Author: Daniele Funaro Publisher: Springer Science & Business Media ISBN: 3540467831 Category : Science Languages : en Pages : 315
Book Description
This book is devoted to the analysis of approximate solution techniques for differential equations, based on classical orthogonal polynomials. These techniques are popularly known as spectral methods. In the last few decades, there has been a growing interest in this subject. As a matter offact, spectral methods provide a competitive alternative to other standard approximation techniques, for a large variety of problems. Initial ap plications were concerned with the investigation of periodic solutions of boundary value problems using trigonometric polynomials. Subsequently, the analysis was extended to algebraic polynomials. Expansions in orthogonal basis functions were preferred, due to their high accuracy and flexibility in computations. The aim of this book is to present a preliminary mathematical background for be ginners who wish to study and perform numerical experiments, or who wish to improve their skill in order to tackle more specific applications. In addition, it furnishes a com prehensive collection of basic formulas and theorems that are useful for implementations at any level of complexity. We tried to maintain an elementary exposition so that no experience in functional analysis is required.
Author: Max-Olivier Hongler Publisher: Springer Science & Business Media ISBN: 3540484485 Category : Science Languages : en Pages : 92
Book Description
Inspired by the general configuration characteristics of automatic production lines, the author discusses the modelisation of important sectors of a factory. Typical topics such as parts feeders, part orienting devices, insertion mechanisms and buffered flows are analysed using random evolution models and non-linear dynamical systems theory.
Author: Giampiero Esposito Publisher: Springer Science & Business Media ISBN: 3662144956 Category : Science Languages : en Pages : 343
Book Description
This book is aimed at theoretical and mathematical physicists and mathematicians interested in modern gravitational physics. I have thus tried to use language familiar to readers working on classical and quantum gravity, paying attention both to difficult calculations and to existence theorems, and discussing in detail the current literature. The first aim of the book is to describe recent work on the problern of boundary conditions in one-loop quantum cosmology. The motivation of this research was to under stand whether supersymmetric theories are one-loop finite in the presence of boundaries, with application to the boundary-value problems occurring in quantum cosmology. Indeed, higher-loop calculations in the absence of boundaries are already available in the litera ture, showing that supergravity is not finite. I believe, however, that one-loop calculations in the presence of boundaries are more fundamental, in that they provide a more direct check of the inconsistency of Supersymmetrie quantum cosmology from the perturbative point of view. It therefore appears that higher-order calculations are not strictly needed, if the one-loop test already yields negative results. Even though the question is not yet settled, this research has led to many interesting, new applications of areas of theoretical and mathematical physics such as twistor theory in flat space, self-adjointness theory, the generalized lliemann zeta-function, and the theory of boundary counterterms in super gravity.
Author: Mauro Ferrari Publisher: Springer Science & Business Media ISBN: 354049636X Category : Science Languages : en Pages : 225
Book Description
The recently proposed, fully multi-scale theory of doublet mechanics offers unprecented opportunities to reconcile the discrete and continuum representations of solids while maintaining a simple analytical format and full compatibility with lattice dynamics and continuum mechanics. In this monograph, a self-contained account of the state of the art in doublet mechanics is presented. Novel results in the elastodynamics of microstructured media are reported, including the identification of a new class of dispersive surface waves, and the presentation of methods for the experimental determination of the essential microstructural parameters. The relationships between doublet mechanics, lattice dynamics, and continuum theories are examined, leading to the identification of the subject areas in which the use of doublet mechanics is most advantageous. These areas include the analysis of domains as diverse as micro-electro-mechanical systems (MEMS), granular and particulate media, nanotubes, and peptide arrays.
Author: Cherif Bendjaballah Publisher: Springer Science & Business Media ISBN: 3540492062 Category : Science Languages : en Pages : 203
Book Description
In recent years, progress in the generation of squeezed states of light, mainly characterized by a reduced noise property, has stimulated important work in relation to their potential use to improve the sensitivity of optical communication systems. These notes are devoted to the detection and information processing of optical signals at very low levels of power. A survey of recent developments from the quantum and classical points of view is presented. Ultimate limits of performance under the criteria of detection and information are established. Some of the results are detailed and may be utilized for the design of practical systems of communication using present technology. The book addresses physicists and engineers interested in present and future developments in optical communications.
Author: Giovanni Landi Publisher: Springer Science & Business Media ISBN: 354014949X Category : Science Languages : en Pages : 216
Book Description
These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'*-algebras, module theory and K-theory, spectral calculus, forms and connection theory. Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated. Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topological spaces. They have been used to construct quantum-mechanical and field-theory models, alternative models to lattice gauge theory, with nontrivial topological content. This book will be essential to physicists and mathematicians with an interest in noncommutative geometry and its uses in physics.
Author: Ludwig Pittner Publisher: Springer Science & Business Media ISBN: 3540478019 Category : Science Languages : en Pages : 476
Book Description
Quantum groups and quantum algebras as well as non-commutative differential geometry are important in mathematics and considered to be useful tools for model building in statistical and quantum physics. This book, addressing scientists and postgraduates, contains a detailed and rather complete presentation of the algebraic framework. Introductory chapters deal with background material such as Lie and Hopf superalgebras, Lie super-bialgebras, or formal power series. Great care was taken to present a reliable collection of formulae and to unify the notation, making this volume a useful work of reference for mathematicians and mathematical physicists.
Author: Stephen Childress Publisher: Springer Science & Business Media ISBN: 3540447784 Category : Science Languages : en Pages : 414
Book Description
The study of the magnetic fields of the Earth and Sun, as well as those of other planets, stars, and galaxies, has a long history and a rich and varied literature, including in recent years a number of review articles and books dedicated to the dynamo theories of these fields. Against this background of work, some explanation of the scope and purpose of the present monograph, and of the presentation and organization of the material, is therefore needed. Dynamo theory offers an explanation of natural magnetism as a phenomenon of magnetohydrodynamics (MHD), the dynamics governing the evolution and interaction of motions of an electrically conducting fluid and electromagnetic fields. A natural starting point for a dynamo theory assumes the fluid motion to be a given vector field, without regard for the origin of the forces which drive it. The resulting kinematic dynamo theory is, in the non-relativistic case, a linear advection-diffusion problem for the magnetic field. This kinematic theory, while far simpler than its magnetohydrodynamic counterpart, remains a formidable analytical problem since the interesting solutions lack the easiest symmetries. Much ofthe research has focused on the simplest acceptable flows and especially on cases where the smoothing effect of diffusion can be exploited. A close analog is the advection and diffusion of a scalar field by laminar flows, the diffusion being measured by an appropriate Peclet number. This work has succeeded in establishing dynamo action as an attractive candidate for astrophysical magnetism.
Author: Peter Kopietz Publisher: Springer Science & Business Media ISBN: 3540684956 Category : Science Languages : en Pages : 263
Book Description
The author presents in detail a new non-perturbative approach to the fermionic many-body problem, improving the bosonization technique and generalizing it to dimensions d1 via functional integration and Hubbard--Stratonovich transformations. In Part I he clearly illustrates the approximations and limitations inherent in higher-dimensional bosonization and derives the precise relation with diagrammatic perturbation theory. He shows how the non-linear terms in the energy dispersion can be systematically included into bosonization in arbitrary d, so that in d1 the curvature of the Fermi surface can be taken into account. Part II gives applications to problems of physical interest. The book addresses researchers and graduate students in theoretical condensed matter physics.
Author: Mohamed Gad-el-Hak Publisher: Springer Science & Business Media ISBN: 3540696725 Category : Science Languages : en Pages : 533
Book Description
No be certain it can is not based mathematics. knowledge if upon da Vinci, (Leonardo 1452 1519) the humankind. Thinking is one greatest of Joys of Galilei, (Galileo 1564 1642) Now I think is to be the root all hydrodynamics and is at of physical science, second the to none in its mathematics. present beauty of Thomson (William (Lord Kelvin), 1824 1907) The book contains the lecture notes of of the nine instructors at present eight the short Flow Control: Fundamentals and which held course was Practices, in the week 24 28 June and Carg6se, Corsica, France, during 1996, repeated at the of Notre 9 13 1996. University Dame, Indiana, September Following the week in the course a on same was held. Corsica, 5 day workshop topic Selected from the scheduled to 1998 workshop are papers appear early special volume of the International Journal Heat Thermo of Experimental Transfer, and Fluid All Mechanics. three events were Jean Paul dynamics, organized by Bonnet of Universit6 de Andrew Pollard of Univer Poitiers, France, Queen's at and Mohamed Gad el Hak of the of sity Kingston, Canada, University Notre U.S.A.
Author: Daniele Funaro
Author: Max-Olivier Hongler
Author: Giampiero Esposito
Author: Mauro Ferrari
Author: Cherif Bendjaballah
Author: Giovanni Landi
Author: Ludwig Pittner
Author: Stephen Childress
Author: Peter Kopietz
Author: Mohamed Gad-el-Hak