Download or read book Metric Myth Quasicrystals written by Antony J. Bourdillon and published by AuthorHouse. This book was released on 2012-08-30 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metric, Myth & Quasicrystallography describes the first measurement of the metric in quasicrystals and the first measurement at atomic scale. Quasicrystals are ordinary as window glass, but they have been mistified owing to their sharp diffraction patterns with 5-fold symmetries, impossible in crystals. Out of the fog, the patterns are not in Bragg order; the series is not properly Fibonacci: simplified indexation of the pattern is used to simulate a structure due to a single, aligned, edge-sharing unit-cell that is consistent with all data. Since it is unlikely that the sharp diffraction pattern is due to unmeasured poly polyhedra, does the International Union of Crystallography have to redefine crystals yet again? In modern physics, the metric relates the covariant components of invariant vectors with corresponding contravariant components. In crystallography it relates dimensions in momentum space to atomic locations in real space. In quasicrystals, the pattern in momentum space is logarithmic. Theory and simulation show why this has to be. Consequences follow. In particular, we show not only where the atoms are but also why they are there. A debate is reported so that the reader will be encouraged to make his own mind. When logarithmic periodicity is discovered and explained in one branch of physics, it should be expected in others.
Download or read book Metric Myth and Quasicrystals written by A. Bourdillon and published by . This book was released on 2012-09-11 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Group Theory in a Nutshell for Physicists written by A. Zee and published by Princeton University Press. This book was released on 2016-03-29 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise, modern textbook on group theory written especially for physicists Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a modern, accessible, and self-contained textbook on the subject written especially for physicists. Group Theory in a Nutshell for Physicists fills this gap, providing a user-friendly and classroom-tested text that focuses on those aspects of group theory physicists most need to know. From the basic intuitive notion of a group, A. Zee takes readers all the way up to how theories based on gauge groups could unify three of the four fundamental forces. He also includes a concise review of the linear algebra needed for group theory, making the book ideal for self-study. Provides physicists with a modern and accessible introduction to group theory Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more Topics include finite group and character tables; real, pseudoreal, and complex representations; Weyl, Dirac, and Majorana equations; the expanding universe and group theory; grand unification; and much more The essential textbook for students and an invaluable resource for researchers Features a brief, self-contained treatment of linear algebra An online illustration package is available to professors Solutions manual (available only to professors)
Download or read book The Mathematics of Harmony written by Alexey Stakhov and published by World Scientific. This book was released on 2009 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science."
Download or read book Symmetry A Very Short Introduction written by Ian Stewart and published by OUP Oxford. This book was released on 2013-05-30 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 1800s mathematicians introduced a formal theory of symmetry: group theory. Now a branch of abstract algebra, this subject first arose in the theory of equations. Symmetry is an immensely important concept in mathematics and throughout the sciences, and its applications range across the entire subject. Symmetry governs the structure of crystals, innumerable types of pattern formation, how systems change their state as parameters vary; and fundamental physics is governed by symmetries in the laws of nature. It is highly visual, with applications that include animal markings, locomotion, evolutionary biology, elastic buckling, waves, the shape of the Earth, and the form of galaxies. In this Very Short Introduction, Ian Stewart demonstrates its deep implications, and shows how it plays a major role in the current search to unify relativity and quantum theory. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Download or read book Logarithmically Periodic Solids written by A. Bourdillon and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The cluster model, also called the logarithmically periodic solid or LPS, can be used to represent a supercluster and is infinitely extensive, uniquely aligned and uniquely icosahedral. This book presents a review of logarithmically periodic solids with important new properties for ready access.
Download or read book The Second Kind of Impossible written by Paul Steinhardt and published by Simon & Schuster. This book was released on 2020-01-07 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: *Shortlisted for the 2019 Royal Society Insight Investment Science Book Prize* One of the most fascinating scientific detective stories of the last fifty years, an exciting quest for a new form of matter. “A riveting tale of derring-do” (Nature), this book reads like James Gleick’s Chaos combined with an Indiana Jones adventure. When leading Princeton physicist Paul Steinhardt began working in the 1980s, scientists thought they knew all the conceivable forms of matter. The Second Kind of Impossible is the story of Steinhardt’s thirty-five-year-long quest to challenge conventional wisdom. It begins with a curious geometric pattern that inspires two theoretical physicists to propose a radically new type of matter—one that raises the possibility of new materials with never before seen properties, but that violates laws set in stone for centuries. Steinhardt dubs this new form of matter “quasicrystal.” The rest of the scientific community calls it simply impossible. The Second Kind of Impossible captures Steinhardt’s scientific odyssey as it unfolds over decades, first to prove viability, and then to pursue his wildest conjecture—that nature made quasicrystals long before humans discovered them. Along the way, his team encounters clandestine collectors, corrupt scientists, secret diaries, international smugglers, and KGB agents. Their quest culminates in a daring expedition to a distant corner of the Earth, in pursuit of tiny fragments of a meteorite forged at the birth of the solar system. Steinhardt’s discoveries chart a new direction in science. They not only change our ideas about patterns and matter, but also reveal new truths about the processes that shaped our solar system. The underlying science is important, simple, and beautiful—and Steinhardt’s firsthand account is “packed with discovery, disappointment, exhilaration, and persistence...This book is a front-row seat to history as it is made” (Nature).
Download or read book The Fourth Dimension Toward a Geometry of Higher Reality written by Rudy Rucker and published by Courier Corporation. This book was released on 2014-09-17 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most talented contemporary authors of cutting-edge math and science books conducts a fascinating tour of a higher reality, the Fourth Dimension. Includes problems, puzzles, and 200 drawings. "Informative and mind-dazzling." — Martin Gardner.
Download or read book Shadows of Reality written by Tony Robbin and published by Yale University Press. This book was released on 2008-10-01 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this insightful book, which is a revisionist math history as well as a revisionist art history, Tony Robbin, well known for his innovative computer visualizations of hyperspace, investigates different models of the fourth dimension and how these are applied in art and physics. Robbin explores the distinction between the slicing, or Flatland, model and the projection, or shadow, model. He compares the history of these two models and their uses and misuses in popular discussions. Robbin breaks new ground with his original argument that Picasso used the projection model to invent cubism, and that Minkowski had four-dimensional projective geometry in mind when he structured special relativity. The discussion is brought to the present with an exposition of the projection model in the most creative ideas about space in contemporary mathematics such as twisters, quasicrystals, and quantum topology. Robbin clarifies these esoteric concepts with understandable drawings and diagrams. Robbin proposes that the powerful role of projective geometry in the development of current mathematical ideas has been long overlooked and that our attachment to the slicing model is essentially a conceptual block that hinders progress in understanding contemporary models of spacetime. He offers a fascinating review of how projective ideas are the source of some of today’s most exciting developments in art, math, physics, and computer visualization.
Download or read book Thermal Physics and Thermal Analysis written by Jaroslav Šesták and published by Springer. This book was released on 2017-03-24 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features twenty-five chapter contributions from an international array of distinguished academics based in Asia, Eastern and Western Europe, Russia, and the USA. This multi-author contributed volume provides an up-to-date and authoritative overview of cutting-edge themes involving the thermal analysis, applied solid-state physics, micro- and nano-crystallinity of selected solids and their macro- and microscopic thermal properties. Distinctive chapters featured in the book include, among others, calorimetry time scales from days to microseconds, glass transition phenomena, kinetics of non-isothermal processes, thermal inertia and temperature gradients, thermodynamics of nanomaterials, self-organization, significance of temperature and entropy. Advanced undergraduates, postgraduates and researchers working in the field of thermal analysis, thermophysical measurements and calorimetry will find this contributed volume invaluable. This is the third volume of the triptych volumes on thermal behaviour of materials; the previous two receiving thousand of downloads guaranteeing their worldwide impact.
Download or read book From Riemann to Differential Geometry and Relativity written by Lizhen Ji and published by Springer. This book was released on 2017-10-03 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.
Download or read book Quantum Theory and the Schism in Physics written by Karl Popper and published by Routledge. This book was released on 2013-04-15 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Theory and the Schism in Physics is one of the three volumes of Karl Popper’s Postscript to the Logic of scientific Discovery. The Postscript is the culmination of Popper’s work in the philosophy of physics and a new famous attack on subjectivist approaches to philosophy of science. Quantum Theory and the Schism in Physics is the third volume of the Postscript. It may be read independently, but it also forms part of Popper’s interconnected argument in the Postscript. It presents Popper’s classic statement on quantum physics and offers important insights into his thinking on problems of method within science and physics as a whole.
Download or read book Solvation Thermodynamics written by Arieh Y. Ben-Naim and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with a subject that has been studied since the beginning of physical chemistry. Despite the thousands of articles and scores of books devoted to solvation thermodynamics, I feel that some fundamen tal and well-established concepts underlying the traditional approach to this subject are not satisfactory and need revision. The main reason for this need is that solvation thermodynamics has traditionally been treated in the context of classical (macroscopic) ther modynamics alone. However, solvation is inherently a molecular pro cess, dependent upon local rather than macroscopic properties of the system. Therefore, the starting point should be based on statistical mechanical methods. For many years it has been believed that certain thermodynamic quantities, such as the standard free energy (or enthalpy or entropy) of solution, may be used as measures of the corresponding functions of solvation of a given solute in a given solvent. I first challenged this notion in a paper published in 1978 based on analysis at the molecular level. During the past ten years, I have introduced several new quantities which, in my opinion, should replace the conventional measures of solvation thermodynamics. To avoid confusing the new quantities with those referred to conventionally in the literature as standard quantities of solvation, I called these "nonconventional," "generalized," and "local" standard quantities and attempted to point out the advantages of these new quantities over the conventional ones.
Download or read book The Hidden Pattern written by Ben Goertzel and published by Universal-Publishers. This book was released on 2006 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Hidden Pattern presents a novel philosophy of mind, intended to form a coherent conceptual framework within which it is possible to understand the diverse aspects of mind and intelligence in a unified way. The central concept of the philosophy presented is the concept of "pattern" minds and the world they live in and co-create are viewed as patterned systems of patterns, evolving over time, and various aspects of subjective experience and individual and social intelligence are analyzed in detail in this light. Many of the ideas presented are motivated by recent research in artificial intelligence and cognitive science, and the author's own AI research is discussed in moderate detail in one chapter. However, the scope of the book is broader than this, incorporating insights from sources as diverse as Vedantic philosophy, psychedelic psychotherapy, Nietzschean and Peircean metaphysics and quantum theory. One of the unique aspects of the patternist approach is the way it seamlessly fuses the mechanistic, engineering-oriented approach to intelligence and the introspective, experiential approach to intelligence.
Download or read book Huygens and Barrow Newton and Hooke written by Vladimir I. Arnold and published by Birkhäuser. This book was released on 2012-12-06 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translated from the Russian by E.J.F. Primrose "Remarkable little book." -SIAM REVIEW V.I. Arnold, who is renowned for his lively style, retraces the beginnings of mathematical analysis and theoretical physics in the works (and the intrigues!) of the great scientists of the 17th century. Some of Huygens' and Newton's ideas. several centuries ahead of their time, were developed only recently. The author follows the link between their inception and the breakthroughs in contemporary mathematics and physics. The book provides present-day generalizations of Newton's theorems on the elliptical shape of orbits and on the transcendence of abelian integrals; it offers a brief review of the theory of regular and chaotic movement in celestial mechanics, including the problem of ports in the distribution of smaller planets and a discussion of the structure of planetary rings.
Download or read book Symmetrical Analysis Techniques for Genetic Systems and Bioinformatics Advanced Patterns and Applications written by Petoukhov, Sergey and published by IGI Global. This book was released on 2009-10-31 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book compiles studies that demonstrate effective approaches to the structural analysis of genetic systems and bioinformatics"--Provided by publisher.
Download or read book The Silicon Web written by Michael G. Raymer and published by CRC Press. This book was released on 2022-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: From computers to optical communication, this text explores core principles underlying those technologies that continue to revolutionize our lives. Designed for nonscientists, this book requires no higher math or prior physics. It details basic physics principles at the core of information technology; examines the quantum era, discussing digital
