3,616 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
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
Surface crossover exponent for branched polymers in two dimensions
Transfer-matrix methods on finite-width strips with free boundary conditions
are applied to lattice site animals, which provide a model for randomly
branched polymers in a good solvent. By assigning a distinct fugacity to sites
along the strip edges, critical properties at the special (adsorption) and
ordinary transitions are assessed. The crossover exponent at the adsorption
point is estimated as , consistent with recent
predictions that exactly for all space dimensionalities.Comment: 10 pages, LaTeX with Institute of Physics macros, to appear in
Journal of Physics
Solving 1ODEs with functions
Here we present a new approach to deal with first order ordinary differential
equations (1ODEs), presenting functions. This method is an alternative to the
one we have presented in [1]. In [2], we have establish the theoretical
background to deal, in the extended Prelle-Singer approach context, with
systems of 1ODEs. In this present paper, we will apply these results in order
to produce a method that is more efficient in a great number of cases.
Directly, the solving of 1ODEs is applicable to any problem presenting
parameters to which the rate of change is related to the parameter itself.
Apart from that, the solving of 1ODEs can be a part of larger mathematical
processes vital to dealing with many problems.Comment: 31 page
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