Bose-Einstein condensates in fast rotation

In this short review we present our recent results concerning the rotation of atomic Bose-Einstein condensates confined in quadratic or quartic potentials, and give an overview of the field. We first describe the procedure used to set an atomic gas in rotation and briefly discuss the physics of condensates containing a single vortex line. We then address the regime of fast rotation in harmonic traps, where the rotation frequency is close to the trapping frequency. In this limit the Landau Level formalism is well suited to describe the system. The problem of the condensation temperature of a fast rotating gas is discussed, as well as the equilibrium shape of the cloud and the structure of the vortex lattice. Finally we review results obtained with a quadratic + quartic potential, which allows to study a regime where the rotation frequency is equal to or larger than the harmonic trapping frequency.Comment: Laser Physics Letters 2, 275 (2005

Cellular automaton development for the study of the neighborhood effect within polycrystals stress-fields

The objective of this Ph.D. project was to develop an analytical model able to predict the heterogeneous micromechanical fields within polycrystals for a very low computational cost in order to evaluate a material fatigue life probability. Many analytical models already exist for that matter, but they have disadvantages: either they are not efficient enough to rapidly generate a large database and perform a static analysis, or the impacts of certain heterogeneities on the stress fields, such as the neighborhood effect, are neglected. The mechanisms underlying the neighborhood effect, which is the grain stress variations due to a given close environment, are unheralded or misunderstood. A finite element analysis has been carried out on this question in the case of polycrystals oriented randomly with a single phase submitted to an elastic loading. The study revealed that a grain stress level is as much dependent on the crystallographic orientation of the grain as the neighborhood effect. Approximations were drawn from this analysis leading to the development of an analytical model, the cellular automaton. The model applies to regular polycrystalline structures with spherical grains and its development was conducted in two steps: first in elasticity then in elasto-plasticity. In elasticity, the model showed excellent predictions of micromechanical in comparison to the finite element predictions. The model was then used to evaluate the worst grain-neighborhood configurations and their probability to occur. It has been shown in the case of the iron crystal that certain neighborhood configurations can increase by 2 times a grain stress level. In elasto-plasticity, the model underestimates the grains plasticity in comparison to the finite element predictions. Nonetheless, the model proved its capacity to identify the worst grain-neighborhood configurations leading important localized plasticity. It has been shown that grains elastic behaviors determine the location and the level of plasticity within polycrystals in the context of high cycle fatigue regime. The grains undergoing the highest resolved shear stress in elasticity are the grains plastifying the most in high cycle fatigue regime. A statistical study of the neighborhood effect was conducted to evaluate the probability of the true yield stress (stress level applied to the material for which the first sign of plasticity would occur in a grain). The study revealed, in the case of the 316L steel, a significant difference between the true elastic limit at 99% and 1% probability, which could be one of the causes of the fatigue life scatter often observed experimentally in high cycle fatigue regime. Further studies on the effect of a free surface and the morphology of the grains were carried out. The study showed that a free surface have the effect to spread even more the grains stress levels distributions. The neighborhood effect approximations used in the developed model were unaffected by a free area. The grains morphology also has shown to have a significant impact on the stress fields. It has been shown that in the case of a high morphology ratio, the stress variations induced by the morphology of the grains are as important as those induced by the neighborhood effect

Interactions and thermoelectric effects in a parallel-coupled double quantum dot

We investigate the nonequilibrium transport properties of a double quantum dot system connected in parallel to two leads, including intradot electron-electron interaction. In the absence of interactions the system supports a bound state in the continuum. This state is revealed as a Fano antiresonance in the transmission when the energy levels of the dots are detuned. Using the Keldysh nonequilibrium Green's function formalism, we find that the occurrence of the Fano antiresonance survives in the presence of Coulomb repulsion. We give precise predictions for the experimental detection of bound states in the continuum. First, we calculate the differential conductance as a function of the applied voltage and the dot level detuning and find that crossing points in the diamond structure are revealed as minima due to the transmission antiresonances. Second, we determine the thermoelectric current in response to an applied temperature bias. In the linear regime, quantum interference gives rise to sharp peaks in the thermoelectric conductance. Remarkably, we find interaction induced strong current nonlinearities for large thermal gradients that may lead to several nontrivial zeros in the thermocurrent. The latter property is especially attractive for thermoelectric applications.Comment: 9 pages, 8 figure

Phase field method for mean curvature flow with boundary constraints

International audienceThis paper is concerned with the numerical approximation of mean curvature flow $t \to \Omega(t)$ satisfying an additional inclusion-exclusion constraint $\Omega_1 \subset \Omega(t) \subset \Omega_2$. Classical phase field model to approximate these evolving interfaces consists in solving the Allen-Cahn equation with Dirichlet boundary conditions. In this work, we introduce a new phase field model, which can be viewed as an Allen Cahn equation with a penalized double well potential. We first justify this method by a $\Gamma$-convergence result and then show some numerical comparisons of these two different models