4,634 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
Further Results on Strict Lyapunov Functions for Rapidly Time-Varying Nonlinear Systems
We explicitly construct global strict Lyapunov functions for rapidly
time-varying nonlinear control systems. The Lyapunov functions we construct are
expressed in terms of oftentimes more readily available Lyapunov functions for
the limiting dynamics which we assume are uniformly globally asymptotically
stable. This leads to new sufficient conditions for uniform global exponential,
uniform global asymptotic, and input-to-state stability of fast time-varying
dynamics. We also construct strict Lyapunov functions for our systems using a
strictification approach. We illustrate our results using a friction control
example.Comment: 10 pages, 0 figues, revised and accepted for publication as a regular
paper in Automatica in May 2006. To appear in October 2006 issu
- …