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Topological Crystallography
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Book Synopsis Topological Crystallography by : Toshikazu Sunada
Download or read book Topological Crystallography written by Toshikazu Sunada and published by Springer Science & Business Media. This book was released on 2012-12-23 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s Elements. Since then, geometry has taken its own path and the study of crystals has not been a central theme in mathematics, with the exception of Kepler’s work on snowflakes. Only in the nineteenth century did mathematics begin to play a role in crystallography as group theory came to be applied to the morphology of crystals. This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title Topological Crystallography has been chosen. Topological crystals can be described as “living in the logical world, not in space,” leading to the question of how to place or realize them “canonically” in space. Proposed here is the notion of standard realizations of topological crystals in space, including as typical examples the crystal structures of diamond and lonsdaleite. A mathematical view of the standard realizations is also provided by relating them to asymptotic behaviors of random walks and harmonic maps. Furthermore, it can be seen that a discrete analogue of algebraic geometry is linked to the standard realizations. Applications of the discussions in this volume include not only a systematic enumeration of crystal structures, an area of considerable scientific interest for many years, but also the architectural design of lightweight rigid structures. The reader therefore can see the agreement of theory and practice.
Book Synopsis Chemical Topology by : Danail Bonchev
Download or read book Chemical Topology written by Danail Bonchev and published by CRC Press. This book was released on 2000-07-06 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology has been extensively applied in the study of chemically linked and knotted structures, and also in the study of many biologically significant molecules such as proteins and DNA. These are the themes that are addressed in this volume of the Mathematical Chemistry series. The topological chirality of knotted and linked molecular species and the invariants that may characterize them are explored in detail.
Book Synopsis Highlights in Mineralogical Crystallography by : Thomas Armbruster
Download or read book Highlights in Mineralogical Crystallography written by Thomas Armbruster and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-11-13 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Highlights in Mineralogical Crystallography" presents a collection of review articles with the common topic: structural properties of minerals and synthetic analogues. It is a valuable resource for mineralogists, materials scientists, crystallographers, and earth scientists. This book includes: An introduction to the RRUFF database for structural, spectroscopic, and chemical mineral identification. A systematic evaluation of structural complexity of minerals. ab initio computer modelling of mineral surfaces. Natural quasicrystals of meteoritic origin. The potential role of terrestrial ringwoodite on the water content of the Earth's mantle. Structural characterization of nanocrystalline bio-related minerals by electron-diffraction tomography. The uniqueness of mayenite-type compounds as minerals and high-tech ceramics.
Book Synopsis Introduction to Crystallography by : Frank Hoffmann
Download or read book Introduction to Crystallography written by Frank Hoffmann and published by Springer Nature. This book was released on 2020-07-31 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book invites you on a systematic tour through the fascinating world of crystals and their symmetries. The reader will gain an understanding of the symmetry of external crystal forms (morphology) and become acquainted with all the symmetry elements needed to classify and describe crystal structures. The book explains the context in a very vivid, non-mathematical way and captivates with clear, high-quality illustrations. Online materials accompany the book; including 3D models the reader can explore on screen to aid in the spatial understanding of the structure of crystals. After reading the book, you will not only know what a space group is and how to read the International Tables for Crystallography, but will also be able to interpret crystallographic specifications in specialist publications. If questions remain, you also have the opportunity to ask the author on the book's website.
Book Synopsis Trivalent Discrete Surfaces and Carbon Structures by : Hisashi Naito
Download or read book Trivalent Discrete Surfaces and Carbon Structures written by Hisashi Naito and published by Springer Nature. This book was released on 2023-12-02 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses discrete geometric analysis, especially topological crystallography and discrete surface theory for trivalent discrete surfaces. Topological crystallography, based on graph theory, provides the most symmetric structure among given combinatorial structures by using the variational principle, and it can reproduce crystal structures existing in nature. In this regard, the topological crystallography founded by Kotani and Sunada is explained by using many examples. Carbon structures such as fullerenes are considered as trivalent discrete surfaces from the viewpoint of discrete geometric analysis. Discrete surface theories usually have been considered discretization of smooth surfaces. Here, consideration is given to discrete surfaces modeled by crystal/molecular structures, which are essentially discrete objects.
Book Synopsis Electronic Structure Crystallography and Functional Motifs of Materials by : Guo-Cong Guo
Download or read book Electronic Structure Crystallography and Functional Motifs of Materials written by Guo-Cong Guo and published by John Wiley & Sons. This book was released on 2024-01-09 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electronic Structure Crystallography and Functional Motifs of Materials Detailed resource on the method of electronic structure crystallography for revealing the experimental electronic structure and structure-property relationships of functional materials Electronic Structure Crystallography and Functional Motifs of Materials describes electronic structure crystallography and functional motifs of materials, two of the most challenging topics to realize the rational design of high-performance functional materials, emphasizing the physical properties and structure-property relationships of functional materials using nonlinear optical materials as examples. The text clearly illustrates how to extract experimental electronic structure information and relevant physicochemical properties of materials based on the theories and methods in X-ray crystallography and quantum chemistry. Practical skills of charge density studies using experimental X-ray sources are also covered, which are particularly important for the future popularization and development of electron structure crystallography. This book also introduces the related theories and refinement techniques involved in using scattering methods (mainly X-ray single-crystal diffraction, as well as polarized neutron scattering and Compton scattering) to determine experimental electronic structures, including the experimental electron density, experimental electron wavefunction, and experimental electron density matrix of crystalline materials. Electronic Structure Crystallography and Functional Motifs of Materials includes information on: Basic framework and assumptions of the first-principle calculations, density matrix and density function, and Hartree-Fock (HF) and Kohn-Sham (KS) methods Analysis of topological atoms in molecules, chemical interaction analysis, coarse graining and energy partition of the density matrix, and restricted space partition Principles of electronic structure measurement, including thermal vibration analysis, scattering experiments, and refinement algorithm for experimental electronic structure Independent atom model, multipole model, X-ray constrained wavefunction model, and other electron density models Electronic Structure Crystallography and Functional Motifs of Materials is an ideal textbook or reference book for graduate students and researchers in chemistry, physics, and material sciences for studying the structures and properties of functional crystalline materials.
Book Synopsis The Chemistry of Metal-Organic Frameworks by : Stefan Kaskel
Download or read book The Chemistry of Metal-Organic Frameworks written by Stefan Kaskel and published by John Wiley & Sons. This book was released on 2016-06-14 with total page 904 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing vital knowledge on the design and synthesis of specific metal-organic framework (MOF) classes as well as their properties, this ready reference summarizes the state of the art in chemistry. Divided into four parts, the first begins with a basic introduction to typical cluster units or coordination geometries and provides examples of recent and advanced MOF structures and applications typical for the respective class. Part II covers recent progress in linker chemistries, while special MOF classes and morphology design are described in Part III. The fourth part deals with advanced characterization techniques, such as NMR, in situ studies, and modelling. A final unique feature is the inclusion of data sheets of commercially available MOFs in the appendix, enabling experts and newcomers to the field to select the appropriate MOF for a desired application. A must-have reference for chemists, materials scientists, and engineers in academia and industry working in the field of catalysis, gas and water purification, energy storage, separation, and sensors.
Book Synopsis Topological Approaches to the Chemical Bond by : Ángel Martín Pendás
Download or read book Topological Approaches to the Chemical Bond written by Ángel Martín Pendás and published by Springer Nature. This book was released on 2023-02-22 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate textbook provides comprehensive information on topological analysis in real space of the electronic structure. Application of the topological tools is becoming routine for understanding the outcome of quantum chemical calculations. This title thoroughly reviews a selection of currently available topological tools, their use and spectrum of applications and provides graduate students and researchers with information not easily obtained from the available textbooks. The book is accompanied by worked examples, exercises and solutions and is a great tool for any quantum chemistry or computational chemistry course at the graduate and advanced undergraduate levels.
Author :Tullio Ceccherini-Silberstein Publisher :Cambridge University Press ISBN 13 :1316817784 Total Pages :539 pages Book Rating :4.3/5 (168 download)
Book Synopsis Groups, Graphs and Random Walks by : Tullio Ceccherini-Silberstein
Download or read book Groups, Graphs and Random Walks written by Tullio Ceccherini-Silberstein and published by Cambridge University Press. This book was released on 2017-06-29 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubtedly stem.
Book Synopsis Formation and Interactions of Topological Defects by : Anne-Christine Davis
Download or read book Formation and Interactions of Topological Defects written by Anne-Christine Davis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological defects have recently become of great interest in condensed matter physics, particle physics and cosmology. They are the unavoidable remnants of many symmetry breaking phase transitions. Topological defects can play an important role in describing the properties of many condensed matter systems (e.g. superfluids and superconduc tors); they can catalyze many unusual effects in particle physics models and they may be responsible for seeding the density perturbations in the early Universe which de velop into galaxies and the large-scale structure of the Universe. Topological defects are also of great interest in mathematics as nontrivial solutions of nonlinear differential equations stabilized by topological effects. The purpose of the Advanced Study Institute "Formation and Interactions of Topo logical Defects" was to bring together students and practitioners in condensed matter physics, particle physics and cosmology, to give a detailed exposition of the role of topo logical defects in these fields; to explore similarities and differences in the approaches; and to provide a common basis for discussion and future collaborative research on common problems.
Book Synopsis Structural Crystallography of Inorganic Oxysalts by : Sergey V. Krivovichev
Download or read book Structural Crystallography of Inorganic Oxysalts written by Sergey V. Krivovichev and published by OUP Oxford. This book was released on 2009-01-22 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first book dealing with structural crystallography of inorganic oxysalts in general. A special emphasis is placed upon structural topology and methods of its description. The latter include graph theory, nets, 2-D and 3-D tilings, polyhedra, etc. The structures considered range from minerals to organically templated oxysalts, for all of which this book provides a unified approach to structure interpretation and classification. Most of the structures have been analysed from the proposed viewpoint for the first time and it has been shown that they possess the same topological genealogy and relationships, sometimes despite their obvious chemical differences. In order to expand the range of oxysalts considered, the book offers not only traditional schemes but also alternative approaches such as anion topologis, anion-centered polyhedra and cation arrays. As such, this book can be considered as a comprehensive introduction into the amazingly complex and diverse world of inorganic oxysalts.
Download or read book Framboids written by David Rickard and published by Oxford University Press. This book was released on 2021-06-11 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Framboids may be the most astonishing and abundant natural features you've never heard of. These microscopic spherules of golden pyrite consist of thousands of even smaller microcrystals, often arranged in stunning geometric arrays. They are rarely more than twenty micrometers across, and often look like miniscule raspberries under the microscope. The formation of a framboid is the result of self-assembly of pyrite micro- and nano-crystals under the influence of surface forces. They can be found all around us in rocks of all ages and present-day sediments, soils, and natural waters. Our planet makes billions every second and has been doing so for most of recorded geologic time. As a result, there are more framboids on our planet than there are sand grains on Earth or stars in the observable universe. The microscopic size of framboids belies their importance to contemporary science. They help us better understand inorganic self-assembly and self-organization, and studying them illuminates Earth's evolutionary history. In this book, David Rickard explains what framboids are, how they are formed, and what we can learn from them. The book's thirteen chapters trace everything from their basic attributes and mineralogy to their biogeochemistry and paleoenvironmental significance. Rickard expands on the most updated research and recent developments in geology, chemistry, biology, materials science, biogeochemistry, mineralogy, and crystallography, making this a must-have guide for researchers.
Book Synopsis Joint Polish-German Crystallographic Meeting, February 24–27, 2020, Wrocław, Poland by :
Download or read book Joint Polish-German Crystallographic Meeting, February 24–27, 2020, Wrocław, Poland written by and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-02-24 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zeitschrift für Kristallographie. Supplement Volume 40 presents the complete Abstracts of all contributions to the Joint Polish-German Crystallographic Meeting in Wroclaw (Poland) 2020: - Plenary Talks - Microsymposia - Poster Session Supplement Series of Zeitschrift für Kristallographie publishes Abstracts of international conferences on the interdisciplinary field of crystallography.
Book Synopsis Quantum Crystallography: Expectations vs Reality by : Piero Macchi
Download or read book Quantum Crystallography: Expectations vs Reality written by Piero Macchi and published by Springer Nature. This book was released on 2022-03-05 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the potential of quantum crystallography. The field accompanied the major milestones of x-ray diffraction and it has undergone a rapid evolution in the past few years. For this reason, some reflections are necessary in order to scrutinize the next steps and anticipate the future developments. After a short survey of the historical background and in depth description of the state of the art, some examples are provided of current and future applications of the know-how in this discipline. This implies attracting readership of both experts in the field and neophytes. The former will test their own views with the one exposed in the book; the newcomers, instead, will learn both what has been done and what could be done with quantum crystallography.
Book Synopsis A New Direction in Mathematics for Materials Science by : Susumu Ikeda
Download or read book A New Direction in Mathematics for Materials Science written by Susumu Ikeda and published by Springer. This book was released on 2015-12-08 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first volume of the SpringerBriefs in the Mathematics of Materials and provides a comprehensive guide to the interaction of mathematics with materials science. The anterior part of the book describes a selected history of materials science as well as the interaction between mathematics and materials in history. The emergence of materials science was itself a result of an interdisciplinary movement in the 1950s and 1960s. Materials science was formed by the integration of metallurgy, polymer science, ceramics, solid state physics, and related disciplines. We believe that such historical background helps readers to understand the importance of interdisciplinary interaction such as mathematics–materials science collaboration. The middle part of the book describes mathematical ideas and methods that can be applied to materials problems and introduces some examples of specific studies—for example, computational homology applied to structural analysis of glassy materials, stochastic models for the formation process of materials, new geometric measures for finite carbon nanotube molecules, mathematical technique predicting a molecular magnet, and network analysis of nanoporous materials. The details of these works will be shown in the subsequent volumes of this SpringerBriefs in the Mathematics of Materials series by the individual authors. The posterior section of the book presents how breakthroughs based on mathematics–materials science collaborations can emerge. The authors' argument is supported by the experiences at the Advanced Institute for Materials Research (AIMR), where many researchers from various fields gathered and tackled interdisciplinary research.
Book Synopsis Soviet Physics, Crystallography by :
Download or read book Soviet Physics, Crystallography written by and published by . This book was released on 1992 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Science – ICCS 2009 by : Gabrielle Allen
Download or read book Computational Science – ICCS 2009 written by Gabrielle Allen and published by Springer. This book was released on 2009-05-21 with total page 920 pages. Available in PDF, EPUB and Kindle. Book excerpt: “There is something fascinating about science. One gets such wholesale returns of conjecture out of such a tri?ing investment of fact. ” Mark Twain, Life on the Mississippi The challenges in succeeding with computational science are numerous and deeply a?ect all disciplines. NSF’s 2006 Blue Ribbon Panel of Simulation-Based 1 Engineering Science (SBES) states ‘researchers and educators [agree]: com- tational and simulation engineering sciences are fundamental to the security and welfare of the United States. . . We must overcome di?culties inherent in multiscale modeling, the development of next-generation algorithms, and the design. . . of dynamic data-driven application systems. . . We must determine better ways to integrate data-intensive computing, visualization, and simulation. - portantly,wemustoverhauloureducationalsystemtofostertheinterdisciplinary study. . . The payo?sformeeting these challengesareprofound. ’The International Conference on Computational Science 2009 (ICCS 2009) explored how com- tational sciences are not only advancing the traditional hard science disciplines, but also stretching beyond, with applications in the arts, humanities, media and all aspects of research. This interdisciplinary conference drew academic and industry leaders from a variety of ?elds, including physics, astronomy, mat- matics,music,digitalmedia,biologyandengineering. Theconferencealsohosted computer and computational scientists who are designing and building the - ber infrastructure necessary for next-generation computing. Discussions focused on innovative ways to collaborate and how computational science is changing the future of research. ICCS 2009: ‘Compute. Discover. Innovate. ’ was hosted by the Center for Computation and Technology at Louisiana State University in Baton Rouge.
