Existence results for non-smooth second order differential inclusions, Convergence result for a numerical scheme and applications for modelling inelastic collisions

We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal normal cone to a time-dependent set. Moreover we extend a numerical scheme, introduced in [8] and proved a convergence result. We propose applications in modelling inelastic collisions between rigid particles too.Comment: 22 pages, 1 figur

Micro-Macro Modelling of an Array of Spheres Interacting Through Lubrication Forces

We consider here a discrete system of spheres interacting through a lubrication force. This force is dissipative, and singular near contact: it behaves like the reciprocal of interparticle distance. We propose a macroscopic constitutive equation which is built as the natural continuous counterpart of this microscopic lubrication model. This model, which is of the newtonian type, relies on an elongational viscosity, which is proportional to the reciprocal of the local fluid fraction. We then establish the convergence in a weak sense of solutions to the discrete problem towards the solution to the partial differential equation which we identified as the macroscopic constitutive equation

Numerical Simulation of Gluey Particles

We propose here a model and a numerical scheme to compute the motion of rigid particles interacting through the lubrication force. In the case of a particle approaching a plane, we propose an algorithm and prove its convergence towards the solutions to the gluey particle model proposed by B. Maury. We propose a multi-particle version of this gluey model which is based on the projection of the velocities onto a set of admissible velocities. Then, we describe a multi-particle algorithm for the simulation of such systems and present numerical results

Numerical simulation of rigid particles in Stokes flow: lubrication correction for any (regular) shape of particles

We address the problem of numerical simulation of suspensions of rigid particles in a Stokes flow. We focus on the inclusion of the singular short range interaction effects (lubrication effects) in the simulations when the particles come close one to another. The problem is solved without introducing new hypothesis nor model. As in [Lefebvre-Lepot, Merlet, Nguyen, JFM, 2015], the key idea is to decompose the velocity and pressure flows in a sum of a singular and a regular part. In this article, the singular part is computed using an explicit asymptotic expansion of the solution when the distance goes to zero. This expansion is similar to the asymptotic expansion proposed in [Hillairet, Kelai, Asymptotic Analysis, 2015] but is more appropriate for numerical simulations of suspensions. It can be computed for any shape of particles. Using [Hillairet, Kelai, Asymptotic Analysis, 2015] as an intermediate result, we prove that the remaining part is regular in the sense that it is bounded independently of the distance. As a consequence, only a small number of degrees of freedom are necessary to obtain accurate results. The method is tested in dimension 2 for clusters of two or three aligned particles with general rigid velocities. We show that, as expected, the convergence is independent on the distance

Problèmes de contact pour des particules en écoulement cisaillé

National audienceSee http://hal.archives-ouvertes.fr/docs/00/59/28/28/ANNEX/r_X8K316T9.pd

The Sparse Cardinal Sine Decomposition applied to Stokes integral equations

International audienceNumerical simulations of two-phase flows driven by viscosity (e.g. for bubble motions in glass melting process) rely on the ability to efficiently compute the solutions to discretized Stokes equations. When using boundary element methods to track fluid interfaces, one usually faces the problem of solving linear systems with a dense matrix with a size proportional to the system number of degrees of freedom. Acceleration techniques, based on the compression of the underlying matrix and efficient matrix vector products are known (Fast Multipole Method, H-matrices, etc.) but are usually rather cumbersome to develop. More recently, a new method was proposed, called the " Sparse Cardinal Sine Decomposition " , in the context of acoustic problems to tackle this kind of problem in some generality (in particular with respect to the Green kernel of the problem). The proposed contribution aims at showing the potential applicability of the method in the context of viscous flows governed by Stokes equations

Ecoulement dense autour d'une sphère traversant un nuage de grains

Une simulation bidimensionnelle d'une sphère se déplaçant à vitesse constante à l'intérieur d'un nuage de petits grains est présentée avec une méthode de type ?'Non-Smooth Contact Dynamic'' (sans effet de la gravité). Une zone granulaire dense, appelée ?'cluster'', à fraction volumique constante se construit progressivement autour de la sphère jusqu'à ce qu'un régime stationnaire apparaisse caractérisée par une taille constante du cluster en amont de la sphère qui augmente avec la fraction volumique initiale \phi_0 du nuage. Une analyse détaillée du champ de taux de déformation et du champ de contrainte à l'intérieur du cluster révèle que, malgré les variations spatiales de ces champs, le coefficient local de friction \mu et la fraction volumique \phi dépendent uniquement du nombre d'inertie I, ce qui signifie que la rhéologie du milieu granulaire est bien locale dans cet écoulement non parallèle. Les variations spatiales de I à l'intérieur même du cluster ne dépendent pas de la vitesse de déplacement de la sphère et explore une faible gamme allant de 0.01 à 0.1. L'influence des parois latérales sur l'écoulement et les forces est ensuite étudiée

Time of Lactation and Maternal Fucosyltransferase Genetic Polymorphisms Determine the Variability in Human Milk Oligosaccharides

Rationale: Human milk oligosaccharides (HMOs) vary among mothers and genetic factors contribute to this variability.We assessed changes in HMO concentrations during the first year of lactation and the relationship with FUT2 Secretor group and FUT3 Lewis group defining genetic polymorphisms. Methods: Milk samples were collected from lactating mothers participating in the LIFE Child cohort in Leipzig, Germany. The concentrations of 24 HMOs in milk samples collected at 3 months (N = 156), 6 months (N = 122), and 12 months (N = 28) were measured using liquid chromatography. Concentrations of HMOs were compared at all time-points and were tested for their associations with FUT2 and FUT3 genetic variations by sPLS regression. Results: FUT2 SNP rs601338 was found to predominantly define the Secretor status Se-: 11.8% and it was highly correlated with 2′-fucosyllactose (2′FL, p < 0.001) and lacto-N-fucosylpentaose-I (LNFP-I, p < 0.001). FUT3 SNPs rs28362459 and rs812936 were found to define Lewis status (Le-: 5.9%) and correlated with lacto-N-fucosylpentaose-II (LNFP-II, p < 0.001). A polygenic score predicted the abundance of 2′FL levels within Secretors’ milk (adj. R2 = 0.58, p < 0.001). Mean concentrations of most of the individual HMOs, as well as the sums of the measured HMOs, the fucosylated HMOs, and the neutral HMOs were lower at 6 and 12 months compared to 3 months (p < 0.001). Conclusions: Secretor and Lewis status defined by specific FUT2 and FUT3 SNPs are confirmed to be good proxies for specific individual HMOs and milk group variabilities. The polygenic score developed here is an opportunity for clinicians to predict 2′FL levels in milk of future mothers. These results show opportunities to strengthen our understanding of factors controlling FUT2 and FUT3 functionality, the temporal changes and variability of HMO composition during lactation and eventually their significance for infant development