Speaker
Tobias Ambjörnsson
(Computational Biology and Biological Physics, Lund University)
Description
There is an increasing amount of interest in the problem of
INTERACTING random walkers (due to the strong connection of
this problem to the fields of, for instance, biophysics,
nanofluidics, and cell biology). We have focused on the
non-equilibrium problem of interacting walkers in (quasi)one
dimensional systems, so called single-file diffusion (SFD),
where we recently showed that the tracer paricle motion in
an SFD system belong to the same universality class as that
of fractional Langevin dynamics [1]. An interesting, not yet
fully understood, problem in this field is that of
first-passage times for this type of non-Markovian dynamics.
We have investigated the first passage time densities (FPTD)
of a tracer particle in a SFD system whose population is:
(i) homogeneous i.e. all particles having the same dffusion
constant and (ii) heterogeneous with diffusion constants
drawn from a heavy-tailed power-law distribution. Extensive
stochastic SFD simulations are performed and compared to two
analytical estimates: the Method of Images approximation
(MIA) and the Willemski-Fixman approximation (WFA). We find
that the MIA cannot approximate well any temporal scale of
the FPTD. Our exact inversion of the Willemski-Fixman
integral equation captures the long-term power-law exponent
predicted by Molchan [1999] for fractional Brownian motion
for certain Hurst exponents. A simple new functional form is
proposed to describe the FPTD for all times, and to guide
further research into this phenomenon.
[1] T. Ambjornsson, L. Lizana, A. Taloni, E. Barkai and M.A.
Lomholt, Foundation of fractional Langevin equations:
Harmonization of a many-body problem, Phys. Rev. E 81,
051118 (2010).
[2]. L. P. Sanders and T. Ambjornsson, in preparation.
Primary author
Tobias Ambjörnsson
(Computational Biology and Biological Physics, Lund University)
