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Author ORCID Identifier
Open Access Dissertation
Doctor of Philosophy (PhD)
Year Degree Awarded
Month Degree Awarded
Condensed Matter Physics | Statistical, Nonlinear, and Soft Matter Physics
In equilibrium, matter condenses into ordered phases due to the combined effects of inter-particle interactions and entropy. In this dissertation, we explore the self-propulsion of particles as an additional nonequilibrium consideration in the mechanisms for ordering. Our experiments employ square-shaped hard particles; in equilibrium, when particle motions are randomly directed, squares form entropically-stabilized phases in which first their orientations, and then their positions, get locked in relative to each other, depending on the density of coverage. When the square tiles are modified to have small propulsion along some body-fixed axis we find that their tendency to order is profoundly altered. Adding such 'activity'(quantified by the persistence length of motion along the mobility direction) to particles can produce new ‘phases’ and mechanisms for ordering not seen in equilibrium materials.
In the first study, we study a system of vibrated self-propelled granular particles with high persistence length on a horizontal plane within a circular boundary. The particles are square and designed to have polar motion along one body diagonal. When they hit the boundary they align along the boundary but also 'walk' along the boundary. Given a large enough initial density in the plane, particles spontaneously migrate to the boundary, form a ring, and perform a stable 1D rotational gear-like motion with a direction chosen by their net polarization. For a fully polarized single ring, we find that the collective velocity surpasses the free single-particle velocity. This collective velocity increases as the density of particles in the ring increases, which is counterintuitive for a normal traffic problem. The spatial correlations of particle velocity fluctuations decay exponentially with a length scale that increases with density. There is thus increased cooperativity in the system. However, the temporal correlation shows that velocity fluctuations are very short-lived.
In a second project, we study the effect of varying the persistence length of individual particle motion in an ensemble of squares held at fixed density. We find that adding activity to the particles qualitatively modifies their phase diagram relative to that of passive squares. At large enough activity (just as in the previous study), particles always migrate to the boundary and form a high-density ordered state. At smaller values of activity, different phases are seen as a function of density. At low density, the particles form an isotropic fluid. As the density increases, particles separate into a high-density ordered region while the remaining particles remain in the fluid state. Above a finite density, the phase coexistence curve terminates and all particles freeze into an ordered state. The start and end density of the coexistence region is found to be a function of activity. %(NM). The coexistence region emerges purely due to the effect of activity in the system. We also discuss dynamics within the dense, ordered state.
In the final project in this thesis, we studied by simulation the effect on collective behavior of changing the symmetry of single particle activity. In addition to passive squares (that is, squares with isotropic mobility), we study polar, bipolar, and chiral mobilities. For each of these choices of symmetry we also choose different axes for the activity relative to the particle shape. We thus have six different kinds of particles and compare their corresponding phase behavior. We find that different symmetries of activity have quite different phase states. For a fixed symmetry of activity, changing the direction of symmetry leads to much smaller changes in phase behavior.
Shen, Zhejun, "COLLECTIVE MOTION AND PHASE DIAGRAM OF SELF-PROPELLED VIBRATED HARD SQUARES" (2022). Doctoral Dissertations. 2570.