlomo Havlin
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642514357
Fractals and disordered systems have recently become the focus of intense interest in research. This book discusses in great detail the effects of disorder on mesoscopic scales (fractures, aggregates, colloids, surfaces and interfaces, glasses, and polymers) and presents tools to describe them in mathematical language. A substantial part is devoted to the development of scaling theories based on fractal concepts. In 10 chapters written by leading experts in the field, including E. Stanley and B. Mandelbrot, the reader is introduced to basic concepts and techniques in disordered systems and is lead to the forefront of current research. In each chapter the connection between theory and experiment is emphasized, and a special chapter entitled "Fractals and Experiments" presents experimental studies of fractal systems in the laboratory. The book is written pedagogically. It can be used as a textbook for graduate students, by university teachers to prepare courses and seminars, and by active scientists who want to become familiar with a fascinating new field.
Author : Yuri P. Kalmykov,William T. Coffey,Stuart A. Rice
Publisher : John Wiley & Sons
Page : 756 pages
File Size : 49,7 Mb
Release : 2006-06-30
Category : Science
ISBN : 9780471725084
Fractals, Diffusion and Relaxation in Disordered Complex Systems is a special guest-edited, two-part volume of Advances in Chemical Physics that continues to report recent advances with significant, up-to-date chapters by internationally recognized researchers.
Author : Yuri P. Kalmykov,William T. Coffey,Stuart A. Rice
Publisher : John Wiley & Sons
Page : 432 pages
File Size : 43,7 Mb
Release : 2006-07-18
Category : Science
ISBN : 9780471790259
Fractals, Diffusion, and Relaxation in Disordered Complex Systems is a special guest-edited, two-part volume of Advances in Chemical Physics that continues to report recent advances with significant, up-to-date chapters by internationally recognized researchers.
Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Page : 1885 pages
File Size : 48,5 Mb
Release : 2011-10-05
Category : Mathematics
ISBN : 9781461418054
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Author : Mihai V. Putz
Publisher : CRC Press
Page : 414 pages
File Size : 44,7 Mb
Release : 2020-05-10
Category : Technology & Engineering
ISBN : 9780429663161
New Frontiers in Nanochemistry: Concepts, Theories, and Trends, Volume 1: Structural Nanochemistry is the first volume of the new three-volume set that explains and explores the important concepts from various areas within the nanosciences. This first volume focuses on structural nanochemistry and encompasses the general fundamental aspects of nanochemistry while simultaneously incorporating crucial material from other fields, in particular mathematic and natural sciences, with specific attention to multidisciplinary chemistry. Under the broad expertise of the editor, the volume contains 50 concise yet comprehensive entries from world-renowned scholars, alphabetically organizing a multitude of essential basic and advanced concepts, ranging from algebraic chemistry to new energy technology, from the bondonic theory of chemistry to spintronics, and from fractal dimension and kinetics to quantum dots and tight binding—and much more. The entries contain definitions, short characterizations, uses and usefulness, limitations, references, and more.
Author : Mihai V. Putz
Publisher : CRC Press
Page : 1479 pages
File Size : 40,7 Mb
Release : 2022-05-30
Category : Science
ISBN : 9780429634093
New Frontiers in Nanochemistry: Concepts, Theories, and Trends, 3-Volume Set explains and explores the important fundamental and advanced modern concepts from various areas of nanochemistry and, more broadly, the nanosciences. This innovative and one-of-a kind set consists of three volumes that focus on structural nanochemistry, topological nanochemistry, and sustainable nanochemistry respectively, collectively forming an explicative handbook in nanochemistry. The compilation provides a rich resource that is both thorough and accessible, encompassing the core concepts of multiple areas of nanochemistry. It also explores the content through a trans-disciplinary lens, integrating the basic and advanced modern concepts in nanochemistry with various examples, applications, issues, tools, algorithms, and even historical notes on the important people from physical, quantum, theoretical, mathematical, and even biological chemistry.
Author : David A. Weitz,Leonard M. Sander,Benoit B. Mandelbrot
Publisher : Unknown
Page : 382 pages
File Size : 53,9 Mb
Release : 1988
Category : Fractals
ISBN : UOM:39015032285077
Author : David Carfi,Michel L. Lapidus,Erin P. J. Pearse,Machiel van Frankenhuijsen
Publisher : American Mathematical Soc.
Page : 384 pages
File Size : 49,8 Mb
Release : 2013-10-24
Category : Mathematics
ISBN : 9780821891483
This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.
Author : N. Le Novère
Publisher : Springer Science & Business Media
Page : 569 pages
File Size : 44,5 Mb
Release : 2012-07-20
Category : Medical
ISBN : 9789400738584
Computational neurosciences and systems biology are among the main domains of life science research where mathematical modeling made a difference. This book introduces the many different types of computational studies one can develop to study neuronal systems. It is aimed at undergraduate students starting their research in computational neurobiology or more senior researchers who would like, or need, to move towards computational approaches. Based on their specific project, the readers would then move to one of the more specialized excellent textbooks available in the field. The first part of the book deals with molecular systems biology. Functional genomics is introduced through examples of transcriptomics and proteomics studies of neurobiological interest. Quantitative modelling of biochemical systems is presented in homogeneous compartments and using spatial descriptions. A second part deals with the various approaches to model single neuron physiology, and naturally moves to neuronal networks. A division is focused on the development of neurons and neuronal systems and the book closes on a series of methodological chapters. From the molecules to the organ, thinking at the level of systems is transforming biology and its impact on society. This book will help the reader to hop on the train directly in the tank engine.
Author : Harendra Singh,Devendra Kumar,Dumitru Baleanu
Publisher : CRC Press
Page : 168 pages
File Size : 46,9 Mb
Release : 2019-09-17
Category : Technology & Engineering
ISBN : 9781000606485
This book features original research articles on the topic of mathematical modelling and fractional differential equations. The contributions, written by leading researchers in the field, consist of chapters on classical and modern dynamical systems modelled by fractional differential equations in physics, engineering, signal processing, fluid mechanics, and bioengineering, manufacturing, systems engineering, and project management. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate level students, educators, researchers, and scientists interested in mathematical modelling and its diverse applications. Features Presents several recent developments in the theory and applications of fractional calculus Includes chapters on different analytical and numerical methods dedicated to several mathematical equations Develops methods for the mathematical models which are governed by fractional differential equations Provides methods for models in physics, engineering, signal processing, fluid mechanics, and bioengineering Discusses real-world problems, theory, and applications
Author : Paul Meakin
Publisher : Cambridge University Press
Page : 700 pages
File Size : 53,6 Mb
Release : 1998
Category : Mathematics
ISBN : 0521452538
A comprehensive, 1998 account of the practical aspects and pitfalls of the applications of fractal modelling in the physical sciences.
Author : Richard Paul Shaw
Publisher : Geological Society of London
Page : 180 pages
File Size : 55,5 Mb
Release : 2005
Category : Science
ISBN : 1862391866
Understanding how fluids flow through though rocks is very important in a number of fields. Almost all of the world's oil and gas are produced from underground reservoirs. Knowledge of how they got where they are, what keeps them there and how they migrate through the rock is very important in the search for new resources, as well as for maximising the extraction of as much of the contained oil/gas as possible. Some contributors to this volume have been trying to understand real rocks in real situations and others have been working on computer models and laboratory simulations. Put together, these approaches have yielded very useful results, many of which are discussed in this volume.
