Geometry And Thermodynamics PDF Download
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Author | : J.C. Tolédano |
Publisher | : Springer Science & Business Media |
Total Pages | : 453 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 1461538165 |
Download Geometry and Thermodynamics Book in PDF, ePub and Kindle
Distinct scientific communities are usually involved in the three fields of quasi-crystals, of liquid crystals, and of systems having modulated crystalline structures. However, in recent years, there has been a growing feeling that a number of common problems were encountered in the three fields. These comprise the need to recur to "exotic" spaces for describing the type of order of the atomic or molecular configurations of these systems (Euclidian "superspaces" of dimensions greater than 3, or 4-dimensional curved spaces); the recognition that one has to deal with geometrically frustrated systems, and also the occurence of specific excitations (static or dynamic) resulting from the continuous degeneracies of the stable structures considered. In the view of discussing these problems, aNA TO-Advance Research Workshop has assembled in Preveza (Greece), in september 1989,50 experts of the three considered fields (with an equal proportion of theorists and experimentalists). 35 hours of conferences and discussions have led to a more detailed evaluation of the similarities and of the differences in the approaches implemented in the studies of the three types of systems. The papers contained in this NATO-series book provide the substance of this workshop. The reader will find three types of papers. Some very short papers giving the main ideas stated on a subject. Papers comprising 8-10 pages which stick closely to the contents of the talks presented. Longer papers providing more extensively the background and results relative to a given topic. It is worth summarizing the principal outputs of the workshop.
Author | : J. C. Toledano |
Publisher | : |
Total Pages | : 480 |
Release | : 1991-02-01 |
Genre | : |
ISBN | : 9781461538172 |
Download Geometry and Thermodynamics Book in PDF, ePub and Kindle
Author | : William L. Burke |
Publisher | : Cambridge University Press |
Total Pages | : 440 |
Release | : 1985-05-31 |
Genre | : Mathematics |
ISBN | : 9780521269292 |
Download Applied Differential Geometry Book in PDF, ePub and Kindle
This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.
Author | : Frank Weinhold |
Publisher | : John Wiley & Sons |
Total Pages | : 506 |
Release | : 2009-02-17 |
Genre | : Science |
ISBN | : 0470435054 |
Download Classical and Geometrical Theory of Chemical and Phase Thermodynamics Book in PDF, ePub and Kindle
Because it is grounded in math, chemical thermodynamics is often perceived as a difficult subject and many students are never fully comfortable with it. The first authoritative textbook presentation of equilibrium chemical and phase thermodynamics in a reformulated geometrical framework, Chemical and Phase Thermodynamics shows how this famously difficult subject can be accurately expressed with only elementary high-school geometry concepts. Featuring numerous suggestions for research-level extensions, this simplified alternative to standard calculus-based thermodynamics expositions is perfect for undergraduate and beginning graduate students as well as researchers.
Author | : D. E. Blair |
Publisher | : Springer |
Total Pages | : 153 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540381546 |
Download Contact Manifolds in Riemannian Geometry Book in PDF, ePub and Kindle
Author | : Frédéric Barbaresco |
Publisher | : Springer Nature |
Total Pages | : 466 |
Release | : 2021-06-27 |
Genre | : Mathematics |
ISBN | : 3030779572 |
Download Geometric Structures of Statistical Physics, Information Geometry, and Learning Book in PDF, ePub and Kindle
Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces. This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing.
Author | : Viorel Badescu |
Publisher | : Springer |
Total Pages | : 207 |
Release | : 2016-05-19 |
Genre | : Technology & Engineering |
ISBN | : 3319337890 |
Download Modeling Thermodynamic Distance, Curvature and Fluctuations Book in PDF, ePub and Kindle
This textbook aims to briefly outline the main directions in which the geometrization of thermodynamics has been developed in the last decades. The textbook is accessible to people trained in thermal sciences but not necessarily with solid formation in mathematics. For this, in the first chapters a summary of the main mathematical concepts is made. In some sense, this makes the textbook self-consistent. The rest of the textbook consists of a collection of results previously obtained in this young branch of thermodynamics. The manner of presentation used throughout the textbook is adapted for ease of access of readers with education in natural and technical sciences.
Author | : J.M. Souriau |
Publisher | : Springer Science & Business Media |
Total Pages | : 427 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461202817 |
Download Structure of Dynamical Systems Book in PDF, ePub and Kindle
The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization.
Author | : Nihat Ay |
Publisher | : Springer |
Total Pages | : 407 |
Release | : 2017-08-25 |
Genre | : Mathematics |
ISBN | : 3319564781 |
Download Information Geometry Book in PDF, ePub and Kindle
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.
Author | : Michal Pavelka |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 292 |
Release | : 2018-08-06 |
Genre | : Science |
ISBN | : 3110350955 |
Download Multiscale Thermo-Dynamics Book in PDF, ePub and Kindle
One common feature of new emerging technologies is the fusion of the very small (nano) scale and the large scale engineering. The classical environment provided by single scale theories, as for instance by the classical hydrodynamics, is not anymore satisfactory. The main challenge is to keep the important details while still be able to keep the overall picture and simplicity. It is the thermodynamics that addresses this challenge. Our main reason for writing this book is to explain such general viewpoint of thermodynamics and to illustrate it on a very wide range of examples. Contents Levels of description Hamiltonian mechanics Irreversible evolution Reversible and irreversible evolution Multicomponent systems Contact geometry Appendix: Mathematical aspects