341,221 research outputs found
Sample path large deviations for a class of Markov chains related to disordered mean field models
We prove a large deviation principle on path space for a class of discrete
time Markov processes whose state space is the intersection of a regular domain
\L\subset \R^d with some lattice of spacing \e. Transitions from to
are allowed if \e^{-1}(x-y)\in \D for some fixed set of vectors \D. The
transition probabilities p_\e(t,x,y), which themselves depend on \e, are
allowed to depend on the starting point and the time in a sufficiently
regular way, except near the boundaries, where some singular behaviour is
allowed. The rate function is identified as an action functional which is given
as the integral of a Lagrange function. %of time dependent relativistic
classical mechanics. Markov processes of this type arise in the study of mean
field dynamics of disordered mean field models.Comment: 56pp, AMS-Te
The Persistence Length of a Strongly Charged, Rod-like, Polyelectrolyte in the Presence of Salt
The persistence length of a single, intrinsically rigid polyelectrolyte
chain, above the Manning condensation threshold is investigated theoretically
in presence of added salt. Using a loop expansion method, the partition
function is consistently calculated, taking into account corrections to
mean-field theory. Within a mean-field approximation, the well-known results of
Odijk, Skolnick and Fixman are reproduced. Beyond mean-field, it is found that
density correlations between counterions and thermal fluctuations reduce the
stiffness of the chain, indicating an effective attraction between monomers for
highly charged chains and multivalent counterions. This attraction results in a
possible mechanical instability (collapse), alluding to the phenomenon of DNA
condensation. In addition, we find that more counterions condense on slightly
bent conformations of the chain than predicted by the Manning model for the
case of an infinite cylinder. Finally, our results are compared with previous
models and experiments.Comment: 13 pages, 2 ps figure
Differential equation approximations of stochastic network processes: an operator semigroup approach
The rigorous linking of exact stochastic models to mean-field approximations
is studied. Starting from the differential equation point of view the
stochastic model is identified by its Kolmogorov equations, which is a system
of linear ODEs that depends on the state space size () and can be written as
. Our results rely on the convergence of the transition
matrices to an operator . This convergence also implies that the
solutions converge to the solution of . The limiting ODE
can be easily used to derive simpler mean-field-type models such that the
moments of the stochastic process will converge uniformly to the solution of
appropriately chosen mean-field equations. A bi-product of this method is the
proof that the rate of convergence is . In addition, it turns
out that the proof holds for cases that are slightly more general than the
usual density dependent one. Moreover, for Markov chains where the transition
rates satisfy some sign conditions, a new approach for proving convergence to
the mean-field limit is proposed. The starting point in this case is the
derivation of a countable system of ordinary differential equations for all the
moments. This is followed by the proof of a perturbation theorem for this
infinite system, which in turn leads to an estimate for the difference between
the moments and the corresponding quantities derived from the solution of the
mean-field ODE
Pair Density Waves in coupled doped two-leg Ladders
Motivated by Resonant X-ray scattering experiments in cuprate ladder
materials showing charge order modulation of period and 5 at
specific hole densities, we investigate models involving the electronic t-J
ladders and bosonic chains coupled via screened Coulomb repulsion. Extensive
density matrix renormalization group calculations applied to the ladders/chains
supplemented by a self-consistent mean-field treatment of the
inter-ladder/chain coupling provide quantitative estimates of the charge order
for and 5. As previously proposed, such patterns correspond to
the emergence of pair density waves which stem from the strong electronic
correlations. We comment on the existence of a modulation not seen
so far in experiment.Comment: 4 pages, 4 figure
Macromolecular theory of solvation and structure in mixtures of colloids and polymers
The structural and thermodynamic properties of mixtures of colloidal spheres
and non-adsorbing polymer chains are studied within a novel general
two-component macromolecular liquid state approach applicable for all size
asymmetry ratios. The dilute limits, when one of the components is at infinite
dilution but the other concentrated, are presented and compared to field theory
and models which replace polymer coils with spheres. Whereas the derived
analytical results compare well, qualitatively and quantitatively, with
mean-field scaling laws where available, important differences from ``effective
sphere'' approaches are found for large polymer sizes or semi-dilute
concentrations.Comment: 23 pages, 10 figure
Static Rouse Modes and Related Quantities: Corrections to Chain Ideality in Polymer Melts
Following the Flory ideality hypothesis intrachain and interchain excluded
volume interactions are supposed to compensate each other in dense polymer
systems. Multi-chain effects should thus be neglected and polymer conformations
may be understood from simple phantom chain models. Here we provide evidence
against this phantom chain, mean-field picture. We analyze numerically and
theoretically the static correlation function of the Rouse modes. Our numerical
results are obtained from computer simulations of two coarse-grained polymer
models for which the strength of the monomer repulsion can be varied, from full
excluded volume (`hard monomers') to no excluded volume (`phantom chains'). For
nonvanishing excluded volume we find the simulated correlation function of the
Rouse modes to deviate markedly from the predictions of phantom chain models.
This demonstrates that there are nonnegligible correlations along the chains in
a melt. These correlations can be taken into account by perturbation theory.
Our simulation results are in good agreement with these new theoretical
predictions.Comment: 9 pages, 7 figures, accepted for publication in EPJ
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