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 #  AuthorTitleAccn#YearItem Type Claims
1 Dribus, Benjamin F Discrete Causal Theory I10462 2017 eBook  
2 Taylor, Alexander John Analysis of Quantised Vortex Tangle I10040 2017 eBook  
3 Papadimitriou, Fivos Spatial Complexity I09027 2020 eBook  
4 Antoniou, Stathis Mathematical Modeling Through Topological Surgery and Applications I08861 2018 eBook  
5 Szabo, Richard J Equivariant Cohomology and Localization of Path Integrals I11316 2000 eBook  
6 Mecke, Klaus R Morphology of Condensed Matter I11236 2002 eBook  
7 Cotsakis, Spiros Mathematical and Quantum Aspects of Relativity and Cosmology I11099 2000 eBook  
8 Labastida, Jose Topological Quantum Field Theory and Four Manifolds I06905 2005 eBook  
9 Rosenberg, Ivo G Algebras and Orders I05135 1993 eBook  
10 Jack Avrin Knots, braids, and mobius stripe: Particle Physics and the Geometry of Elementarity: An Alternative View 025989 2015 Book  
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TitleDiscrete Causal Theory : Emergent Spacetime and the Causal Metric Hypothesis
Author(s)Dribus, Benjamin F
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionXXX, 558 p. 154 illus : online resource
Abstract NoteThis book evaluates and suggests potentially critical improvements to causal set theory, one of the best-motivated approaches to the outstanding problems of fundamental physics. Spacetime structure is of central importance to physics beyond general relativity and the standard model. The causal metric hypothesis treats causal relations as the basis of this structure. The book develops the consequences of this hypothesis under the assumption of a fundamental scale, with smooth spacetime geometry viewed as emergent. This approach resembles causal set theory, but differs in important ways; for example, the relative viewpoint, emphasizing relations between pairs of events, and relationships between pairs of histories, is central. The book culminates in a dynamical law for quantum spacetime, derived via generalized path summation
ISBN,Price9783319500836
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. COSMOLOGY 3. EBOOK 4. EBOOK - SPRINGER 5. GEOMETRY 6. GRAVITATION 7. TOPOLOGY
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TitleAnalysis of Quantised Vortex Tangle
Author(s)Taylor, Alexander John
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionXVI, 197 p. 95 illus., 84 illus. in color : online resource
Abstract NoteIn 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.
ISBN,Price9783319485560
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. MATHEMATICAL PHYSICS 4. Numerical and Computational Physics, Simulation 5. PHYSICS 6. Statistical Theory and Methods 7. Statistics?? 8. TOPOLOGY
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TitleSpatial Complexity : Theory, Mathematical Methods and Applications
Author(s)Papadimitriou, Fivos
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2020.
DescriptionXXI, 298 p. 178 illus., 149 illus. in color : online resource
Abstract NoteThis book delivers stimulating input for a broad range of researchers, from geographers and ecologists to psychologists interested in spatial perception and physicists researching in complex systems. How can one decide whether one surface or spatial object is more complex than another? What does it require to measure the spatial complexity of small maps, and why does this matter for nature, science and technology? Drawing from algorithmics, geometry, topology, probability and informatics, and with examples from everyday life, the reader is invited to cross the borders into the bewildering realm of spatial complexity, as it emerges from the study of geographic maps, landscapes, surfaces, knots, 3D and 4D objects. The mathematical and cartographic experiments described in this book lead to hypotheses and enigmas with ramifications in aesthetics and epistemology.
ISBN,Price9783030596712
Keyword(s)1. BIODIVERSITY 2. Cognitive psychology 3. COMPLEX SYSTEMS 4. EBOOK 5. EBOOK - SPRINGER 6. GEOGRAPHY 7. Geography, general 8. SYSTEM THEORY 9. TOPOLOGY
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TitleMathematical Modeling Through Topological Surgery and Applications
Author(s)Antoniou, Stathis
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2018.
DescriptionXVII, 85 p. 37 illus., 27 illus. in color : online resource
Abstract NoteTopological surgery is a mathematical technique used for creating new manifolds out of known ones. In this book the authors observe that it also occurs in natural phenomena of all scales: 1-dimensional surgery happens during DNA recombination and when cosmic magnetic lines reconnect; 2-dimensional surgery happens during tornado formation and cell mitosis; and they conjecture that 3-dimensional surgery happens during the formation of black holes from cosmic strings, offering an explanation for the existence of a black hole???s singularity. Inspired by such phenomena, the authors present a new topological model that extends the formal definition to a continuous process caused by local forces. Lastly, they describe an intrinsic connection between topological surgery and a chaotic dynamical system exhibiting a ???hole drilling??? behavior. The authors??? model indicates where to look for the forces causing surgery and what deformations should be observed in the local submanifolds involved. These predictions are significant for the study of phenomena exhibiting surgery and they also open new research directions. This novel study enables readers to gain a better understanding of the topology and dynamics of various natural phenomena, as well as topological surgery itself and serves as a basis for many more insightful observations and new physical implications
ISBN,Price9783319970677
Keyword(s)1. COSMOLOGY 2. Dynamical Systems and Ergodic Theory 3. DYNAMICS 4. EBOOK 5. EBOOK - SPRINGER 6. ERGODIC THEORY 7. Mathematical Methods in Physics 8. PHYSICS 9. STATISTICAL PHYSICS 10. Statistical Physics and Dynamical Systems 11. TOPOLOGY
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TitleEquivariant Cohomology and Localization of Path Integrals
Author(s)Szabo, Richard J
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2000.
DescriptionXI, 315 p : online resource
Abstract NoteThis book, addressing both researchers and graduate students, reviews equivariant localization techniques for the evaluation of Feynman path integrals. The author gives the relevant mathematical background in some detail, showing at the same time how localization ideas are related to classical integrability. The text explores the symmetries inherent in localizable models for assessing the applicability of localization formulae. Various applications from physics and mathematics are presented
ISBN,Price9783540465508
Keyword(s)1. ALGEBRAIC TOPOLOGY 2. EBOOK 3. EBOOK - SPRINGER 4. Elementary particles (Physics) 5. Elementary Particles, Quantum Field Theory 6. GLOBAL ANALYSIS (MATHEMATICS) 7. Global Analysis and Analysis on Manifolds 8. Manifolds (Mathematics) 9. Mathematical Methods in Physics 10. NUCLEAR PHYSICS 11. Particle and Nuclear Physics 12. PHYSICS 13. QUANTUM FIELD THEORY 14. TOPOLOGY
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TitleMorphology of Condensed Matter : Physics and Geometry of Spatially Complex Systems
Author(s)Mecke, Klaus R;Stoyan, Dietrich
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2002.
DescriptionXVIII, 442 p. 147 illus., 5 illus. in color : online resource
Abstract NoteThe morphology of spatially stuctured materials is a rapidly growing field of research at the interface of statistical physics, applied mathematics and materials science. A wide spectrum of applications encompasses the flow through porous and composite materials as well as microemulsions and foams. Written as a set of lectures and tutorial reviews leading up to the forefront of research, this book will be both a compendium for the experienced researcher as well as a high level introductory text for postgraduate students and nonspecialist researchers working in related areas
ISBN,Price9783540457824
Keyword(s)1. COMPLEX SYSTEMS 2. CONDENSED MATTER 3. CONDENSED MATTER PHYSICS 4. DYNAMICAL SYSTEMS 5. EBOOK 6. EBOOK - SPRINGER 7. MECHANICS 8. Mechanics, Applied 9. STATISTICAL PHYSICS 10. Statistical Physics and Dynamical Systems 11. Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences 12. Statistics?? 13. Theoretical and Applied Mechanics 14. TOPOLOGY
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TitleMathematical and Quantum Aspects of Relativity and Cosmology : Proceedings of the Second Samos Meeting on Cosmology, Geometry and Relativity Held at Pythagoreon, Samos, Greece, 31 August ??? 4 September 1998
Author(s)Cotsakis, Spiros;Gibbons, Gary W
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2000.
DescriptionIX, 254 p : online resource
Abstract NoteThis book is written in a pedagogical style intelligible for graduate students. It reviews recent progress in black-hole and wormhole theory and in mathematical cosmology within the framework of Einstein's field equations and beyond, including quantum effects. This collection of essays, written by leading scientists of long standing reputation, should become an indispensable source for future research
ISBN,Price9783540466710
Keyword(s)1. Astronomy, Observations and Techniques 2. Astronomy???Observations 3. ASTROPHYSICS 4. Astrophysics and Astroparticles 5. Classical and Quantum Gravitation, Relativity Theory 6. EBOOK 7. EBOOK - SPRINGER 8. GEOMETRY 9. GRAVITATION 10. Observations, Astronomical 11. TOPOLOGY
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I11099     On Shelf    

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TitleTopological Quantum Field Theory and Four Manifolds
Author(s)Labastida, Jose;Marino, Marcos
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2005.
DescriptionX, 224 p : online resource
Abstract NoteThe present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory material that it can be read by mathematicians and theoretical physicists. On the one hand, it contains a chapter dealing with topological aspects of four manifolds, on the other hand it provides a full introduction to supersymmetry. The book constitutes an essential tool for researchers interested in the basics of topological quantum field theory, since these theories are introduced in detail from a general point of view. In addition, the book describes Donaldson theory and Seiberg-Witten theory, and provides all the details that have led to the connection between these theories using topological quantum field theory. It provides a full account of Witten???s magic formula relating Donaldson and Seiberg-Witten invariants. Furthermore, the book presents some of the recent developments that have led to important applications in the context of the topology of four manifolds
ISBN,Price9781402031779
Keyword(s)1. DIFFERENTIAL GEOMETRY 2. EBOOK 3. EBOOK - SPRINGER 4. MATHEMATICAL PHYSICS 5. Theoretical, Mathematical and Computational Physics 6. TOPOLOGY
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9.     
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TitleAlgebras and Orders
Author(s)Rosenberg, Ivo G;Sabidussi, Gert
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1993.
DescriptionXVIII, 558 p : online resource
Abstract NoteIn the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in its own right. One of the objectives of the ASI was to cover a broad spectrum of topics in this field, and to put in evidence the natural links to, and interactions with, boolean algebra, lattice theory, topology, graphs, relations, automata, theoretical computer science and (partial) orders. The theory of orders is a relatively young and vigorous discipline sharing certain topics as well as many researchers and meetings with universal algebra and lattice theory. W. Taylor surveyed the abstract clone theory which formalizes the process of compos?? ing operations (i.e., the formation of term operations) of an algebra as a special category with countably many objects, and leading naturally to the interpretation and equivalence of varieties
ISBN,Price9789401706971
Keyword(s)1. ALGEBRA 2. Computer science???Mathematics 3. Discrete Mathematics in Computer Science 4. EBOOK 5. EBOOK - SPRINGER 6. MATHEMATICAL LOGIC 7. Mathematical Logic and Foundations 8. NUMBER THEORY 9. Order, Lattices, Ordered Algebraic Structures 10. Ordered algebraic structures 11. TOPOLOGY
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10.    
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TitleKnots, braids, and mobius stripe: Particle Physics and the Geometry of Elementarity: An Alternative View
Author(s)Jack Avrin
PublicationNew Jersey, World Scientific Publishing Co. Pvt. Ltd., 2015.
Descriptionxx, 332p.
Series(Series on Knots and Everything)
Abstract NoteElementary particles in this book exist as Solitons in-and-of the fabric of spacetime itself. As such they are characterized by their geometry, that is their topology and configuration which lead directly to their physical attributes and behavior as well as to a simplification and reduction of assumptions and the importation of parameter values. The emphasis of the book is thus on that geometry, the algebraic geometry associated with taxonomical issues and the differential geometry that determines the physics as well as on simplifying the results. In itself, however, the process of assembling and developing what eventually went into the book has been a singularly rewarding journey. Along the way some fascinating insights and connections to known physical attributes and theories emerge, some predictable but others unbidden and even unanticipated. The book is intended to summarize that journey in a way that, readers with a range of backgrounds will find interesting and provocative. Connections to other physical theories and subjects are also discussed. A most gratifying development is the emergence of a unifying principle underlying the epistemological structure of not only the elementary particles but of such diverse fields as Radar, Quantum mechanics, Biology, Cosmology and the Philosophy of science.
ISBN,Price9789814616003 : US $98.00(HB)
Classification514:539.12
Keyword(s)1. ALGEBRIC GEOMETRY 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - WORLD SCIENTIFIC 5. GEOMETRY 6. PARTICLE PHYSICS 7. TOPOLOGY
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025989   514:539.12/AVR/025989  On Shelf    
OB1229   514:539.12/AVR/  On Shelf    

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