291 research outputs found
Violating conformal invariance: Two-dimensional clusters grafted to wedges, cones, and branch points of Riemann surfaces
We present simulations of 2-d site animals on square and triangular lattices
in non-trivial geomeLattice animals are one of the few critical models in
statistical mechanics violating conformal invariance. We present here
simulations of 2-d site animals on square and triangular lattices in
non-trivial geometries. The simulations are done with the newly developed PERM
algorithm which gives very precise estimates of the partition sum, yielding
precise values for the entropic exponent (). In particular, we studied animals grafted to the tips of wedges
with a wide range of angles , to the tips of cones (wedges with the
sides glued together), and to branching points of Riemann surfaces. The latter
can either have sheets and no boundary, generalizing in this way cones to
angles degrees, or can have boundaries, generalizing wedges. We
find conformal invariance behavior, , only for small
angles (), while for
. These scalings hold both for wedges and cones. A heuristic
(non-conformal) argument for the behavior at large is given, and
comparison is made with critical percolation.Comment: 4 pages, includes 3 figure
Noise driven translocation of short polymers in crowded solutions
In this work we study the noise induced effects on the dynamics of short
polymers crossing a potential barrier, in the presence of a metastable state.
An improved version of the Rouse model for a flexible polymer has been adopted
to mimic the molecular dynamics by taking into account both the interactions
between adjacent monomers and introducing a Lennard-Jones potential between all
beads. A bending recoil torque has also been included in our model. The polymer
dynamics is simulated in a two-dimensional domain by numerically solving the
Langevin equations of motion with a Gaussian uncorrelated noise. We find a
nonmonotonic behaviour of the mean first passage time and the most probable
translocation time, of the polymer centre of inertia, as a function of the
polymer length at low noise intensity. We show how thermal fluctuations
influence the motion of short polymers, by inducing two different regimes of
translocation in the molecule transport dynamics. In this context, the role
played by the length of the molecule in the translocation time is investigated.Comment: 11 pages, 3 figures, to appear in J. Stat. Mechanics: Theory and
Experiment, 200
DNA unzipped under a constant force exhibits multiple metastable intermediates
Single molecule studies, at constant force, of the separation of
double-stranded DNA into two separated single strands may provide information
relevant to the dynamics of DNA replication. At constant applied force, theory
predicts that the unzipped length as a function of time is characterized by
jumps during which the strands separate rapidly, followed by long pauses where
the number of separated base pairs remains constant. Here, we report previously
uncharacterized observations of this striking behavior carried out on a number
of identical single molecules simultaneously. When several single lphage
molecules are subject to the same applied force, the pause positions are
reproducible in each. This reproducibility shows that the positions and
durations of the pauses in unzipping provide a sequence-dependent molecular
fingerprint. For small forces, the DNA remains in a partially unzipped state
for at least several hours. For larger forces, the separation is still
characterized by jumps and pauses, but the double-stranded DNA will completely
unzip in less than 30 min
DNA in nanopore-counterion condensation and coion depletion
Molecular dynamics simulations are used to study the equilibrium distribution
of monovalent ions in a nanopore connecting two water reservoirs separated by a
membrane, both for the empty pore and that with a single stranded DNA molecule
inside. In the presence of DNA, the counterions condense on the stretched
macromolecule effectively neutralizing it, and nearly complete depletion of
coions from the pore is observed. The implications of our results for
experiments on DNA translocation through alpha-hemolysin nanopores are
discussed.Comment: 8 pages, 2 figure
Unzipping Kinetics of Double-Stranded DNA in a Nanopore
We studied the unzipping kinetics of single molecules of double-stranded DNA
by pulling one of their two strands through a narrow protein pore. PCR analysis
yielded the first direct proof of DNA unzipping in such a system. The time to
unzip each molecule was inferred from the ionic current signature of DNA
traversal. The distribution of times to unzip under various experimental
conditions fit a simple kinetic model. Using this model, we estimated the
enthalpy barriers to unzipping and the effective charge of a nucleotide in the
pore, which was considerably smaller than previously assumed.Comment: 10 pages, 5 figures, Accepted: Physics Review Letter
Unzipping Vortices in Type-II Superconductors
The unzipping of vortex lines using magnetic-force microscopy from extended
defects is studied theoretically. We study both the unzipping isolated vortex
from common defects, such as columnar pins and twin-planes, and the unzipping
of a vortex from a plane in the presence of other vortices. We show, using
analytic and numerical methods, that the universal properties of the unzipping
transition of a single vortex depend only on the dimensionality of the defect
in the presence and absence of disorder. For the unzipping of a vortex from a
plane populated with many vortices is shown to be very sensitive to the
properties of the vortices in the two-dimensional plane. In particular such
unzipping experiments can be used to measure the ``Luttinger liquid parameter''
of the vortices in the plane. In addition we suggest a method for measuring the
line tension of the vortex directly using the experiments.Comment: 19 pages 15 figure
Polymer Translocation in Crowded Environments
We study the effect of the crowded nature of the cellular cytoplasm on the
translocation of a polymer through a pore in a membrane. By systematically
treating the entropic penalty due to crowding, we show that the translocation
dynamics are significantly altered, leading to novel scaling behaviors of the
translocation time in terms of chain length. We also observe new and
qualitatively different translocation regimes depending upon the extent of
crowding, transmembrane chemical potential asymmetry, and polymer length.Comment: 4 figure
Influence of polymer-pore interactions on translocation
We investigate the influence of polymer-pore interactions on the
translocation dynamics using Langevin dynamics simulations. An attractive
interaction can greatly improve translocation probability. At the same time, it
also increases translocation time slowly for weak attraction while exponential
dependence is observed for strong attraction. For fixed driving force and chain
length the histogram of translocation time has a transition from Gaussian
distribution to long-tailed distribution with increasing attraction. Under a
weak driving force and a strong attractive force, both the translocation time
and the residence time in the pore show a non-monotonic behavior as a function
of the chain length. Our simulations results are in good agreement with recent
experimental data.Comment: 4 pages, 5 figures, Submitted to Phys. Rev. Let
A Classification of random Dirac fermions
We present a detailed classification of random Dirac hamiltonians in two
spatial dimensions based on the implementation of discrete symmetries. Our
classification is slightly finer than that of random matrices, and contains
thirteen classes. We also extend this classification to non-hermitian
hamiltonians with and without Dirac structure.Comment: 15 pages, version2: typos in the table of classes are correcte
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