Browsing by Autor "Mario Sandoval"

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Active matter on Riemannian manifolds
(Royal Society of Chemistry, 2018) Leonardo Apaza; Mario Sandoval
We formulate the dynamics of overdamped Brownian active particles (swimmers) moving on any Riemannian 2-manifold. To characterize such dynamics at short times, an analytical expression for the variance of swimmers diffusing on any Riemmanian 2-manifold is derived. To show the generality of the present work, we apply the latter dynamics to swimmers moving on the surface of a spheroid and a torus, and offer analytical expressions for both their long-time variances and steady angular marginal probability density functions. Finally, Brownian dynamics simulations are used to validate our theoretical findings.
Ballistic behavior and trapping of self-driven particles in a Poiseuille flow
(American Physical Society, 2016) Leonardo Apaza; Mario Sandoval
We study the two- and three-dimensional dynamics of a Brownian self-driven particle at low Reynolds number in a Poiseuille flow. A deterministic analysis is also performed and we find that under certain conditions the swimmer becomes trapped, thus performing closed orbits as observed in related experiments. Further analysis enables us to provide an analytic expression to achieve this trapping phenomenon. We then turn to Brownian dynamics simulations, where we show the effect of a Poiseuille flow, self-propulsion, and confinement on the diffusion of the swimmer in both two and three dimensions. It is found that for long times the mean-square displacement (MSD) along the flow direction is always quadratic in time, whereas for shorter times (before the particle reaches the walls) its MSD has also a quartic time behavior. It is also found that self-propelled particles will spread less in a Poiseuille flow than passive ones under the same circumstances.
Brownian self-driven particles on the surface of a sphere
(American Physical Society, 2017) Leonardo Apaza; Mario Sandoval
We present the dynamics of overdamped Brownian self-propelled particles moving on the surface of a sphere. The effect of self-propulsion on the diffusion of these particles is elucidated by determining their angular (azimuthal and polar) mean-square displacement. Short- and long-times analytical expressions for their angular mean-square displacement are offered. Finally, the particles' steady marginal angular probability density functions are also elucidated.