Topological Crystallography PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Topological Crystallography PDF full book. Access full book title Topological Crystallography by Toshikazu Sunada. Download full books in PDF and EPUB format.
Author: Toshikazu Sunada
Publisher: Springer Science & Business Media
ISBN: 4431541772
Category : Mathematics
Languages : en
Pages : 236
Get Book Here
Book Description
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.
Author: Toshikazu Sunada
Publisher: Springer Science & Business Media
ISBN: 4431541772
Category : Mathematics
Languages : en
Pages : 236
Get Book Here
Book Description
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.
Author: Hisashi Naito
Publisher: Springer Nature
ISBN: 9819957699
Category : Mathematics
Languages : en
Pages : 113
Get Book Here
Book Description
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.
Author: Danail Bonchev
Publisher: CRC Press
ISBN: 9789056992408
Category : Science
Languages : en
Pages : 392
Get Book Here
Book Description
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.
Author: Tullio Ceccherini-Silberstein
Publisher: Cambridge University Press
ISBN: 1316817784
Category : Mathematics
Languages : en
Pages : 539
Get Book Here
Book Description
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.
Author: David Rickard
Publisher: Oxford University Press
ISBN: 0197571921
Category : Science
Languages : en
Pages : 320
Get Book Here
Book Description
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.
Author: Hayit Greenspan
Publisher: Springer Nature
ISBN: 3031439937
Category : Computers
Languages : en
Pages : 726
Get Book Here
Book Description
The ten-volume set LNCS 14220, 14221, 14222, 14223, 14224, 14225, 14226, 14227, 14228, and 14229 constitutes the refereed proceedings of the 26th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2023, which was held in Vancouver, Canada, in October 2023. The 730 revised full papers presented were carefully reviewed and selected from a total of 2250 submissions. The papers are organized in the following topical sections: Part I: Machine learning with limited supervision and machine learning – transfer learning; Part II: Machine learning – learning strategies; machine learning – explainability, bias, and uncertainty; Part III: Machine learning – explainability, bias and uncertainty; image segmentation; Part IV: Image segmentation; Part V: Computer-aided diagnosis; Part VI: Computer-aided diagnosis; computational pathology; Part VII: Clinical applications – abdomen; clinical applications – breast; clinical applications – cardiac; clinical applications – dermatology; clinical applications – fetal imaging; clinical applications – lung; clinical applications – musculoskeletal; clinical applications – oncology; clinical applications – ophthalmology; clinical applications – vascular; Part VIII: Clinical applications – neuroimaging; microscopy; Part IX: Image-guided intervention, surgical planning, and data science; Part X: Image reconstruction and image registration.
Author: P. Engel
Publisher: Springer Science & Business Media
ISBN: 9400947607
Category : Science
Languages : en
Pages : 273
Get Book Here
Book Description
In the last decade mathematical crystallography has found increasing interest. Siginificant results have been obtained by algebraic, geometric, and group theoretic methods. Also classical crystallography in three-dimen sional Euclidean space has been extended to higher dimen sions in order to understand better the dimension independent crystallographic properties. The aim of this note is to introduce the reader to the fascinating and rich world of geometric crystallography. The prerequisites for reading it are elementary geometry and topological notations, and basic knowledge of group theory and linear algebra. Crystallography is geometric by its nature. In many cases, geometric arguments are the most appropriate and can thus best be understood. Thus the geometric point of view is emphasized here. The approach is axiomatic start ing from discrete point sets in Euclidean space. Symmetry comes in very soon and plays a central role. Each chapter starts with the necessary definitions and then the subject is treated in two- and three-dimensional space. Subsequent sections give an extension to higher dimensions. Short historical remarks added at the end of the chapters will show the development of the theory. The chapters are main ly self-contained. Frequent cross references, as well as an extended subject index, will help the reader who is only interested in a particular subject.
Author: Susumu Ikeda
Publisher: Springer
ISBN: 4431558640
Category : Mathematics
Languages : en
Pages : 93
Get Book Here
Book Description
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.
Author: Elena Pereloma
Publisher: Elsevier
ISBN: 0857096117
Category : Technology & Engineering
Languages : en
Pages : 673
Get Book Here
Book Description
The processing-microstructure-property relationships in steels continue to present challenges to researchers because of the complexity of phase transformation reactions and the wide spectrum of microstructures and properties achievable. This major two-volume work summarises the current state of research on phase transformations in steels and its implications for the emergence of new steels with enhanced engineering properties.Volume 2 reviews current research on diffusionless transformations and phase transformations in high strength steels, as well as advances in modelling and analytical techniques which underpin this research. Chapters in part one discuss the crystallography and kinetics of martensite transformations, the morphology, substructure and tempering of martensite as well as shape memory in ferrous alloys. Part two summarises research on phase transformations in high strength low alloy (HSLA) steels, transformation induced plasticity (TRIP)-assisted multiphase steels, quenched and partitioned steels, advanced nanostructured bainitic steels, high manganese twinning induced plasticity (TWIP) and maraging steels. The final two parts of the book review advances in modelling and the use of advanced analytical techniques to improve our understanding of phase transformations in steels.With its distinguished editors and distinguished international team of contributors, the two volumes of Phase transformations in steels is a standard reference for all those researching the properties of steel and developing new steels in such areas as automotive engineering, oil and gas and energy production. - Alongside its companion volume, this major two-volume work summarises the current state of research on phase transformations in steels - Reviews research on diffusionless transformations and phase transformations in high strength steels - Examines advances in modelling and the use of advanced analytical techniques to improve understanding of phase transformations in steels
Author: Frank Hoffmann
Publisher: Springer Nature
ISBN: 3030351106
Category : Science
Languages : en
Pages : 313
Get Book Here
Book Description
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.
