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Loopy Lévy flights enhance tracer diffusion in active suspensions
##manager.scheduler.building##: Edificio Santa Maria
##manager.scheduler.room##: Auditorio San Agustin
Date: 2019-07-10 12:00 PM – 03:45 PM
Last modified: 2019-06-14
Abstract
The diffusion process followed by a tracer in a medium out of equilibrium typically exhibits anomalous diffusive characteristics that cannot be captured by Brownian motion. Modeling the tracer fluctuating dynamics is thus a challenging task that can provide fundamental insight into the rheological and thermodynamic properties of active systems. Prototypical active media are suspensions of swimming microorganisms, like algae and bacteria, where the tracer is dragged by the hydrodynamic flow generated by the swimmers. Several experiments have characterized the tracer diffusion in dilute conditions in terms of a greatly enhanced diffusion coefficient, non-Gaussian tails of the displacement statistics, and crossover phenomena from non-Gaussian to Gaussian scaling. Despite the abundance of experimental results, there is so far no comprehensive theory that can describe all the observed diffusional characteristics of the tracer. Here we present a theoretical framework of the enhanced tracer diffusion in active suspensions from microscopic dynamics by coarse-graining the hydrodynamic interactions between the tracer and the active particles as a stochastic process. The random driving force in the Langevin equation of motion is a colored Lévy Poisson process that induces power-law distributed position displacements. This theory predicts a non-monotonic transition of the scaling exponents of the displacement statistics at different timescales, manifest in the distribution tail becoming fatter from short to intermediate timescales and converging to a Gaussian scaling for long ones. Our framework not only provides the toolkit necessary to characterize theoretically the tracer diffusion in active suspensions but also paves the way to the study of the tracer stochastic thermodynamics.