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Quantum Fractals

Author: Arkadiusz Jadczyk
Publisher: World Scientific
ISBN: 9814569887
Size: 68.49 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: 70.38 MB
Format: PDF
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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?

Fractional Order Systems

Author: Riccardo Caponetto
Publisher: World Scientific
ISBN: 9814304204
Size: 13.12 MB
Format: PDF
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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.

A Glossary Of Literary And Cultural Theory

Author: Peter Brooker
Publisher: Taylor & Francis
ISBN: 131735477X
Size: 73.62 MB
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The Glossary of Literary and Cultural Theory provides researchers and students with an up-to-date guide through the vibrant and changing debates in Literary and Cultural Studies. In a field where meanings are frequently complex and ambiguous, this text is remarkable for its clarity and usefulness. This third edition includes 17 entirely new entries and updates to more than a dozen others which address key concepts and contemporary positions in both literary and cultural theory. New entries include: • Actor Network Theory • Anthropocene • Ecocriticism • Digital Humanities • Postcapitalism • World Literature

Complexity Cognition And The City

Author: Juval Portugali
Publisher: Springer Science & Business Media
ISBN: 3642194508
Size: 47.80 MB
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Complexity, Cognition and the City aims at a deeper understanding of urbanism, while invoking, on an equal footing, the contributions both the hard and soft sciences have made, and are still making, when grappling with the many issues and facets of regional planning and dynamics. In this work, the author goes beyond merely seeing the city as a self-organized, emerging pattern of some collective interaction between many stylized urban "agents" – he makes the crucial step of attributing cognition to his agents and thus raises, for the first time, the question on how to deal with a complex system composed of many interacting complex agents in clearly defined settings. Accordingly, the author eventually addresses issues of practical relevance for urban planners and decision makers. The book unfolds its message in a largely nontechnical manner, so as to provide a broad interdisciplinary readership with insights, ideas, and other stimuli to encourage further research – with the twofold aim of further pushing back the boundaries of complexity science and emphasizing the all-important interrelation of hard and soft sciences in recognizing the cognitive sciences as another necessary ingredient for meaningful urban studies.

Chaos And Fractals

Author: Heinz-Otto Peitgen
Publisher: Springer Science & Business Media
ISBN: 1475747403
Size: 23.24 MB
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For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.

Chaotic Logic

Author: Ben Goertzel
Publisher: Springer Science & Business Media
ISBN: 1475721978
Size: 26.56 MB
Format: PDF
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This book summarizes a network of interrelated ideas which I have developed, off and on, over the past eight or ten years. The underlying theme is the psychological interplay of order and chaos. Or, to put it another way, the interplay of deduction and induction. I will try to explain the relationship between logical, orderly, conscious, rule-following reason and fluid, self organizing, habit-governed, unconscious, chaos-infused intuition. My previous two books, The Structure of Intelligence and The Evolving Mind, briefly touched on this relationship. But these books were primarily concerned with other matters: SI with constructing a formal language for discussing mentality and its mechanization, and EM with exploring the role of evolution in thought. They danced around the edges of the order/chaos problem, without ever fully entering into it. My goal in writing this book was to go directly to the core of mental process, "where angels fear to tread" -- to tackle all the sticky issues which it is considered prudent to avoid: the nature of consciousness, the relation between mind and reality, the justification of belief systems, the connection between creativity and mental illness,.... All of these issues are dealt with here in a straightforward and unified way, using a combination of concepts from my previous work with ideas from chaos theory and complex systems science.

Artificial General Intelligence

Author: Ben Goertzel
Publisher: Springer
ISBN: 331909274X
Size: 15.23 MB
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This book constitutes the refereed proceedings of the 7th International Conference on Artificial General Intelligence, AGI 2014, held in Quebec City, QC, Canada, in August 2014. The 22 papers and 8 posters were carefully reviewed and selected from 65 submissions. Researchers have recognized the necessity of returning to the original goals of the field by treating intelligence as a whole. Increasingly, there is a call for a transition back to confronting the more difficult issues of "human-level intelligence" and more broadly artificial general intelligence. AGI research differs from the ordinary AI research by stressing on the versatility and wholeness of intelligence and by carrying out the engineering practice according to an outline of a system comparable to the human mind in a certain sense. The AGI conference series has played and continues to play, a significant role in this resurgence of research on artificial intelligence in the deeper, original sense of the term of "artificial intelligence". The conferences encourage interdisciplinary research based on different understandings of intelligence and exploring different approaches.