6 research outputs found
Free Energy Evaluation in Polymer Translocation via Jarzynski Equality
We perform, with the help of cloud computing resources, extensive Langevin
simulations which provide free energy estimates for unbiased three dimensional
polymer translocation. We employ the Jarzynski equality in its rigorous
setting, to compute the variation of the free energy in single monomer
translocation events. In our three-dimensional Langevin simulations, the
excluded-volume and van der Waals interactions between beads (monomers and
membrane atoms) are modeled through a repulsive Lennard-Jones (LJ) potential
and consecutive monomers are subject to the Finite-Extension Nonlinear Elastic
(FENE) potential. Analysing data for polymers with different lengths, the free
energy profile is noted to have interesting finite size scaling properties.Comment: 14 pages, 5 figures, Accepted for publication in Physics Letters
Markovian Description of Unbiased Polymer Translocation
We perform, with the help of cloud computing resources, extensive Langevin
simulations which provide compelling evidence in favor of a general markovian
framework for unbiased polymer translocation. Our statistical analysis consists
of careful evaluations of (i) two-point correlation functions of the
translocation coordinate and (ii) the empirical probabilities of complete
polymer translocation (taken as a function of the initial number of monomers on
a given side of the membrane). We find good agreement with predictions derived
from the Markov chain approach recently addressed in the literature by the
present authors.Comment: 11 pages, 4 figure
Markov Chain Modeling of Polymer Translocation Through Pores
We solve the Chapman-Kolmogorov equation and study the exact splitting
probabilities of the general stochastic process which describes polymer
translocation through membrane pores within the broad class of Markov chains.
Transition probabilities which satisfy a specific balance constraint provide a
refinement of the Chuang-Kantor-Kardar relaxation picture of translocation,
allowing us to investigate finite size effects in the evaluation of dynamical
scaling exponents. We find that (i) previous Langevin simulation results can be
recovered only if corrections to the polymer mobility exponent are taken into
account and that (ii) the dynamical scaling exponents have a slow approach to
their predicted asymptotic values as the polymer's length increases. We also
address, along with strong support from additional numerical simulations, a
critical discussion which points in a clear way the viability of the Markov
chain approach put forward in this work.Comment: 17 pages, 5 figure
Disordered two-dimensional superconductors: roles of temperature and interaction strength
We have considered the half-filled disordered attractive Hubbard model on a
square lattice, in which the on-site attraction is switched off on a fraction
of sites, while keeping a finite on the remaining ones. Through Quantum
Monte Carlo (QMC) simulations for several values of and , and for system
sizes ranging from to , we have calculated the
configurational averages of the equal-time pair structure factor , and,
for a more restricted set of variables, the helicity modulus, , as
functions of temperature. Two finite-size scaling {\it ansatze} for have
been used, one for zero-temperature and the other for finite temperatures. We
have found that the system sustains superconductivity in the ground state up to
a critical impurity concentration, , which increases with , at least up
to U=4 (in units of the hopping energy). Also, the normalized zero-temperature
gap as a function of shows a maximum near , for . Analyses of the helicity modulus and of the pair structure factor
led to the determination of the critical temperature as a function of , for
4 and 6: they also show maxima near , with the highest
increasing with in this range. We argue that, overall, the observed
behavior results from both the breakdown of CDW-superconductivity degeneracy
and the fact that free sites tend to "push" electrons towards attractive sites,
the latter effect being more drastic at weak couplings.Comment: 9 two-column pages, 14 figures, RevTe
Destruction of Superconductivity by Impurities in the Attractive Hubbard Model
We study the effect of U=0 impurities on the superconducting and
thermodynamic properties of the attractive Hubbard model on a square lattice.
Removal of the interaction on a critical fraction of of the sites results in the destruction of off-diagonal long range order
in the ground state. This critical fraction is roughly independent of filling
in the range , although our data suggest that might be somewhat larger below half-filling than at . We also
find that the two peak structure in the specific heat is present at both
below and above the value which destroys long range pairing order. It is
expected that the high peak associated with local pair formation should be
robust, but apparently local pairing fluctuations are sufficient to generate a
low temperature peak