Tag: Mechanics

January 30, 2024

Multiscale Methods in Quantum Mechanics Theory and Experiment

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Free Download Multiscale Methods in Quantum Mechanics: Theory and Experiment by Philippe Blanchard, Gianfausto Dell’Antonio
English | PDF | 2004 | 223 Pages | ISBN : 0817632565 | 21 MB
In the last few years, multiscale methods have lead to spectacular progress in our understanding of complex physical systems and have stimulated the development of very refined mathematical techniques. At the same time on the experimental side, equally spectacular progress has been made in developing experimental machinery and techniques to test the foundations of quantum mechanics. In view of this progress, this volume is very timely; it is the first text totally devoted to multiscale methods as applied to various areas of physics and to the relative developments in mathematics.

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January 30, 2024

Multiscale Buckling Modes in the Mechanics of Fiber-Reinforced Plastics

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Free Download Multiscale Buckling Modes in the Mechanics of Fiber-Reinforced Plastics by Vitaly Paimushin , Andris K. Chate , Sergey Kholmogorov , Maksim Makarov , Ruslan Gazizullin
English | PDF EPUB (True) | 2024 | 175 Pages | ISBN : 3031482158 | 27.8 MB
This book is a useful source of knowledge for engineers and scientists in the field of mechanics of deformation and destruction of composite materials.

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January 30, 2024

Mathematical Aspects of Fluid Mechanics

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Free Download James C. Robinson, "Mathematical Aspects of Fluid Mechanics "
English | ISBN: 1107609259 | 2012 | 276 pages | PDF | 12 MB
The rigorous mathematical theory of the equations of fluid dynamics has been a focus of intense activity in recent years. This volume is the product of a workshop held at the University of Warwick to consolidate, survey and further advance the subject. The Navier-Stokes equations feature prominently: the reader will find new results concerning feedback stabilisation, stretching and folding, and decay in norm of solutions to these fundamental equations of fluid motion. Other topics covered include new models for turbulent energy cascade, existence and uniqueness results for complex fluids and certain interesting solutions of the SQG equation. The result is an accessible collection of survey articles and more traditional research papers that will serve both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.

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January 30, 2024

Integrability and Nonintegrability in Geometry and Mechanics

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Free Download Integrability and Nonintegrability in Geometry and Mechanics by A. T. Fomenko
English | PDF | 1988 | 358 Pages | ISBN : 9027728186 | 28.7 MB
Approach your problems from the right end It isn’t that they can’t see the solution. It is and begin with the answers. 1hen one day, that they can’t see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father ‘The Hermit Oad in Crane Feathers’ in R. Brown ‘The point of a Pin’ . * 1111 Oulik’. n. . Chi" *. * ~ Mm~ Mu,d. ", Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

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January 21, 2024

The Matrix Perturbation Method in Quantum Mechanics

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Free Download The Matrix Perturbation Method in Quantum Mechanics
English | 2024 | ISBN: 3031485459 | 201 Pages | PDF EPUB (True) | 36 MB
This book provides an alternative approach to time-independent perturbation theory in non-relativistic quantum mechanics. It allows easy application to any initial condition because it is based on an approximation to the evolution operator and may also be used on unitary evolution operators for the unperturbed Hamiltonian in the case where the eigenvalues cannot be found. This flexibility sets it apart from conventional perturbation theory. The matrix perturbation method also gives new theoretical insights; for example, it provides corrections to the energy and wave function in one operation. Another notable highlight is the facility to readily derive a general expression for the normalization constant at m-th order, a significant difference between the approach within and those already in the literature. Another unique aspect of the matrix perturbation method is that it can be extended directly to the Lindblad master equation. The first and second-order corrections are obtained for this equation and the method is generalized for higher orders. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained. Throughout the book, several benchmark examples and practical applications underscore the potential, accuracy and good performance of this novel approach. Moreover, the method’s applicability extends to some specific time-dependent Hamiltonians. This book represents a valuable addition to the literature on perturbation theory in quantum mechanics and is accessible to students and researchers alike.

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January 21, 2024

Relativistic Quantum Mechanics and Related Topics

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Free Download Relativistic Quantum Mechanics and Related Topics by Eduardo Guendelman, David Owen
English | July 8, 2022 | ISBN: 9811248753 | 212 pages | MOBI | 32 Mb
This book describes Relativistic Quantum Mechanics, starting from the free field equations for spin-zero particles and for spin-one-half particles, leading to the Klein-Gordon equation and Dirac equations. Interactions of these particles with the electromagnetic field through minimal coupling are introduced as well as other interactions between particles. It includes the calculation of the fundamental processes of Quantum Electrodynamics by means of Feynman’s propagator theory, which allows for a proper treatment of diverse scattering and particle creation processes. In addition to this, a number of special topics are discussed, such as spontaneous symmetry breaking, the global and local cases, the Higgs mechanism, axion-photon interactions using techniques borrowed from scalar QED, pair creation in a strong external electric field, the two-dimensional representation of the Klein-Gordon propagator, bound states in the Greens functions approach, and the Breit equation for bound states. Also, the photon-electron interactions are treated in the context of a symmetric treatment within electrons and photons for eg. Compton scattering, pair creation and pair annihilation. Finally, non-abelian gauge theories, the Glashow-Weinberg-Salam model, some electroweak processes, and Feynman diagrams are also discussed.

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