Saverio Spagnolie
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MATHEMATICS COLLOQUIUM
Speaker: Saverio Spagnolie Abstract. The swimming kinematics and trajectories of many microorganisms are altered by the presence of nearby boundaries, be they solid or deformable, and often in perplexing fashion. When an organism's swimming dynamics vary near a boundary a natural question arises: is the change in behavior fluid mechanical, biological, or perhaps mediated by other physical laws? We isolate the first possibility by exploring a far-field description of swimming organisms, providing a general framework for studying the fluid-mediated modifications to swimming trajectories. We address the hydrodynamic entrapment of a self-propelled body near a stationary wall or spherical obstacle. Simulations of model equations show that the swimmer can be trapped by a spherical colloid larger than a critical size, that sub-critical interactions tend to result in short residence times on the surface, and that the basin of attraction around the colloid is set by a power-law dependence on the colloid size and dipole strength. With the introduction of Brownian fluctuations, swimmers otherwise trapped in the deterministic setting can escape from the colloid at randomly distributed times. The distribution of trapping times is governed by an Ornstein-Uhlenbeck process, resulting in nearly inverse-Gaussian or exponential distributions. Analytical predictions are found to match very favorably with the numerical simulations. We also explore the billiard-like motion of such a body inside a regular polygon and in a patterned environment, and show that the dynamics can settle towards a stable periodic orbit or can be chaotic depending on the nature of the scattering dynamics. We envision applications in bioremediation, sorting techniques, and the study of motile suspensions in heterogeneous or porous environments. |