Knotted Fields
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Knotted Fields
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Author : Renzo L. Ricca
language : en
Publisher: Springer Nature
Release Date : 2024-06-19
Knotted Fields written by Renzo L. Ricca and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-19 with Mathematics categories.
This book provides a remarkable collection of contributions written by some of the most accredited world experts in the modern area of Knotted Fields. Scope of the book is to provide an updated view of some of the key aspects of contemporary research, with the purpose to cover basic concepts and techniques commonly used in the context of Knotted Fields. The material is presented to help the interested reader to become familiar with the fundamentals, from fluid flows to electromagnetism, from knot theory to numerical visualization, while presenting the new ideas and results in an accessible way to beginners and young researchers. No advanced knowledge is required, and at the end of each chapter, key references are provided to offer further information on particular topics of interest. All those keen on modern applications of topological techniques to the study of knotted fields in mathematical physics will find here a valuable and unique source of information. The work will be of interest to many researchers in the field.
Gauge Fields Knots And Gravity
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Author : John C Baez
language : en
Publisher: World Scientific Publishing Company
Release Date : 1994-10-24
Gauge Fields Knots And Gravity written by John C Baez and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-24 with Science categories.
This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.
Being And Motion
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Author : Thomas Nail
language : en
Publisher:
Release Date : 2019
Being And Motion written by Thomas Nail and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Philosophy categories.
More than at any other time in human history, we live in an age defined by movement and mobility; and yet, we lack a unifying theory which takes this seriously as a starting point for philosophy. The history of philosophy has systematically explained movement as derived from something else that does not move: space, eternity, force, and time. Why, when movement has always been central to human societies, did a philosophy based on movement never take hold? This book finally overturns this long-standing metaphysical tradition by placing movement at the heart of philosophy. In doing so, Being and Motion provides a completely new understanding of the most fundamental categories of ontology from a movement-oriented perspective: quality, quantity, relation, modality, and others. It also provides the first history of the philosophy of motion, from early prehistoric mythologies up to contemporary ontologies. Through its systematic ontology of movement, Being and Motion provides a path-breaking historical ontology of our present.
Ideal Knots
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Author : A. Stasiak
language : en
Publisher: World Scientific
Release Date : 1998
Ideal Knots written by A. Stasiak and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Crafts & Hobbies categories.
In this book, experts in different fields of mathematics, physics, chemistry and biology present unique forms of knots which satisfy certain preassigned criteria relevant to a given field. They discuss the shapes of knotted magnetic flux lines, the forms of knotted arrangements of bistable chemical systems, the trajectories of knotted solitons, and the shapes of knots which can be tied using the shortest piece of elastic rope with a constant diameter.
Analysis Of Quantised Vortex Tangle
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Author : Alexander John Taylor
language : en
Publisher: Springer
Release Date : 2016-11-24
Analysis Of Quantised Vortex Tangle written by Alexander John Taylor and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-24 with Science categories.
In this thesis, the author develops numerical techniques for tracking and characterising the convoluted nodal lines in three-dimensional space, analysing their geometry on the small scale, as well as their global fractality and topological complexity---including knotting---on the large scale. The work is highly visual, and illustrated with many beautiful diagrams revealing this unanticipated aspect of the physics of waves. Linear superpositions of waves create interference patterns, which means in some places they strengthen one another, while in others they completely cancel each other out. This latter phenomenon occurs on 'vortex lines' in three dimensions. In general wave superpositions modelling e.g. chaotic cavity modes, these vortex lines form dense tangles that have never been visualised on the large scale before, and cannot be analysed mathematically by any known techniques.
Bifurcations And Periodic Orbits Of Vector Fields
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Author : Dana Schlomiuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Bifurcations And Periodic Orbits Of Vector Fields written by Dana Schlomiuk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The last thirty years were a period of continuous and intense growth in the subject of dynamical systems. New concepts and techniques and at the same time new areas of applications of the theory were found. The 31st session of the Seminaire de Mathematiques Superieures (SMS) held at the Universite de Montreal in July 1992 was on dynamical systems having as its center theme "Bifurcations and periodic orbits of vector fields". This session of the SMS was a NATO Advanced Study Institute (ASI). This ASI had the purpose of acquainting the participants with some of the most recent developments and of stimulating new research around the chosen center theme. These developments include the major tools of the new resummation techniques with applications, in particular to the proof of the non-accumulation of limit-cycles for real-analytic plane vector fields. One of the aims of the ASI was to bring together methods from real and complex dy namical systems. There is a growing awareness that an interplay between real and complex methods is both useful and necessary for the solution of some of the problems. Complex techniques become powerful tools which yield valuable information when applied to the study of the dynamics of real vector fields. The recent developments show that no rigid frontiers between disciplines exist and that interesting new developments occur when ideas and techniques from diverse disciplines are married. One of the aims of the ASI was to show these multiple interactions at work.
Theory Of The Earth
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Author : Thomas Nail
language : en
Publisher: Stanford University Press
Release Date : 2021-04-27
Theory Of The Earth written by Thomas Nail and has been published by Stanford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-27 with Philosophy categories.
We need a new philosophy of the earth. Geological time used to refer to slow and gradual processes, but today we are watching land sink into the sea and forests transform into deserts. We can even see the creation of new geological strata made of plastic, chicken bones, and other waste that could remain in the fossil record for millennia or longer. Crafting a philosophy of geology that rewrites natural and human history from the broader perspective of movement, Thomas Nail provides a new materialist, kinetic ethics of the earth that speaks to this moment. Climate change and other ecological disruptions challenge us to reconsider the deep history of minerals, atmosphere, plants, and animals and to take a more process-oriented perspective that sees humanity as part of the larger cosmic and terrestrial drama of mobility and flow. Building on his earlier work on the philosophy of movement, Nail argues that we should shift our biocentric emphasis from conservation to expenditure, flux, and planetary diversity. Theory of the Earth urges us to rethink our ethical relationship to one another, the planet, and the cosmos at large.
Knots Topology And Quantum Field Theory Proceedings Of The 13th Johns Hopkins Workshop
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Author : Luca Lusanna
language : en
Publisher: World Scientific
Release Date : 1989-12-01
Knots Topology And Quantum Field Theory Proceedings Of The 13th Johns Hopkins Workshop written by Luca Lusanna and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-12-01 with categories.
This book fills a gap in literature for the important interdisciplinary area of biochemical physics, adopting the chemist's view of this topic in the process. The present status of the theory of electron spin effects in fundamental processes such as spin exchange, dipole-dipole interactions, electron transfer, triplet-triplet energy transfer, and annihilation intersystem crossing is reviewed. These effects form a basis for the understanding of the molecular mechanisms essential to chemical and biological reactions including photosynthesis and magnetic field influence, and for the creation of advanced organic magnets and catalysts, as well as the development of new methods of studying the structural and molecular dynamics of biological and non-biological objects.
Knots And Physics Second Edition
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Author : Louis H Kauffman
language : en
Publisher: World Scientific
Release Date : 1994-01-15
Knots And Physics Second Edition written by Louis H Kauffman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-15 with Mathematics categories.
In this second edition, the following recent papers have been added: “Gauss Codes, Quantum Groups and Ribbon Hopf Algebras”, “Spin Networks, Topology and Discrete Physics”, “Link Polynomials and a Graphical Calculus” and “Knots Tangles and Electrical Networks”. An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included.This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of knot theory, coupled with a quantum statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems.
Knots And Physics
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Author : Louis H. Kauffman
language : en
Publisher: World Scientific
Release Date : 2001
Knots And Physics written by Louis H. Kauffman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This invaluable book is an introduction to knot and link invariants as generalised amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.