10 research outputs found
Quantitative Tube Model for Semiflexible Polymer Solutions
We develop a analytical and quantitative theory of the tube model concept for
entangled networks of semiflexible polymers. The absolute value of the tube
diameter L_perp is derived as a function of the polymers' persistence length
l_p and mesh size xi of the network. To leading order we find L_\perp = 0.32
xi^{6/5} l_p^{-1/5}, which is consistent with known asymptotic scaling laws.
Additionally, our theory provides corrections to scaling that account for
finite polymer length effects and are dominated by the mesh size to polymer
length ratio. We support our analytical studies by extensive computer
simulations. These allow to verify assumptions essential to our theoretical
description and provide an excellent agreement with the analytically calculated
tube diameter. Furthermore, we present simulation data for the distribution
function of tube widths in the network.Comment: 13 pages, 10 figure
Generic principles of active transport
Nonequilibrium collective motion is ubiquitous in nature and often results in
a rich collection of intringuing phenomena, such as the formation of shocks or
patterns, subdiffusive kinetics, traffic jams, and nonequilibrium phase
transitions. These stochastic many-body features characterize transport
processes in biology, soft condensed matter and, possibly, also in nanoscience.
Inspired by these applications, a wide class of lattice-gas models has recently
been considered. Building on the celebrated {\it totally asymmetric simple
exclusion process} (TASEP) and a generalization accounting for the exchanges
with a reservoir, we discuss the qualitative and quantitative nonequilibrium
properties of these model systems. We specifically analyze the case of a
dimeric lattice gas, the transport in the presence of pointwise disorder and
along coupled tracks.Comment: 21 pages, 10 figures. Pedagogical paper based on a lecture delivered
at the conference on "Stochastic models in biological sciences" (May 29 -
June 2, 2006 in Warsaw). For the Banach Center Publication
Bulk-driven non-equilibrium phase transitions in a mesoscopic ring
We study a periodic one-dimensional exclusion process composed of a driven
and a diffusive part. In a mesoscopic limit where both dynamics compete we
identify bulk-driven phase transitions. We employ mean-field theory
complemented by Monte-Carlo simulations to characterize the emerging
non-equilibrium steady states. Monte-Carlo simulations reveal interesting
correlation effects that we explain phenomenologically.Comment: 4 pages, 3 figure