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Study of a non-Galilean Hamiltonian liquid : collective motion without activity

Abstract : Collective motion, the spontaneous ordering of the velocities across a macroscopic system, is a hallmark of living systems like flocks of birds.It is captured by models of self-propelled particles, that are usually active: they do not conserve energy nor momentum. In my thesis, using notions from the theory of liquids, magnetism, and statistical mechanics, I study a conservative model of collective motion, composed of particles that carry spins, which are coupled to their velocities. I show that the alignment of spins creates an effective attraction, that is responsible for a phase separation between an isotropic gas and a ferroliquid. This phase separation ends in a tricritical point, from which stems the Curie line. I then establish the full phase diagram of the model with a spin-velocity coupling, varying its amplitude, the number of particles, the density, and the temperature.The conservation of momentum imposes that all polar phases move collectively. At low temperatures and densities, I show that the system spontaneously generates alignment defects so as to stop moving, and thus escapes a high kinetic energy cost. I also show that the system can go from an apolar state to a polar one as the temperature increases, betraying an order-by-disorder phenomenon. Finally, I show that the dynamics of the system is well described by an effective model of self-propelled particles, with a rotational inertia that soars at the rigidity transition. At high inertia, the system moves with spontaneous turns and rotations caused by the conservation of angular momentum.
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Submitted on : Friday, September 17, 2021 - 12:36:09 PM
Last modification on : Saturday, September 18, 2021 - 3:32:31 AM


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  • HAL Id : tel-03347594, version 1


Mathias Casiulis. Study of a non-Galilean Hamiltonian liquid : collective motion without activity. Condensed Matter [cond-mat]. Sorbonne Université, 2019. English. ⟨NNT : 2019SORUS647⟩. ⟨tel-03347594⟩



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