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Author : Laurent Nottale
Publisher :
Page : 0 pages
File Size : 42,29 MB
Release : 1998
Category : Science
ISBN : 9789810208783
1. General introduction -- 2. Relativity and quantum physics -- 3. From fractal objects to fractal spaces -- 4. Fractal dimension of a quantum path -- 5. The fractal structure of quantum space-time -- 6. Towards a special theory of scale relativity -- 7. Prospects
Author : Laurent Nottale
Publisher : World Scientific
Page : 358 pages
File Size : 40,36 MB
Release : 1993
Category : Science
ISBN : 9789810208783
This is the first detailed account of a new approach to microphysics based on two leading ideas: (i) the explicit dependence of physical laws on scale encountered in quantum physics, is the manifestation of a fundamental principle of nature, scale relativity. This generalizes Einstein's principle of (motion) relativity to scale transformations; (ii) the mathematical achievement of this principle needs the introduction of a nondifferentiable space-time varying with resolution, i.e. characterized by its fractal properties.The author discusses in detail reactualization of the principle of relativity and its application to scale transformations, physical laws which are explicitly scale dependent, and fractals as a new geometric description of space-time.
Author : Laurent Nottale
Publisher : World Scientific
Page : 766 pages
File Size : 43,77 MB
Release : 2011
Category : Science
ISBN : 1848166508
This book provides a comprehensive survey of the state-of-the-art in the development of the theory of scale relativity and fractal space-time. It suggests an original solution to the disunified nature of the classical-quantum transition in physical systems, enabling quantum mechanics to be based on the principle of relativity provided this principle is extended to scale transformations of the reference system. In the framework of such a newly-generalized relativity theory (including position, orientation, motion and now scale transformations), the fundamental laws of physics may be given a general form that goes beyond and integrates the classical and the quantum regimes. A related concern of this book is the geometry of space-time, which is described as being fractal and nondifferentiable. It collects and organizes theoretical developments and applications in many fields, including physics, mathematics, astrophysics, cosmology and life sciences.
Author : Laurent Nottale
Publisher : World Scientific
Page : 766 pages
File Size : 50,9 MB
Release : 2011
Category : Science
ISBN : 1848166516
This book provides a comprehensive survey of the development of the theory of scale relativity and fractal space-time. It suggests an original solution to the disunified nature of the classical-quantum transition in physical systems, enabling the basis of quantum mechanics on the principle of relativity, provided this principle is extended to scale transformations of the reference system. In the framework of such a newly generalized relativity theory (including position, orientation, motion and now scale transformations), the fundamental laws of physics may be given a general form that unifies and thus goes beyond the classical and quantum regimes taken separately. A related concern of this book is the geometry of space-time, which is described as being fractal and nondifferentiable. It collects and organizes theoretical developments and applications in many fields, including physics, mathematics, astrophysics, cosmology and life sciences.
Author : Ioan Merches
Publisher : World Scientific
Page : 299 pages
File Size : 33,66 MB
Release : 2015-08-28
Category : Science
ISBN : 9814678406
Using Cartan's differential 1-forms theory, and assuming that the motion variables depend on Euclidean invariants, certain dynamics of the material point and systems of material points are developed. Within such a frame, the Newtonian force as mass inertial interaction at the intragalactic scale, and the Hubble-type repulsive interaction at intergalactic distances, are developed.The wave-corpuscle duality implies movements on curves of constant informational energy, which implies both quantizations and dynamics of velocity limits.Analysis of motion of a charged particle in a combined field which is electromagnetic and with constant magnetism implies fractal trajectories. Mechanics of material points in a fractalic space is constructed, and various applications — fractal atom, potential well, free particle, etc. — are discussed.
Author : Patrice Abry
Publisher : John Wiley & Sons
Page : 382 pages
File Size : 19,30 MB
Release : 2013-03-01
Category : Mathematics
ISBN : 1118622901
Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling — self-similarity, long-range dependence and multi-fractals — are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space.
Author : R. Buccheri
Publisher : Springer Science & Business Media
Page : 441 pages
File Size : 40,45 MB
Release : 2012-12-06
Category : Science
ISBN : 9401001553
There are very few concepts that fascinate equally a theoretical physicist studying black holes and a patient undergoing seriolls mental psychosis. Time, undoubtedly, can well be ranked among them. For the measure of time inside a black hole is no less bizarre than the perception of time by a schizophrenic, who may perceive it as completely "suspended," "standing still," or even "reversing its direction. " The nature of time is certainly shrouded in profound mystery. This, perhaps, since the concept entails multifarious, and occasionally incongruous, facets. No wonder the subject attracts the serious attention of scholars on the one hand, and of the lay public on the other. Our Advanced Research Workshop is an excellent il lustration of this point, as the reader will soon discover. It turned out to be a unique professional forum for an unusually lively, effective and fruitful exchange of ideas and beliefs among 48 participants from 20 countries worldwide, selected out of more than a hundred applicants. The present book is based on the select talks presented at the meeting, and aims to provide the interested layperson and specialist alike with a multidisciplinary sampling of the most up-to-date scholarly research on the nature of time. It represents a coherent, state-of-the-art volume showing that research relevant to this topic is necessarily interdisciplinary and does not ignore such delicate issues as "altered" states of consciousness, religion and metaphysics.
Author : M.M. Novak
Publisher : CRC Press
Page : 414 pages
File Size : 21,83 MB
Release : 1995-08-01
Category : Mathematics
ISBN : 9780412710209
This book contains state of the art contributions to this rapidly growing research area. It will be of essential value to mathematicians, physicists and engineers working in the fields of fractals and related phenomena and to researchers working in medicine and the life sciences.
Author : Christos H Skiadas
Publisher : World Scientific
Page : 467 pages
File Size : 22,97 MB
Release : 2011-05-31
Category : Science
ISBN : 9814460478
The work done in chaotic modeling and simulation during the last decades has changed our views of the world around us and has introduced new scientific tools, methods and techniques. Advanced topics of these achievements are included in this volume on Chaos Theory which focuses on Chaotic Modeling, Simulation and Applications of the nonlinear phenomena. This volume includes the best papers presented in the 3rd International Conference on CHAOS. This interdisciplinary conference attracted people from many scientific fields dealing with chaos, nonlinear dynamics, fractals and the works presented and the papers included here are of particular interest that could provide a broad understanding of chaos in its various forms.The chapters relate to many fields of chaos including Dynamical and Nonlinear Systems, Attractors and Fractals, Hydro-Fluid Dynamics and Mechanics, Chaos in Meteorology and Cosmology, Chaos in Biology and Genetics, Chaotic Control, Chaos in Economy and Markets, and Computer Composition and Chaotic Simulations, including related applications.
Author : Rodrigo Sobreiro
Publisher : BoD – Books on Demand
Page : 114 pages
File Size : 37,3 MB
Release : 2012-02-15
Category : Science
ISBN : 9535100890
The unification between gravity and quantum field theory is one of the major problems in contemporary fundamental Physics. It exists for almost one century, but a final answer is yet to be found. Although string theory and loop quantum gravity have brought many answers to the quantum gravity problem, they also came with a large set of extra questions. In addition to these last two techniques, many other alternative theories have emerged along the decades. This book presents a series of selected chapters written by renowned authors. Each chapter treats gravity and its quantization through known and alternative techniques, aiming a deeper understanding on the quantum nature of gravity. Quantum Gravity is a book where the reader will find a fine collection of physical and mathematical concepts, an up to date research, about the challenging puzzle of quantum gravity.