Boundary value for a nonlinear transport equation emerging from a stochastic coagulation-fragmentation type model

We investigate the connection between two classical models of phase transition phenomena, the (discrete size) stochastic Becker-D\"oring, a continous time Markov chain model, and the (continuous size) deterministic Lifshitz-Slyozov model, a nonlinear transport partial differential equation. For general coefficients and initial data, we introduce a scaling parameter and prove that the empirical measure associated to the stochastic Becker-D\"oring system converges in law to the weak solution of the Lifshitz-Slyozov equation when the parameter goes to 0. Contrary to previous studies, we use a weak topology that includes the boundary of the state space (\ie\ the size $x=0$) allowing us to rigorously derive a boundary value for the Lifshitz-Slyozov model in the case of incoming characteristics. The condition reads $\lim_{x\to 0} (a(x)u(t)-b(x))f(t,x) = \alpha u(t)^2$ where $f$ is the volume distribution function, solution of the Lifshitz-Slyozov equation, $a$ and $b$ the aggregation and fragmentation rates, $u$ the concentration of free particles and $\alpha$ a nucleation constant emerging from the microscopic model. It is the main novelty of this work and it answers to a question that has been conjectured or suggested by both mathematicians and physicists. We emphasize that this boundary value depends on a particular scaling (as opposed to a modeling choice) and is the result of a separation of time scale and an averaging of fast (fluctuating) variables.Comment: 42 pages, 3 figures, video on supplementary materials at http://yvinec.perso.math.cnrs.fr/video.htm

La construction d’une sanction: Le cas des pénalités de retard dans les centres de loisirs de la commune d’Asnières-sur-Seine

This paper presents a natural experiment where a French city decided to fine parents who pick up their children late in municipal day-care centers. After five months of implementation of this scheme, contrary to the findings of Gneezy and Rustichini (2000a), the number of delay has been significantly decreased. We attribute this difference to three specific features of the French city sanction system: 1/ it has not been imposed top-down but built afterimplication of all stakeholders, including parents (involved in a working group); 2/ Communication towards parents in order to justify the fine focused on non-financial elements such as the problems that delay induce for day-care centers personals rather than on the financial costs of delays; 3/ the fine is proportional to the length of the delay and to the income of the parents and, in extreme cases, there is the possibility to exclude children.Cet article présente une expérience naturelle où une commune française a décidé de sanctionner financièrement les parents venant chercher leurs enfants avec retard dans les centres de loisirs communaux. Après cinq mois de mise en œuvre de ce dispositif, contrairement aux conclusions obtenues par Gneezy et Rustichini (2000a), il est constaté une diminution significative du nombre de retards. Nous attribuons cette différence à trois caractéristiques spécifiques du dispositif de sanction français : 1/ celui-ci n’a pas été imposé de manière brutale mais construit après consultation des différentes parties prenantes, y compris les parents (impliqués dans un groupe de travail) ; 2/ La communication auprès des parents pour justifierl’introduction de cette sanction a été centrée sur les motivations non financières c’est-à-dire sur les nuisances que les retards induisaient pour le personnel plutôt que sur le coût financier des retards ; 3/ la sanction financière est proportionnelle à la durée du retard et au revenu des parents et, en dernier ressors, existe la possibilité d’exclure les enfants

Characteristic spatial scale of vesicle pair interactions in a plane linear flow

We report the experimental studies on interaction of two vesicles trapped in a microfluidic analog of four-roll mill, where a plane linear flow is realized. We found that the dynamics of a single vesicle is significantly altered by the presence of another vesicle at separation distances up to about 3.2 \div 3.7 times of effective radius of the vesicles. This is supported by direct measurements of a single vesicle back-reaction on the velocity field. Thus, the experiment provides the lower bound for the interaction scale of vesicles and so the corresponding upper bound for the volume fraction \phi=0.08 \div 0.13 of non-interacting vesicle suspensions.Comment: 5 pages, 8 figures, PRE accepted for publicatio

Dynamics of Vesicles in shear and rotational flows: Modal Dynamics and Phase Diagram

Despite the recent upsurge of theoretical reduced models for vesicle shape dynamics, comparisons with experiments have not been accomplished. We review the implications of some of the recently proposed models for vesicle dynamics, especially the Tumbling-Trembling domain regions of the phase plane and show that they all fail to capture the essential behavior of real vesicles for excess areas, \Delta, greater than 0.4. We emphasize new observations of shape harmonics and the role of thermal fluctuations.Comment: (removed forgotten leftover figure files

Impact of the key determinants of a distributed planning process on the performance of a supply chain

International audienceIn today's highly competitive world, firms try to maximize value for their customers and other stakeholders through the effective management of their supply chains. Given that performance measurement considerably affects the actions of firms' decision makers, it is increasingly important to understand the key factors that can significantly affect the performance of the supply chain. Using analytical models and simulations, this article aims to identify and analyse the key determinants (both financial and nonfinancial) of a distributed planning process that affect the performance of the supply chain. The identified determinants are discussed with respect to three performance dimensions: efficiency, effectiveness, and responsiveness. Our results show that different combinations of the determining factors have varying positive or negative effects on these three performance dimensions

Tank-treading of microcapsules in shear flow

International audienceWe investigated experimentally the deformation of soft microcapsules and the dynamics of their membrane in simple shear flows. Firstly, the tank-treading motion, i.e. the rotation of the membrane, was visualized and quantified by tracking particles included in the membrane by a new protocol. The period of membrane rotation increased quadratically with the extension of the large axis. The tracking of the distance between two close micro-particles showed membrane contraction at the tips and stretching on the sides, a specific property of soft particles such as capsules. Present experimental results are discussed in regard to previous numerical simulations. This analysis showed that the variation of the tank-treading period with the Taylor parameter (deformation) cannot be explained by purely elastic membrane models. It suggests a strong effect of membrane viscosity whose order of magnitude is determined. Secondly, two distinct shapes of sheared microcapsules were observed. For moderate deformations, the shape was a steady ellipsoid in the shear plane. For larger deformations, the capsule became asymmetric and presented a S-like shape. When the viscous shear stress increased by three orders of magnitude, the small axis decreased by 70 % whereas the large axis increased by 100% before any break-up. The inclination angle decreased from 40 • to 8 • , almost aligned with the flow direction as expected by theory/numerics on capsules and experiments/theory/numerics on drops and vesicles. Whatever the microcapsule size and the concentration of proteins, the characteristic lengths of the shape, the Taylor parameter and the inclination angle satisfy master curves versus the longest axis or the normalized shear stress or the capillary number in agreement with theory for non negligible membrane viscosity in the regime of moderate deformations. Finally, we observed that very small deviation from sphericity gave rise to swinging motion, i.e. shape oscillations, in the small deformation regime. In conclusion, this study of tank-treading motion supports the role of membrane viscosity on the dynamics of microcapsules in shear flow by both independent methods which compare experimental data with numerical results in the regime of large deformations and with the theory in the regime of moderate deformations

Level 0 trigger decision unit for the LHCb experiment

The Level-0 Decision Unit (L0DU) is the central part of the first trigger level of the LHCb detector. The L0DU receives information from the Calorimeter, Muon and Pile-Up sub-triggers, with fixed latencies, at 40 MHz via 24 high speed optical fiber links running at 1.6 Gb/s. The L0DU performs simple physics algorithm to compute the decision in order to reduce the data flow down to 1 MHz for the next trigger level and a L0Block is constructed. The processing is implemented in FPGA using a 40 MHz synchronous pipelined architecture. The algorithm can be easily configured with the Experiment Control System (ECS) without FPGA reprogramming. The L0DU is a 16 layer custom board

Grandes déformations de microcapsules en écoulement élongationel et en cisaillement simple

Nous étudions expérimentalement des microcapsules dans toute la gamme de déformations accessibles avant leur rupture dans des écoulements élongationel plan et de cisaillement simple. La membrane élastique est faite de protéines réticulées et enferme une goutte de même viscosité que le fluide externe. En écoulement élongationel, nous avons développé un système micro-fluidique en croix permettant de visualiser les deux plans principaux de déformation de la capsule. L’analyse géométrique dans les deux vues permet d’identifier la loi de comportement et le coefficient de Poisson de la membrane. Pour des déformations modérées et en écoulement de cisaillement, la capsule a une forme ellipsoïdale. Au delà d’une valeur critique de déformation, la capsule devient asymétrique et présente une forme en ‘S’. Des microparticules attachées à la membrane nous permettent de quantifier localement le phénomène de ‘tank-treading’, c.à.d de rotation de la membrane. La période de rotation augmente avec la déformation. De plus, la vitesse de rotation instantanée est fortement dépendante de la position angulaire pour les grandes déformations ; les microparticules ralentissent aux pointes de la capsule

Adsorption process with carbon xerogel cylinders for Refractory Organic Compounds removal in water, coupled with innovative in situ regeneration by H2O2 electrogeneration

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