Geometry And Topology In Hamiltonian Dynamics And Statistical Mechanics
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Geometry And Topology In Hamiltonian Dynamics And Statistical Mechanics
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Author : Marco Pettini
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-14
Geometry And Topology In Hamiltonian Dynamics And Statistical Mechanics written by Marco Pettini 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 2007-06-14 with Mathematics categories.
Itisaspecialpleasureformetowritethisforewordforaremarkablebookbya remarkableauthor.MarcoPettiniisadeepthinker,whohasspentmanyyears probing the foundations of Hamiltonian chaos and statistical mechanics, in particular phase transitions, from the point of view of geometry and topology. Itisinparticularthequalityofmindoftheauthorandhisdeepphysical,as well as mathematical insights which make this book so special and inspiring. It is a “must” for those who want to venture into a new approach to old problems or want to use new tools for new problems. Although topology has penetrated a number of ?elds of physics, a broad participationoftopologyintheclari?cationandprogressoffundamentalpr- lems in the above-mentioned ?elds has been lacking. The new perspectives topology gives to the above-mentioned problems are bound to help in their clari?cation and to spread to other ?elds of science. The sparsity of geometric thinking and of its use to solve fundamental problems, when compared with purely analytical methods in physics, could be relieved and made highly productive using the material discussed in this book. It is unavoidable that the physicist reader may have then to learn some new mathematics and be challenged to a new way of thinking, but with the author as a guide, he is assured of the best help in achieving this that is presently available.
An Introduction To The Geometry And Topology Of Fluid Flows
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Author : Renzo L. Ricca
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Introduction To The Geometry And Topology Of Fluid Flows written by Renzo L. Ricca 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.
Leading experts present a unique, invaluable introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and links, the reader is gradually led to explore the fascinating world of geometric and topological fluid mechanics. Geodesics and chaotic orbits, magnetic knots and vortex links, continual flows and singularities become alive with more than 160 figures and examples. In the opening article, H. K. Moffatt sets the pace, proposing eight outstanding problems for the 21st century. The book goes on to provide concepts and techniques for tackling these and many other interesting open problems.
Computational Psychiatry
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Author : Rodrick Wallace
language : en
Publisher: Springer
Release Date : 2017-04-20
Computational Psychiatry written by Rodrick Wallace and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-20 with Science categories.
This book explores mental disorders from a uniquely evolutionary perspective. Although there have been many attempts to mathematically model neural processes and, to some extent, their dysfunction, there is very little literature that models mental function within a sociocultural, socioeconomic, and environmental context. Addressing this gap in the extant literature, this book explores essential aspects of mental disorders, recognizing the ubiquitous role played by the exaptation of crosstalk between cognitive modules at many different scales and levels of organization, the missing heritability of complex diseases, and cultural epigenetics. Further, it introduces readers to valuable control theory tools that permit the exploration of the environmental induction of neurodevelopmental disorders, as well as the study of the synergism between culture, psychopathology and sleep disorders, offering a distinctively unique resource.
Essays On The Extended Evolutionary Synthesis
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Author : Rodrick Wallace
language : en
Publisher: Springer Nature
Release Date : 2023-05-18
Essays On The Extended Evolutionary Synthesis written by Rodrick Wallace and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-18 with Science categories.
From the ‘punctuated equilibrium' of Eldrege and Gould, through Lewontin's ‘triple helix' and the various visions and revisions of the Extended Evolutionary Synthesis (EES) of Laland and others, both data and theory have demanded an opening-up of the 1950's Evolutionary Synthesis that so firmly wedded evolutionary theory to the mathematics of gene frequency analysis. It can, however, be argued that a single deep and comprehensive mathematical theory may simply not be possible for the almost infinite varieties of evolutionary process active at and across the full range of scales of biological, social, institutional, and cultural phenomena. Indeed, the case history of 'meme theory' should have raised a red flag that narrow gene-centered models of evolutionary process may indeed have serious limitations. What is attempted here is less grand, but still broader than a gene-centered analysis. Following the instruction of Maturana and Varela that all living systems are cognitive, in a certainsense, and that living as a process is a process of cognition, the asymptotic limit theorems of information and control theories that bound all cognition provide a basis for constructing an only modestly deep but wider-ranging series of probability models that might be converted into useful statistical tools for the analysis of observational and experimental data related to evolutionary process. The line of argument in this series of interrelated essays proves to be surprisingly direct.
Dynamical Systems With Applications Using Mapletm
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Author : Stephen Lynch
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-23
Dynamical Systems With Applications Using Mapletm written by Stephen Lynch 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 2009-12-23 with Mathematics categories.
Excellent reviews of the first edition (Mathematical Reviews, SIAM, Reviews, UK Nonlinear News, The Maple Reporter) New edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions Two new chapters on neural networks and simulation have also been added Wide variety of topics covered with applications to many fields, including mechanical systems, chemical kinetics, economics, population dynamics, nonlinear optics, and materials science Accessible to a broad, interdisciplinary audience of readers with a general mathematical background, including senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering A hands-on approach is used with Maple as a pedagogical tool throughout; Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author’s website with additional applications and further links of interest at Maplesoft’s Application Center
Progress In Physics Vol 2 2009
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Author : Dmitri Rabounski
language : en
Publisher: Infinite Study
Release Date :
Progress In Physics Vol 2 2009 written by Dmitri Rabounski and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, including related themes from mathematics.
Information Geometry
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Author : Geert Verdoolaege
language : en
Publisher: MDPI
Release Date : 2019-04-04
Information Geometry written by Geert Verdoolaege and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-04 with Juvenile Nonfiction categories.
This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience.
Handbook Of Applications Of Chaos Theory
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Author : Christos H. Skiadas
language : en
Publisher: CRC Press
Release Date : 2017-12-19
Handbook Of Applications Of Chaos Theory written by Christos H. Skiadas and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-19 with Mathematics categories.
In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.
100 Years Of Chronogeometrodynamics The Status Of The Einstein S Theory Of Gravitation In Its Centennial Year
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Author : Lorenzo Iorio
language : en
Publisher: MDPI
Release Date : 2018-07-10
100 Years Of Chronogeometrodynamics The Status Of The Einstein S Theory Of Gravitation In Its Centennial Year written by Lorenzo Iorio and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-10 with Mathematics categories.
This book is a printed edition of the Special Issue "100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year" that was published in Universe
Dynamical Systems And Geometric Mechanics
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Author : Jared Maruskin
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-08-21
Dynamical Systems And Geometric Mechanics written by Jared Maruskin and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-21 with Science categories.
Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.