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: Antenucci Название: Statistical Physics of Wave Interactions ISBN: 3319412248 ISBN-13(EAN): 9783319412245 Издательство: Springer Рейтинг: Цена: 14365.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This thesis reveals the utility of pursuing a statistical physics approach in the description of wave interactions in multimode optical systems. To that end, the appropriate Hamiltonian models are derived and their limits of applicability are discussed. The versatility of the framework allows the characterization of ordered and disordered lasers in open and closed cavities in a unified scheme, from standard mode-locking to random lasers. With the use of replica method and Monte Carlo simulations, the models are categorized on the basis of universal properties, and nontrivial predictions of experimental relevance are obtained. In particular, the approach makes it possible to nonperturbatively treat the interplay between disorder and nonlinearity and to envisage novel and fascinating physical phenomena such as glassy random lasers, providing a novel way to experimentally investigate replica symmetry breaking.
Название: Guided wave optics and photonic devices ISBN: 1138077313 ISBN-13(EAN): 9781138077317 Издательство: Taylor&Francis Рейтинг: Цена: 12554.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Guided Wave Optics and Photonic Devices introduces readers to a broad cross-section of topics in this area, from the basics of guided wave optics and nonlinear optics to biophotonics. The book is inspired by and expands on lectures delivered by distinguished speakers at a three-week school on guided wave optics and devices organized at the CSIR-Central Glass and Ceramic Research Institute in Kolkata in 2011.
An Introduction to Guided Wave Optics and Photonic Devices: Principles, Applications, and Future Directions
The book discusses the concept of modes in a guided medium from first principles, emphasizing the importance of dispersion properties in optical fibers. It describes fabrication and characterization techniques of rare-earth-doped optical fibers for amplifiers and lasers, with an eye to future applications. Avoiding complex mathematical formalism, it also presents the basic theory and operational principles of fiber amplifiers and lasers. The book examines techniques for writing fiber Bragg gratings, which are of particular interest for smart sensing applications. A chapter focuses on the fundamental principles of Fourier optics and its implementation in guided wave optics.
In addition, the book explains the critical phenomena of soliton dynamics and supercontinuum generation in photonic crystal fiber, including its fabrication process and characteristics. It also looks at plasmonics in guided media and nonlinearity in stratified media--both key areas for future research. The last chapter explores the importance of lasers in biophotonic applications.
Written by experts engaged in teaching, research, and development in optics and photonics, this reference brings together fundamentals and recent advances in one volume. It offers a valuable overview of the field for students and researchers alike and identifies directions for future research in guided wave and photonic device technology.
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: Wayne D. Kimura Название: Electromagnetic Waves and Lasers ISBN: 1681746123 ISBN-13(EAN): 9781681746128 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 6237.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Reviews basic electromagnetic (EM) wave theory and applies it specifically to lasers in order to give the reader not only tangible examples of how the theory is manifested in real life, but also practical knowledge about lasers, and their operation and usage. This book offers a quick overview, which will allow the reader to gain a competent general understanding of EM waves and lasers.
ООО "Логосфера " Тел:+7(495) 980-12-10 www.logobook.ru
