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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:
At the end of the workshop on "New Theoretical Concepts in Physical Chemistry", one of the participants made an attempt to present a first impression of its achievements from his own personal standpoint. Appar ently his views reflected a general feeling, so that the organizers thought they would be suitable as a presentation of the proceedings for future readers. That is the background from which this foreword was born. The scope of the workshop is a very broad one. There are contribu tions from mathematics, physics, crystallography, chemistry and biology; the problems are approached either by means of axiomatic and rigorous methods, or at an empirical phenomenological level. This same diversifi cation can be found in the new basic concepts presented. Some arise from pure theoretical investigation in C*-algebra or in quantum probability theory; others from an analysis of very complex experimental data like nuclear energy levels, or processes on the frontier between classical and quantum physics; others again have their origin in the discovery of new ordered structures like the icosahedral crystal phases, or the knots of DNA molecules; others follow from the application of ideas like frac tals or chaos to new fields like spectral theory or chemical reactions. It is to be expected that readers will have to face the same sort of difficulties as did the participants in understanding such diverse languages, in applying themselves to subjects possibly far from their own experience, and in grasping highly sophisticated new concepts.
Preface -- Prologue -- Prelude -- part I. The butterfly fractal -- 0. Kiss precise -- 0.1. Apollonian gaskets and integer wonderlands -- Appendix. An Apollonian sand painting--the world's largest artwork
This volume is the second edition of the highly successful Fractals Everywhere. The Focus of this text is how fractal geometry can be used to model real objects in the physical world.
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?
Class-tested textbook that shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Delivers dozens of fully interactive examples for learning and implementation, constants and formulae can readily be altered and adapted for the user’s purposes. New edition offers enlarged two-volume format suitable to courses in mechanics and electrodynamics, while offering dozens of new examples and a more rewarding interactive learning environment.
The only book to successfully integrate social, economic and environmental considerations with an accessible, quantitative approach to energy science.Energy Science introduces the latest energy technologies, explaining the physical principles underlying technology and discussing their environmental, economic, and social impacts. With a focus on the transition from fossil fuels to low-carbon sources of energy, the text enables students to evaluatethe key sources of energy available, and introduces potential solutions to the energy problems facing us today.A core text in the field, Energy Science is full of topical case studies and examples using current data to highlight the practical application of relevant theory. Discussion questions throughout the text encourage the development of deep critical thinking skills, ensuring that students are properlyequipped to approach the energy challenges that lie ahead.Digital formats and resources.The book is available for students and institutions to purchase in a variety of formats, and is supported by online resources:DT The e-book offers a mobile experience and convenient access along with functionality tools, naviigation features, and links that offer extra learning support: www.oxfordtextbooks.co.uk/ebooksDT Online resources include multiple choice questions and further reading links for students to enhance their understanding, and, for registered adopters, a solutions manual, PowerPoint slides, figures and tables from the book.
Mythic Imagination Today is an illustrated guide to the interpenetration of mythology and science throughout the ages. This monograph brings alive our collective need for story as a guide to the rules, roles, and relationships of everyday life.