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Quantum Fractals

Author: Arkadiusz Jadczyk
Publisher: World Scientific
ISBN: 9814569887
Size: 11.86 MB
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Starting with numerical algorithms resulting in new kinds of amazing fractal patterns on the sphere, this book describes the theory underlying these phenomena and indicates possible future applications. The book also explores the following questions: What are fractals?How do fractal patterns emerge from quantum observations and relativistic light aberration effects?What are the open problems with iterated function systems based on Mobius transformations?Can quantum fractals be experimentally detected?What are quantum jumps?Is quantum theory complete and/or universal?Is the standard interpretation of Heisenberg's uncertainty relations accurate?What is Event Enhanced Quantum Theory and how does it differ from spontaneous localization theories?What are the possible applications of quantum fractals? Contents:IntroductionWhat are Quantum Fractals?:Cantor SetIterated Function SystemsCantor Set Through Matrix EigenvectorQuantum Iterated Function SystemsExample: The "Impossible" Quantum FractalAction on the PlaneLorentz Group, SL(2,ℂ), and Relativistic AberrationExamples:Hyperbolic Quantum FractalsControlling Chaotic Behavior and Fractal DimensionQuantum Fractals on n-SpheresAlgorithms for Generating Hyperbolic Quantum FractalsFoundational Questions:Stochastic Nature of Quantum Measurement ProcessesAre There Quantum Jumps?Bohmian MechanicsEvent Enhanced Quantum TheoryGhirardi–Rimini–Weber Spontaneous LocalizationHeisenberg's Uncertainty Principle and Quantum FractalsAre Quantum Fractals Real?Appendix A. Mathematical Concepts:Metric SpacesNormed SpacesMeasure and IntegralMarkov, Frobenius-Perron and Koopman OperatorsAppendix B. Minkowski Space Generalization of Euler-Rodrigues Formula:Alternative Derivation via SL(2,ℂ) Readership: Advanced undergraduate students and professionals in quantum chaos, as well as philosophers of science. Keywords:Fractals;Quantum Theory;Measurement;Uncertainty;Quantum Jumps;Mobius Transformations;IFS;Spin;Lorentz Group;Relativity;Aberration;Time;GRW;EEQT

Quantum Fractals

Author: Arkadiusz Jadczyk
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789814569866
Size: 12.56 MB
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1. Introduction -- 2. What are quantum fractals? 2.1. Cantor set. 2.2. Iterated function systems. 2.3. Cantor set throughmatrix eigenvector. 2.4. Quantum iterated function systems. 2.5. Example: The "impossible" quantum fractal. 2.6. Action on the plane. 2.7 Lorentz group, SL(2,C), and relativistic aberration -- 3. Examples. 3.1. Hyperbolic quantum fractals. 3.2. Controlling chaotic behavior and fractal dimension. 3.3. Quantum fractals on n-spheres. 3.4. Algorithms for generating hyperbolic quantum fractals -- 4. Foundational questions. 4.1. Stochastic nature of quantum measurement processes. 4.2. Are there quantum jumps? 4.3. Bohmian mechanics. 4.4. Event enhanced quantum theory. 4.5. Ghirardi-Rimini-Weber spontaneous localization. 4.6. Heisenberg's uncertainty principle and quantum fractals. 4.7. Are quantum fractals real?

Fractals Chaos Power Laws

Author: Manfred Schroeder
Publisher: Courier Corporation
ISBN: 0486472043
Size: 37.73 MB
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This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author - hailed by Publishers Weekly as a modern Lewis Carroll - conveys memorable insights in the form of puns and puzzles. 1992 edition.

Fractal Cities

Author: Michael Batty
Publisher:
ISBN: 9780124555709
Size: 40.50 MB
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Fractal Cities is the pioneering study of the development and use of fractal geometry for understanding and planning the physical form of cities, showing how this geometry enables cities to be simulated throughcomputer graphics. The book explains how the structure of cities evolve in ways which at first sight may appear irregular, but when understood in terms of fractals reveal a complex and diverse underlying order. The book includes numerous illustrations and 16 pages full-color plates of stunning computer graphics, along with explanations of how to construct them. The authors provide an accessible and thought-provoking introduction to fractal geometry, as well as an exciting visual understanding of the formof cities. This approach, bolstered by new insights into the complexity of social systems, provides one of the best introductions to fractal geometry available for non-mathematicians and social scientists. Fractal Cities is useful as a textbook for courses on geographic information systems, urban geography, regional science, and fractal geometry. Planners and architects will find that many aspects of fractal geometry covered in this book are relevant to their own interests. Those involved in fractals and chaos, computer graphics, and systems theory will also find important methods and examples germane to their work. Michael Batty is Director of the National Center for Geographic Information and analysis in the State University of New York at Buffalo, and has worked in planning theory and urban modeling. Paul Longley is a lecturer in geography at the University of Bristol, and is involved in the development of geographic information systems in urban policy analysis. Richly illustrated, including 16 pages of full-color plates of brilliant computer graphics Provides an introduction to fractal geometry for the non-mathematician and social scientist Explains the influence of fractals on the evolution of the physical form of cities

Fractional Order Systems

Author: Riccardo Caponetto
Publisher: World Scientific
ISBN: 9814304204
Size: 54.89 MB
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This book aims to propose implementations and applications of Fractional Order Systems (FOS). It is well known that FOS can be applied in control applications and systems modeling, and their effectiveness has been proven in many theoretical works and simulation routines. A further and mandatory step for FOS real world utilization is their hardware implementation and applications on real systems modeling. With this viewpoint, introductive chapters on FOS are included, on the definition of stability region of Fractional Order PID Controller and Chaotic FOS, followed by the practical implementation based on Microcontroller, Field Programmable Gate Array, Field Programmable Analog Array and Switched Capacitor. Another section is dedicated to FO modeling of Ionic Polymeric Metal Composite (IPMC). This new material may have applications in robotics, aerospace and biomedicine.

Systems Science

Author: Yi Lin
Publisher: CRC Press
ISBN: 1439895511
Size: 21.57 MB
Format: PDF
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By making use of the principles of systems science, the scientific community can explain many complicated matters of the world and shed new light on unsettled problems. Each real science has its own particular methodology for not only qualitative but also quantitative analyses, so it is important to understand the organic whole of systems research with operable mathematical methods. Systems Science: Methodological Approaches presents a mathematical explanation of systems science, giving readers a complete technical formulation of different systemic laws. It enables them to use a unified methodology to attack different problems that are hard, if not impossible, for modern science to handle. Following a brief history of systems science, the book explores: Basic concepts, characteristics, properties, and classifications of general systems Nonlinear systems dynamics and the theory of catastrophe Dissipative structures and synergistics Studies of chaos, including logistic mapping, phase space reconstruction, Lyapunov exponents, and chaos of general single relation systems Different aspects and concepts of fractals, including a presentation of L systems analysis and design Complex systems and complexity, with a discussion of how the phenomena of "three" and complexity are related, and how various cellular automata can be constructed to generate useful simulations and figurative patterns Complex adaptive systems and open complex giant systems, with introduction of the yoyo model and practical applications Complex networks and related concepts and methods The book concludes with several case studies that demonstrate how various concepts and the logic of systems can be practically applied to resolve real-life problems, such as the prediction of natural disasters. The book will be useful in directing future research and applications of systems science on a commonly accepted platform and playground.

Benoit Mandelbrot

Author: Michael Frame
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789814366069
Size: 64.58 MB
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Presents a biographical sketch of Polish mathematician Benoit Mandelbrot (b. 1924), compiled as part of the MacTutor History of Mathematics Archive of the School of Mathematics and Statistics at the University of Saint Andrews in Scotland. Explains that Mandelbrot is mainly responsible for the current interest in fractal geometry.

Thermodynamics Kinetics And Microphysics Of Clouds

Author: Vitaly I. Khvorostyanov
Publisher: Cambridge University Press
ISBN: 1107016037
Size: 79.98 MB
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This book advances understanding of cloud microphysics and provides a unified theoretical foundation for modeling cloud processes, for researchers and advanced students.