15 research outputs found
Polymer dynamics in time-dependent periodic potentials
Dynamics of a discrete polymer in time-dependent external potentials is
studied with the master equation approach. We consider both stochastic and
deterministic switching mechanisms for the potential states and give the
essential equations for computing the stationary state properties of molecules
with internal structure in time-dependent periodic potentials on a lattice. As
an example, we consider standard and modified Rubinstein-Duke polymers and
calculate their mean drift and effective diffusion coefficient in the two-state
non-symmetric flashing potential and symmetric traveling potential. Rich
non-linear behavior of these observables is found. By varying the polymer
length, we find current inversions caused by the rebound effect that is only
present for molecules with internal structure. These results depend strongly on
the polymer type. We also notice increased transport coherence for longer
polymers.Comment: 22 pages, 7 figure
Finite-size effects in dynamics of zero-range processes
The finite-size effects prominent in zero-range processes exhibiting a
condensation transition are studied by using continuous-time Monte Carlo
simulations. We observe that, well above the thermodynamic critical point, both
static and dynamic properties display fluid-like behavior up to a density
{\rho}c (L), which is the finite-size counterpart of the critical density
{\rho}c = {\rho}c (L \rightarrow \infty). We determine this density from the
cross-over behavior of the average size of the largest cluster. We then show
that several dynamical characteristics undergo a qualitative change at this
density. In particular, the size distribution of the largest cluster at the
moment of relocation, the persistence properties of the largest cluster and
correlations in its motion are studied.Comment: http://pre.aps.org/abstract/PRE/v82/i3/e03111
Characteristics of the polymer transport in ratchet systems
Molecules with complex internal structure in time-dependent periodic
potentials are studied by using short Rubinstein-Duke model polymers as an
example. We extend our earlier work on transport in stochastically varying
potentials to cover also deterministic potential switching mechanisms,
energetic efficiency and non-uniform charge distributions. We also use currents
in the non-equilibrium steady state to identify the dominating mechanisms that
lead to polymer transportation and analyze the evolution of the macroscopic
state (e.g., total and head-to-head lengths) of the polymers. Several numerical
methods are used to solve the master equations and nonlinear optimization
problems. The dominating transport mechanisms are found via graph optimization
methods. The results show that small changes in the molecule structure and the
environment variables can lead to large increases of the drift. The drift and
the coherence can be amplified by using deterministic flashing potentials and
customized polymer charge distributions. Identifying the dominating transport
mechanism by graph analysis tools is found to give insight in how the molecule
is transported by the ratchet effect.Comment: 35 pages, 17 figures, to appear in Phys. Rev.
Single-layer metal-on-metal islands driven by strong time-dependent forces
Non-linear transport properties of single-layer metal-on-metal islands driven
with strong static and time-dependent forces are studied. We apply a
semi-empirical lattice model and use master equation and kinetic Monte Carlo
simulation methods to compute observables such as the velocity and the
diffusion coefficient. Two types of time-dependent driving are considered: a
pulsed rotated field and an alternating field with a zero net force
(electrophoretic ratchet). Small islands up to 12 atoms were studied in detail
with the master equation method and larger ones with simulations. Results are
presented mainly for a parametrization of Cu on Cu(001) surface, which has been
the main system of interest in several previous studies. The main results are
that the pulsed field can increase the current in both diagonal and axis
direction when compared to static field, and there exists a current inversion
in the electrophoretic ratchet. Both of these phenomena are a consequence of
the coupling of the internal dynamics of the island with its transport. In
addition to the previously discovered "magic size" effect for islands in
equilibrium, a strong odd-even effect was found for islands driven far out of
equilibrium. Master equation computations revealed non-monotonous behavior for
the leading relaxation constant and effective Arrhenius parameters. Using cycle
optimization methods, typical island transport mechanisms are identified for
small islands.Comment: 39 pages, 20 figures, to appear in Phys. Rev. E [corrected typo of
the x-axis label in Fig. 6
Accelerated transport and growth with symmetrized dynamics
In this paper we consider a model of accelerated dynamics with the rules modified from those of the
recently proposed [Dong et al., Phys. Rev. Lett. 109, 130602 (2012)] accelerated exclusion process (AEP)
such that particle-vacancy symmetry is restored to facilitate a mapping to a solid-on-solid growth model in 1 + 1
dimensions. In addition to kicking a particle ahead of the moving particle, as in the AEP, in our model another
particle from behind is drawn, provided it is within the “distance of interaction” denoted by max. We call our
model the doubly accelerated exclusion process (DAEP). We observe accelerated transport and interface growth
and widening of the cluster size distribution for cluster sizes above max, when compared with the ordinary
totally asymmetric exclusion process (TASEP). We also characterize the difference between the TASEP, AEP,
and DAEP by computing a “staggered” order parameter, which reveals the local order in the steady state. This
order in part explains the behavior of the particle current as a function of density. The differences of the steady
states are also reflected by the behavior of the temporal and spatial correlation functions in the interface picture.peerReviewe
Totally asymmetric exclusion process fed by using a non-Poissonian clock
In this article we consider the one-dimensional totally asymmetric open-boundary exclusion process fed by
a process with power-law-distributed waiting times. More specifically, we use a modified Pareto distribution to
define the jump rate for jumps into the system. We then characterize the propagation of fluctuations through the
system by kinetic Monte Carlo simulations and by numerical evaluation of the steady-state partition function.peerReviewe