Topology And Geometry In Polymer Science

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Topology And Geometry In Polymer Science
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Author : Stuart G. Whittington
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topology And Geometry In Polymer Science written by Stuart G. Whittington 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 2012-12-06 with Mathematics categories.
This IMA Volume in Mathematics and its Applications TOPOLOGY AND GEOMETRY IN POLYMER SCIENCE is based on the proceedings of a very successful one-week workshop with the same title. This workshop was an integral part of the 1995-1996 IMA program on "Mathematical Methods in Materials Science." We would like to thank Stuart G. Whittington, De Witt Sumners, and Timothy Lodge for their excellent work as organizers of the meeting and for editing the proceedings. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE This book is the product of a workshop on Topology and Geometry of Polymers, held at the IMA in June 1996. The workshop brought together topologists, combinatorialists, theoretical physicists and polymer scientists, who share an interest in characterizing and predicting the microscopic en tanglement properties of polymers, and their effect on macroscopic physical properties.
Topology And Geometry In Polymer Science
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Author : Stuart G. Whittington
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-08-13
Topology And Geometry In Polymer Science written by Stuart G. Whittington 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 1998-08-13 with Mathematics categories.
This book contains contributions from a workshop on topology and geometry of polymers, held at the IMA in June 1996, which brought together topologists, combinatorialists, theoretical physicists and polymer scientists, with a common interest in polymer topology. Polymers can be highly self-entangled even in dilute solution. In the melt the inter- and intra-chain entanglements can dominate the rheological properties of these phenomena. Although the possibility of knotting in ring polymers has been recognized for more than thirty years it is only recently that the powerful methods of algebraic topology have been used in treating models of polymers. This book contains a series of chapters which review the current state of the field and give an up to date account of what is known and perhaps more importantly, what is still unknown. The field abounds with open problems. The book is of interest to workers in polymer statistical mechanics but will also be useful as an introduction to topological methods for polymer scientists, and will introduce mathematicians to an area of science where topological approaches are making a substantial contribution.
Energy Of Knots And Conformal Geometry
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Author : Jun O'hara
language : en
Publisher: World Scientific
Release Date : 2003-03-25
Energy Of Knots And Conformal Geometry written by Jun O'hara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-25 with Mathematics categories.
Energy of knots is a theory that was introduced to create a “canonical configuration” of a knot — a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a “canonical configuration” of a knot in each knot type. It also considers this problems in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting through numerical experiments.
The Role Of Topology In Materials
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Author : Sanju Gupta
language : en
Publisher: Springer
Release Date : 2018-04-21
The Role Of Topology In Materials written by Sanju Gupta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-21 with Science categories.
This book presents the most important advances in the class of topological materials and discusses the topological characterization, modeling and metrology of materials. Further, it addresses currently emerging characterization techniques such as optical and acoustic, vibrational spectroscopy (Brillouin, infrared, Raman), electronic, magnetic, fluorescence correlation imaging, laser lithography, small angle X-ray and neutron scattering and other techniques, including site-selective nanoprobes. The book analyzes the topological aspects to identify and quantify these effects in terms of topology metrics. The topological materials are ubiquitous and range from (i) de novo nanoscale allotropes of carbons in various forms such as nanotubes, nanorings, nanohorns, nanowalls, peapods, graphene, etc. to (ii) metallo-organic frameworks, (iii) helical gold nanotubes, (iv) Möbius conjugated polymers, (v) block co-polymers, (vi) supramolecular assemblies, to (vii) a variety of biological and soft-matter systems, e.g. foams and cellular materials, vesicles of different shapes and genera, biomimetic membranes, and filaments, (viii) topological insulators and topological superconductors, (ix) a variety of Dirac materials including Dirac and Weyl semimetals, as well as (x) knots and network structures. Topological databases and algorithms to model such materials have been also established in this book. In order to understand and properly characterize these important emergent materials, it is necessary to go far beyond the traditional paradigm of microscopic structure–property–function relationships to a paradigm that explicitly incorporates topological aspects from the outset to characterize and/or predict the physical properties and currently untapped functionalities of these advanced materials. Simulation and modeling tools including quantum chemistry, molecular dynamics, 3D visualization and tomography are also indispensable. These concepts have found applications in condensed matter physics, materials science and engineering, physical chemistry and biophysics, and the various topics covered in the book have potential applications in connection with novel synthesis techniques, sensing and catalysis. As such, the book offers a unique resource for graduate students and researchers alike.
Introduction To Polymer Dynamics
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Author : Pierre-Gilles de Gennes
language : en
Publisher: CUP Archive
Release Date : 1990-09-20
Introduction To Polymer Dynamics written by Pierre-Gilles de Gennes and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-09-20 with Mathematics categories.
This book, based on lectures given at the Polytechnic of Milan, gives a broad overview of the field of polymer dynamics. In these lectures the aim is to stress the fundamental concepts of the behaviour of polymers without drawing on the more advanced mathematical formalism which often obscures the natural elegance of the subject matter. Professor De Gennes is one of the most distinguished workers in the field of material science. Therefore this book will be welcomed by both the experienced researcher in the area and the interested layman. It will be of particular value to graduate students.
The Statistical Mechanics Of Interacting Walks Polygons Animals And Vesicles
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Author : E. J. Janse Van Rensburg
language : en
Publisher: Oxford University Press (UK)
Release Date : 2015
The Statistical Mechanics Of Interacting Walks Polygons Animals And Vesicles written by E. J. Janse Van Rensburg and has been published by Oxford University Press (UK) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
This monograph examines the self-avoiding walk, a classical model in statistical mechanics, probability theory and mathematical physics, paying close attention to recent developments in the field, such as models in the hexagonal lattice and the Monte Carlo methods.
Integration Of Fundamental Polymer Science And Technology 3
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Author : P.J. Lemstra
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integration Of Fundamental Polymer Science And Technology 3 written by P.J. Lemstra 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 2012-12-06 with Science categories.
The Rolduc Polymer Meetings, of which the contents of this volume represent the third, are already on their way to occupying a unique place in the crowded calendar of symposia on every aspect of polymer science and engineering. They combine manageable meeting size with a theme, 'Integration of Fundamental Polymer Science and Technology', which is often discussed but seldom realized in practice. The technological, or applied, areas of polymers have perhaps received more emphasis historically than those of other allied disciplines. Indeed, various plastic and rubber materials were successful items of commerce long before the macromolecular concept itself was firmly established. The more fundamental aspects of the field were also largely developed in industrial laboratories. The early work of Mark and Meyer at IG Farben, and that of Carrothers and Flory at Du Pont, are good examples of this. The present situation, in which polymers are being applied to more and more demanding end uses, from high performance materials on the one hand to the biomedical and electronics fields on the other, caIls for an ever greater understanding of the basic scientific principles governing their behavior. It is evident, therefore, that interactions between those engaged in the 'pure' and 'applied' parts of the field must be promoted effectively. The Rolduc Polymer Meetings contribute significantly to such interactions, not only by interweaving technological and scientific presentations, but also by providing a forum for the participants to discuss problems of mutual interest in all their complexity.
Physical And Numerical Models In Knot Theory
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Author : Jorge Alberto Calvo
language : en
Publisher: World Scientific
Release Date : 2005
Physical And Numerical Models In Knot Theory written by Jorge Alberto Calvo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
The physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appreciated and valuable progress continues to be made each year. This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable. While computations have long been used to analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. The volume also includes contributions concentrating on models researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics include properties of knot invariants, knot tabulation, studies of hyperbolic structures, knot energies, the exploration of spaces of knots, knotted umbilical cords, studies of knots in DNA and proteins, and the structure of tight knots. Together, the chapters explore four major themes: physical knot theory, knot theory in the life sciences, computational knot theory, and geometric knot theory.
Geometries Of Nature Living Systems And Human Cognition New Interactions Of Mathematics With Natural Sciences And Humanities
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Author : Luciano Boi
language : en
Publisher: World Scientific
Release Date : 2005-11-02
Geometries Of Nature Living Systems And Human Cognition New Interactions Of Mathematics With Natural Sciences And Humanities written by Luciano Boi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-02 with Science categories.
The collection of papers forming this volume is intended to provide a deeper study of some mathematical and physical subjects which are at the core of recent developments in the natural and living sciences. The book explores some far-reaching interfaces where mathematics, theoretical physics, and natural sciences seem to interact profoundly. The main goal is to show that an accomplished movement of geometrisation has enabled the discovery of a great variety of amazing structures and behaviors in physical reality and in living matter. The diverse group of expert mathematicians, physicists and natural scientists present numerous new results and original ideas, methods and techniques. Both academic and interdisciplinary, the book investigates a number of important connections between mathematics, theoretical physics and natural sciences including biology.
Physical Knots Knotting Linking And Folding Geometric Objects In Mathbb R 3
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Author : Jorge Alberto Calvo
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Physical Knots Knotting Linking And Folding Geometric Objects In Mathbb R 3 written by Jorge Alberto Calvo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
The properties of knotted and linked configurations in space have long been of interest to physicists and mathematicians. More recently and more widely, they have become important to biologists, chemists, computer scientists, and engineers. The depth and breadth of their applications are widely appreciated. Nevertheless, fundamental and challenging questions remain to be answered. Based on a Special Session at the AMS Sectional Meeting in Las Vegas (NV) in April 2001, this volumediscusses critical questions and introduces new ideas that will stimulate multi-disciplinary applications. Some of the papers are primarily theoretical; others are experimental. Some are purely mathematical; others deal with applications of mathematics to theoretical computer science, engineering,physics, biology, or chemistry. Connections are made between classical knot theory and the physical world of macromolecules, such as DNA, geometric linkages, rope, and even cooked spaghetti. This book introduces the world of physical knot theory in all its manifestations and points the way for new research. It is suitable for a diverse audience of mathematicians, computer scientists, engineers, biologists, chemists, and physicists.