Non-equilibrium Dynamics of Nonlinear Wave Systems

Download Non-equilibrium Dynamics of Nonlinear Wave Systems PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 184 pages
Book Rating : 4.:/5 (758 download)

DOWNLOAD NOW!


Book Synopsis Non-equilibrium Dynamics of Nonlinear Wave Systems by : Gustavo Düring H.

Download or read book Non-equilibrium Dynamics of Nonlinear Wave Systems written by Gustavo Düring H. and published by . This book was released on 2010 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dans cette thèse des problèmes relatifs à deux sujets différents ont été étudié. Tous les deux liés à la description statistique des systèmes avec nombreux degrés de liberté, mais d'une nature très différente.La première partie de ce travail est consacrée à l'étude des systèmes d'ondes faiblement non linéaires. La théorie bien établie de la turbulence des ondes est appliquée à différents systèmes, en étudiant la validité et les limites de celle-ci. Les propriétés statistiques à long terme pour les ondes élastiques dans les plaques et coques, et les ondes capillaires dans un fluide ont été considérées en fonction d'une équation cinétique pour la répartition des densités spectrales. Parmi d'autres situations, on analyse le régime turbulent, l'effet de la dissipation et la limite non dispersive. D'autre part, la description de la dynamique d'un condensat d'ondes a été mis en place, cela élargit la théorie de la turbulence d'ondes en incluant cette structure cohérente simple.Dans la deuxième partie on a étudié le problème du signe, qui représente une grosse limitation dans de nombreuses simulations numériques. Une bonne compréhension de la mécanique statistique des échantillonnages de Monte Carlo avec le problème du signe, est réalisée par analogie avec les systèmes vitreux. Une nouvelle approche est également proposée avec l'utilisation du recuit quantique, qui, loin de résoudre le problème du signe donne une compréhension plus approfondie de la structure de celui-ci.

Pattern Formation and Dynamics in Nonequilibrium Systems

Download Pattern Formation and Dynamics in Nonequilibrium Systems PDF Online Free

Author :
Publisher : Cambridge University Press
ISBN 13 : 0521770505
Total Pages : 547 pages
Book Rating : 4.5/5 (217 download)

DOWNLOAD NOW!


Book Synopsis Pattern Formation and Dynamics in Nonequilibrium Systems by : Michael Cross

Download or read book Pattern Formation and Dynamics in Nonequilibrium Systems written by Michael Cross and published by Cambridge University Press. This book was released on 2009-07-16 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: An account of how complex patterns form in sustained nonequilibrium systems; for graduate students in biology, chemistry, engineering, mathematics, and physics.

Nonlinear Waves 1

Download Nonlinear Waves 1 PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3642742890
Total Pages : 250 pages
Book Rating : 4.6/5 (427 download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Waves 1 by : Andrei V. Gaponov-Grekhov

Download or read book Nonlinear Waves 1 written by Andrei V. Gaponov-Grekhov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1972 the Schools on Nonlinear Physics in Gorky have been a meeting place for Soviet scientists working in this field. Instead of producing for the first time English proceedings it has been decided to present a good cross section of nonlinear physics in the USSR. Thus the participants at the last School were invited to provide English reviews and research papers for these two volumes (which in the years to come will be followed by the proceedings of forthcoming schools). The first volume starts with a historical overview of nonlinear dynamics from Poincaré to the present day and touches topics like attractors, nonlinear oscillators and waves, turbulence, pattern formation, and dynamics of structures in nonequilibrium dissipative media. It then deals with structures, bistabilities, instabilities, chaos, dynamics of defects in 1d systems, self-organizations, solitons, spatio-temporal structures and wave collapse in optical systems, lasers, plasmas, reaction-diffusion systems and solids.

New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena

Download New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1468474790
Total Pages : 341 pages
Book Rating : 4.4/5 (684 download)

DOWNLOAD NOW!


Book Synopsis New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena by : Pierre Coullet

Download or read book New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena written by Pierre Coullet and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic aim of the NATO Advanced Research Workshop on "New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena: The Geometry of Nonequilibrium" was to bring together researchers from various areas of physics to review and explore new ideas regarding the organisation of systems driven far from equilibrium. Such systems are characterized by a close relationship between broken spatial and tempo ral symmetries. The main topics of interest included pattern formation in chemical systems, materials and convection, traveling waves in binary fluids and liquid crystals, defects and their role in the disorganisa tion of structures, spatio-temporal intermittency, instabilities and large-scale vortices in open flows, the mathematics of non-equilibrium systems, turbulence, and last but not least growth phenomena. Written contributions from participants have been grouped into chapters addressing these different areas. For additional clarity, the first chapter on pattern formation has been subdivided into sections. One of the main concerns was to focus on the unifying features between these diverse topics. The various scientific communities repre sented were encouraged to discuss and compare their approach so as to mutually benefit their respective fields. We hope that, to a large degree, these goals have been met and we thank all the participants for their efforts. The workshop was held in Cargese (Corsica, France) at the Institut d'Etudes Scientifiques from August 2nd to August 12th, 1988. We greatly thank Yves Pomeau and Daniel Walgraef who, as members of the organising committee, gave us valuable advice and encouragements.

Nonlinear Waves and Pattern Dynamics

Download Nonlinear Waves and Pattern Dynamics PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 3319781936
Total Pages : 238 pages
Book Rating : 4.3/5 (197 download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Waves and Pattern Dynamics by : Nizar Abcha

Download or read book Nonlinear Waves and Pattern Dynamics written by Nizar Abcha and published by Springer. This book was released on 2018-04-20 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physics of the Russian Academy of Sciences in Nizhny Novgorod (Russia). The chapters have been written by leading scientists in Nonlinear Physics, and the topics chosen so as to cover all the fields to which Prof. Ezersky himself contributed, by means of experimental, theoretical and numerical approaches. The volume will appeal to advanced students and researchers studying nonlinear waves and pattern dynamics, as well as other scientists interested in their applications in various natural media.

Nonlinear Waves 1

Download Nonlinear Waves 1 PDF Online Free

Author :
Publisher : Springer
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4.F/5 ( download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Waves 1 by : Andrei V. Gaponov-Grekhov

Download or read book Nonlinear Waves 1 written by Andrei V. Gaponov-Grekhov and published by Springer. This book was released on 1989-08-10 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1972 the Schools on Nonlinear Physics in Gorky have been a meeting place for Soviet scientists working in this field. Instead of producing for the first time English proceedings it has been decided to present a good cross section of nonlinear physics in the USSR. Thus the participants at the last School were invited to provide English reviews and research papers for these two volumes (which in the years to come will be followed by the proceedings of forthcoming schools). The first volume starts with a historical overview of nonlinear dynamics from Poincaré to the present day and touches topics like attractors, nonlinear oscillators and waves, turbulence, pattern formation, and dynamics of structures in nonequilibrium dissipative media. It then deals with structures, bistabilities, instabilities, chaos, dynamics of defects in 1d systems, self-organizations, solitons, spatio-temporal structures and wave collapse in optical systems, lasers, plasmas, reaction-diffusion systems and solids.

Nonlinear Wave Dynamics

Download Nonlinear Wave Dynamics PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9401588910
Total Pages : 197 pages
Book Rating : 4.4/5 (15 download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Wave Dynamics by : J. Engelbrecht

Download or read book Nonlinear Wave Dynamics written by J. Engelbrecht and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.

Non-Equilibrium Dynamics in Chemical Systems

Download Non-Equilibrium Dynamics in Chemical Systems PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3642701965
Total Pages : 260 pages
Book Rating : 4.6/5 (427 download)

DOWNLOAD NOW!


Book Synopsis Non-Equilibrium Dynamics in Chemical Systems by : C. Vidal

Download or read book Non-Equilibrium Dynamics in Chemical Systems written by C. Vidal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markedly apart from elementary particle physics, another current has been building up and cont i nuous ly growi ng within contemporary phys i cs for severa 1 decades, and even expanding into many other disciplines, especially chemistry, biology and, quite recently, economics. Several reasons account for this: presumably the most impor tant one lies in the fact that, whatever the specific problem, model or material concerned, the same basic mathematical features are always involved. In this way, a general phenomenology has emerged which, unlike thermodynamics, is no longer depen dent upon the details or specifics: what largely prevails is the nonlinear charac ter of the underlying dynamics. Perhaps we are witnessing the emergence of a "non linear physics"--In a way similar to the birth of "quantum physics" in the twen ties - a physics which deals with the general behaviour of systems, whatever they are or may be. Over the past fifteen years, chemical systems evolving sufficiently far from equilibrium have proved to be particularly well fitted to experimental research on nonlinear behaviour: oscillation, multistability, birhythmicity, chaotic evolution, spatial self-organization and hysteresis are displayed by chemical reactions whose number is growing each year. In this volume are collected the lectures, communica tions and posters (abstracts) presented at an international meeting entitled: "Non-Equilibrium Dynamics in Chemical Systems", held in Bordeaux (France), Septem ber 3 rd-lth, 1984.

Pattern Formation and Non-linear Dynamics of Non-equilibrium Systems

Download Pattern Formation and Non-linear Dynamics of Non-equilibrium Systems PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 234 pages
Book Rating : 4.:/5 (318 download)

DOWNLOAD NOW!


Book Synopsis Pattern Formation and Non-linear Dynamics of Non-equilibrium Systems by : Leonid Pechenik

Download or read book Pattern Formation and Non-linear Dynamics of Non-equilibrium Systems written by Leonid Pechenik and published by . This book was released on 2000 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Non-Linear Waves in Gas Dynamics and Mechanics

Download Non-Linear Waves in Gas Dynamics and Mechanics PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (227 download)

DOWNLOAD NOW!


Book Synopsis Non-Linear Waves in Gas Dynamics and Mechanics by :

Download or read book Non-Linear Waves in Gas Dynamics and Mechanics written by and published by . This book was released on 1994 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear wave propagation in gas flows, MHD, combustions, elasticity, multiphase flows etc. is studied. Shock waves which are either more or less compressive than the classical gas shocks are shown to be nonlinearly stable, but in the sense distinct from each other. This resolves the longstanding paradox on their physical admissibility by pointing out the sensitive role of dissipations. The phenomenon of non-equilibrium is systematically studied. The problem of zero relaxation limit is resolved for models in mechanics and phase transition. Nonlinear wave propagation, Mechanics, Gas dynamics.

Non-Linear Dynamics Near and Far from Equilibrium

Download Non-Linear Dynamics Near and Far from Equilibrium PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 9789048110971
Total Pages : 304 pages
Book Rating : 4.1/5 (19 download)

DOWNLOAD NOW!


Book Synopsis Non-Linear Dynamics Near and Far from Equilibrium by : J.K. Bhattacharjee

Download or read book Non-Linear Dynamics Near and Far from Equilibrium written by J.K. Bhattacharjee and published by Springer. This book was released on 2009-09-03 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text gives a detailed account of various techniques that are used in the study of dynamics of continuous systems, near as well as far from equilibrium. The analytic methods covered include diagrammatic perturbation theory, various forms of the renormalization group, and self-consistent mode coupling.

New Approaches to Nonlinear Waves

Download New Approaches to Nonlinear Waves PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 3319206907
Total Pages : 309 pages
Book Rating : 4.3/5 (192 download)

DOWNLOAD NOW!


Book Synopsis New Approaches to Nonlinear Waves by : Elena Tobisch

Download or read book New Approaches to Nonlinear Waves written by Elena Tobisch and published by Springer. This book was released on 2015-08-19 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the applicability of these novel methods and approaches to a wide class of evolutionary dispersive PDEs, e.g. equations from Benjamin-Oro, Boussinesq, Hasegawa-Mima, KdV-type, Klein-Gordon, NLS-type, Serre, Shamel , Whitham and Zakharov. This makes the book interesting for professionals in the fields of nonlinear physics, applied mathematics and fluid mechanics as well as students who are studying these subjects. The book can also be used as a basis for a one-semester lecture course in applied mathematics or mathematical physics.

Nonlinear Dispersive Wave Systems

Download Nonlinear Dispersive Wave Systems PDF Online Free

Author :
Publisher : World Scientific
ISBN 13 : 9814554960
Total Pages : 683 pages
Book Rating : 4.8/5 (145 download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Dispersive Wave Systems by : Lokenath Debnath

Download or read book Nonlinear Dispersive Wave Systems written by Lokenath Debnath and published by World Scientific. This book was released on 1992-09-09 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together a comprehensive account of major developments in the theory and applications of nonlinear dispersive waves, nonlinear water waves, KdV and nonlinear Schrodinger equations, Davey-Stewartson equation, Benjamin-Ono equation and nonlinear instability phenomena. In order to give the book a wider readership, chapters have been written by internationally known researchers who have made significant contributions to nonlinear waves and nonlinear instability. This volume will be invaluable to applied mathematicians, physicists, geophysicists, oceanographers, engineering scientists, and to anyone interested in nonlinear dynamics.

Non-Linear Wave Propagation With Applications to Physics and Magnetohydrodynamics by A Jeffrey and T Taniuti

Download Non-Linear Wave Propagation With Applications to Physics and Magnetohydrodynamics by A Jeffrey and T Taniuti PDF Online Free

Author :
Publisher : Elsevier
ISBN 13 : 0080957803
Total Pages : 381 pages
Book Rating : 4.0/5 (89 download)

DOWNLOAD NOW!


Book Synopsis Non-Linear Wave Propagation With Applications to Physics and Magnetohydrodynamics by A Jeffrey and T Taniuti by :

Download or read book Non-Linear Wave Propagation With Applications to Physics and Magnetohydrodynamics by A Jeffrey and T Taniuti written by and published by Elsevier. This book was released on 2000-04-01 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. - Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering

Dynamical Systems and Nonlinear Waves in Plasmas

Download Dynamical Systems and Nonlinear Waves in Plasmas PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 1000404765
Total Pages : 207 pages
Book Rating : 4.0/5 (4 download)

DOWNLOAD NOW!


Book Synopsis Dynamical Systems and Nonlinear Waves in Plasmas by : Santo Banerjee

Download or read book Dynamical Systems and Nonlinear Waves in Plasmas written by Santo Banerjee and published by CRC Press. This book was released on 2021-09-10 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical systems and Nonlinear Waves in Plasmas is written in a clear and comprehensible style to serve as a compact volume for advanced postgraduate students and researchers working in the areas of Applied Physics, Applied Mathematics, Dynamical Systems, Nonlinear waves in Plasmas or other nonlinear media. It provides an introduction to the background of dynamical systems, waves, oscillations and plasmas. Basic concepts of dynamical systems and phase plane analysis for the study of dynamical properties of nonlinear waves in plasmas are presented. Different kinds of waves in plasmas are introduced. Reductive perturbative technique and its applications to derive different kinds of nonlinear evolution equations in plasmas are discussed. Analytical wave solutions of these nonlinear evolution equations are presented using the concept of bifurcation theory of planar dynamical systems in a very simple way. Bifurcations of both small and arbitrary amplitudes of various nonlinear acoustic waves in plasmas are presented using phase plots and time-series plots. Super nonlinear waves and its bifurcation behaviour are discussed for various plasma systems. Multiperiodic, quasiperiodic and chaotic motions of nonlinear plasma waves are discussed in presence of external periodic force. Multistability of plasma waves is investigated. Stable oscillation of plasma waves is also presented in dissipative plasmas. The book is meant for undergraduate and postgraduate students studying plasma physics. It will also serve a reference to the researchers, scientists and faculties to pursue the dynamics of nonlinear waves and its properties in plasmas. It describes the concept of dynamical systems and is useful in understanding exciting features, such as solitary wave, periodic wave, supernonlinear wave, chaotic, quasiperiodic and coexisting structures of nonlinear waves in plasmas. The concepts and approaches, discussed in the book, will also help the students and professionals to study such features in other nonlinear media.

Nonlinear Dynamics, Chaotic and Complex Systems

Download Nonlinear Dynamics, Chaotic and Complex Systems PDF Online Free

Author :
Publisher : Cambridge University Press
ISBN 13 : 9780521582018
Total Pages : 358 pages
Book Rating : 4.5/5 (82 download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Dynamics, Chaotic and Complex Systems by : Eryk Infeld

Download or read book Nonlinear Dynamics, Chaotic and Complex Systems written by Eryk Infeld and published by Cambridge University Press. This book was released on 1997-06-19 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: The physics and mathematics of nonlinear dynamics, chaotic and complex systems constitute some of the most fascinating developments of late twentieth century science. It turns out that chaotic bahaviour can be understood, and even utilized, to a far greater degree than had been suspected. Surprisingly, universal constants have been discovered. The implications have changed our understanding of important phenomena in physics, biology, chemistry, economics, medicine and numerous other fields of human endeavor. In this book, two dozen scientists and mathematicians who were deeply involved in the "nonlinear revolution" cover most of the basic aspects of the field.

Advances In Wave Turbulence

Download Advances In Wave Turbulence PDF Online Free

Author :
Publisher : World Scientific
ISBN 13 : 9814520802
Total Pages : 294 pages
Book Rating : 4.8/5 (145 download)

DOWNLOAD NOW!


Book Synopsis Advances In Wave Turbulence by : Victor Shrira

Download or read book Advances In Wave Turbulence written by Victor Shrira and published by World Scientific. This book was released on 2013-05-10 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave or weak turbulence is a branch of science concerned with the evolution of random wave fields of all kinds and on all scales, from waves in galaxies to capillary waves on water surface, from waves in nonlinear optics to quantum fluids. In spite of the enormous diversity of wave fields in nature, there is a common conceptual and mathematical core which allows to describe the processes of random wave interactions within the same conceptual paradigm, and in the same language. The development of this core and its links with the applications is the essence of wave turbulence science (WT) which is an established integral part of nonlinear science.The book comprising seven reviews aims at discussing new challenges in WT and perspectives of its development. A special emphasis is made upon the links between the theory and experiment. Each of the reviews is devoted to a particular field of application (there is no overlap), or a novel approach or idea. The reviews cover a variety of applications of WT, including water waves, optical fibers, WT experiments on a metal plate and observations of astrophysical WT.