1,763 research outputs found
Domain wall theory and non-stationarity in driven flow with exclusion
We study the dynamical evolution toward steady state of the stochastic
non-equilibrium model known as totally asymmetric simple exclusion process, in
both uniform and non-uniform (staggered) one-dimensional systems with open
boundaries. Domain-wall theory and numerical simulations are used and, where
pertinent, their results are compared to existing mean-field predictions and
exact solutions where available. For uniform chains we find that the inclusion
of fluctuations inherent to the domain-wall formulation plays a crucial role in
providing good agreement with simulations, which is severely lacking in the
corresponding mean-field predictions. For alternating-bond chains the
domain-wall predictions for the features of the phase diagram in the parameter
space of injection and ejection rates turn out to be realized only in an
incipient and quantitatively approximate way. Nevertheless, significant
quantitative agreement can be found between several additional domain-wall
theory predictions and numerics.Comment: 12 pages, 12 figures (published version
Correlation--function distributions at the Nishimori point of two-dimensional Ising spin glasses
The multicritical behavior at the Nishimori point of two-dimensional Ising
spin glasses is investigated by using numerical transfer-matrix methods to
calculate probability distributions and associated moments of spin-spin
correlation functions on strips. The angular dependence of the shape of
correlation function distributions provides a stringent test of how well
they obey predictions of conformal invariance; and an even symmetry of reflects the consequences of the Ising spin-glass gauge (Nishimori)
symmetry. We show that conformal invariance is obeyed in its strictest form,
and the associated scaling of the moments of the distribution is examined, in
order to assess the validity of a recent conjecture on the exact localization
of the Nishimori point. Power law divergences of are observed near C=1
and C=0, in partial accord with a simple scaling scheme which preserves the
gauge symmetry.Comment: Final version to be published in Phys Rev
Scaling treatment of the random field Ising model
Analytic phenomenological scaling is carried out for the random field Ising
model in general dimensions using a bar geometry. Domain wall configurations
and their decorated profiles and associated wandering and other exponents
are obtained by free energy minimization. Scaling
between different bar widths provides the renormalization group (RG)
transformation. Its consequences are (1) criticality at in
with correlation length diverging like for and
for , where is a decoration constant; (2) criticality in dimensions at , , where
, .
Finite temperature generalizations are outlined. Numerical transfer matrix
calculations and results from a ground state algorithm adapted for strips in
confirm the ingredients which provide the RG description.Comment: RevTex v3.0, 5 pages, plus 4 figures uuencode
Smoothly-varying hopping rates in driven flow with exclusion
We consider the one-dimensional totally asymmetric simple exclusion process
(TASEP) with position-dependent hopping rates. The problem is solved,in a mean
field/adiabatic approximation, for a general (smooth) form of spatial rate
variation. Numerical simulations of systems with hopping rates varying linearly
against position (constant rate gradient), for both periodic and open boundary
conditions, provide detailed confirmation of theoretical predictions,
concerning steady-state average density profiles and currents, as well as
open-system phase boundaries, to excellent numerical accuracy.Comment: RevTeX 4.1, 14 pages, 9 figures (published version
Exact probability function for bulk density and current in the asymmetric exclusion process
We examine the asymmetric simple exclusion process with open boundaries, a
paradigm of driven diffusive systems, having a nonequilibrium steady state
transition. We provide a full derivation and expanded discussion and digression
on results previously reported briefly in M. Depken and R. Stinchcombe, Phys.
Rev. Lett. {\bf 93}, 040602, (2004). In particular we derive an exact form for
the joint probability function for the bulk density and current, both for
finite systems, and also in the thermodynamic limit. The resulting distribution
is non-Gaussian, and while the fluctuations in the current are continuous at
the continuous phase transitions, the density fluctuations are discontinuous.
The derivations are done by using the standard operator algebraic techniques,
and by introducing a modified version of the original operator algebra. As a
byproduct of these considerations we also arrive at a novel and very simple way
of calculating the normalization constant appearing in the standard treatment
with the operator algebra. Like the partition function in equilibrium systems,
this normalization constant is shown to completely characterize the
fluctuations, albeit in a very different manner.Comment: 10 pages, 4 figure
Connectivity-dependent properties of diluted sytems in a transfer-matrix description
We introduce a new approach to connectivity-dependent properties of diluted
systems, which is based on the transfer-matrix formulation of the percolation
problem. It simultaneously incorporates the connective properties reflected in
non-zero matrix elements and allows one to use standard random-matrix
multiplication techniques. Thus it is possible to investigate physical
processes on the percolation structure with the high efficiency and precision
characteristic of transfer-matrix methods, while avoiding disconnections. The
method is illustrated for two-dimensional site percolation by calculating (i)
the critical correlation length along the strip, and the finite-size
longitudinal DC conductivity: (ii) at the percolation threshold, and (iii) very
near the pure-system limit.Comment: 4 pages, no figures, RevTeX, Phys. Rev. E Rapid Communications (to be
published
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