A general formulation of Bead Models applied to flexible fibers and active filaments at low Reynolds number

This contribution provides a general framework to use Lagrange multipliers for the simulation of low Reynolds number fiber dynamics based on Bead Models (BM). This formalism provides an efficient method to account for kinematic constraints. We illustrate, with several examples, to which extent the proposed formulation offers a flexible and versatile framework for the quantitative modeling of flexible fibers deformation and rotation in shear flow, the dynamics of actuated filaments and the propulsion of active swimmers. Furthermore, a new contact model called Gears Model is proposed and successfully tested. It avoids the use of numerical artifices such as repulsive forces between adjacent beads, a source of numerical difficulties in the temporal integration of previous Bead Models.Comment: 41 pages, 15 figure

Large-scale simulation of steady and time-dependent active suspensions with the force-coupling method

We present a new development of the force-coupling method (FCM) to address the accurate simulation of a large number of interacting micro-swimmers. Our approach is based on the squirmer model, which we adapt to the FCM framework, resulting in a method that is suitable for simulating semi-dilute squirmer suspensions. Other effects, such as steric interactions, are considered with our model. We test our method by comparing the velocity field around a single squirmer and the pairwise interactions between two squirmers with exact solutions to the Stokes equations and results given by other numerical methods. We also illustrate our method's ability to describe spheroidal swimmer shapes and biologically-relevant time-dependent swimming gaits. We detail the numerical algorithm used to compute the hydrodynamic coupling between a large collection ($10^4-10 ^5$) of micro-swimmers. Using this methodology, we investigate the emergence of polar order in a suspension of squirmers and show that for large domains, both the steady-state polar order parameter and the growth rate of instability are independent of system size. These results demonstrate the effectiveness of our approach to achieve near continuum-level results, allowing for better comparison with experimental measurements while complementing and informing continuum models.Comment: 37 pages, 21 figure

Light scattering from cold rolled aluminum surfaces

We present experimental light scattering measurements from aluminum surfaces obtained by cold rolling. We show that our results are consistent with a scale invariant description of the roughness of these surfaces. The roughness parameters that we obtain from the light scattering experiment are consistent with those obtained from Atomic Force Microscopy measurements

Mechanical Integrity of 3D Rough Surfaces during Contact

Rough surfaces are in contact locally by the peaks of roughness. At this local scale, the pressure of contact can be sharply superior to the macroscopic pressure. If the roughness is assumed to be a random morphology, a well-established observation in many practical cases, mechanical indicators built from the contact zone are then also random variables. Consequently, the probability density function (PDF) of any mechanical random variable obviously depends upon the morphological structure of the surface. The contact pressure PDF, or the probability of damage of this surface can be determined for example when plastic deformation occurs. In this study, the contact pressure PDF is modeled using a particular probability density function, the generalized Lambda distributions (GLD). The GLD are generic and polymorphic. They approach a large number of known distributions (Weibull, Normal, and Lognormal). The later were successfully used to model damage in materials. A semi-analytical model of elastic contact which takes into account the morphology of real surfaces is used to compute the contact pressure. In a first step, surfaces are simulated by Weierstrass functions which have been previously used to model a wide range of surfaces met in tribology. The Lambda distributions adequacy is qualified to model contact pressure. Using these functions, a statistical analysis allows us to extract the probability density of the maximal pressure. It turns out that this density can be described by a GLD. It is then possible to determine the probability that the contact pressure generates plastic deformation

Coupled transport onto complex geometries

TOULOUSE3-BU Sciences (315552104) / SudocSudocFranceF

Étude statistique de la conductance d'un joint d'étanchéité statique

Cette thèse est motivée par l'étude de l'étanchéité des systèmes boulonnés où un joint métallique est placé entre deux brides de serrage. L'objectif est de mieux comprendre les mécanismes de la fuite en développant de nouveaux outils de calculs afin de la modéliser et l'estimer. Dans ce travail, le champ d'ouverture entre les deux surfaces en contact est modélisé par un champ Gaussien aléatoire isotrope corrélé à courte portée. Le système est découpé en pavés élémentaires représentatifs. La conductance à l'échelle du joint est déduite de l'étude statistique à l'échelle du pavé. Nous avons développé dans le cadre de l'approximation de lubrification un code de calcul fondé sur une approche réseau, qui permet de ramener le calcul de la conductance à l'échelle du pavé à un problème de résistances distribuées sur un réseau aléatoire. Le réseau est construit à partir de l'identification des points critiques du champ d'ouverture. Les maxima de ce champ sont reliés entre eux, via les cols, par des liens. La conductance d'un lien est calculée en fonction des caractéristiques géométriques du col. Dans un premier temps, on considère que le champ d'ouverture se déforme de façon purement plastique selon un modèle d'écrêtage géométrique. Prés du seuil de percolation, on trouve que l'évolution de la conductance à l'échelle du pavé suit une loi puissance nouvelle. Loin du seuil, les résultats numériques ont été favorablement comparés avec une approximation de champ moyen. Dans un deuxième temps, nous nous sommes intéressé à l'impact de déformations élastiques. Un code de calcul fondé sur l'approximation de Boussinesq a été couplé à l'approche réseau. Les résultats indiquent un impact non négligeable des déformations élastiques sur les conductances. Enfin, l'approche réseau a été adaptée pour simuler à l'aide d'un algorithme de percolation d'invasion le processus de drainage quasi-statique. Une bonne adéquation entre résultats numériques et expérimentaux a été obtenueThis work is motivated by thightness technological problems associated with metallic gasket. The objective is a better understanding of leakage mecanisms, through the development of new computationals tools. In this study, the aperture field between two rough surfaces in contact is described by a short correlated isotropic random Gaussian process. The system is studied as a set of independant elementary surfaces. Joint conductances are evalueted from a statistical study on those elementary surfaces. A computational code is developed using a network approach based on lubrification theory estimation of local conductances. The global conductance computation becomes analogous to an electrical problem for wich the resistances are distributed on a random network. The network is built from the identification of the aperture field critical points. Maxima are linked through saddle points. Bond conductances are estimated at the aperture field's saddle points. First, a purely plastic model of deformations is considered. Near percolation threshold the conductances display a power behaviour. Far from percolation threshold, numerical results are favourably compared with an effective medium approximation. Secondly, we study the impact of elastic deformations. A computational code based on Boussinesq approximation is coupled to the network approach. The results indicate a significant impact of elastic deformations on conductances. Finally, the network approach is adapted to simulate quasi-static drainage thanks to a classical invasion percolation algorithm. A good comparison between previous experiments and numerical predictions is obtained.TOULOUSE-ENSEEIHT (315552331) / SudocSudocFranceF

Learing Induced Criticality In Consumers' Adoption Pattern: A Neural Network Approach

The aim of this paper is to lay the foundations of 3 social influence based approach for the diffusion of an innovation or a technological standard. A model built on the principles of a neural network is proposed and a learning procedure is set up, making the network formation endogenous, the strength of connections among agents being determined by their shared histories, Referring to the concept of criticality developed by physicists, it shall be shown that learning, in a social structure, can lead the network to a critical state, called 'learning induced criticality, where some agents are able to exert a macroscopic influence over the network. The distribution of influence spheres' size follows a Pareto law. This approach shows an interesting similatry with that of the social coherence in sociology, whereby individuals within a social structure are led to share a close assessment of a given innovation.diffusion, adoption, social influence, network externality, learning, criticality JEL Classification: A12, A14, DI1, D83, 033,

Learing Induced Criticality In Consumers' Adoption Pattern: A Neural Network Approach

The aim of this paper is to lay the foundations of 3 social influence based approach for the diffusion of an innovation or a technological standard. A model built on the principles of a neural network is proposed and a learning procedure is set up, making the network formation endogenous, the strength of connections among agents being determined by their shared histories, Referring to the concept of criticality developed by physicists, it shall be shown that learning, in a social structure, can lead the network to a critical state, called 'learning induced criticality, where some agents are able to exert a macroscopic influence over the network. The distribution of influence spheres' size follows a Pareto law. This approach shows an interesting similatry with that of the social coherence in sociology, whereby individuals within a social structure are led to share a close assessment of a given innovation.diffusion, adoption, social influence, network externality, learning, criticality JEL Classification: A12, A14, DI1, D83, 033,