19 research outputs found
Fluctuations of a long, semiflexible polymer in a narrow channel
We consider an inextensible, semiflexible polymer or worm-like chain, with
persistence length and contour length , fluctuating in a cylindrical
channel of diameter . In the regime , corresponding to a long,
tightly confined polymer, the average length of the channel
occupied by the polymer and the mean square deviation from the average vary as
and , respectively, where
and are dimensionless amplitudes. In earlier work
we determined and the analogous amplitude for a
channel with a rectangular cross section from simulations of very long chains.
In this paper we estimate and from the simulations.
The estimates are compared with exact analytical results for a semiflexible
polymer confined in the transverse direction by a parabolic potential instead
of a channel and with a recent experiment. For the parabolic confining
potential we also obtain a simple analytic result for the distribution of
or radial distribution function, which is asymptotically exact
for large and has the skewed shape seen experimentally.Comment: 21 pages, including 4 figure
First-passage and extreme-value statistics of a particle subject to a constant force plus a random force
We consider a particle which moves on the x axis and is subject to a constant
force, such as gravity, plus a random force in the form of Gaussian white
noise. We analyze the statistics of first arrival at point of a particle
which starts at with velocity . The probability that the particle
has not yet arrived at after a time , the mean time of first arrival,
and the velocity distribution at first arrival are all considered. We also
study the statistics of the first return of the particle to its starting point.
Finally, we point out that the extreme-value statistics of the particle and the
first-passage statistics are closely related, and we derive the distribution of
the maximum displacement .Comment: Contains an analysis of the extreme-value statistics not included in
first versio
Occupation time statistics of the random acceleration model
The random acceleration model is one of the simplest non-Markovian stochastic
systems and has been widely studied in connection with applications in physics
and mathematics. However, the occupation time and related properties are
non-trivial and not yet completely understood. In this paper we consider the
occupation time of the one-dimensional random acceleration model on the
positive half-axis. We calculate the first two moments of analytically
and also study the statistics of with Monte Carlo simulations. One goal
of our work was to ascertain whether the occupation time and the time
at which the maximum of the process is attained are statistically
equivalent. For regular Brownian motion the distributions of and
coincide and are given by L\'evy's arcsine law. We show that for randomly
accelerated motion the distributions of and are quite similar but
not identical. This conclusion follows from the exact results for the moments
of the distributions and is also consistent with our Monte Carlo simulations.Comment: 10 pages, 4 figure