A Random Walk Through Fractal Dimensions
A Random Walk Through Fractal Dimensions

Author: Brian H. Kaye

Publisher: John Wiley & Sons

Published: 2008-07-11

Total Pages: 452

ISBN-13: 3527615989

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Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science. From reviews of the first edition: "...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems." MRS Bulletin

A Random Walk Through Fractal Dimensions
A Random Walk Through Fractal Dimensions

Author: Brian Howard Kaye

Publisher: Weinheim, Germany : VCH Verlagsgesellschaft ; New York, NY, USA : VCH Publishers

Published: 1989

Total Pages: 421

ISBN-13: 9780895738882

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Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science. From reviews of the first edition: '...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems.' MRS Bulletin

Fractals in Probability and Analysis
Fractals in Probability and Analysis

Author: Christopher J. Bishop

Publisher: Cambridge University Press

Published: 2017

Total Pages: 415

ISBN-13: 1107134110

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A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.

Random Walk and the Heat Equation
Random Walk and the Heat Equation

Author: Gregory F. Lawler

Publisher: American Mathematical Soc.

Published: 2010-11-22

Total Pages: 170

ISBN-13: 0821848291

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The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation and considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equations and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. This first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For example, solving the heat equation in the discrete setting becomes a problem of diagonalization of symmetric matrices, which becomes a problem in Fourier series in the continuous case. Random walk and Brownian motion are introduced and developed from first principles. The latter two chapters discuss different topics: martingales and fractal dimension, with the chapters tied together by one example, a random Cantor set. The idea of this book is to merge probabilistic and deterministic approaches to heat flow. It is also intended as a bridge from undergraduate analysis to graduate and research perspectives. The book is suitable for advanced undergraduates, particularly those considering graduate work in mathematics or related areas.

A Random Walk Through Fractal Dimensions
A Random Walk Through Fractal Dimensions

Author: Brian Howard Kaye

Publisher:

Published: 1989

Total Pages: 456

ISBN-13:

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The aim of this book is both to stimulate interest in fractal geometry and to be useful as a first text to those who use fractal geometry in their work. It contains many suggestions for experiments, and tends to rely on graphic examples, rather than swamping the reader with equations and symbols.

Galileo Unbound
Galileo Unbound

Author: David D. Nolte

Publisher: Oxford University Press

Published: 2018-07-12

Total Pages: 384

ISBN-13: 0192528505

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Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

The Fractal Dimension of Architecture
The Fractal Dimension of Architecture

Author: Michael J. Ostwald

Publisher: Birkhäuser

Published: 2016-09-01

Total Pages: 429

ISBN-13: 3319324268

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Fractal analysis is a method for measuring, analysing and comparing the formal or geometric properties of complex objects. In this book it is used to investigate eighty-five buildings that have been designed by some of the twentieth-century’s most respected and celebrated architects. Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world’s most famous designs. Starting with 625 reconstructed architectural plans and elevations, and including more than 200 specially prepared views of famous buildings, this book presents the results of the largest mathematical study ever undertaken into architectural design and the largest single application of fractal analysis presented in any field. The data derived from this study is used to test three overarching hypotheses about social, stylistic and personal trends in design, along with five celebrated arguments about twentieth-century architecture. Through this process the book offers a unique mathematical insight into the history and theory of design.

Gaussian Self-Affinity and Fractals
Gaussian Self-Affinity and Fractals

Author: Benoit Mandelbrot

Publisher: Springer Science & Business Media

Published: 2002

Total Pages: 672

ISBN-13: 9780387989938

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This third volume of the Selected Works focusses on a detailed study of fraction Brownian motions. The fractal themes of "self-affinity" and "globality" are presented, while extensive introductory material, written especially for this book, precedes the papers and presents a number of striking new observations and conjectures. The mathematical tools so discussed will be valuable to diverse scientific communities.

Elementary Introduction to Spatial and Temporal Fractals
Elementary Introduction to Spatial and Temporal Fractals

Author: L.T. Fan

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 179

ISBN-13: 3642456901

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Fractals play an important role in modeling natural phenomena and engineering processes. And fractals have a close connection to the concepts of chaotic dynamics. This monograph presents definitions, concepts, notions and methodologies of both spatial and temporal fractals. It addresses students and researchers in chemistry and in chemical engineering. The authors present the concepts and methodologies in sufficient detail for uninitiated readers. They include many simple examples and graphical illustrations. They outline some examples in more detail: Perimeter fractal dimension of char particles, surface fractal dimension of charcoal; fractal analysis of pressure fluctuation in multiphase flow systems. Readers who master the concepts in this book, can confidently apply them to their fields of interest.

Proceedings of the 2011 International Conference on Informatics, Cybernetics, and Computer Engineering (ICCE2011) November 19-20, 2011, Melbourne, Australia
Proceedings of the 2011 International Conference on Informatics, Cybernetics, and Computer Engineering (ICCE2011) November 19-20, 2011, Melbourne, Australia

Author: Liangzhong Jiang

Publisher: Springer Science & Business Media

Published: 2011-11-24

Total Pages: 689

ISBN-13: 3642251854

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The volume includes a set of selected papers extended and revised from the International Conference on Informatics, Cybernetics, and Computer Engineering. Intelligent control is a class of control techniques, that use various AI computing approaches like neural networks, Bayesian probability, fuzzy logic, machine learning, evolutionary computation and genetic algorithms. Intelligent control can be divided into the following major sub-domains: Neural network control Bayesian control Fuzzy (logic) control Neuro-fuzzy control Expert Systems Genetic control Intelligent agents (Cognitive/Conscious control) New control techniques are created continuously as new models of intelligent behavior are created and computational methods developed to support them. Networks may be classified according to a wide variety of characteristics such as medium used to transport the data, communications protocol used, scale, topology, organizational scope, etc. ICCE 2011 Volume 1 is to provide a forum for researchers, educators, engineers, and government officials involved in the general areas of Intelligent Control and Network Communication to disseminate their latest research results and exchange views on the future research directions of these fields. 90 high-quality papers are included in the volume. Each paper has been peer-reviewed by at least 2 program committee members and selected by the volume editor Special thanks to editors, staff of association and every participants of the conference. It’s you make the conference a success. We look forward to meeting you next year.