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SUMMARY:Microscopic derivation of coloured Lévy flights in active swimmer
s' suspensions
DTSTART;VALUE=DATE-TIME:20170908T073500Z
DTEND;VALUE=DATE-TIME:20170908T075000Z
DTSTAMP;VALUE=DATE-TIME:20230206T091200Z
UID:indico-contribution-48@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Adrian Baule (Queen Mary University of London)\, Kiy
oshi Kanazawa (Institute of Innovative Research\, Tokyo Institute of Techn
ology)\, Tomohiko G. Sano (Department of Physical Sciences\, Ritsumeikan U
niversity)\, Andrea Cairoli (Imperial College London)\n\nThe motion of a t
racer particle in a complex medium typically exhibits anomalous diffusive
patterns\, characterised\, e.g\, by a non-liner mean-squared displacement
and/or non-Gaussian statistics. \nModelling such fluctuating dynamics is
in general a challenging task\, that provides\, despite all\, a fundamenta
l tool to probe the rheological properties of the environment. \nA promi
nent example is the dynamics of a tracer in a suspension of swimming micro
organisms\, like bacteria\, which is driven by the hydrodynamic fields gen
erated by the active swimmers. \nFor dilute systems\, several experiments
confirmed the existence of non-Gaussian fat tails in the displacement dist
ribution of the probe particle\, that has been recently shown to fit well
a truncated Lévy distribution. \nThis result was obtained by applying an
argument first proposed by Holtsmark in the context of gravitation: the f
orce acting on the tracer is the superposition of the hydrodynamic fields
of spatially random distributed swimmers. \nThis theory\, however\, does
not clarify the stochastic dynamics of the tracer\, nor it predicts the n
on monotonic behaviour of the non-Gaussian parameter of the displacement d
istribution. \nHere we derive the Langevin description of the stochast
ic motion of the tracer from microscopic dynamics using tools from kinetic
theory. \nThe random driving force in the equation of motion is a coloure
d Lévy Poisson process\, that induces power-law distributed position disp
lacements. \nThis theory predicts a novel transition of their characterist
ic exponents at different timescales. For short ones\, the Holtzmark-type
scaling exponent is recovered\; for intermediate ones\, it is larger. \nCo
nsistently with previous works\, for even longer ones the truncation appea
rs and the distribution converge to a Gaussian. \nOur approach allows
to employ well established functional methods to characterize the displac
ement statistics and correlations of the tracer. In particular\, it qualit
atively reproduces the non monotonic behaviour of the non-Gaussian paramet
er measured in recent experiments.\n\nhttps://zakopane.if.uj.edu.pl/event/
4/contributions/48/
LOCATION:56
RELATED-TO:indico-event-4@zakopane.if.uj.edu.pl
URL:https://zakopane.if.uj.edu.pl/event/4/contributions/48/
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