A Geometrical Approach to Physics, Burton, David A ; Noble, Adam
Автор: Burton, David A ; Noble, Adam Название: A Geometrical Approach to Physics ISBN: 103212928X ISBN-13(EAN): 9781032129280 Издательство: Taylor&Francis Рейтинг: Цена: 7501.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: K. Bleuler; M. Werner Название: Differential Geometrical Methods in Theoretical Physics ISBN: 9048184592 ISBN-13(EAN): 9789048184590 Издательство: Springer Рейтинг: Цена: 41647.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Proceedings of the NATO Advanced Research Workshop and the 16th International Conference, Como, Italy, August 24-29, 1987
Автор: Carfora Название: Einstein Constraints and Ricci Flow ISBN: 9811985391 ISBN-13(EAN): 9789811985393 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold. This is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface. The book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory. This work is intended for advanced students in mathematical physics and researchers alike.
Автор: Carfora Название: Einstein Constraints and Ricci Flow ISBN: 9811985421 ISBN-13(EAN): 9789811985423 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold. This is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface. The book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory. This work is intended for advanced students in mathematical physics and researchers alike.
Modern Geometrical Machinery; 1 .1 Introduction; 1 .2 Smooth Manifolds; 1.2.1 Intuition Behind a Smooth Manifold; 1.2.2 Definition of a Smooth Manifold; 1.2.3 Smooth Maps Between Manifolds; 1.2.4 (Co)Tangent Bundles of a Smooth Manifold; 1.2.5 Tensor Fields and Bundles of a Smooth Manifold; 1.2.6 Lie Derivative on a Smooth Manifold; 1.2.7 Lie Groups and Associated Lie Algebras; 1.2.8 Lie Symmetries and Prolongations on Manifolds;1.2.9 Riemannian Manifolds; 1.2.10 Finsler Manifolds; 1.2.11 Symplectic Manifolds; 1.2.12 Complex and Kдhler Manifolds; 1.2.13 Conformal Killing-Riemannian Geometry; 1.3 Fibre Bundles; 1.3.1 Intuition Behind a Fibre Bundle; 1.3.2 Definition of a Fibre Bundle;1.3.3 Vector and Affine Bundles; 1.3.4 Principal Bundles; 1.3.5 Multivector-Fields and Tangent-Valued Forms; 1.4 Jet Spaces; 1.4.1 Intuition Behind a Jet Space; 1.4.2 Definition of a 1-Jet Space; 1.4.3 Connections as Jet Fields; 1.4.4 Definition of a 2-Jet Space; 1.4.5 Higher-Order Jet Spaces; 1.4.6 Jets in Mechanics;1.4.7 Jets and Action Principle; 1.5 Path Integrals: Extending Smooth Geometrical Machinery; 1.5.1 Intuition Behind a Path Integral; 1.5.2 Path Integral History; 1.5.3 Standard Path-Integral Quantization; 1.5.4 Sum over Geometries/Topologies; 1.5.5 TQFT and Stringy Path Integrals; 2 Dynamics of High-Dimensional Nonlinear Systems; 2.1 Mechanical Systems; 2.1.1 Autonomous Lagrangian/Hamiltonian Mechanics; 2.1.2 Non-Autonomous Lagrangian/Hamiltonian Mechanics; 2.1.3 Semi-Riemannian Geometrical Dynamics; 2.1.4 Relativistic and Multi-Time Rheonomic Dynamics; 2.1.5 Geometrical Quantization; 2.2 Physical Field Systems; 2.2.1 n-Categorical Framework; 2.2.2 Lagrangian Field Theory on Fibre Bundles; 2.2.3 Finsler-Lagrangian Field Theory; 2.2.4 Hamiltonian Field Systems: Path-Integral Quantization; 2.2.5 Gauge Fields on Principal Connections; 2.2.6 Modern Geometrodynamics; 2.2.7 Topological Phase Transitions and Hamiltonian Chaos; 2.2.8 Topological Superstring Theory; 2.2.9 Turbulence and Chaos Field Theory; 2.3 Nonlinear Control Systems; 2.3.1 The Basis of Modern Geometrical Control;2.3.2 Geometrical Control of Mechanical Systems;2.3.3 Hamiltonian Optimal Control and Maximum Principle; 2.3.4 Path-Integral Optimal Control of Stochastic Systems; 2.4 Human-Like Biomechanics; 2.4.1 Lie Groups and Symmetries in Biomechanics; 2.4.2 Muscle-Driven Hamiltonian Biomechanics; 2.4.3 Biomechanical Functors; 2.4.4 Biomechanical Topology; 2.5 Neurodynamics; 2.5.1 Microscopic Neurodynamics and Quantum Brain; 2.5.2 Macroscopic Neurodynamics; 2.5.3 Oscillatory Phase Neurodynamics;2.5.4 Neural Path-Integral Model for the Cerebellum; 2.5.5 Intelligent Robot Control; 2.5.6 Brain-Like Control Functor in Biomechanics; 2.5.7 Concurrent and Weak Functorial Machines; 2.5.8 Brain-Mind Functorial Machines; 26 Psycho-Socio-Economic Dynamics; 2.6.1 Force-Field Psychodynamics; 2.6.2 Geometrical Dynamics of Human Crowd; 2.6.3 Dynamical Games on Lie Groups; 2.6.4 Nonlinear Dynamics of Option Pricing; 2.6.5 Command/Control in Human-Robot Interactions; 2.6.6 Nonlinear Dynamics of Complex Nets; 2.6.7 Complex Adaptive Systems: Common Characteristics; 2.6.8 FAM Functors and Real-Life Games; 2.6.9 Riemann-Finsler Approach to Information Geometry; 3 Appendix: Tensors and Functors; 3.1 Elements of Classical Tensor Analysis; 3.1.1 Transformation of Coordinates and Elementary Tensors; 3.1.2 Euclidean Tensors; 3. 1 .3 Tensor Derivatives on Riemannian Manifolds; 3.1.4 Tensor Mechanics in Brief; 3.1.5 The Covariant Force Law in Robotics and Biomechanics; 3.2 Categories and Functors; 3.2.1 Maps; 3.2.2 Categories; 3.2.3 Functors; 3.2.4 Natural Transformations; 3.2.5 Limits and Colimits; 3.2.6 The Adjunction; 3.2.7 ri-Categories; 3.2.8 Abelian Functorial Algebra; References; Index.
Автор: Angela Slavova, Petar Popivanov Название: Nonlinear Waves: A Geometrical Approach ISBN: 9813271604 ISBN-13(EAN): 9789813271609 Издательство: World Scientific Publishing Рейтинг: Цена: 12672.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.
Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used.
This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.
Автор: Lin Название: Advanced Geometrical Optics ISBN: 9811022984 ISBN-13(EAN): 9789811022982 Издательство: Springer Рейтинг: Цена: 22359.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book computes the first- and second-order derivative matrices of skew ray and optical path length, while also providing an important mathematical tool for automatic optical design. This book consists of three parts. Part One reviews the basic theories of skew-ray tracing, paraxial optics and primary aberrations – essential reading that lays the foundation for the modeling work presented in the rest of this book. Part Two derives the Jacobian matrices of a ray and its optical path length. Although this issue is also addressed in other publications, they generally fail to consider all of the variables of a non-axially symmetrical system. The modeling work thus provides a more robust framework for the analysis and design of non-axially symmetrical systems such as prisms and head-up displays. Lastly, Part Three proposes a computational scheme for deriving the Hessian matrices of a ray and its optical path length, offering an effective means of determining an appropriate search direction when tuning the system variables in the system design process.
Автор: Rajeev, S. G. (professor Of Physics And Mathematics, University Of Rochester) Название: Fluid mechanics ISBN: 0198805020 ISBN-13(EAN): 9780198805021 Издательство: Oxford Academ Рейтинг: Цена: 11246.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book emphasizes general principles of physics illustrated by simple examples in fluid mechanics. Advanced mathematics (e.g., Riemannian geometry and Lie groups) commonly used in other parts of theoretical physics (e.g. General Relativity or High Energy Physics) are explained and applied to Fluid Mechanics.
Автор: E.G.Peter Rowe Название: Geometrical Physics in Minkowski Spacetime ISBN: 1849968667 ISBN-13(EAN): 9781849968669 Издательство: Springer Рейтинг: Цена: 11753.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: From the reviews: "This attractive book provides an account of the theory of special relativity from a geometrical viewpoint, explaining the unification and insights that are given by such a treatment. [ ] Can be read with profit by all who have taken a first course in relativity physics." ASLIB Book Guide
Описание: This book presents a comprehensive account of the renormalization-group (RG) method and its extension, the doublet scheme, in a geometrical point of view. It extract long timescale macroscopic/mesoscopic dynamics from microscopic equations in an intuitively understandable way rather than in a mathematically rigorous manner and introduces readers to a mathematically elementary, but useful and widely applicable technique for analyzing asymptotic solutions in mathematical models of nature. The book begins with the basic notion of the RG theory, including its connection with the separation of scales. Then it formulates the RG method as a construction method of envelopes of the naive perturbative solutions containing secular terms, and then demonstrates the formulation in various types of evolution equations. Lastly, it describes successful physical examples, such as stochastic and transport phenomena including second-order relativistic as well as nonrelativistic fluid dynamics with causality and transport phenomena in cold atoms, with extensive numerical expositions of transport coefficients and relaxation times. Requiring only an undergraduate-level understanding of physics and mathematics, the book clearly describes the notions and mathematical techniques with a wealth of examples. It is a unique and can be enlightening resource for readers who feel mystified by renormalization theory in quantum field theory.
Автор: Dino Boccaletti; Giuseppe Pucacco Название: Theory of Orbits ISBN: 364208222X ISBN-13(EAN): 9783642082221 Издательство: Springer Рейтинг: Цена: 11753.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Half a century ago, S. Chandrasekhar wrote these words in the preface to his 1 celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy- namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. ... ] Indeed, several of the problems of modern stellar dy- namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var- ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con- sidered from the point of view of celestial mechanics (the N-body problem with N 1), fluid mechanics (the system is represented by a material con- tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).
Автор: Psang Dain Lin Название: New Computation Methods for Geometrical Optics ISBN: 9811013411 ISBN-13(EAN): 9789811013416 Издательство: Springer Рейтинг: Цена: 14365.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book employs homogeneous coordinate notation to compute the first- and second-order derivative matrices of various optical quantities. It will serve as an important mathematical tool for automatic optical design.
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