2,893 research outputs found
Probabilistic Phase Space Trajectory Description for Anomalous Polymer Dynamics
It has been recently shown that the phase space trajectories for the
anomalous dynamics of a tagged monomer of a polymer --- for single polymeric
systems such as phantom Rouse, self-avoiding Rouse, Zimm, reptation, and
translocation through a narrow pore in a membrane; as well as for
many-polymeric system such as polymer melts in the entangled regime --- is
robustly described by the Generalized Langevin Equation (GLE). Here I show that
the probability distribution of phase space trajectories for all these
classical anomalous dynamics for single polymers is that of a fractional
Brownian motion (fBm), while the dynamics for polymer melts between the
entangled regime and the eventual diffusive regime exhibits small, but
systematic deviations from that of a fBm.Comment: 8 pages, two figures, 3 eps figure files, minor changes,
supplementary material included moved to the appendix, references expanded,
to appear in J. Phys.: Condens. Matte
Pore-blockade Times for Field-Driven Polymer Translocation
We study pore blockade times for a translocating polymer of length ,
driven by a field across the pore in three dimensions. The polymer performs
Rouse dynamics, i.e., we consider polymer dynamics in the absence of
hydrodynamical interactions. We find that the typical time the pore remains
blocked during a translocation event scales as ,
where is the Flory exponent for the polymer. In line with our
previous work, we show that this scaling behaviour stems from the polymer
dynamics at the immediate vicinity of the pore -- in particular, the memory
effects in the polymer chain tension imbalance across the pore. This result,
along with the numerical results by several other groups, violates the lower
bound suggested earlier in the literature. We discuss why
this lower bound is incorrect and show, based on conservation of energy, that
the correct lower bound for the pore-blockade time for field-driven
translocation is given by , where is the viscosity of
the medium surrounding the polymer.Comment: 14 pages, 6 figures, slightly shorter than the previous version; to
appear in J. Phys.: Cond. Ma
An Elementary Proof of Lyapunov Exponent Pairing for Hard-Sphere Systems at Constant Kinetic Energy
The conjugate pairing of Lyapunov exponents for a field-driven system with
smooth inter-particle interaction at constant total kinetic energy was first
proved by Dettmann and Morriss [Phys. Rev. E {\bf 53}, R5545 (1996)] using
simple methods of geometry. Their proof was extended to systems interacting via
hard-core inter-particle potentials by Wojtkowski and Liverani [Comm. Math.
Phys. {\bf 194}, 47 (1998)], using more sophisticated methods. Another, and
somewhat more direct version of the proof for hard-sphere systems has been
provided by Ruelle [J. Stat. Phys. {\bf 95}, 393 (1999)]. However, these
approaches for hard-sphere systems are somewhat difficult to follow. In this
paper, a proof of the pairing of Lyapunov exponents for hard-sphere systems at
constant kinetic energy is presented, based on a very simple explicit geometric
construction, similar to that of Ruelle. Generalizations of this construction
to higher dimensions and arbitrary shapes of scatterers or particles are
trivial. This construction also works for hard-sphere systems in an external
field with a Nos\'e-Hoover thermostat. However, there are situations of
physical interest, where these proofs of conjugate pairing rule for systems
interacting via hard-core inter-particle potentials break down.Comment: 16 pages, 4 figures, to appear in J. Stat. Phy
Fluctuating Fronts as Correlated Extreme Value Problems: An Example of Gaussian Statistics
In this paper, we view fluctuating fronts made of particles on a
one-dimensional lattice as an extreme value problem. The idea is to denote the
configuration for a single front realization at time by the set of
co-ordinates of the
constituent particles, where is the total number of particles in that
realization at time . When are arranged in the ascending order
of magnitudes, the instantaneous front position can be denoted by the location
of the rightmost particle, i.e., by the extremal value
. Due to interparticle
interactions, at two different times for a single front
realization are naturally not independent of each other, and thus the
probability distribution [based on an ensemble of such front
realizations] describes extreme value statistics for a set of correlated random
variables. In view of the fact that exact results for correlated extreme value
statistics are rather rare, here we show that for a fermionic front model in a
reaction-diffusion system, is Gaussian. In a bosonic front model
however, we observe small deviations from the Gaussian.Comment: 6 pages, 3 figures, miniscule changes on the previous version, to
appear in Phys. Rev.
Front Propagation and Diffusion in the A <--> A + A Hard-core Reaction on a Chain
We study front propagation and diffusion in the reaction-diffusion system A
A + A on a lattice. On each lattice site at most one A
particle is allowed at any time. In this paper, we analyze the problem in the
full range of parameter space, keeping the discrete nature of the lattice and
the particles intact. Our analysis of the stochastic dynamics of the foremost
occupied lattice site yields simple expressions for the front speed and the
front diffusion coefficient which are in excellent agreement with simulation
results.Comment: 5 pages, 5 figures, to appear in Phys. Rev.
Long-time-tail Effects on Lyapunov Exponents of a Random, Two-dimensional Field-driven Lorentz Gas
We study the Lyapunov exponents for a moving, charged particle in a
two-dimensional Lorentz gas with randomly placed, non-overlapping hard disk
scatterers placed in a thermostatted electric field, . The low density
values of the Lyapunov exponents have been calculated with the use of an
extended Lorentz-Boltzmann equation. In this paper we develop a method to
extend these results to higher density, using the BBGKY hierarchy equations and
extending them to include the additional variables needed for calculation of
Lyapunov exponents. We then consider the effects of correlated collision
sequences, due to the so-called ring events, on the Lyapunov exponents. For
small values of the applied electric field, the ring terms lead to
non-analytic, field dependent, contributions to both the positive and negative
Lyapunov exponents which are of the form , where is a dimensionless parameter
proportional to the strength of the applied field. We show that these
non-analytic terms can be understood as resulting from the change in the
collision frequency from its equilibrium value, due to the presence of the
thermostatted field, and that the collision frequency also contains such
non-analytic terms.Comment: 45 pages, 4 figures, to appear in J. Stat. Phy
Asymptotic Scaling of the Diffusion Coefficient of Fluctuating "Pulled" Fronts
We present a (heuristic) theoretical derivation for the scaling of the
diffusion coefficient for fluctuating ``pulled'' fronts. In agreement
with earlier numerical simulations, we find that as ,
approaches zero as , where is the average number of particles per
correlation volume in the stable phase of the front. This behaviour of
stems from the shape fluctuations at the very tip of the front, and is
independent of the microscopic model.Comment: Some minor algebra corrected, to appear in Rapid Comm., Phys. Rev.
Field dependent collision frequency of the two-dimensional driven random Lorentz gas
In the field-driven, thermostatted Lorentz gas the collision frequency
increases with the magnitude of the applied field due to long-time
correlations. We study this effect with computer simulations and confirm the
presence of non-analytic terms in the field dependence of the collision
frequency as predicted by kinetic theory.Comment: 6 pages, 2 figures. Submitted to Phys. Rev.
Validity of the Brunet-Derrida formula for the speed of pulled fronts with a cutoff
We establish rigorous upper and lower bounds for the speed of pulled fronts
with a cutoff. We show that the Brunet-Derrida formula corresponds to the
leading order expansion in the cut-off parameter of both the upper and lower
bounds. For sufficiently large cut-off parameter the Brunet-Derrida formula
lies outside the allowed band determined from the bounds. If nonlinearities are
neglected the upper and lower bounds coincide and are the exact linear speed
for all values of the cut-off parameter.Comment: 8 pages, 3 figure
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