2,888 research outputs found
Response of Single Polymers to Localized Step Strains
In this paper, the response of single three-dimensional phantom and
self-avoiding polymers to localized step strains are studied for two cases in
the absence of hydrodynamic interactions: (i) polymers tethered at one end with
the strain created at the point of tether, and (ii) free polymers with the
strain created in the middle of the polymer. The polymers are assumed to be in
their equilibrium state before the step strain is created. It is shown that the
strain relaxes as a power-law in time as . While the strain
relaxes as for the phantom polymer in both cases; the self-avoiding
polymer relaxes its strain differently in case (i) than in case (ii): as
and as respectively. Here is
the Flory exponent for the polymer, with value in three
dimensions. Using the mode expansion method, exact derivations are provided for
the strain relaxation behavior for the phantom polymer. However, since
the mode expansion method for self-avoiding polymers is nonlinear, similar
theoretical derivations for the self-avoiding polymer proves difficult to
provide. Only simulation data are therefore presented in support of the
and the behavior. The relevance of
these exponents for the anomalous dynamics of polymers are also discussed.Comment: 10 pages, 1 figure; minor errors corrected, introduction slightly
modified and references expanded; to appear in Phys. Rev.
Extreme Associated Functions: Optimally Linking Local Extremes to Large-scale Atmospheric Circulation Structures
We present a new statistical method to optimally link local weather extremes
to large-scale atmospheric circulation structures. The method is illustrated
using July-August daily mean temperature at 2m height (T2m) time-series over
the Netherlands and 500 hPa geopotential height (Z500) time-series over the
Euroatlantic region of the ECMWF reanalysis dataset (ERA40). The method
identifies patterns in the Z500 time-series that optimally describe, in a
precise mathematical sense, the relationship with local warm extremes in the
Netherlands. Two patterns are identified; the most important one corresponds to
a blocking high pressure system leading to subsidence and calm, dry and sunny
conditions over the Netherlands. The second one corresponds to a rare, easterly
flow regime bringing warm, dry air into the region. The patterns are robust;
they are also identified in shorter subsamples of the total dataset. The method
is generally applicable and might prove useful in evaluating the performance of
climate models in simulating local weather extremes.Comment: 10 pages, 7 figures, 14 eps figure files; to appear in J. Atmos.
Chem. Phy
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
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.
Rouse Modes of Self-avoiding Flexible Polymers
Using a lattice-based Monte Carlo code for simulating self-avoiding flexible
polymers in three dimensions in the absence of explicit hydrodynamics, we study
their Rouse modes. For self-avoiding polymers, the Rouse modes are not expected
to be statistically independent; nevertheless, we demonstrate that numerically
these modes maintain a high degree of statistical independence. Based on
high-precision simulation data we put forward an approximate analytical
expression for the mode amplitude correlation functions for long polymers. From
this, we derive analytically and confirm numerically several scaling properties
for self-avoiding flexible polymers, such as (i) the real-space end-to-end
distance, (ii) the end-to-end vector correlation function, (iii) the
correlation function of the small spatial vector connecting two nearby monomers
at the middle of a polymer, and (iv) the anomalous dynamics of the middle
monomer. Importantly, expanding on our recent work on the theory of polymer
translocation, we also demonstrate that the anomalous dynamics of the middle
monomer can be obtained from the forces it experiences, by the use of the
fluctuation-dissipation theorem.Comment: 16 pages (double spaced), 5 figures, small changes and corrections,
to appear in J. Chem. Phy
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
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
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.
Monomer dynamics of a wormlike chain
We derive the stochastic equations of motion for a tracer that is tightly
attached to a semiflexible polymer and confined or agitated by an externally
controlled potential. The generalised Langevin equation, the power spectrum,
and the mean-square displacement for the tracer dynamics are explicitly
constructed from the microscopic equations of motion for a weakly bending
wormlike chain by a systematic coarse-graining procedure. Our accurate
analytical expressions should provide a convenient starting point for further
theoretical developments and for the analysis of various single-molecule
experiments and of protein shape fluctuations.Comment: 6 pages, 4 figure
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