Contribution à la modélisation numérique des phénomènes couples magneto-élastiques

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ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.:/5 (49 download)

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Book Synopsis Contribution à la modélisation numérique des phénomènes couples magneto-élastiques by : Mondher Besbes

Download or read book Contribution à la modélisation numérique des phénomènes couples magneto-élastiques written by Mondher Besbes and published by . This book was released on 1995 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Les travaux présentés dans ce mémoire traitent de la modélisation numérique dans l'hypothèse bidimensionnelle des phénomènes couples magneto-elastiques dans les dispositifs electromagnetiques. L'objectif est particulièrement cible a l'étude théorique et expérimentale des vibrations d'origine magnétique dans les machines a reluctance variable a double saillance. Dans le but de quantifier la réponse vibratoire d'une telle machine, nous avons introduit dans un code de calcul du champ magnétique, base sur la méthode des éléments finis, un module qui permet la détermination de la répartition des forces magnétiques locales pour calculer les déformations mécaniques résultantes. Le choix de la méthode de calcul de force magnétique, qui se base sur l'application locale du principe des travaux virtuels, a été justifie par la précision de cette méthode, sa generalite (milieux satures) et sa souplesse de mise en ouvre. L'analyse spectrale des forces magnétiques nous a permis de prédire quelles sont les modes de vibrations qui vont être excites. Le calcul du spectre des vibrations a été réalise en cherchant la solution de l'équation d'équilibre relative a chaque harmonique de force. Une analyse modale a été aussi effectuée pour déterminer les fréquences de résonance et les modes de vibrations associées. Parallèlement a cette approche numérique, nous avons analyse expérimentalement, en se basant sur des mesures accelerometriques, le comportement vibratoire de la machine. Grâce a cette analyse, nous avons pu valider le code de calcul des vibrations ainsi développe. L'ensemble de ces travaux a montre que la source principale du bruit acoustique, ou des vibrations qui le produisent, dans la machine d'étude réside sur l'action des forces magnétiques radiales d'attraction des dents statoriques et rotoriques en particulier lorsque celles-ci sont en conjonction. A la fin de ce mémoire, nous avons mis au point un modèle de couplage fort qui permet la résolution simultanée des problèmes couples magneto-elastiques. Ce type de modèle trouve son importance dans le cas ou les propriétés magnétiques et élastiques sont en forte interaction. Nous avons spécialement évoque dans cette partie le calcul des déformations des matériaux fortement magnétostrictifs et la résolution des problèmes de grandes déformations élastiques

CONTRIBUTION A LA MODELISATION NUMERIQUE DE PHENOMENES COUPLES MAGNETIQUE-MECANIQUE. ETUDE DES VIBRATIONS D'ORIGINE ELECTROMAGNETIQUE D'UNE PLAQUE ELASTIQUE

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ISBN 13 :
Total Pages : 182 pages
Book Rating : 4.:/5 (49 download)

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Book Synopsis CONTRIBUTION A LA MODELISATION NUMERIQUE DE PHENOMENES COUPLES MAGNETIQUE-MECANIQUE. ETUDE DES VIBRATIONS D'ORIGINE ELECTROMAGNETIQUE D'UNE PLAQUE ELASTIQUE by : DAN.. MIRESCU

Download or read book CONTRIBUTION A LA MODELISATION NUMERIQUE DE PHENOMENES COUPLES MAGNETIQUE-MECANIQUE. ETUDE DES VIBRATIONS D'ORIGINE ELECTROMAGNETIQUE D'UNE PLAQUE ELASTIQUE written by DAN.. MIRESCU and published by . This book was released on 1996 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: L'ETUDE DES PHENOMENES COMPLEXES IMPOSE UNE ANALYSE DE L'ENSEMBLE DES INTERACTIONS ENTRE DIFFERENTS DOMAINES DE LA PHYSIQUE. LA MECANIQUE ET L'ELECTROMAGNETISME Y OCCUPENT UNE PLACE SPECIALE CAR LES COURANTS INDUITS DANS UN CORPS CONDUCTEUR DEPENDENT DE LA VITESSE DE MOUVEMENT ET LES FORCES QUI MODIFIERONT LE MOUVEMENT DEPENDENT DES COURANTS INDUITS. UNE ANALYSE DE CE TYPE DE PROBLEMES A ETE EFFECTUE DANS CETTE THESE POUR UNE PLAQUE ELASTIQUE, PLANE, RECTANGULAIRE ET CONDUCTRICE PLACEE DANS UN CHAMP MAGNETIQUE VARIABLE DANS LE TEMPS. DES ASPECTS SPECIFIQUES AUX PROBLEMES DE COUPLAGE ONT ETE REVELES AINSI QUE LEUR RESOLUTION ET LES RESULTATS DE MODELISATIONS ONT ETE COMPARES AVEC DES RESULTATS EXPERIMENTAUX ET CEUX DES AUTRES CHERCHEURS

CONTRIBUTION A LA MODELISATION PAR ELEMENTS FINIS DES PHENOMENES ELECTROMAGNETIQUES RELATIFS AU MAGNETOFORMAGE

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ISBN 13 :
Total Pages : 151 pages
Book Rating : 4.:/5 (49 download)

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Book Synopsis CONTRIBUTION A LA MODELISATION PAR ELEMENTS FINIS DES PHENOMENES ELECTROMAGNETIQUES RELATIFS AU MAGNETOFORMAGE by : BRAHIM.. BENDJIMA

Download or read book CONTRIBUTION A LA MODELISATION PAR ELEMENTS FINIS DES PHENOMENES ELECTROMAGNETIQUES RELATIFS AU MAGNETOFORMAGE written by BRAHIM.. BENDJIMA and published by . This book was released on 1997 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: L'ETUDE DU COMPORTEMENT DYNAMIQUE DES SYSTEMES DE MAGNETOFORMAGE PASSE PAR L'ANALYSE DES PHENOMENES COUPLES MAGNETO-MECANIQUES. UNE PRESENTATION DU MAGNETOFORMAGE EST EFFECTUEE ; ELLE RAPPELLE LE PRINCIPE, LE MATERIEL ET LES MODELES PHYSIQUES ET MATHEMATIQUES DE REPRESENTATION DES DISPOSITIFS. LES MODELES MAGNETODYNAMIQUES GENERALEMENT UTILISES DANS LE TRAITEMENT DU PROBLEME DE LA VITESSE, AINSI QUE LES METHODES UTILISEES POUR LA SOLUTION DE CE PROBLEME SONT PRESENTES. DEUX MODELES BASES SUR LA METHODE DES ELEMENTS FINIS POUR L'ANALYSE DU COMPORTEMENT DYNAMIQUE D'UN TUBE EN EXPANSION LIBRE SONT PROPOSES. CES MODELES DIFFERENT PAR LE CHOIX DE LA TECHNIQUE DE PRISE EN COMPTE DU MOUVEMENT DE L'OBJET EN DEFORMATION, LE PREMIER MODELE UTILISE UNE TECHNIQUE DE BANDE DE MOUVEMENT SANS REMAILLAGE, LE SECOND UTILISE LA TECHNIQUE DU MACRO-ELEMENT. LE MODELE NUMERIQUE UTILISANT LA BANDE DE MOUVEMENT EST APPLIQUE A UN SYSTEME AXISYMETRIQUE A TUBE LONG CARACTERISE PAR UNE DEFORMATION NON-UNIFORME LE LONG DE L'AXE DU TUBE. LE MODELE ANALYTICO-NUMERIQUE UTILISANT LE MACRO-ELEMENT EST APPLIQUE AU SYSTEME A TUBE COURT A DEFORMATION UNIFORME. LES MODELES DEVELOPPES SONT VALIDES EN LES CONFRONTANT ENTRE EUX, ET EN LES COMPARANT AUX RESULTATS EXPERIMENTAUX DONT NOUS DISPOSONS.

CONTRIBUTION A LA MODELISATION TRIDIMENSIONNELLE DES PHENOMENES TRANSITOIRES COUPLES MAGNETIQUE MECANIQUE

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ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.:/5 (492 download)

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Book Synopsis CONTRIBUTION A LA MODELISATION TRIDIMENSIONNELLE DES PHENOMENES TRANSITOIRES COUPLES MAGNETIQUE MECANIQUE by : MATHIAS.. VOISIN

Download or read book CONTRIBUTION A LA MODELISATION TRIDIMENSIONNELLE DES PHENOMENES TRANSITOIRES COUPLES MAGNETIQUE MECANIQUE written by MATHIAS.. VOISIN and published by . This book was released on 2000 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: NOUS AVONS DEVELOPPE UN MODELE NUMERIQUE POUR LES PHENOMENES COUPLES MAGNETIQUE-MECANIQUE BIDIRECTIONNELS QUI APPARAISSENT DANS LES DISPOSITIFS ELECTROMAGNETIQUES. L'ALGORITHME DU SCHEMA DE COUPLAGE DEVELOPPE INTEGRE UNE BOUCLE DE CORRECTION DES HYPOTHESES, SIMILAIRE A CELLE DES SCHEMAS NON-LINEAIRES. LA BOUCLE EFFECTUE LA RESOLUTION DU PROBLEME MAGNETIQUE, LE CALCUL DES FORCES, LA RESOLUTION DU PROBLEME MECANIQUE ET PRENDS EN COMPTE LES DEFORMATIONS DANS L'ENSEMBLE DU PROBLEME COUPLE. LE PROBLEME MAGNETODYNAMIQUE EST ECRIT EN POTENTIELS COMBINES T-PHI DANS LE REPERE LAGRANGIEN. IL EST RESOLU PAR UNE METHODE COMBINEE ELEMENTS FINIS INTEGRALES DE FRONTIERES, AVEC DES ELEMENTS DE WHITNEY 3D. LE CALCUL PAS A PAS DANS LE TEMPS AVEC LA METHODE DES GRADIENTS CONJUGUES CONVERGE RAPIDEMENT. LES FORCES MAGNETIQUES SONT EVALUEES PAR LA METHODE DES TRAVAUX VIRTUELS. LES HYPOTHESES SONT AISEMENT VERIFIEES GRACE AU MODELE MAGNETIQUE. LA VARIATION DE LA COENERGIE EST CALCULEE PAR DERIVATION DE LA MATRICE JACOBIENNE. CECI REDUIT LES CALCULS ET AMELIORE LA PRECISION. LE CHAMP DE FORCE NODAL OBTENU DEPEND DU MAILLAGE UTILISE ET NE CORRESPOND A RIEN DE PHYSIQUE. EN REVANCHE, IL CORRESPOND AUX DONNEES DU PROBLEME MECANIQUE SUR LE MEME MAILLAGE. LE CALCUL D'ELASTICITE LINEAIRE DYNAMIQUE EST MENE EN EQUATIONS MODALES. LE SYSTEME EST ALORS DIAGONAL ET NE REQUIERT QU'UN SEUL CALCUL PREPARATOIRE. ON NEGLIGE LES MODES HAUTES FREQUENCES POUR REDUIRE LA TAILLE DU SYSTEME. LA DEFORMATION DU MAILLAGE, OBTENU PAR DEPLACEMENT DES NUDS, SUFFIT A REPRESENTER LA DEFORMATION DE LA STRUCTURE. LA FORMULATION LAGRANGIENNE DU PROBLEME MAGNETIQUE PREND EN COMPTE LES DEFORMATIONS GEOMETRIQUES ET LES MOUVEMENTS DE CONDUCTEURS. LES DERIVEES GLOBALES INTEGRENT LES MATRICES DU SYSTEME MAGNETIQUE. LA DEFORMATION CONDUIT A DES MAILLAGES IMPROPRES AU CALCUL. UNE METHODE DE REPARTITION DES DISTORSIONS Y REMEDIE. L'EXEMPLE UTILISE POUR LA VALIDATION EST UN EXEMPLE IDEAL POUR REVELER LA COMPLEXITE DES PHENOMENES. LES RESULTATS OBTENUS CONCORDENT AVEC LES RESULTATS NUMERIQUES ET EXPERIMENTAUX DES AUTRES CHERCHEURS. LE MODELE AMELIORE LA VITESSE ET LA STABILITE DES CALCULS, CONTRIBUANT AINSI A AUGMENTER LA PRECISION. IL PRESENTE D'AUTRES CAPACITES ANALYSEES QUALITATIVEMENT, A DEFAUT DE MESURES DISPONIBLES.

Physics on Manifolds

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Publisher : Springer Science & Business Media
ISBN 13 : 9401119384
Total Pages : 365 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Physics on Manifolds by : M. Flato

Download or read book Physics on Manifolds written by M. Flato and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Colloquium "Analysis, Manifolds and Physics" organized in honour of Yvonne Choquet-Bruhat by her friends, collaborators and former students, on June 3, 4 and 5, 1992 in Paris. Its title accurately reflects the domains to which Yvonne Choquet-Bruhat has made essential contributions. Since the rise of General Relativity, the geometry of Manifolds has become a non-trivial part of space-time physics. At the same time, Functional Analysis has been of enormous importance in Quantum Mechanics, and Quantum Field Theory. Its role becomes decisive when one considers the global behaviour of solutions of differential systems on manifolds. In this sense, General Relativity is an exceptional theory in which the solutions of a highly non-linear system of partial differential equations define by themselves the very manifold on which they are supposed to exist. This is why a solution of Einstein's equations cannot be physically interpreted before its global behaviour is known, taking into account the entire hypothetical underlying manifold. In her youth, Yvonne Choquet-Bruhat contributed in a spectacular way to this domain stretching between physics and mathematics, when she gave the proof of the existence of solutions to Einstein's equations on differential manifolds of a quite general type. The methods she created have been worked out by the French school of mathematics, principally by Jean Leray. Her first proof of the local existence and uniqueness of solutions of Einstein's equations inspired Jean Leray's theory of general hyperbolic systems.

Flexoelectricity in Liquid Crystals

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Publisher : World Scientific
ISBN 13 : 1848167997
Total Pages : 299 pages
Book Rating : 4.8/5 (481 download)

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Book Synopsis Flexoelectricity in Liquid Crystals by : Agnes Buka

Download or read book Flexoelectricity in Liquid Crystals written by Agnes Buka and published by World Scientific. This book was released on 2013 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book intends to give a state-of-the-art overview of flexoelectricity, a linear physical coupling between mechanical (orientational) deformations and electric polarization, which is specific to systems with orientational order, such as liquid crystals. Chapters written by experts in the field shed light on theoretical as well as experimental aspects of research carried out since the discovery of flexoelectricity. Besides a common macroscopic (continuum) description the microscopic theory of flexoelectricity is also addressed. Electro-optic effects due to or modified by flexoelectricity as well as various (direct and indirect) measurement methods are discussed. Special emphasis is given to the role of flexoelectricity in pattern-forming instabilities. While the main focus of the book lies in flexoelectricity in nematic liquid crystals, peculiarities of other mesophases (bent-core systems, cholesterics, and smectics) are also reviewed. Flexoelectricity has relevance to biological (living) systems and can also offer possibilities for technical applications. The basics of these two interdisciplinary fields are also summarized.

Submarine Mass Movements and Their Consequences

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Publisher : Springer Science & Business Media
ISBN 13 : 1402065124
Total Pages : 407 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Submarine Mass Movements and Their Consequences by : Vasilios Lykousis

Download or read book Submarine Mass Movements and Their Consequences written by Vasilios Lykousis and published by Springer Science & Business Media. This book was released on 2007-09-14 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions from leading researchers in science and engineering, this book provides a global perspective on submarine mass movements and their consequences. Authors report on new findings from fundamental as well as site-specific studies from around the world. All studies relied on the most recent technologies, including multi-beam sonar imaging techniques, 3D seismic analysis, slope stability analysis, debris flow, and tsunami modeling.

Statistical Mechanics of Elasticity

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Publisher : Courier Corporation
ISBN 13 : 0486161234
Total Pages : 497 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Statistical Mechanics of Elasticity by : J.H. Weiner

Download or read book Statistical Mechanics of Elasticity written by J.H. Weiner and published by Courier Corporation. This book was released on 2012-02-10 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced, self-contained treatment illustrates general principles and elastic behavior of solids. Topics include thermoelastic behavior of crystalline and polymeric solids, interatomic force laws, behavior of solids, and thermally activated processes. 1983 edition.

Ventricular Wall Motion

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Publisher : Thieme-Stratton Corporation
ISBN 13 : 9780865771468
Total Pages : 327 pages
Book Rating : 4.7/5 (714 download)

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Book Synopsis Ventricular Wall Motion by : Ulrich Sigwart

Download or read book Ventricular Wall Motion written by Ulrich Sigwart and published by Thieme-Stratton Corporation. This book was released on 1984 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Methods and Instrumentation for the Investigation of Groundwater Systems

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ISBN 13 :
Total Pages : 716 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Methods and Instrumentation for the Investigation of Groundwater Systems by :

Download or read book Methods and Instrumentation for the Investigation of Groundwater Systems written by and published by . This book was released on 1983 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Effective Properties of Heterogeneous Materials

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Publisher : Springer Science & Business Media
ISBN 13 : 9400757158
Total Pages : 393 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Effective Properties of Heterogeneous Materials by : Mark Kachanov

Download or read book Effective Properties of Heterogeneous Materials written by Mark Kachanov and published by Springer Science & Business Media. This book was released on 2013-01-21 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains state-of the-art reviews in the area of effective properties of heterogeneous materials - the classical field at interface of materials science and solid mechanics. The primary focus is on thermo-mechanical properties, materials science applications, as well as computational aspects and new opportunities provided by rapidly increasing computer powers. The reviews are at the level that is appropriate for a substantial community of researchers working in this field, both at universities and in the industry, and to graduate students. The book can be used as supplementary reading to graduate level courses.

Selected Papers on Linear Optical Composite Materials

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Publisher : SPIE-International Society for Optical Engineering
ISBN 13 :
Total Pages : 730 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Selected Papers on Linear Optical Composite Materials by : Akhlesh Lakhtakia

Download or read book Selected Papers on Linear Optical Composite Materials written by Akhlesh Lakhtakia and published by SPIE-International Society for Optical Engineering. This book was released on 1996 with total page 730 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in this volume include: a physical model for the daguerrotype; experimental relations of gold; electromagnetic properties of random material; and local-field effects and effective-medium theory: a microscopic perspective.

Neutron Data Booklet

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Publisher : Old City Pub Incorporated
ISBN 13 : 9780970414373
Total Pages : 210 pages
Book Rating : 4.4/5 (143 download)

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Book Synopsis Neutron Data Booklet by : A. J. Dianoux

Download or read book Neutron Data Booklet written by A. J. Dianoux and published by Old City Pub Incorporated. This book was released on 2003-01-01 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Optical Materials

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Publisher : Springer Science & Business Media
ISBN 13 : 9780387985817
Total Pages : 270 pages
Book Rating : 4.9/5 (858 download)

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Book Synopsis Nonlinear Optical Materials by : Jerome V. Moloney

Download or read book Nonlinear Optical Materials written by Jerome V. Moloney and published by Springer Science & Business Media. This book was released on 1998-08-13 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical methods play a significant role in the rapidly growing field of nonlinear optical materials. This volume discusses a number of successful or promising contributions. The overall theme of this volume is twofold: (1) the challenges faced in computing and optimizing nonlinear optical material properties; and (2) the exploitation of these properties in important areas of application. These include the design of optical amplifiers and lasers, as well as novel optical switches. Research topics in this volume include how to exploit the magnetooptic effect, how to work with the nonlinear optical response of materials, how to predict laser-induced breakdown in efficient optical devices, and how to handle electron cloud distortion in femtosecond processes.

Physical Properties of Amorphous Materials

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Publisher : Springer Science & Business Media
ISBN 13 : 1489922601
Total Pages : 448 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Physical Properties of Amorphous Materials by : David Adler

Download or read book Physical Properties of Amorphous Materials written by David Adler and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Institute for Amorphous Studies was founded in 1982 as the international center for the investigation of amorphous mate rials. It has since played an important role in promoting the und er standing of disordered matter in general. An Institute lecture series on "Fundamentals of Amorphous Materials and Devices" was held during 1982-83 with distinguished speakers from universities and industry. These events were free and open to the public ,and were attended by many representatives of the scientific community. The lectures themselves were highly successful inasmuch as they provided not only formal instruction but also an opportunity for vigorous and stimulating debate. That last element could not be captured within the pages of a book I but the lectures concentrated on the latest advances in the field I which is why their essential contents are he re reproduced in collective form. Together they constitute an interdisciplinary status report of the field. The speakers brought many different viewpoints and a variety of back ground experiences io bear on the problems involved I but though language and conventions vary I the essential unity of the concerns is very clear I as indeed are the ultimate benefits of the many-sided approach.

Canada Enters the Nuclear Age

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Publisher : McGill-Queen's Press - MQUP
ISBN 13 : 9780773516014
Total Pages : 466 pages
Book Rating : 4.5/5 (16 download)

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Book Synopsis Canada Enters the Nuclear Age by : Atomic Energy of Canada Limited

Download or read book Canada Enters the Nuclear Age written by Atomic Energy of Canada Limited and published by McGill-Queen's Press - MQUP. This book was released on 1997 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nuclear energy company has overseen the production of its own history, focusing on programs at its laboratories in Chalk River, Ontario, and Whiteshell, Manitoba between 1943 and 1985. The 16 scientists who wrote the narrative discuss the organization and operations of the laboratories, nuclear safety and radiation protection, radioisotopes, basic research, developing the CANDU reactor, managing the radioactive wastes, business development, and revenue generation. Canadian card order number: C97-900188-9. Annotation copyrighted by Book News, Inc., Portland, OR

Time Machine Tales

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Publisher : Springer
ISBN 13 : 3319488643
Total Pages : 423 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Time Machine Tales by : Paul J. Nahin

Download or read book Time Machine Tales written by Paul J. Nahin and published by Springer. This book was released on 2016-12-24 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a broad overview of time travel in science fiction, along with a detailed examination of the philosophical implications of time travel. The emphasis of this book is now on the philosophical and on science fiction, rather than on physics, as in the author's earlier books on the subject. In that spirit there are, for example, no Tech Notes filled with algebra, integrals, and differential equations, as there are in the first and second editions of TIME MACHINES. Writing about time travel is, today, a respectable business. It hasn’t always been so. After all, time travel, prima facie, appears to violate a fundamental law of nature; every effect has a cause, with the cause occurring before the effect. Time travel to the past, however, seems to allow, indeed to demand, backwards causation, with an effect (the time traveler emerging into the past as he exits from his time machine) occurring before its cause (the time traveler pushing the start button on his machine’s control panel to start his trip backward through time). Time Machine Tales includes new discussions of the advances by physicists and philosophers that have appeared since the publication of TIME MACHINES in 1999, examples of which are the chapters on time travel paradoxes. Those chapters have been brought up-to-date with the latest philosophical thinking on the paradoxes.