42 research outputs found
Geometry and topology of knotted ring polymers in an array of obstacles
We study knotted polymers in equilibrium with an array of obstacles which
models confinement in a gel or immersion in a melt. We find a crossover in both
the geometrical and the topological behavior of the polymer. When the polymers'
radius of gyration, , and that of the region containing the knot,
, are small compared to the distance b between the obstacles, the knot
is weakly localised and scales as in a good solvent with an amplitude
that depends on knot type. In an intermediate regime where ,
the geometry of the polymer becomes branched. When exceeds b, the
knot delocalises and becomes also branched. In this regime, is
independent of knot type. We discuss the implications of this behavior for gel
electrophoresis experiments on knotted DNA in weak fields.Comment: 4 pages, 6 figure
Rate dependence of current and fluctuations in jump models with negative differential mobility
Negative differential mobility is the phenomenon in which the velocity of a
particle decreases when the force driving it increases. We study this
phenomenon in Markov jump models where a particle moves in the presence of
walls that act as traps. We consider transition rates that obey local detailed
balance but differ in normalisation, the inclusion of a rate to cross a wall
and a load factor. We illustrate the full counting statistics for different
choices of the jumping rates. We also show examples of thermodynamic
uncertainty relations. The variety of behaviours we encounter highlights that
negative differential mobility depends crucially on the chosen rates and points
out the necessity that such choices should be based on proper coarse-graining
studies of a more microscopic description
Validity of the additivity principle in the weakly asymmetric exclusion process with open boundaries
The additivity principle allows a calculation of current fluctuations and
associated density profiles in large diffusive systems. In order to test its
validity in the weakly asymmetric exclusion process with open boundaries, we
use a numerical approach based on the density matrix renormalisation. With this
technique, we determine the cumulant generating function of the current and the
density profile corresponding to atypical currents in finite systems. We find
that these converge to those predicted by the additivity principle. No evidence
for dynamical phase transitions is found.Comment: 5 pages, 5 figure