In the rings of Saturn, self gravity is dominated by the tidal forces from the planet. Therefore, the boulders consituting the rings can not aggregate. However, the rings evolve viscously and spread (e.g. Salmon et al. 2010). As they spread beyond the Roche radius, the tides become weaker than the self gravity, and new satellites form. I will describe this process, and show that the smallest moons of Saturn (Prometheus, Pandora, Epimetheus, Janus) most likely formed this way, less than a hundred million years ago (Charnoz et al. 2010) !

Actually, the mid-sized moons of Saturn --namely the 8 ones inside the orbit of Titan-- probably formed this way too : this model explains naturally their partial differentiation and their variable silicate/ice ratio (Charnoz, Crida et al. 2011).

Finally, I'll present an analytical, general model of this process (Crida & Charnoz 2012). We demonstrate that the spreading of rings beyond the Roche radius leads to the formation of a satellite system with a precise mass-distance distribution. This distribution fits very well that of the regular satellites of Saturn. SURPRISE 1: Uranus and Neptune's regular satellites follow the same distribution... Did they have massive rings ? SURPRISE 2: If the rings are more than 1% of the planet mass, our model predicts the formation of 1 single large satellite, like Charon or our Moon !

Conclusion: The spreading of rings beyond the Roche radius may be the most general process of satellite formation in the Solar System.

La majeure partie de l'intérieur de la Terre se comporte comme un fluide convectif, mais son enveloppe superficielle externe se refroidit de manière conductive et se comporte comme un solide. Les équations de la mécanique du solide s'appliquent en effet à de nombreuses structures observées sur Terre, généralement associées a la “tectonique des plaques”. Au premier ordre ces plaques peuvent être considérées comme des bloques rigides, mais elles endossent aussi de la deformation interne, résultant en la formation de bassins et de montagnes. Les travaux de modélisation présentés ici traitent de processus de convergence, cependant de nombreuses structures sont aussi issues de conditions extensives ou cisaillantes (par exemple la faille de San Andreas). Je citerai d'abord nos connaissances sur le comportement à la fois élastique, visqueux et cassant, de l'échelle expérimentale à l'échelle tectonique. J'illustrerai ensuite comment des scénarios classiques de mécanique tels que le flambage d'une plaque homogène s'applique à l'Ocean Indien Central, ou encore comment un indenteur rigide structure un large domaine tel que l'Himalaya.

On considère ensuite le processus de subduction en bordure de plaque, qui décrit comment une plaque passe sous l'autre, mûe par son propre excès de poids (selon les connaissances conventionelles). Je présenterai rapidement la structure des Andes Chiliennes, rectiligne sur plus de 3000 km de long. Le relief colossal de l'Altiplano au nord s'oppose au relief du sud, et la subduction est plane par endroits. Je montrerai le rôle des hétéorogeneités de comportement sur cette structuration, alors que l'identification des forces motrices de cette zone de subduction font toujours polémique. Nos travaux récents de modélisation proposent une explication selon laquelle l'enregistrement géologique de périodes de régime compressif ou extensif caracterisant le relief des Andes dépendrait de la manière dont la plaque subductante “tombe” sur la discontinuité de viscosité à 660 km de profondeur. En fonction des conditions aux limites cinématiques, une plaque en subduction peut se déposer en glissant uniformément sur cette barrière à 660 km, ou bien au contraire s'y déposer en se plissant. Dans ce cas un état de contraintes oscillant se transmet jusqu'en surface et modifie le régime des déformations. Je discuterai la validité de ce scénario, fonction de la cohérence de la plaque au fur et à mesure qu'elle s'enfonce dans le manteau et s'échauffe. L'originalité de ce travail consiste à montrer l'existence d'interactions mecaniques en profondeur capables de générer des déformations en surface, en plus de la vision classique de plumes ou point-chauds mantelliques venant percer la surface terrestre.

Capture of micron-sized magnetic particles on high gradient magnetic separators (HGMS) has been studied for decades in view of broad applications to ore beneficiation and to magnetic separation of biological cells. Filtration of magnetic nanoparticles, as small as 10-20 nm in diameter, is often considered as practically irrelevant because of the weakness of magnetic interactions as compared to Brownian effects. We show in this work that, despite a strong Brownian motion, the nanoparticles can be effectively captured by a magnetic filter element if the interparticle interactions are large enough to provoke a condensation phase transition in the vicinity of the filter element. In experiments, we observe formation of thick anisotropic “clouds” of nanoparticles around a micron-sized spherical filter element, and try to estimate the shape and the concentration profile of these clouds both in the absence and in the presence of the external flow. This study is motivated by a potential application to magnetically assisted water purification.

First part - I will show some recent experimental results with three mutants of the gliding bacterium Myxococcus xanthus. We found that mutants lacking biochemical signaling and moving unidirectionally exhibit collective motion in the form of large moving clusters at intermediate densities, while self-organize into vortices at very high densities. Our measurements indicate that there is a critical density at which arbitrary large clusters and giant number fluctuations are observed. These findings are consistent with what is known from self-propelled rod models which strongly suggests that the combined effect of self-propulsion and volume exclusion interactions is the pattern formation mechanism leading to the observed phenomena. On the other hand, if mutants reverse periodically their moving direction -- as the wild-type does -- the emerging macroscopic patterns are remarkably different, particularly at high density where the bacteria self-organize into a mesh-like structure.

Second part - Most bacteria do not leave in clean and homogeneous media, but rather in highly heterogeneous environments. Despite of this evident fact, little is known about collective motion on heterogeneous media and most, if not all, theoretical efforts have focused on homogeneous media. In the second part of the talk, I will show through a simple model that due to the presence of few heterogeneities the transition to collective motion is radically different from what we know from homogeneous media. For instance, our “homogeneous-based” intuition tells us that low noise intensities should favor collective motion. However, we found that in heterogeneous media this is no longer true. There is a optimal noise amplitude that maximizes collective motion. Counterintuitively, at vanishing noise intensities the system becomes disordered again. These results may shed light on bacterial adaptation and evolution, particularly concerning the bacterial tumbling rate.

Under quasi-static assumptions, Maxwell’s equations governing the spatial behaviour of the electromagnetic fields lead to partial differential equations (PDE) of elliptic type in domains of R³.

We will mainly consider the case of an electrical potential solution to such a PDE, which depends on the electrical conductivity and of the current density of the medium. In electroencephalography (EEG), an important application in medical engineering, a spherical model of the head is classically taken, with piecewise constant conductivity in spherical layers representing the scalp, the skull and the brain, and pointwise dipolar current sources located within the brain. It appears that the potential is then solution to Laplace equation in the outermost layers and to Laplace-Poisson equation in the innermost one (where the sources are situated). The inverse EEG source problem is the following, assuming the conductivity val- ues to be known: being given a set of pointwise values of the electrical potential (measured by electrodes) on the scalp, and the current flux, find the quantity, the locations, and the moments of the pointwise dipolar sources in the brain. We will see how to solve this issue by a first data transmission step from the scalp to the cortex (cortical mapping), followed with a singularities localisation step, performed using best approximation techniques on planar slices [1, 2]. Numerical examples will be presented, from the software FindSources3D [3]. Maxwell’s and Newton’s equation are to the effect that under suitable assumptions, many other physical quantities, like magnetic or gravitational potentials, possess such a PDE model. The particular examples of magnetic plasma confinment in tokamaks and of some geodesy problems will be briefly discussed.

References:

[1] L. Baratchart, J. Leblond, J.-P. Marmorat, Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices, Elec. Trans. Numerical Anal- ysis (ETNA), 25, 41–53, 2006.

[2] M. Clerc, J. Leblond, J.-P. Marmorat, T. Papadopoulo, Source localization in EEG using rational approximation on plane sections, Inverse Problems, 28, 055018, 2012.

[3] FindSources3D, http://www-sop.inria.fr/apics/FindSources3D/

Laser-cooled clouds of atoms constitute an original medium to revisit experiments in the field of non linear optics. Among the interesting features of cold atoms, one can cite the absence of "defects" of the samples, the possibility to engineer their optical response, and the fact that a full ab initio description of the physics is possible starting from the microscopic building block of the atom-light interaction. I will illustrate this with three examples of experiments performed at INLN, of increasing complexity (and interest): self-focussing, spatial soliton, and transverse self-organization.