Emmanuel PLAUT. Example of an hypertext Report written with L A TEX. This is a public document.

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1 Emmanuel PLAUT Example of an hypertext Report written with L A TEX This is a public document.

2 Contents Introduction 3 1 Presentation of the corporation UL ENSMN Logo Lemta Logo Presentation of my work Teaching activities Research activities Organization Conclusion 8 A Curriculum Vitae 9 A.1 Initial training A.2 Career A.3 Main responsibility Bibliography 10

3 Introduction This is an example of a Report that you can download on the web page Please modify it! Nancy - March 13, Emmanuel PLAUT.

4 Chapter 1 Presentation of the corporation I am a Professor at Université de Lorraine (UL) and Researcher in LEMTA. My CV is available in the appendix A. 1.1 UL The Université de Lorraine is a great French University that contains ten Engineering Schools. I teach in one of them, the ENSMN. 1.2 ENSMN ENSMN is the École Nationale Supérieure des Mines de Nancy Logo I present the logo of ENSMN on figure 1.1. Fig. 1.1 : small font. Notice that the Figure number appears in bold font and that the caption appears with a

5 Chapter 1. Presentation of the corporation 5 Fig. 1.2 : This Figure appears at the top of the page because of the option [t] in the latex file. 1.3 Lemta Lemta is the Laboratoire d Énergétique et de Mécanique Théorique et Appliquée. It depends on the Centre National de la Recherche Scientifique (CNRS) and on the UL Logo I present the logo of Lemta on figure 1.2.

6 Chapter 2 Presentation of my work 2.1 Teaching activities I teach tensorial calculus, as a tool for continuum mechanics... My students should know that the stress vector T depends on the Cauchy stress tensor σ and on the normal unit vector n through the relation: T = σ n. They should also understand the physics of the equation that expresses mass conservation in a fluid: ρ t + div(ρv) = 0, or the physics of the Navier-Stokes equation: ρ dv dt [ v = ρ t + ( xv ) v Note the order of magnitude of the viscosity of a fluid ] η = 1, m/s, = ρg p + η v. for air in standard conditions. Presently one of the sophisticated topics that I teach concerns Turbulence modelling. I present to my students the K ɛ model, which I like to write using intrinsic tensor notations, as follows: ɛ t V t K t + ( V ) V = g 1 ρ P 2 3 K + 2 div[ (ν + ν t )D(V) ], (2.1) [( ) ] + ( K) V = div ν + νt K + ( ɛ) V = div [( ) ν + νt σ ɛ σ K ] ɛ + 2ν t V : D(V) ɛ, (2.2) + 2C 1ɛ ν t ɛ K V : D(V) C 2ɛ ɛ 2 K. (2.3)

7 Chapter 2. Presentation of my work 7 Task Teaching Research Theoretical proportion 50% 50% Experimental observation 60% 40% Tab. 2.1 : Sketch of the partition of my working time between Teaching and Research. Teaching activities also encompass duties linked to my responsibilities, as the Head of a Department of Mines Nancy. To close the set of equations (2.1), (2.2) and (2.3), one has to specify the turbulent or eddy viscosity ν t. It is given by ν t K 2 = C ν. (2.4) ɛ 2.2 Research activities I try to advance the study of the nonlinear dynamics of extended systems. For instance I developed for this purpose a reformulation of the Reynolds stress tensor τ created by pure bidimensional waves at the lowest nonlinear order. This work has been published in Plaut et al. (2008). It helps to analyze the instability mechanisms in shear flows, by pushing farther the study performed by Pedlosky (1987), or to better understand the form of zonal flows in rotating convection, see e.g. Morin & Dormy (2006). In Cartesian geometry xy, with x the periodic direction of the wave, the reformulation reads as follows: τ xx = 2E cx, τ yy = 2E cy, τ xy = τ yy tan α. (2.5) There E cx = 1 v 2 2, E x cy = 1 v 2 x 2 y (2.6) x are the mean kinetic energies associated to the x and y components of the wave velocity field, α is the angle between the wave separatrices and the y direction. 2.3 Organization In table 2.1 I sketch the partition of my working time between Teaching and Research. This partition evolves slowly with time, hopefully, I will soon verify an equipartition principle...

8 Conclusion I wish you a good play with L A TEX...

9 Appendix A Curriculum Vitae A.1 Initial training 1989 : École Polytechnique, Palaiseau, France 1992 : DEA (Master) of Theoretical Physics, Paris, France 1996 : PhD in Physics, Université d Orsay, France A.2 Career : Post-doc at the Theoretical Physics Institute of the University of Bayreuth, Germany : Assistant professor at École Nationale Supérieure d Électricité et de Mécanique (ENSEM), France : Professor at ENSMN, France : Researcher in Lemta A.3 Main responsibility Responsibility of the department Energy: Production, Transformation at ENSMN. In this department we have roughly, each year, 20 students at the Master 1 level, 20 students at the Master 2 level.

10 Bibliography Morin, V. & Dormy, E Dissipation mechanisms for convection in rapidly rotating spheres and the formation of banded structures. Phys. Fluids 18, Pedlosky, J Geophysical fluid dynamics. Springer-Verlag. Plaut, E., Lebranchu, Y., Simitev, R. & Busse, F. H Reynolds stresses and mean fields generated by pure waves: applications to shear flows and convection in a rotating shell. J. Fluid Mech. 602,