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Continuous and Stochastic Descriptions of Active Matter

Abstract : This thesis purpose is to study simple "self-propelled" agents models: they are able to generate motion by consumming energy comming from their environment, without external forcing. Two models of that kind have been studied:-In the first part a Vicsek-style model has been studied, that is we particles are modeled by a couple (position,velocity) which evolution is dictated by simple rules of alignment and self-propulsion at constant speed. Here the alignment is nematic particles align along their long axis and alignment is not polar, contrarily to a polar alignment particles don't discriminate between head and tail . Compared to previous models of this type, the first novelty is the introduction of a pseudo-repulsion (in the Vicsek-spirit, modelized by a torque-like term) providing spatial extension to these particles. The second addition is a flipping rate which renders the persistence time of the direction of self-propulsion. In this part we describe several phase diagrams of this new model which show new phases not previously classified: arches but also "smectic" bands, some propreties of these structures have been measured. Hydrodynamic equations from the "Boltzmann-Ginzburg-Landau" method have been also developped, comparisons are performed: the hydrodynamic model recovers most phases and some of their propreties.-In the second part we study Neisseria Meningitidis, a bacteria which particularity is to generate pili: filamentous structures several micrometers long. By depolymerizing these structures at constant speed (~1µm/s), it is able to generate gigantic forces for the living word (~ 100pN). This bacteria has a tendancy to form spherical aggregates, showing all propreties of a liquid, in order to colonize the host organism. Viscosity and surface tension measure of these aggregates have shown the crucial role of the pili number. Using these data we've built a microscopic model which particularity is the presence of a stochastically attractive potential, that is to say that particles are transiting between an attractive state and a diffusive one. This part relates the model evolution in time. We've ben able to reproduce some aggregate propreties, in particular we've highlighted a variation of the diffusion between aggregate center and edges which fits experimental data.
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Submitted on : Wednesday, September 27, 2017 - 10:31:51 AM
Last modification on : Monday, February 10, 2020 - 6:12:22 PM


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  • HAL Id : tel-01596008, version 1



Ilyas Djafer-Cherif. Continuous and Stochastic Descriptions of Active Matter. Statistical Mechanics [cond-mat.stat-mech]. Université Paris-Saclay, 2017. English. ⟨NNT : 2017SACLS216⟩. ⟨tel-01596008⟩



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