Fractional Laplacians and Nilpotent Lie Groups

The aim of this short article is to generalize, with a slighthly different point of view, some new results concerning the fractional powers of the Laplace operator to the setting of Nilpotent Lie Groups and to study its relationship with the solutions of a partial differential equation in the spirit of the articles of Caffarelli & Silvestre and Stinga & Torrea.Comment: 10

Efficient Delivery of Cash Transfers to the Poor: Improving the Design of a Conditional Cash Transfer Program in Equador

Many governments provide monetary transfers to low-income families. The mechanism through which these subsidies are distributed may contain several inefficiencies that diminish the net-value obtained by the recipients. In this paper, we build and estimate a behavioral dynamic model that allows us to evaluate the efficiency of current and alternative distribution mechanisms. The proposed model is simple and resembles the individual’s decision to collect the transfer. To estimate it, we use data from a cash transfer program in Ecuador where recipients incur high transaction costs each time they collect their benefits. Despite its simplicity, our model is able to replicate the observed data remarkably well. We use it to simulate alternative payment mechanisms and show that an adequate design of the delivery of payments can substantially increase the value of cash transfer programs.Cash Transfer Programs, Behavioral Model, Distribution of Payments

Frequency decay for Navier-Stokes stationary solutions

We consider stationary Navier-Stokes equations in R 3 with a regular external force and we prove exponential frequency decay of the solutions. Moreover, if the external force is small enough, we give a pointwise exponential frequency decay for such solutions according to the K41 theory. If a damping term is added to the equation, a pointwise decay is obtained without the smallness condition over the force

Modélisation des effets de déplacements atomiques induits par irradiation dans les matériaux pour la microélectronique

Les domaines de l'ingénierie spatiale et nucléaire requièrent le développement et l'utilisation de composants opto et microélectroniques spécifiques. Or, pour des applications dans les domaines cités, les composants sont immergés dans des environnements fortement radiatifs et sont donc soumis à des flux importants de particules énergétiques qui dégradent leur fonctionnement en induisant la formation de charges libres par ionisation de la matière ainsi que la création de défauts cristallins par déplacements atomiques. Ce dernier mécanisme est le sujet de la présente thèse. D'un point de vue technologique, les effets des déplacements atomiques sont assez bien connus. Par exemple, on sait qu'ils sont responsables d'une forte augmentation du courant d'obscurité mesuré dans les capteurs d'images, ou de la perte de puissance maximale délivrée par les cellules photovoltaïques. En revanche, les origines physiques fondamentales des effets mesurés technologiquement sont encore sujettes à débat. Les difficultés rencontrées quant à l'établissement du lien entre la physique et les effets observés dans les technologies résident en partie dans la durée extrêmement courte des temps caractéristiques (de la femtoseconde à la picoseconde pour une collision atomique par exemple) des phénomènes dynamiques en jeu dans les premiers instants de la dégradation d'un composant, rendant impossible ou extrêmement compliquée la réalisation d'expériences. C'est la raison pour laquelle, dans cette thèse, nous avons recours à la simulation numérique afin de mieux comprendre le lien entre phénomènes physiques et effets observés et ainsi prédire la réponse des matériaux utilisés en microélectronique aux effets de déplacements atomiques. Une chaîne de simulation multi-échelle, décrite dans ce manuscrit, a été développée en ce sens, permettant de simuler tout le processus de déplacements atomiques : l'interaction particule-matière en Monte Carlo, la propagation de la cascade de collisions dans la matière en Dynamique Moléculaire, la guérison des structures endommagées en Monte Carlo-cinétique et enfin la caractérisation ab initio de l'activité électronique des défauts suspectés comme responsables de la dégradation de composants. Toutes les étapes, excepté la dernière, ont été adressées dans cette thèse. Plus spécifiquement, nous nous sommes appliqués à améliorer la seconde étape de Dynamique Moléculaire en insistant sur le caractère stochastique des cascades de collisions et sur l'inclusion des effets électroniques. En particulier sur ce dernier aspect, une méthode basée sur des calculs ab initio de Théorie de la Fonctionnelle de la Densité Dépendante du Temps est utilisée. Les résultats des études effectuées dans le but d'améliorer l'étape de Dynamique Moléculaire sont décrits dans la thèse. De plus, les trois premières étapes de la chaîne de simulation sont appliquées à Si, Ge et aux alliages Si-Ge, et les résultats obtenus présentés dans le manuscrit.The development and usage of dedicated opto and microelectronic devices is an essential aspect of space and nuclear research and industries. However, in space and nuclear environments, devices are subject to intense flux of energetic particles jeopardizing their correct working by inducing the formation of free charges via ionization of materials as well as creation of crystalline defects following atomic displacements. The latter mechanism is the subject of the present PhD thesis. Atomic displacements are quite well known from a technological point of view. For example, it is acknowledged they are responsible for the drastic increase of dark current observed in image sensors, or for the loss of maximum output power of solar cells. Nonetheless, the fundamental physical origins of experimentally measured effects are still subject to debate. The difficulties encountered in the establishment of a clear link between the effects observed in technologies and the fundamental mechanisms are partly due to the very short (of the order of the femtosecond to the picosecond for an atomic collision for example) characteristic timescales of the dynamic process at stake. Indeed, experiments cannot cover dynamic process of so small characteristic times. This is the reason why, in this PhD thesis, we resort to numerical modelling to understand the links between basic physical mechanisms and deleterious effects witnessed in technologies and thus predict the response to atomic displacements effects of materials used in microelectronic applications. Aiming at this ultimate purpose, a multiscale simulation approach has been developed, allowing simulating the entire process of atomic displacements: particle-matter interactions with Monte Carlo techniques, collision cascades propagation using Molecular Dynamics, healing of the damaged structures with a kinetic- Monte Carlo code and finally the electronic characterization of defects thought to be responsible for devices degradation with ab initio methods. All the mentioned steps of this approach, except the last one, have been addressed in this thesis. In more details, lots of efforts have been undertaken to improve the models and methodologies employed in the second molecular dynamics step, regarding the stochastic aspects of cascades as well as the inclusion of electronic effects. Concerning this last aspect, a method based on ab initio Time-Dependent Density Function Theory calculations of electronic stopping power is employed. The results of the studies carried out with the objective of improving the second step of Molecular Dynamics are presented in this thesis. In addition, the three first steps of the global simulation approach are applied to Si, Ge and Si-Ge alloys, and obtained results are presented and discussed in the manuscript

On the existence, regularity and uniqueness of LpL^p-solutions to the steady-state 3D Boussinesq system in the whole space

We consider the steady-state Boussinesq system in the whole three-dimensional space, with the action of external forces and the gravitational acceleration. First, for $3<p\leq +\infty$ we prove the existence of weak $L^p$-solutions. Moreover, within the framework of a slightly modified system, we discuss the possibly non-existence of $L^p-$solutions for $1\leq p \leq 3$. Then, we use the more general setting of the $L^{p,\infty}-$spaces to show that weak solutions and their derivatives are H\"older continuous functions, where the maximum gain of regularity is determined by the initial regularity of the external forces and the gravitational acceleration. As a bi-product, we get a new regularity criterion for the steady-state Navier-Stokes equations. Furthermore, in the particular homogeneous case when the external forces are equal to zero; and for a range of values of the parameter $p$, we show that weak solutions are not only smooth enough, but also they are identical to the trivial (zero) solution. This result is of independent interest, and it is also known as the Liouville-type problem for the steady-state Boussinesq system.Comment: 28 page

On the regularity of very weak solutions for an elliptic coupled system of liquid crystal flows

We consider here an elliptic coupled system describing the dynamics of liquid crystals flows. This system is posed on the whole n-dimensional space. We introduce first the notion of very weak solutions for this system. Then, within the fairly general framework of the Morrey spaces, we derive some sufficient conditions on the very weak solutions which improve their regularity. As a bi-product, we also prove a new regularity criterium for the time-independing Navier-Stokes equations.Comment: 14 page

Asymptotic behavior of a generalized Navier-Stokes-Bardina's model and applications to related models

We consider here a general theoretical equation on the whole three-dimensional space, which contains as a particular case some relevant equations of the fluid dynamics as the Navier-Stokes-Bardina's model, the fractional and the classical Navier-Stokes equations with an additional drag/friction term. These equations arise from ocean and atmospheric models. For the general equation, we study first the existence and in some cases the uniqueness of finite energy solutions. Then, we use a general framework to study their long behavior with respect to the weak and the strong topology of the phase space. We thus prove the existence of a weak global attractor and in some cases the existence of a strong global attractor. Moreover, we study some sufficient conditions to insure the weak global attractor becomes a strong global attractor. As a bi-product, we obtain some new results on the long time description of the fractional and classical Navier-Stokes models with a damping term.Comment: 29 page