Fractals in Engineering: Theoretical Aspects and Numerical Approximations
Fractals in Engineering: Theoretical Aspects and Numerical Approximations

Author: Maria Rosaria Lancia

Publisher: Springer Nature

Published: 2021-03-17

Total Pages: 173

ISBN-13: 303061803X

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Fractal structures or geometries currently play a key role in all models for natural and industrial processes that exhibit the formation of rough surfaces and interfaces. Computer simulations, analytical theories and experiments have led to significant advances in modeling these phenomena across wild media. Many problems coming from engineering, physics or biology are characterized by both the presence of different temporal and spatial scales and the presence of contacts among different components through (irregular) interfaces that often connect media with different characteristics. This work is devoted to collecting new results on fractal applications in engineering from both theoretical and numerical perspectives. The book is addressed to researchers in the field.

Fractals in Engineering
Fractals in Engineering

Author: Jacques Lévy-Véhel

Publisher: Springer Science & Business Media

Published: 2005-12-06

Total Pages: 288

ISBN-13: 1846280486

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The application of fractals in the engineering sciences is evolving swiftly and the editors have turned to Springer for the third time to bring you the latest research emerging from the rapid growth in techniques available for the employment of the ideas of fractals and complexity to a variety of disciplines in and associated with the engineering field. The strong potential of this research can be seen in real industrial situations with recent progress being made in areas such as chemical engineering, internet traffic, physics and finance. Image processing continues to be a major field of application for fractal analysis and is well-represented here. It is important to note that the applications models are presented with a firm basis in theoretical argument, the qualitative observation of fractal phenomena no longer being sufficient. Consisting of papers written by a world-wide pool of experts, the multidisciplinary approach of this third volume will be of particular interest to industrial researchers and practitioners as well as to academics from many backgrounds. Fractals in Engineering: New Trends in Theory and Applications continues the publication of engineering-related research in fractal techniques begun in Fractals in Engineering and Fractals: Theory and Applications in Engineering (Springer London 1997 and 1999).

Fractals in Reservoir Engineering
Fractals in Reservoir Engineering

Author: H. H. Hardy

Publisher: World Scientific

Published: 1994

Total Pages: 390

ISBN-13: 9789810220693

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Many natural objects have been found to be fractal and fractal mathematics has been used to generate many beautiful ?nature? scenes. Fractal mathematics is used in image compression and for movies and is now becoming an engineering tool as well. This book describes the application of fractal mathematics to one engineering specialty ? reservoir engineering. This is the process of engineering the production of oil and gas. The reservoir engineer's job is to design and predict production from underground oil and gas reservoirs. The successful application of fractal mathematics to this engineering discipline should be of interest, not only to reservoir engineers, but to other engineers with their own potential applications as well. Geologists will find surprisingly good numerical descriptions of subsurface rock distributions. Physicists will be interested in the application of renormalization and percolation theory described in the book. Geophysicists will find the description of fluid flow scaling problems faced by the reservoir engineer similar to their problems of scaling the transport of acoustic signals.

Chaos and Fractals in Engineering
Chaos and Fractals in Engineering

Author: Masao Nakagawa

Publisher: World Scientific

Published: 1999

Total Pages: 960

ISBN-13: 9789810238339

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This book is written for all engineers, graduate students and beginners working in the application fields, and for experimental scientists in general. It is not presented as a purely theoretical treatise but shows mathematics at a workshop, so to speak, through important applications originating in a deep pure mathematical theory. Widely spread subjects which the author has encountered hitherto are briefly addressed in the book, as chaos and fractal science is a frontier of new research fields nowadays.

African Fractals
African Fractals

Author: Ron Eglash

Publisher:

Published: 1999

Total Pages: 258

ISBN-13: 9780813526140

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Fractals are characterized by the repetition of similar patterns at ever-diminishing scales. Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced by computer graphics. It has become a new tool for modeling in biology, geology, and other natural sciences. Anthropologists have observed that the patterns produced in different cultures can be characterized by specific design themes. In Europe and America, we often see cities laid out in a grid pattern of straight streets and right-angle corners. In contrast, traditional African settlements tend to use fractal structures-circles of circles of circular dwellings, rectangular walls enclosing ever-smaller rectangles, and streets in which broad avenues branch down to tiny footpaths with striking geometric repetition. These indigenous fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs and knowledge systems. Drawing on interviews with African designers, artists, and scientists, Ron Eglash investigates fractals in African architecture, traditional hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, practical craft, quantitative techniques, and symbolic systems. He also examines the political and social implications of the existence of African fractal geometry. His book makes a unique contribution to the study of mathematics, African culture, anthropology, and computer simulations.

Fractals in Rock Mechanics
Fractals in Rock Mechanics

Author: Heping Xie

Publisher: CRC Press

Published: 2020-12-18

Total Pages: 472

ISBN-13: 1000150348

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Important developments in the progress of the theory of rock mechanics during recent years are based on fractals and damage mechanics. The concept of fractals has proved to be a useful way of describing the statistics of naturally occurring geometrics. Natural objects, from mountains and coastlines to clouds and forests, are found to have boundaries best described as fractals. Fluid flow through jointed rock masses and clusterings of earthquakes are found to follow fractal patterns in time and space. Fracturing in rocks at all scales, from the microscale (microcracks) to the continental scale (megafaults), can lead to fractal structures. The process of diagenesis and pore geometry of sedimentary rock can be quantitatively described by fractals, etc. The book is mainly concerned with these developments, as related to fractal descriptions of fragmentations, damage and fracture of rocks, rock burst, joint roughness, rock porosity and permeability, rock grain growth, rock and soil particles, shear slips, fluid flow through jointed rocks, faults, earthquake clustering, and so on. The prime concerns of the book are to give a simple account of the basic concepts, methods of fractal geometry, and their applications to rock mechanics, geology, and seismology, and also to discuss damage mechanics of rocks and its application to mining engineering. The book 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.

Fractals in Engineering
Fractals in Engineering

Author: Jacques Levy Vehel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 408

ISBN-13: 1447109953

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Fractal analysis research is expanding into a variety of engineering domains. The strong potential of this work is now beginning to be seen in important applications in real industrial situations. Recent research progress has already led to new developments in domains such as signal processing and chemical engineering, and the major advances in fractal theory that underlie such developments are detailed here. New domains of applications are also presented, among them environmental science and rough surface analysis. Sections include multifractal analysis, iterated function systems, random processes, network traffic analysis, fractals and waves, image compression, and applications in physics. Fractals in Engineering emphasizes the connection between fractal analysis research and applications to industry. It is an important volume that illustrates the scientific and industrial value of this exciting field.

Fractal Control Theory
Fractal Control Theory

Author: Shu-Tang Liu

Publisher: Springer

Published: 2018-04-21

Total Pages: 300

ISBN-13: 9811070504

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This book focuses on the control of fractal behaviors in nonlinear dynamics systems, addressing both the principles and purposes of control. For fractals in different systems, it presents revealing studies on the theory and applications of control, reflecting a spectrum of different control methods used with engineering technology. As such, it will benefit researchers, engineers, and graduate students in fields of fractals, chaos, engineering, etc.

Fractal Analysis
Fractal Analysis

Author: Fernando Brambila

Publisher: BoD – Books on Demand

Published: 2017-06-14

Total Pages: 296

ISBN-13: 9535131915

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Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Let us begin with the fractional calculus-fractal geometry relationship, which allows for modeling with extreme precision of phenomena such as diffusion in porous media with fractional partial differential equations in fractal objects. Where the order of the equation is the same as the fractal dimension, this allows us to make calculations with enormous precision in diffusion phenomena-particularly in the oil industry, for new spillage prevention. Main applications to industry, design of fractal antennas to receive all frequencies and that is used in all cell phones, spacecraft, radars, image processing, measure, porosity, turbulence, scattering theory. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book: "Part I: Petroleum Industry and Numerical Analysis"; "Part II: Fractal Antennas, Spacecraft, Radars, Image Processing, and Measure"; and "Part III: Scattering Theory, Porosity, and Turbulence." It's impossible to picture today's research without fractal analysis.

Fractals In Engineering - Proceedings Of The Conference On Fractals In Engineering 94
Fractals In Engineering - Proceedings Of The Conference On Fractals In Engineering 94

Author: C Trico

Publisher: World Scientific

Published: 1995-01-16

Total Pages: 298

ISBN-13: 9814550574

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Fractal sets serve as excellent models in Physics, Chemistry, Biology and other fields. However, the actual applications of these fascinating models are often unknown even to specialists in fractal theories. The communication of the most recent results utilising fractal concepts in experimental and industrial engineering research was thus a major challenge discussed in the above conference.The resulting proceedings are organised around five main themes: Materials Processing, Flow, Natural Sciences, Signal and Image Analysis and Mathematical Methods. Almost 50 papers are included in this volume. Besides the classical topics, the book also introduces an important session on Fractal Signal and Image Analysis, a subject which is rapidly gaining recognition in computer science and engineering for its promising industrial applications.