Download or read book Equilibrium States in Negative Curvature written by Barbara Schapira and published by . This book was released on 2015 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework (through Patterson-Sullivan densities) allowing us to get rid of compactness assumptions on the manifold, and prove many existence, uniqueness and finiteness results of Gibbs measures. We give many applications to the variational principle, the counting and equidistribution of orbit points and periods, the unique ergodicity of the strong unstable foliation and the classification of Gibbs densities on some Riemannian covers
Download or read book Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees written by Anne Broise-Alamichel and published by Springer Nature. This book was released on 2019-12-16 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a complete exposition of equidistribution and counting problems weighted by a potential function of common perpendicular geodesics in negatively curved manifolds and simplicial trees. Avoiding any compactness assumptions, the authors extend the theory of Patterson-Sullivan, Bowen-Margulis and Oh-Shah (skinning) measures to CAT(-1) spaces with potentials. The work presents a proof for the equidistribution of equidistant hypersurfaces to Gibbs measures, and the equidistribution of common perpendicular arcs between, for instance, closed geodesics. Using tools from ergodic theory (including coding by topological Markov shifts, and an appendix by Buzzi that relates weak Gibbs measures and equilibrium states for them), the authors further prove the variational principle and rate of mixing for the geodesic flow on metric and simplicial trees—again without the need for any compactness or torsionfree assumptions. In a series of applications, using the Bruhat-Tits trees over non-Archimedean local fields, the authors subsequently prove further important results: the Mertens formula and the equidistribution of Farey fractions in function fields, the equidistribution of quadratic irrationals over function fields in their completions, and asymptotic counting results of the representations by quadratic norm forms. One of the book's main benefits is that the authors provide explicit error terms throughout. Given its scope, it will be of interest to graduate students and researchers in a wide range of fields, for instance ergodic theory, dynamical systems, geometric group theory, discrete subgroups of locally compact groups, and the arithmetic of function fields.
Download or read book Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms written by Robert Edward Bowen and published by Springer Science & Business Media. This book was released on 2008-04-18 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details. From the Preface by D. Ruelle: "Rufus Bowen has left us a masterpiece of mathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have been proved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems."
Download or read book Ergodic Theory and Negative Curvature written by Boris Hasselblatt and published by Springer. This book was released on 2017-12-15 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focussing on the mathematics related to the recent proof of ergodicity of the (Weil–Petersson) geodesic flow on a nonpositively curved space whose points are negatively curved metrics on surfaces, this book provides a broad introduction to an important current area of research. It offers original textbook-level material suitable for introductory or advanced courses as well as deep insights into the state of the art of the field, making it useful as a reference and for self-study. The first chapters introduce hyperbolic dynamics, ergodic theory and geodesic and horocycle flows, and include an English translation of Hadamard's original proof of the Stable-Manifold Theorem. An outline of the strategy, motivation and context behind the ergodicity proof is followed by a careful exposition of it (using the Hopf argument) and of the pertinent context of Teichmüller theory. Finally, some complementary lectures describe the deep connections between geodesic flows in negative curvature and Diophantine approximation.
Download or read book Geometry Topology and Dynamics in Negative Curvature written by C. S. Aravinda and published by Cambridge University Press. This book was released on 2016-01-21 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.
Download or read book NASA Technical Translation written by and published by . This book was released on 1965 with total page 978 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book NASA Technical Paper written by United States. National Aeronautics and Space Administration and published by . This book was released on 1989 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Engineering Thermodynamics written by Adrian Bejan and published by John Wiley & Sons. This book was released on 2016-09-06 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt: An advanced, practical approach to the first and second laws of thermodynamics Advanced Engineering Thermodynamics bridges the gap between engineering applications and the first and second laws of thermodynamics. Going beyond the basic coverage offered by most textbooks, this authoritative treatment delves into the advanced topics of energy and work as they relate to various engineering fields. This practical approach describes real-world applications of thermodynamics concepts, including solar energy, refrigeration, air conditioning, thermofluid design, chemical design, constructal design, and more. This new fourth edition has been updated and expanded to include current developments in energy storage, distributed energy systems, entropy minimization, and industrial applications, linking new technologies in sustainability to fundamental thermodynamics concepts. Worked problems have been added to help students follow the thought processes behind various applications, and additional homework problems give them the opportunity to gauge their knowledge. The growing demand for sustainability and energy efficiency has shined a spotlight on the real-world applications of thermodynamics. This book helps future engineers make the fundamental connections, and develop a clear understanding of this complex subject. Delve deeper into the engineering applications of thermodynamics Work problems directly applicable to engineering fields Integrate thermodynamics concepts into sustainability design and policy Understand the thermodynamics of emerging energy technologies Condensed introductory chapters allow students to quickly review the fundamentals before diving right into practical applications. Designed expressly for engineering students, this book offers a clear, targeted treatment of thermodynamics topics with detailed discussion and authoritative guidance toward even the most complex concepts. Advanced Engineering Thermodynamics is the definitive modern treatment of energy and work for today's newest engineers.
Download or read book Understanding Acoustics written by Steven L. Garrett and published by Springer Nature. This book was released on 2020-11-02 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook, like Rayleigh’s classic Theory of Sound, focuses on experiments and on approximation techniques rather than mathematical rigor. The second edition has benefited from comments and corrections provided by many acousticians, in particular those who have used the first edition in undergraduate and graduate courses. For example, phasor notation has been added to clearly distinguish complex variables, and there is a new section on radiation from an unbaffled piston. Drawing on over 40 years of teaching experience at UCLA, the Naval Postgraduate School, and Penn State, the author presents a uniform methodology, based on hydrodynamic fundamentals for analysis of lumped-element systems and wave propagation that can accommodate dissipative mechanisms and geometrically-complex media. Five chapters on vibration and elastic waves highlight modern applications, including viscoelasticity and resonance techniques for measurement of elastic moduli, while introducing analytical techniques and approximation strategies that are revisited in nine subsequent chapters describing all aspects of generation, transmission, scattering, and reception of waves in fluids. Problems integrate multiple concepts, and several include experimental data to provide experience in choosing optimal strategies for extraction of experimental results and their uncertainties. Fundamental physical principles that do not ordinarily appear in other acoustics textbooks, like adiabatic invariance, similitude, the Kramers-Kronig relations, and the equipartition theorem, are shown to provide independent tests of results obtained from numerical solutions, commercial software, and simulations. Thanks to the Veneklasen Research Foundation, this popular textbook is now open access, making the e-book available for free download worldwide. Provides graduate-level treatment of acoustics and vibration suitable for use in courses, for self-study, and as a reference Highlights fundamental physical principles that can provide independent tests of the validity of numerical solutions, commercial software, and computer simulations Demonstrates approximation techniques that greatly simplify the mathematics without a substantial decrease in accuracy Incorporates a hydrodynamic approach to the acoustics of sound in fluids that provides a uniform methodology for analysis of lumped-element systems and wave propagation Emphasizes actual applications as examples of topics explained in the text Includes realistic end-of-chapter problems, some including experimental data, as well as a Solutions Manual for instructors. Features “Talk Like an Acoustician“ boxes to highlight key terms introduced in the text.
Download or read book NASA Technical Paper written by and published by . This book was released on 1989 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Certain Problems in the Theory of Stability of Motion in the Whole written by V. A. Pliss and published by . This book was released on 1958 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Thermodynamic Formalism written by Mark Pollicott and published by Springer Nature. This book was released on 2021-10-01 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume arose from a semester at CIRM-Luminy on “Thermodynamic Formalism: Applications to Probability, Geometry and Fractals” which brought together leading experts in the area to discuss topical problems and recent progress. It includes a number of surveys intended to make the field more accessible to younger mathematicians and scientists wishing to learn more about the area. Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry. This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.
Download or read book Topics in Probability and Lie Groups written by John Christopher Taylor and published by American Mathematical Soc.. This book was released on with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is comprised of two parts: the first contains articles by S. N. Evans, F. Ledrappier, and Figa-Talomanaca. These articles arose from a Centre de Recherches de Mathematiques (CRM) seminar entitiled, ''Topics in Probability on Lie Groups: Boundary Theory''. Evans gives a synthesis of his pre-1992 work on Gaussian measures on vector spaces over a local field. Ledrappier uses the freegroup on $d$ generators as a paradigm for results on the asymptotic properties of random walks and harmonic measures on the Martin boundary. These articles are followed by a case study by Figa-Talamanca using Gelfand pairs to study a diffusion on a compact ultrametric space. The second part of the book is an appendix to the book Compactifications of Symmetric Spaces (Birkhauser) by Y. Guivarc'h and J. C. Taylor. This appendix consists of an article by each author and presents the contents of this book in a more algebraic way. L. Ji and J.-P. Anker simplifies some of their results on the asymptotics of the Green function that were used to compute Martin boundaries. And Taylor gives a self-contained account of Martin boundary theory for manifolds using the theory of second order strictly elliptic partial differential operators.
Download or read book Transport Phenomena for Chemical Reactor Design written by Laurence A. Belfiore and published by John Wiley & Sons. This book was released on 2003-07-04 with total page 910 pages. Available in PDF, EPUB and Kindle. Book excerpt: Laurence Belfiore’s unique treatment meshes two mainstreamsubject areas in chemical engineering: transport phenomena andchemical reactor design. Expressly intended as an extension ofBird, Stewart, and Lightfoot’s classic Transport Phenomena,and Froment and Bischoff’s Chemical Reactor Analysis andDesign, Second Edition, Belfiore’s unprecedented textexplores the synthesis of these two disciplines in a manner theupper undergraduate or graduate reader can readily grasp. Transport Phenomena for Chemical Reactor Designapproaches the design of chemical reactors from microscopic heatand mass transfer principles. It includes simultaneousconsideration of kinetics and heat transfer, both critical to theperformance of real chemical reactors. Complementary topics intransport phenomena and thermodynamics that provide support forchemical reactor analysis are covered, including: Fluid dynamics in the creeping and potential flow regimesaround solid spheres and gas bubbles The corresponding mass transfer problems that employ velocityprofiles, derived in the book’s fluid dynamics chapter, tocalculate interphase heat and mass transfer coefficients Heat capacities of ideal gases via statistical thermodynamicsto calculate Prandtl numbers Thermodynamic stability criteria for homogeneous mixtures thatreveal that binary molecular diffusion coefficients must bepositive In addition to its comprehensive treatment, the text alsocontains 484 problems and ninety-six detailed solutions to assistin the exploration of the subject. Graduate and advancedundergraduate chemical engineering students, professors, andresearchers will appreciate the vision, innovation, and practicalapplication of Laurence Belfiore’s Transport Phenomenafor Chemical Reactor Design.
Download or read book Computational Thermodynamics of Materials written by Zi-Kui Liu and published by Cambridge University Press. This book was released on 2016-06-30 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrates fundamental concepts with experimental data and practical applications, including worked examples and end-of-chapter problems.
Download or read book Polymer Phase Diagrams written by Ronald Koningsveld and published by Oxford University Press, USA. This book was released on 2001 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polymeric materials include plastics, gels, synthetic fibres, and rubbers. They are all-important both in industry and in daily life. Unlike liquid water, ice, or sugar solution, polymers are not homogeneous. They are said to consist of two or more phases, and their production and processing, as well as their properties and uses, depend on an understanding of the transitions that take place between these phases. This new textbook uses fundamental principles to classify phase separation phenomena in polymer systems, and describes simple molecular models explaining the observed behaviour.
Download or read book Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms written by Robert Edward Bowen and published by Springer. This book was released on 2008-04-04 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details. From the Preface by D. Ruelle: "Rufus Bowen has left us a masterpiece of mathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have been proved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems."
