boltzmann-ginzburg-landau approach to simple models of active matter

Abstract : Collective motion is observed in many different biological systems like bird flocks or fish schools. In these systems, collective motion may arise without any leader or external force, and is only due to the interactions among individuals and the out of equilibrium nature of the whole system. We study simple models of such collective motion situations in order to establish universality classes of "dry" active matter, i.e. when the fluid medium in which individuals evolve is neglected. Many of such systems have already been studied at the "microscopic", particle-based, level. In this thesis, we obtain coarse-grained hydrodynamic equations of such models which we compare to the microscopic level results. Their analysis also reveals new collective properties. We introduce the "Boltzmann-Ginzburg-Landau approach" to derive our equations in a controlled manner. The equations are derived for four different Vicsek-type models. The simple polar model (original Vicsek model), a mixed case of polar particles with nematic interactions, a model of nematic particles with nematic interactions and finally a model for polar particles with metric free interactions. In each case, the obtained equations are studied analytically and numerically. We find that our equations reproduce faithfully the qualitative properties of the underlying microscopic models, such as the different observed phases and the nature of the phase transitions between them. Some new phases not previously observed in microscopic models are found. Their existence was confirmed a posteriori in further simulations of the microscopic models.
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Submitted on : Thursday, December 19, 2013 - 3:26:10 PM
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  • HAL Id : tel-00921017, version 1

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Anton Peshkov. boltzmann-ginzburg-landau approach to simple models of active matter. Other [cond-mat.other]. Université Pierre et Marie Curie - Paris VI, 2013. English. ⟨tel-00921017⟩

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