Download or read book The Mathematics and Topology of Fullerenes written by Franco Cataldo and published by Springer Science & Business Media. This book was released on 2011-12-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematics and Topology of Fullerenes presents a comprehensive overview of scientific and technical innovations in theoretical and experimental studies. Topics included in this multi-author volume are: Clar structures for conjugated nanostructures; counting polynomials of fullerenes; topological indices of fullerenes; the wiener index of nanotubes; toroidal fullerenes and nanostars; C60 Structural relatives: a topological study; local combinatorial characterization of fullerenes; computation of selected topological indices of C60 and C80 Fullerenes via the Gap Program; 4valent- analogues of fullerenes; a detailed atlas of Kekule structures of C60. The Mathematics and Topology of Fullerenes is targeted at advanced graduates and researchers working in carbon materials, chemistry and physics.
Download or read book An Atlas of Fullerenes written by P. W. Fowler and published by Courier Corporation. This book was released on 2007-01-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the current state of theory in a new and lively field, this volume offers both students and researchers a practical guide. It features a comprehensive set of pictures of fullerene structures and tabulates their properties. In addition, it lists a computer program that will extend the tables as needed. Seven chapters of descriptive material precede over 200 pages of tables with corresponding diagrams and serve as a self-contained introduction. Topics include fullerene cages, electronic structure, steric strain, symmetry and spectroscopy, fullerene isomerization, and carbon gain and loss. Each chapter concludes with references and notes.
Download or read book Toric Topology written by Victor M. Buchstaber and published by American Mathematical Soc.. This book was released on 2015-07-15 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on moment-angle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and non-Kaehler complex geometry. A related categorical construction of moment-angle complexes and polyhedral products provides for a universal framework for many fundamental constructions of homotopical topology. The study of polyhedral products is now evolving into a separate subject of homotopy theory. A new perspective on torus actions has also contributed to the development of classical areas of algebraic topology, such as complex cobordism. This book includes many open problems and is addressed to experts interested in new ideas linking all the subjects involved, as well as to graduate students and young researchers ready to enter this beautiful new area.
Download or read book Topological Modelling of Nanostructures and Extended Systems written by Ali Reza Ashrafi and published by Springer Science & Business Media. This book was released on 2013-05-19 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological Modelling of Nanostructures and Extended Systems completes and expands upon the previously published title within this series: The Mathematics and Topology of Fullerenes (Vol. 4, 2011) by gathering the latest research and advances in materials science at nanoscale. It introduces a new speculative area and novel concepts like topochemical reactions and colored reactive topological indices and provides a better understanding of the physical-chemical behaviors of extended systems. Moreover, a charming new family of space-filling fullerenic crystals is here analyzed for the first time. Particular attention is given to the fundamental influences exercised by long-range connectivity topological mechanisms on the chemical and physical properties of carbon nanostructures. Systems consisting in graphenic layers with structural and topological defects are investigated in their electronic and magnetic behaviors also in presence of metallic particles. More specifically, the book focuses on: - Electronic Properties of low dimensional nanostructures including negatively-curved carbon surfaces; Pariser-Parr-Pople model hamiltonian approach to graphene studies; - Topochemistry and Toporeactcivity of extended sp2-nanocarbons: PAH, fullerenes, nanoribbons, Moebius-like nanoribbons, nanotubes and grapheme; - Novel class of crystal networks arising from spanning fullerenes; - Nanostructures and eigenvectors of matrices and an extended treatise of topological invariants; - Enumeration hetero-fullerenes by Polya theory. Topological Modelling of Nanostructures and Extended Systems represents a valuable resource to advances graduates and researchers working in mathematics, chemistry, physics and material science.
Download or read book Chemical Topology written by D Bonchev and published by CRC Press. This book was released on 1999-04-23 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology is becoming increasingly important in chemistry because of its rapidly growing number of applications. Here, its many uses are reviewed and the authors anticipate what future developments might bring. This work shows how significant new insights can be gained by representing molecular species as topological structures known as topographs. The text explores carbon structures, establishing how the stability of fullerene species can be accounted for and also predicting which fullerenes will be most stable. It is pointed out that molecular topology, rather than molecular geometry, characterizes molecular shape and various tools for shape characterization are described. Several of the fascinating ideas that arise from regarding topology as a unifying principle in chemical bonding theory are discussed, and in particular, the novel concept of the molecular topoid is shown to have numerous uses. The topological description of polymers is examined and the reader is gently guided through the realms of branched and tangled polymers. Overall, this work outlines the fact that topology is not only a theoretical discipline but also one that has practical applications and high relevance to the whole domain of chemistry.
Download or read book Advances in Mathematical Chemistry and Applications Volume 2 written by Subhash C. Basak and published by Elsevier. This book was released on 2016-02-11 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Mathematical Chemistry and Applications highlights the recent progress in the emerging discipline of discrete mathematical chemistry. Editors Subhash C. Basak, Guillermo Restrepo, and Jose Luis Villaveces have brought together 27 chapters written by 68 internationally renowned experts in these two volumes. Each volume comprises a wise integration of mathematical and chemical concepts and covers numerous applications in the field of drug discovery, bioinformatics, chemoinformatics, computational biology, mathematical proteomics, and ecotoxicology. Volume 2 explores deeper the topics introduced in Volume 1, with numerous additional topics such as topological approaches for classifying fullerene isomers; chemical reaction networks; discrimination of small molecules using topological molecular descriptors; GRANCH methods for the mathematical characterization of DNA, RNA and protein sequences; linear regression methods and Bayesian techniques; in silico toxicity prediction methods; drug design; integration of bioinformatics and systems biology, molecular docking, and molecular dynamics; metalloenzyme models; protein folding models; molecular periodicity; generalized topologies and their applications; and many more. Brings together both the theoretical and practical aspects of the fundamental concepts of mathematical chemistry Covers applications in diverse areas of physics, chemistry, drug discovery, predictive toxicology, systems biology, chemoinformatics, and bioinformatics About half of the book focuses primarily on current work, new applications, and emerging approaches for the mathematical characterization of essential aspects of molecular structure, while the other half describes applications of structural approach to new drug discovery, virtual screening, protein folding, predictive toxicology, DNA structure, and systems biology
Download or read book Distance Symmetry and Topology in Carbon Nanomaterials written by Ali Reza Ashrafi and published by Springer. This book was released on 2016-08-16 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume is inspired by the seminal discovery and identification of C60. Starting with a comprehensive discussion featuring graphene based nanostructures, subsequent chapters include topological descriptions of matrices, polynomials and indices, and an extended analysis of the symmetry and topology of nanostructures. Carbon allotropes such as diamond and its connection to higher-dimensional spaces is explored along with important mathematical and topological considerations. Further topics covered include spontaneous symmetry breaking in graphene, polyhedral carbon structures, nanotube junction energetics, and cyclic polyines as relatives of nanotubes and fullerenes. This book is aimed at researchers active in the study of carbon materials science and technology.
Download or read book The Role of Topology in Materials written by Sanju Gupta and published by Springer. This book was released on 2018-04-21 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Electronic Structure Calculations on Fullerenes and Their Derivatives written by Jerzy Cioslowski and published by Oxford University Press, USA. This book was released on 1995 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive overview of the latest approaches to electronic structure calculations of fullerenes. Topics include C(60) and C(70) molecules, the medium-size fullerenes, large carbon clusters, hypothetical allotropic forms of carbon, small fullerenes, endohedral complexes, heterofullerenes, fullerene derivatives, and solid-state fullerenes. A summary of recent research breakthroughs and a discussion of potential future directions round out the book. Far-reaching and well-written, the book will be welcomed by students and researchers in chemistry and quantum physics.
Download or read book The Fullerenes written by H. W. Kroto and published by Cambridge University Press. This book was released on 1993-09-09 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1985, Buckminsterfullerene (fullerene-60) C60 was discovered serendipitously during graphite laser vaporisation experiments designed to simulate the chemistry in a red giant carbon star. The molecule was isolated for the first time in macroscopic amounts in 1990, a breakthrough which triggered an explosion of research into its chemical and physical properties. The fullerenes hold great potential for material science applications, such as semiconductors and microscopic engineering, and as new compounds for pharmaceuticals, polymers and the chemical industry. In October 1992, a Discussion Meeting of the Royal Society entitled A Post-Buckminsterfullerene View of the Chemistry, Physics and Astrophysics of Carbon, organised by H. W. Kroto, A. L. Makay, G. Turner and D. R. M. Walton, was held to celebrate this exciting advance. The scientists who played key roles in the discovery and who are currently uncovering fascinating problems and the implications of this elegant molecule presented the papers published in this book.
Download or read book Combinatorial And Toric Homotopy Introductory Lectures written by Alastair Darby and published by World Scientific. This book was released on 2017-10-20 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning.The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis-Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics.The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students.
Download or read book Euler s Gem written by David S. Richeson and published by Princeton University Press. This book was released on 2019-07-23 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: How a simple equation reshaped mathematics Leonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.
Download or read book The Physics of Fullerene Based and Fullerene Related Materials written by W. Andreoni and published by Springer Science & Business Media. This book was released on 2000-03-31 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Krätschmer and Huffman's revolutionary discovery of a new solid phase of carbon, solid C60, in 1990 opened the way to an entire new class of materials with physical properties so diverse that their richness has not yet been fully exploited. Moreover, as a by-product of fullerene research, carbon nanotubes were later identified, from which novel nanostructures originated that are currently fascinating materials scientists worldwide. Rivers of words have been written on both fullerenes and nanotubes, in the form of journal articles, conference proceedings and books. The present book offers, in a concise and self-contained manner, the basics of the science of these materials as well as detailed information on those aspects that have so far been better explored. Structural, electronic and dynamical properties are described as obtained from various measurements and state-of-the-art calculations. Their interrelation emerges as well as their possible dependence on, for example, preparation conditions or methods of investigation. By presenting and comparing data from different sources, experiment and theory, this book helps the reader to rapidly master the basic knowledge, to grasp important issues and critically discuss them. Ultimately, it aims to inspire him or her to find novel ways to approach still open questions. As such, this book is addressed to new researchers in the field as well as experts.
Download or read book Recent Advances in the Chemistry and Physics of Fullerenes and Related Materials written by Prashant V. Kamat and published by The Electrochemical Society. This book was released on 1999 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Physics and Chemistry of the Fullerenes written by K. Prassides and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: In September 1985, in an attempt to simulate the chemistry in a carbon star, Harry Kroto, Bob Curl and Richard Smalley set up a mass spectrometry experiment to study the plasma produced by focusing a pulsed laser on solid graphite. Serendipitously, a dominant 720 amu mass peak corresponding to a C60 species was revealed in the time-of-flight mass spectrum of the resulting carbon clusters. It was proposed that this C60 cluster had the closed cage structure of a truncated icosahedron (a soccerball) and was named Buckminsterfullerene because geodesic dome concepts, pioneered by the architect Buckminster Fuller, played an important part in arriving at this solution. The signal for a C70 species (840 amu) , proposed to have the ellipsoidal shape of a rugbyball, was also prominent in the early experiments. Five years later, the seminal work of the Sussex! Rice collaboration was triumphantly confirmed as Wolfgang Krlitschmer and Donald Huffman succeeded in producing, and separating, bulk crystalline samples of fullerene material from arc-processed (in an inert gas atmosphere) carbon deposits. From then onwards, fullerene research continued, and still proceeds, at an exhilarating pace. The materials excited the imagination of many diverse classes of scientists, resulting in a truly interdisciplinary field. Many of our old, seemingly well-founded, preconceptions in carbon science had to be radically altered or totally abandoned, as a new round world of chemistry, physics and materials science began to unfold.
Download or read book Topology in Condensed Matter written by Michael I. Monastyrsky and published by Springer Science & Business Media. This book was released on 2006-02-04 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.
Download or read book New Frontiers in Nanochemistry Concepts Theories and Trends written by Mihai V. Putz and published by CRC Press. This book was released on 2020-05-06 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Frontiers in Nanochemistry: Concepts, Theories, and Trends, Volume 2: Topological Nanochemistry is the second of the new three-volume set that explains and explores the important basic and advanced modern concepts in multidisciplinary chemistry. Under the broad expertise of the editor, this second volume explores the rich research areas of nanochemistry with a specific focus on the design and control of nanotechnology by structural and reactive topology. The objective of this particular volume is to emphasize the application of nanochemistry. With 46 entries from eminent international scientists and scholars, the content in this volume spans concepts from A-to-Z—from entries on the atom-bond connectivity index to the Zagreb indices, from connectivity to vapor phase epitaxy, and from fullerenes to topological reactivity—and much more. The definitions within the text are accompanied by brief but comprehensive explicative essays as well as figures, tables, etc., providing a holistic understanding of the concepts presented.
