IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions

Download IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9781402040481
Total Pages : 352 pages
Book Rating : 4.0/5 (44 download)

DOWNLOAD NOW!


Book Synopsis IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions by : Tom Mullin

Download or read book IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions written by Tom Mullin and published by Springer Science & Business Media. This book was released on 2005-09-19 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exciting new direction in hydrodynamic stability theory and the transition to turbulence is concerned with the role of disconnected states or finite amplitude solutions in the evolution of disorder in fluid flows. This volume contains refereed papers presented at the IUTAM/LMS sponsored symposium on "Non-Uniqueness of Solutions to the Navier-Stokes equations and their Connection with Laminar-Turbulent Transition" held in Bristol 2004. Theoreticians and experimentalists gathered to discuss developments in understanding both the onset and collapse of disordered motion in shear flows such as those found in pipes and channels. The central objective of the symposium was to discuss the increasing amount of experimental and numerical evidence for finite amplitude solutions to the Navier-Stokes equations and to set the work into a modern theoretical context. The participants included many of the leading authorities in the subject and this volume captures much of the flavour of the resulting stimulating and lively discussions.

Seventh IUTAM Symposium on Laminar-Turbulent Transition

Download Seventh IUTAM Symposium on Laminar-Turbulent Transition PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9048137233
Total Pages : 628 pages
Book Rating : 4.0/5 (481 download)

DOWNLOAD NOW!


Book Synopsis Seventh IUTAM Symposium on Laminar-Turbulent Transition by : Philipp Schlatter

Download or read book Seventh IUTAM Symposium on Laminar-Turbulent Transition written by Philipp Schlatter and published by Springer Science & Business Media. This book was released on 2010-03-11 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of turbulent ?ow and the transition from laminar to turbulent ?ow are the most important unsolved problems of ?uid mechanics and aerodynamics. - sides being a fundamental question of ?uid mechanics, there are numerous app- cations relying on information regarding transition location and the details of the subsequent turbulent ?ow. For example, the control of transition to turbulence is - pecially important in (1) skin-friction reduction of energy ef?cient aircraft, (2) the performance of heat exchangers and diffusers, (3) propulsion requirements for - personic aircraft, and (4) separation control. While considerable progress has been made in the science of laminar to turbulent transition over the last 30 years, the c- tinuing increase in computer power as well as new theoretical developments are now revolutionizing the area. It is now starting to be possible to move from simple 1D eigenvalue problems in canonical ?ows to global modes in complex ?ows, all - companied by accurate large-scale direct numerical simulations (DNS). Here, novel experimental techniques such as modern particle image velocimetry (PIV) also have an important role. Theoretically the in?uence of non-normality on the stability and transition is gaining importance, in particular for complex ?ows. At the same time the enigma of transition in the oldest ?ow investigated, Reynolds pipe ?ow tran- tion experiment, is regaining attention. Ideas from dynamical systems together with DNS and experiments are here giving us new insights.

Sixth IUTAM Symposium on Laminar-Turbulent Transition

Download Sixth IUTAM Symposium on Laminar-Turbulent Transition PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1402041594
Total Pages : 466 pages
Book Rating : 4.4/5 (2 download)

DOWNLOAD NOW!


Book Synopsis Sixth IUTAM Symposium on Laminar-Turbulent Transition by : Rama Govindarajan

Download or read book Sixth IUTAM Symposium on Laminar-Turbulent Transition written by Rama Govindarajan and published by Springer Science & Business Media. This book was released on 2006-01-18 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of transition from laminar to turbulent flow remains to this day a major challenge in theoretical and applied mechanics. A series of IUTAM symposia held over the last twenty five years at well-known Centres of research in the subject - Novosibirsk, Stuttgart, Toulouse, Sendai and Sedona (Arizona) - has proved to be a great catalyst which has given a boost to research and our understanding of the field. At this point of time, the field is changing significantly with several emerging directions. The sixth IUTAM meeting in the series, which was held at the Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India, focused on the progress after the fifth meeting held at Sedona in 1999. The s- posium, which adhered to the IUTAM format of a single session, included seven invited lectures, fifty oral presentations and eight posters. During the course of the symposium, the following became evident. The area of laminar-turbulent transition has progressed considerably since 1999. Better theoretical tools, for handling nonlinearities as well as transient behaviour are now available. This is accompanied by an en- mous increase in the level of sophistication of both experiments and direct numerical simulations. The result has been that our understanding of the early stages of the transition process is now on much firmer footing and we are now able to study many aspects of the later stages of the transition process.

Seventh IUTAM Symposium on Laminar-Turbulent Transition

Download Seventh IUTAM Symposium on Laminar-Turbulent Transition PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 9789048137329
Total Pages : 608 pages
Book Rating : 4.1/5 (373 download)

DOWNLOAD NOW!


Book Synopsis Seventh IUTAM Symposium on Laminar-Turbulent Transition by : Philipp Schlatter

Download or read book Seventh IUTAM Symposium on Laminar-Turbulent Transition written by Philipp Schlatter and published by Springer. This book was released on 2011-11-29 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of turbulent ?ow and the transition from laminar to turbulent ?ow are the most important unsolved problems of ?uid mechanics and aerodynamics. - sides being a fundamental question of ?uid mechanics, there are numerous app- cations relying on information regarding transition location and the details of the subsequent turbulent ?ow. For example, the control of transition to turbulence is - pecially important in (1) skin-friction reduction of energy ef?cient aircraft, (2) the performance of heat exchangers and diffusers, (3) propulsion requirements for - personic aircraft, and (4) separation control. While considerable progress has been made in the science of laminar to turbulent transition over the last 30 years, the c- tinuing increase in computer power as well as new theoretical developments are now revolutionizing the area. It is now starting to be possible to move from simple 1D eigenvalue problems in canonical ?ows to global modes in complex ?ows, all - companied by accurate large-scale direct numerical simulations (DNS). Here, novel experimental techniques such as modern particle image velocimetry (PIV) also have an important role. Theoretically the in?uence of non-normality on the stability and transition is gaining importance, in particular for complex ?ows. At the same time the enigma of transition in the oldest ?ow investigated, Reynolds pipe ?ow tran- tion experiment, is regaining attention. Ideas from dynamical systems together with DNS and experiments are here giving us new insights.

IUTAM Symposium on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamics

Download IUTAM Symposium on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamics PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1402041810
Total Pages : 376 pages
Book Rating : 4.4/5 (2 download)

DOWNLOAD NOW!


Book Synopsis IUTAM Symposium on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamics by : Shigeo Kida

Download or read book IUTAM Symposium on Elementary Vortices and Coherent Structures: Significance in Turbulence Dynamics written by Shigeo Kida and published by Springer Science & Business Media. This book was released on 2006-05-05 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary vortices – those tubular swirling vortical structures with concentrated vorticity commonly observed in various kinds of turbulent flows – play key roles in turbulence dynamics (e.g. enhancement of mixing, diffusion and resistance) and characterize turbulence statistics (e.g. intermittency). Because of their dynamical importance, manipulation of elementary vortices is expected to be effective and useful in turbulence control as well as in construction of turbulence modeling. The most advanced research works on elementary vortices and related problems were presented and discussed at the IUTAM Symposium in Kyoto, Japan, 26-28 October 2004. This book contains 40 contributions presented there, the subjects of which cover vortex dynamics, coherent structures, chaotic advection and mixing, statistical properties of turbulence, rotating and stratified turbulence, instability and transition, dynamics of thin vortices, finite-time singularity, and superfluid turbulence. The book should be useful for readers of graduate and advanced levels in the field of fluid turbulence.

IUTAM Laminar-Turbulent Transition

Download IUTAM Laminar-Turbulent Transition PDF Online Free

Author :
Publisher : Springer Nature
ISBN 13 : 3030679020
Total Pages : 809 pages
Book Rating : 4.0/5 (36 download)

DOWNLOAD NOW!


Book Synopsis IUTAM Laminar-Turbulent Transition by : Spencer Sherwin

Download or read book IUTAM Laminar-Turbulent Transition written by Spencer Sherwin and published by Springer Nature. This book was released on 2021-07-30 with total page 809 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the carefully revised papers of the 9th IUTAM Symposium on Laminar-Turbulent Transition, held at the Imperial College, London, UK, in September 2019. The papers focus on the leading research in understanding transition to turbulence, which is a challenging topic of fluid mechanics and arises in many modern technologies as well as in nature. The proceedings are of interest for researchers in fluid mechanics and industry who have to handle these types of problems, such as in the aeronautical sector.

IUTAM Symposium on Computational Approaches to Multiphase Flow

Download IUTAM Symposium on Computational Approaches to Multiphase Flow PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1402049773
Total Pages : 443 pages
Book Rating : 4.4/5 (2 download)

DOWNLOAD NOW!


Book Synopsis IUTAM Symposium on Computational Approaches to Multiphase Flow by : S. Balachandar

Download or read book IUTAM Symposium on Computational Approaches to Multiphase Flow written by S. Balachandar and published by Springer Science & Business Media. This book was released on 2007-01-28 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a broad overview of the full spectrum of state-of-the-art computational activities in multiphase flow as presented by top practitioners in the field. It starts with well-established approaches and builds up to newer methods. These methods are illustrated with applications to a broad spectrum of problems involving particle dispersion and deposition, turbulence modulation, environmental flows, fluidized beds, bubbly flows, and many others.

IUTAM Symposium on Laminar Turbulent Transition ; 3

Download IUTAM Symposium on Laminar Turbulent Transition ; 3 PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (258 download)

DOWNLOAD NOW!


Book Synopsis IUTAM Symposium on Laminar Turbulent Transition ; 3 by :

Download or read book IUTAM Symposium on Laminar Turbulent Transition ; 3 written by and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Laminar-Turbulent Transition

Download Laminar-Turbulent Transition PDF Online Free

Author :
Publisher : Springer
ISBN 13 :
Total Pages : 568 pages
Book Rating : 4.F/5 ( download)

DOWNLOAD NOW!


Book Synopsis Laminar-Turbulent Transition by : Ryoji Kobayashi

Download or read book Laminar-Turbulent Transition written by Ryoji Kobayashi and published by Springer. This book was released on 1995-07-14 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International Union of Theoretical and Applied Mechanics (IUTAM) decided in 1992 to sponsor the fourth Symposium on Laminar-Turbulent Transition, Sendai/Japan, 1994. The objectives of the present Symposium were to deepen the fundamental knowledge of stability and laminar turbulent transition in three-dimensional and compressible flows and to contribute to recent developing technologies in the field. This Symposium followed the three previous IUTAM-Symposia (Stuttgart 1979, Novosibirsk 1984 and Toulouse 1989). The Scientific Committee selected two keynote lectures and 62 technical papers. The Symposium was held on the 5th to 9th of September, 1994, at the Sendai International Center in Sendai. The participants were 82 scientists from 10 countries. The keynote lectures have critically reviewed recent development of researches concerning the laminar-to-turbulent transition phenomena from the fundamental and the application aspects. Many papers presented were concerned about the detailed mechanism of the boundary layer transition (receptivity, secondary instability, turbulent spot and bypass transition). Particular emphasis was further placed on the transition of three-dimensional boundary layers on rotation systems and on swept wings. Attention was also given to compressible hypersonic flows.

Turbulence in Fluids

Download Turbulence in Fluids PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1402064357
Total Pages : 593 pages
Book Rating : 4.4/5 (2 download)

DOWNLOAD NOW!


Book Synopsis Turbulence in Fluids by : Marcel Lesieur

Download or read book Turbulence in Fluids written by Marcel Lesieur and published by Springer Science & Business Media. This book was released on 2008-03-26 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its fully updated fourth edition, this leading text in its field is an exhaustive monograph on turbulence in fluids in its theoretical and applied aspects. The authors examine a number of advanced developments using mathematical spectral methods, direct-numerical simulations, and large-eddy simulations. The book remains a hugely important contribution to the literature on a topic of great importance for engineering and environmental applications, and presents a very detailed presentation of the field.

IUTAM Symposium on Laminar Turbulent Transition ; 2

Download IUTAM Symposium on Laminar Turbulent Transition ; 2 PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (258 download)

DOWNLOAD NOW!


Book Synopsis IUTAM Symposium on Laminar Turbulent Transition ; 2 by :

Download or read book IUTAM Symposium on Laminar Turbulent Transition ; 2 written by and published by . This book was released on 1984 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

IUTAM Laminar-Turbulent Transition

Download IUTAM Laminar-Turbulent Transition PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 9783030679040
Total Pages : 0 pages
Book Rating : 4.6/5 (79 download)

DOWNLOAD NOW!


Book Synopsis IUTAM Laminar-Turbulent Transition by : Spencer Sherwin

Download or read book IUTAM Laminar-Turbulent Transition written by Spencer Sherwin and published by Springer. This book was released on 2022-08-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Invited Papers.- Coherent Structures, Dynamical Systems, Edge States.- Experiments.- Flow Control.- General Stability Analysis.- High Speed and Hypersonics.- Roughness and Receptivity.

Laminar-Turbulent Transition

Download Laminar-Turbulent Transition PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 9783642087523
Total Pages : 686 pages
Book Rating : 4.0/5 (875 download)

DOWNLOAD NOW!


Book Synopsis Laminar-Turbulent Transition by : H.F. Fasel

Download or read book Laminar-Turbulent Transition written by H.F. Fasel and published by Springer. This book was released on 2010-12-08 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of turbulent flow and the transition from laminar to turbulent flow are among the most important unsolved problems of fluid mechanics and aerodynamics. Besides being a fundamental question of fluid mechanics, there are any number of applications for information regarding transition location and the details of the subsequent turbulent flow. The JUT AM Symposium on Laminar-Turbulent Transition, co-hosted by Arizona State University and the University of Arizona, was held in Sedona, Arizona. Although four previous JUT AM Symposia bear the same appellation (Stuttgart 1979, Novosibirsk 1984, Toulouse 1989, and Sendai 1994) the topics that were emphasized at each were different and reflect the evolving nature of our understanding of the transition process. The major contributions of Stuttgart 1979 centered on nonlinear behavior and later stages of transition in two-dimensional boundary layers. Stability of closed systems was also included with Taylor vortices in different geometries. The topics of Novosibirsk 1984 shifted to resonant wave interactions and secondary instabilities in boundary layers. Pipe- and channel-flow transition were discussed as model problems for the boundary layer. Investigations of free shear layers were presented and a heavy dose of supersonic papers appeared for the first time. The character of Toulouse 1989 was also different in that 3-D boundary layers, numerical simulations, streamwise vortices, and foundation papers on receptivity were presented. Sendai 1994 saw a number of papers on swept wings and 3-D boundary layers. Numerical simulations attacked a broader range of problems.

IUTAM Laminar-Turbulent Transition

Download IUTAM Laminar-Turbulent Transition PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 9783030679019
Total Pages : 836 pages
Book Rating : 4.6/5 (79 download)

DOWNLOAD NOW!


Book Synopsis IUTAM Laminar-Turbulent Transition by : Spencer Sherwin

Download or read book IUTAM Laminar-Turbulent Transition written by Spencer Sherwin and published by Springer. This book was released on 2021-09-01 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the carefully revised papers of the 9th IUTAM Symposium on Laminar-Turbulent Transition, held at the Imperial College, London, UK, in September 2019. The papers focus on the leading research in understanding transition to turbulence, which is a challenging topic of fluid mechanics and arises in many modern technologies as well as in nature. The proceedings are of interest for researchers in fluid mechanics and industry who have to handle these types of problems, such as in the aeronautical sector.

IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers

Download IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9400917007
Total Pages : 458 pages
Book Rating : 4.4/5 (9 download)

DOWNLOAD NOW!


Book Synopsis IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers by : Peter W. Duck

Download or read book IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers written by Peter W. Duck and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most fluid flows of practical importance are fully three-dimensional, so the non-linear instability properties of three-dimensional flows are of particular interest. In some cases the three-dimensionality may have been caused by a finite amplitude disturbance whilst, more usually, the unperturbed state is three-dimensional. Practical applications where transition is thought to be associated with non-linearity in a three- dimensional flow arise, for example, in aerodynamics (swept wings, engine nacelles, etc.), turbines and aortic blood flow. Here inviscid `cross-flow' disturbances as well as Tollmien-Schlichting and Görtler vortices can all occur simultaneously and their mutual non-linear behaviour must be understood if transition is to be predicted. The non-linear interactions are so complex that usually fully numerical or combined asymptotic/numerical methods must be used. Moreover, in view of the complexity of the instability processes, there is also a growing need for detailed and accurate experimental information. Carefully conducted tests allow us to identify those elements of a particular problem which are dominant. This assists in both the formulation of a relevant theoretical problem and the subsequent physical validation of predictions. It should be noted that the demands made upon the skills of the experimentalist are high and that the tests can be extremely sophisticated - often making use of the latest developments in flow diagnostic techniques, automated high speed data gathering, data analysis, fast processing and presentation.

Laminar-Turbulent Transition

Download Laminar-Turbulent Transition PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3642824625
Total Pages : 770 pages
Book Rating : 4.6/5 (428 download)

DOWNLOAD NOW!


Book Synopsis Laminar-Turbulent Transition by : Victor V. Kozlov

Download or read book Laminar-Turbulent Transition written by Victor V. Kozlov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 770 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the suggestion of the USSR National Committee of Theo retical and Applied Mechanios the International Union of Theo retical and Applied Meohanics made a deoision to organize the Second IUTAM Symposium on Laminar-Turbulent Transition in No vosibirsk. Professor Yanenko was entrusted to be the chairman of the scientific committee. It was proposed that about 100 scientists would participate in the Symposium and that 60 lectures and invited lectures would be delivered; as for the theme of the Symposium, it was devoted to experimental and theoretical stu dies of laminar-turbulent transition in fluids and gases, i.e. the physical problems of transition and mathematical modeling in shear flows. It was planned to lay a special emphasis on fundamental mechanisms of the transition process. The scienti fio committee approved of the scope of the Symposium having considered the changes in the directions of the stUdies which took place since the First Symposium. For example, there was singled out the problem of transformation of external distur bances into eigenoscillations of shear flows, i.e. the recep tivity problem which was only slightly touched upon at the First Symposium. A new section appeared devoted to the inter relation of the flow separation phenomenon and its stability. It was planned to focus the attention on the secondary instability at transition to turbulence at the non-linear stage of the flow breakdown as well as on the loss of stability and the disturbances development in 3-D flows.

Extremes and Recurrence in Dynamical Systems

Download Extremes and Recurrence in Dynamical Systems PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 111863229X
Total Pages : 314 pages
Book Rating : 4.1/5 (186 download)

DOWNLOAD NOW!


Book Synopsis Extremes and Recurrence in Dynamical Systems by : Valerio Lucarini

Download or read book Extremes and Recurrence in Dynamical Systems written by Valerio Lucarini and published by John Wiley & Sons. This book was released on 2016-04-04 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a team of international experts, Extremes and Recurrence in Dynamical Systems presents a unique point of view on the mathematical theory of extremes and on its applications in the natural and social sciences. Featuring an interdisciplinary approach to new concepts in pure and applied mathematical research, the book skillfully combines the areas of statistical mechanics, probability theory, measure theory, dynamical systems, statistical inference, geophysics, and software application. Emphasizing the statistical mechanical point of view, the book introduces robust theoretical embedding for the application of extreme value theory in dynamical systems. Extremes and Recurrence in Dynamical Systems also features: • A careful examination of how a dynamical system can serve as a generator of stochastic processes • Discussions on the applications of statistical inference in the theoretical and heuristic use of extremes • Several examples of analysis of extremes in a physical and geophysical context • A final summary of the main results presented along with a guide to future research projects • An appendix with software in Matlab® programming language to help readers to develop further understanding of the presented concepts Extremes and Recurrence in Dynamical Systems is ideal for academics and practitioners in pure and applied mathematics, probability theory, statistics, chaos, theoretical and applied dynamical systems, statistical mechanics, geophysical fluid dynamics, geosciences and complexity science. VALERIO LUCARINI, PhD, is Professor of Theoretical Meteorology at the University of Hamburg, Germany and Professor of Statistical Mechanics at the University of Reading, UK. DAVIDE FARANDA, PhD, is Researcher at the Laboratoire des science du climat et de l’environnement, IPSL, CEA Saclay, Université Paris-Saclay, Gif-sur-Yvette, France. ANA CRISTINA GOMES MONTEIRO MOREIRA DE FREITAS, PhD, is Assistant Professor in the Faculty of Economics at the University of Porto, Portugal. JORGE MIGUEL MILHAZES DE FREITAS, PhD, is Assistant Professor in the Department of Mathematics of the Faculty of Sciences at the University of Porto, Portugal. MARK HOLLAND, PhD, is Senior Lecturer in Applied Mathematics in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter, UK. TOBIAS KUNA, PhD, is Associate Professor in the Department of Mathematics and Statistics at the University of Reading, UK. MATTHEW NICOL, PhD, is Professor of Mathematics at the University of Houston, USA. MIKE TODD, PhD, is Lecturer in the School of Mathematics and Statistics at the University of St. Andrews, Scotland. SANDRO VAIENTI, PhD, is Professor of Mathematics at the University of Toulon and Researcher at the Centre de Physique Théorique, France.