The dynamics of singularities in passive, driven, and active matter
by Jacopo Romano
Date of Examination:2024-06-20
Date of issue:2024-12-13
Advisor:Prof. Dr. Ramin Golestanian
Referee:Prof. Dr. Ramin Golestanian
Referee:Prof. Dr. Marcus Mueller
Referee:Prof. Dr. Timo Betz
Persistent Address:
http://dx.doi.org/10.53846/goediss-10851
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Abstract
English
Out-of-equilibrium statistical physics studies the time evolution of large collections of particles in terms of a reduced number of meso- and macroscopic observables. Their nature emerge from of the underlying microscopic theory, with some notable examples being the density for motile particles, the magnetization for Ising-like spins, and the orientation for aligning polar and nematic particles. At the mesoscopic level, these observables can be described in terms of a field theory, which specifies their value as a function of space and time. Topological constraints can induce the formation of singularities in these fields, such as point defects in two-dimensional liquid crystals, domain walls in magnetic systems, and interfaces in phase-separating mixtures. Despite the importance of the study of these defects for the characterization of the large-scale behaviour of the system, the description of their out-of-equilibrium motion still poses unsolved questions. The aim of this thesis is to address the problem, by de- termining the dynamics of the singularities from the underlying field theory and study its consequence on the large-scale behoaviour of the system under consideration. We start from passive matter, which evolve to minimize their free energy. For polar and nematic systems in two dimensions, the relevant singularities are point defects in the angular field. We show how the presence and motion of the defects affects the angular field in diffusive systems. We do so providing the exact expression for the orientation created by multiple moving defects, which we find to depend on their past trajectories and thus to be nonlocal in time. Our results lead to so far unnoticed structures in the orientation field of moving defects which we discuss in light of existing experimental results. We then show how the equation of motion of point defects, domain walls, disclination lines and any other singularities can be understood with one unifying mathematical framework. We will use this framework to obtain an analytical description of two long-lasting problems in point-defects motion, namely the scale dependence of the defect mobility and the role of elastic anisotropy in the motion of defects in liquid crystals. We then turn our attention to conserved systems in which the material proper- ties are modulated in space and time. We study the effect of such modulations on the motion of the interfaces, showing that space dependencies in the surface tension and chemical potential induce two new forces, which are of surface and bulk type respectively. We use our results to study non-isothermal systems, quantifying ther- mophoretic motion experienced by droplets of phase-separating binary mixtures. Our analysis shows that the effective force due to temperature gradients can change signs depending on the size of the droplet due to the competition of bulk and surface con- tributions. Finally, we turn our attention to active matter, in which the microscopic components can perform work to drive the system far from equilibrium. In partic- ular, we study the behavior of phase-separating mixtures with chemically mediated interaction, by supposing that the phase-separating species can produce a chemical that is in turn able to affect their surface tension. For self-chemotactic mixtures, the activity causes the interface of a droplet to undergo shape instabilities, as well as caus- ing reverse Ostwald ripening and affecting coalescence. When two chemically inter- acting mixtures are combined, the non-reciprocal interaction cause the formation of self-propelling clusters. Contrary to what is often observed, these droplets display self-propulsion with purely attractive interactions, due to the non-local nature of the forces governing their behavior.
Keywords: Driven systems; Active matter; Out-of-equilibrium thermodynamics; Topological defects; Liquid crystals; Non-reciprocal interactions
