Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics PDF Download

Author: Marco Pettini
Publisher: Springer Science & Business Media
ISBN: 0387499571
Category : Mathematics
Languages : en
Pages : 460

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Book Description
This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The author focuses on two main areas: Riemannian formulation of Hamiltonian dynamics, providing an original viewpoint about the relationship between geodesic instability and curvature properties of the mechanical manifolds; and a topological theory of thermodynamic phase transitions, relating topology changes of microscopic configuration space with the generation of singularities of thermodynamic observables. The book contains numerous illustrations throughout and it will interest both mathematicians and physicists.

Author: Renzo L. Ricca
Publisher: Springer Science & Business Media
ISBN: 9401004463
Category : Science
Languages : en
Pages : 346

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Book Description
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.

Author: Rodrick Wallace
Publisher: Springer Nature
ISBN: 3031298799
Category : Evolution (Biology)
Languages : en
Pages : 177

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Book Description
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 certain sense, 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.

Author: Rodrick Wallace
Publisher: Springer Nature
ISBN: 3030835782
Category : Political Science
Languages : en
Pages : 242

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Book Description
This book is a collection of essays that explore commonalities and contrasts between strategy in armed conflict and strategy in public health. The first part uses the asymptotic limit theorems of information and control theories to study strategy as an exchange of messages between adversaries, in the context of underlying power relations. The ‘messages’ to be exchanged are constructed from an ‘alphabet’ of tactics available to each contender, in a large sense. The second part of the book explores four case histories from this perspective, ranging across agribusiness-generated pandemics, through tuberculosis and COVID-19. The final chapter attempts a strategic synthesis applicable more specifically to public health than to the remarkably – and disturbingly -- close parallel of armed conflict. Taking a unique approach to public health tactics and strategy this volume will be of interest to social epidemiologists, public health economists, public policy scientists, as well as public health researchers and practitioners.

Author: Robert G. Wallace
Publisher: Springer
ISBN: 3319409409
Category : Medical
Languages : en
Pages : 110

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Book Description
This volume compiles five papers modeling the effects of neoliberal economics on the emergence of Ebola and its aftermath. Neoliberalism is currently the world’s primary economic philosophy. It centers international relations around globalizing laissez-faire economics for multinational companies, promoting free trade, deregulating economic markets, and shifting state expenditures in favor of private property. The multidisciplinary teams represented here place both Ebola Makona, the Zaire Ebola virus variant that has infected 28,000 in West Africa, and Ebola Reston, which is currently emerging in industrial hog farms in the Philippines and China, within a multi-plank modeling framework. Using a stochastic extinction model that one group spatializes, environmental stochasticity across the ecologies in which Ebola evolves is treated as an ecosystemic prophylaxis. An agroecological logic gate is developed for epidemic control. A Black-Scholes model explicitly links economic margins across agricultural systems to success in biocontrol. This new control theory is further developed around the data-rate and rate-distortion theorems, a turbulence model, and cognitive symmetry breaking. Lastly, a model of pandemic penetrance is used to explore the domino effects of serious outbreaks amplifying through the cascades of disasters that can follow deadly pandemics. All the models presented are contextualized by socioeonomic geographies specific to outbreak locales.Together the models suggest shifts in regional agroeconomics under the neoliberal doctrine, driving deforestation and monoculture production, destroying the ecosystemic “friction” with which local forests typically disrupt Ebola transmission. The resulting collapse in such an ecological function accelerates pathogen spillover and propagation across the remaining host populations. The failure on the part of current control efforts to assimilate such a structural context may render even an efficacious vaccine dysfunctional. The authors propose an alternate science of disease and an adjunct program of interventions useful to researchers and public health officials alike.

Author: Rodrick Wallace
Publisher: Springer
ISBN: 3319539108
Category : Science
Languages : en
Pages : 243

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Book Description
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.

Author: Michael Spivak
Publisher:
ISBN: 9780914098324
Category : Mechanics
Languages : en
Pages : 733

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Author: Arkady Leonidovich Kholodenko
Publisher: World Scientific
ISBN: 9814412090
Category : Mathematics
Languages : en
Pages : 492

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Book Description
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.

Author: Lorenzo Iorio
Publisher: MDPI
ISBN: 303842482X
Category : Mathematics
Languages : en
Pages : 469

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Book Description
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

Author: Jared Maruskin
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110597802
Category : Science
Languages : en
Pages : 350

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Book Description
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.