Geometry And Thermodynamics
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Geometry And Thermodynamics
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Author : J. C. Toledano
language : en
Publisher:
Release Date : 1991-02-01
Geometry And Thermodynamics written by J. C. Toledano and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-02-01 with categories.
Geometry And Thermodynamics
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Author : J.C. Tolédano
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometry And Thermodynamics written by J.C. Tolédano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Modeling Thermodynamic Distance Curvature And Fluctuations
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Author : Viorel Badescu
language : en
Publisher: Springer
Release Date : 2016-05-19
Modeling Thermodynamic Distance Curvature And Fluctuations written by Viorel Badescu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-19 with Technology & Engineering categories.
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.
Statistical Thermodynamics And Differential Geometry Of Microstructured Materials
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Author : H.Ted Davis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Statistical Thermodynamics And Differential Geometry Of Microstructured Materials written by H.Ted Davis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Substances possessing heterogeneous microstructure on the nanometer and micron scales are scientifically fascinating and technologically useful. Examples of such substances include liquid crystals, microemulsions, biological matter, polymer mixtures and composites, vycor glasses, and zeolites. In this volume, an interdisciplinary group of researchers report their developments in this field. Topics include statistical mechanical free energy theories which predict the appearance of various microstructures, the topological and geometrical methods needed for a mathematical description of the subparts and dividing surfaces of heterogeneous materials, and modern computer-aided mathematical models and graphics for effective exposition of the salient features of microstructured materials.
Maximum Dissipation Non Equilibrium Thermodynamics And Its Geometric Structure
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Author : Henry W. Haslach Jr.
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-15
Maximum Dissipation Non Equilibrium Thermodynamics And Its Geometric Structure written by Henry W. Haslach Jr. and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-15 with Science categories.
Maximum Dissipation: Non-Equilibrium Thermodynamics and its Geometric Structure explores the thermodynamics of non-equilibrium processes in materials. The book develops a general technique created in order to construct nonlinear evolution equations describing non-equilibrium processes, while also developing a geometric context for non-equilibrium thermodynamics. Solid materials are the main focus in this volume, but the construction is shown to also apply to fluids. This volume also: • Explains the theory behind thermodynamically-consistent construction of non-linear evolution equations for non-equilibrium processes • Provides a geometric setting for non-equilibrium thermodynamics through several standard models, which are defined as maximum dissipation processes • Emphasizes applications to the time-dependent modeling of soft biological tissue Maximum Dissipation: Non-Equilibrium Thermodynamics and its Geometric Structure will be valuable for researchers, engineers and graduate students in non-equilibrium thermodynamics and the mathematical modeling of material behavior.
Classical And Geometrical Theory Of Chemical And Phase Thermodynamics
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Author : Frank Weinhold
language : en
Publisher: John Wiley & Sons
Release Date : 2009-02-17
Classical And Geometrical Theory Of Chemical And Phase Thermodynamics written by Frank Weinhold and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-17 with Science categories.
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.
Applications Of Contact Geometry And Topology In Physics
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Author : Arkady Leonidovich Kholodenko
language : en
Publisher: World Scientific
Release Date : 2013
Applications Of Contact Geometry And Topology In Physics written by Arkady Leonidovich Kholodenko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
Although contact geometry and topology is briefly discussed in V I Arnol''d''s book Mathematical Methods of Classical Mechanics (Springer-Verlag, 1989, 2nd edition), it still remains a domain of research in pure mathematics, e.g. see the recent monograph by H Geiges An Introduction to Contact Topology (Cambridge U Press, 2008). Some attempts to use contact geometry in physics were made in the monograph Contact Geometry and Nonlinear Differential Equations (Cambridge U Press, 2007). Unfortunately, even the excellent style of this monograph is not sufficient to attract the attention of the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc. The book is written in the style of famous Landau-Lifshitz (L-L) multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics (at least at the level of the L-L course). No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. As in the L-L course some problems/exercises are formulated along the way and, again as in the L-L course, these are always supplemented by either solutions or by hints (with exact references). Unlike the L-L course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text.
Dynamics On Differential One Forms
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Author : Troy L. Story
language : en
Publisher: iUniverse
Release Date : 2002
Dynamics On Differential One Forms written by Troy L. Story and has been published by iUniverse this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Black holes (Astronomy) categories.
Dynamics on Differential One-Forms proposes a unifying principle for mathematical models of dynamic systems. In "Thermodynamics on One-Forms (chapter I)", the long-standing problem of deriving irreversibility in thermodynamics from reversibility in Hamiltonian mechanics, is solved. Differential geometric analysis shows thermodynamics and Hamiltonian mechanics are both irreversible on representative extended phase spaces. "Dynamics on Differential One-Forms (II)" generalizes (I) to Hamiltonian mechanics, geometric optics, thermodynamics, black holes, electromagnetic fields and string fields. Mathematical models for these systems are revealed as representations of a unifying principle; namely, description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a tangent vector defining system transformations. Relationships between models using exterior calculus and conventional calculus imply a technical definition of dynamic equilibrium. "Global Analysis of Composite Particles (III)" uses differential topology to develop the theory of large vibration-rotation interactions for composite particles. A global classical Hamiltonian and corresponding quantum Hamiltonian operator are derived, then applied to the molecular vibration-rotation problem. "Characteristic Electromagnetic and Yang-Mills Gauge (IV)" uses differential geometry to remove some of the arbitrariness in the gauge, and shows how gauge functions for electromagnetic and Yang-Mills fields follow the same differential equation.
Geometry Mechanics And Dynamics
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Author : Paul Newton
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-11
Geometry Mechanics And Dynamics written by Paul Newton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-11 with Mathematics categories.
Jerry Marsden, one of the world’s pre-eminent mechanicians and applied mathematicians, celebrated his 60th birthday in August 2002. The event was marked by a workshop on “Geometry, Mechanics, and Dynamics”at the Fields Institute for Research in the Mathematical Sciences, of which he wasthefoundingDirector. Ratherthanmerelyproduceaconventionalp- ceedings, with relatively brief accounts of research and technical advances presented at the meeting, we wished to acknowledge Jerry’s in?uence as a teacher, a propagator of new ideas, and a mentor of young talent. Con- quently, starting in 1999, we sought to collect articles that might be used as entry points by students interested in ?elds that have been shaped by Jerry’s work. At the same time we hoped to give experts engrossed in their own technical niches an indication of the wonderful breadth and depth of their subjects as a whole. This book is an outcome of the e?orts of those who accepted our in- tations to contribute. It presents both survey and research articles in the several ?elds that represent the main themes of Jerry’s work, including elasticity and analysis, ?uid mechanics, dynamical systems theory, g- metric mechanics, geometric control theory, and relativity and quantum mechanics. The common thread running through this broad tapestry is the use of geometric methods that serve to unify diverse disciplines and bring a widevarietyofscientistsandmathematicianstogether,speakingalanguage which enhances dialogue and encourages cross-fertilization.
Nonlinear Pdes Their Geometry And Applications
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Author : Radosław A. Kycia
language : en
Publisher: Springer
Release Date : 2019-05-18
Nonlinear Pdes Their Geometry And Applications written by Radosław A. Kycia and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-18 with Mathematics categories.
This volume presents lectures given at the Summer School Wisła 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures in the first part of this volume were delivered by experts in nonlinear differential equations and their applications to physics. Original research articles from members of the school comprise the second part of this volume. Much of the latter half of the volume complements the methods expounded in the first half by illustrating additional applications of geometric theory of differential equations. Various subjects are covered, providing readers a glimpse of current research. Other topics covered include thermodynamics, meteorology, and the Monge–Ampère equations. Researchers interested in the applications of nonlinear differential equations to physics will find this volume particularly useful. A knowledge of differential geometry is recommended for the first portion of the book, as well as a familiarity with basic concepts in physics.