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| Author | : Fernando Brambila |
| Publisher | : BoD – Books on Demand |
| Total Pages | : 296 |
| Release | : 2017-06-14 |
| Genre | : Mathematics |
| ISBN | : 9535131915 |
Download Fractal Analysis Book in PDF, ePub and Kindle
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.
| Author | : Manuel Fernández-Martínez |
| Publisher | : Springer |
| Total Pages | : 204 |
| Release | : 2019-04-23 |
| Genre | : Mathematics |
| ISBN | : 3030166457 |
Download Fractal Dimension for Fractal Structures Book in PDF, ePub and Kindle
This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts. In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithms for properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Lévy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes. This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.
| Author | : Michael J. Ostwald |
| Publisher | : Birkhäuser |
| Total Pages | : 429 |
| Release | : 2016-09-01 |
| Genre | : Mathematics |
| ISBN | : 3319324268 |
Download The Fractal Dimension of Architecture Book in PDF, ePub and Kindle
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.
| Author | : David Thomas Matthews |
| Publisher | : |
| Total Pages | : 210 |
| Release | : 1997 |
| Genre | : Fractals |
| ISBN | : |
Download On Fractal Dimension and Its Application Book in PDF, ePub and Kindle
| Author | : A.J. Crilly |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 312 |
| Release | : 2013-11-11 |
| Genre | : Computers |
| ISBN | : 3642780970 |
Download Applications of Fractals and Chaos Book in PDF, ePub and Kindle
Applications of Fractals and Chaos presents new developments in this rapidlydeveloping subject area. The presentation is more than merely theoretical, it specifically presents particular applications in a wide range of applications areas. Under the oceans, we consider the ways in which sponges and corals grow; we look, too, at the stability of ships on their surfaces. Land itself is modelled and applications to art, medicineand camouflage are presented. Readers should find general interest in the range of areas considered and should also be able to discover methods of value for their own specific areas of interest from studying the structure of related activities.
| Author | : Eric Rosenberg |
| Publisher | : Springer Nature |
| Total Pages | : 530 |
| Release | : 2020-07-07 |
| Genre | : Computers |
| ISBN | : 303043169X |
Download Fractal Dimensions of Networks Book in PDF, ePub and Kindle
Current interest in fractal dimensions of networks is the result of more than a century of previous research on dimensions. Fractal Dimensions of Networks ties the theory and methods for computing fractal dimensions of networks to the “classic” theory of dimensions of geometric objects. The goal of the book is to provide a unified treatment of fractal dimensions of sets and networks. Since almost all of the major concepts in fractal dimensions originated in the study of sets, the book achieves this goal by first clearly presenting, with an abundance of examples and illustrations, the theory and algorithms for sets, and then showing how the theory and algorithms have been applied to networks. Thus, the book presents the classical theory and algorithms for the box counting dimension for sets, and then presents the box counting dimension for networks. All the major fractal dimensions are studied, e.g., the correlation dimension, the information dimension, the Hausdorff dimension, the multifractal spectrum, as well as many lesser known dimensions. Algorithm descriptions are accompanied by worked examples, many applications of the methods are presented, and many exercises, ranging in difficulty from easy to research level, are included.
| Author | : David D. Nolte |
| Publisher | : Oxford University Press |
| Total Pages | : 384 |
| Release | : 2018-07-12 |
| Genre | : Science |
| ISBN | : 0192528505 |
Download Galileo Unbound Book in PDF, ePub and Kindle
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.
| Author | : Dongjie Xue |
| Publisher | : Springer Nature |
| Total Pages | : 183 |
| Release | : 2022-02-22 |
| Genre | : Science |
| ISBN | : 9811697167 |
Download Fractal Algorithm and Its Application in Rock Mechanics Book in PDF, ePub and Kindle
This book focuses on learning and adapting nonlinear geometry tool in rock engineering through fractal theories, hypotheses, algorithm, practical understandings, and case studies. Understanding self-similarity and self-affinity is a prerequisite to the fractal model in rock mechanics. The book aims to provide a guide for the readers seeking to understand and build nonlinear model by fractal algorithm. The book is motivated by recent rapid advances in rock engineering in China including application of fractal theory, in addition to percolation theory. It is an essential reference to the most promising innovative rock engineering. Chapters are carefully developed to cover (1) new fractal algorithms (2) five engineering cases. This authored book addresses the issue with a holistic and systematic approach that utilizes fractal theory to nonlinear behavior in rock engineering. The book is written for researchers interested in rock and geological engineering as well as organizations engaged in underground energy practices.
| Author | : L. Pietronero |
| Publisher | : Elsevier |
| Total Pages | : 489 |
| Release | : 2012-12-02 |
| Genre | : Science |
| ISBN | : 0444598413 |
Download Fractals in Physics Book in PDF, ePub and Kindle
Fractals in Physics
| Author | : Santo Banerjee |
| Publisher | : CRC Press |
| Total Pages | : 142 |
| Release | : 2020-03-27 |
| Genre | : Mathematics |
| ISBN | : 1351647628 |
Download Fractal Patterns in Nonlinear Dynamics and Applications Book in PDF, ePub and Kindle
Most books on fractals focus on deterministic fractals as the impact of incorporating randomness and time is almost absent. Further, most review fractals without explaining what scaling and self-similarity means. This book introduces the idea of scaling, self-similarity, scale-invariance and their role in the dimensional analysis. For the first time, fractals emphasizing mostly on stochastic fractal, and multifractals which evolves with time instead of scale-free self-similarity, are discussed. Moreover, it looks at power laws and dynamic scaling laws in some detail and provides an overview of modern statistical tools for calculating fractal dimension and multifractal spectrum.
