3 research outputs found
Open boundary conditions in stochastic transport processes with pair-factorized steady states
Using numerical methods we discuss the effects of open boundary conditions on
condensation phenomena in the zero-range process (ZRP) and transport processes
with pair-factorized steady states (PFSS), an extended model of the ZRP with
nearest-neighbor interaction. For the zero-range process we compare to
analytical results in the literature with respect to criticality and
condensation. For the extended model we find a similar phase structure, but
observe supercritical phases with droplet formation for strong boundary drives.Comment: conference contribution for the 27th Annual CSP Workshop on "Recent
Developments in Computer Simulation Studies in Condensed Matter Physics", CSP
2014 5 pages, 5 figure
Order-by-disorder in classical oscillator systems
We consider classical nonlinear oscillators on hexagonal lattices. When the
coupling between the elements is repulsive, we observe coexisting states, each
one with its own basin of attraction. These states differ by their degree of
synchronization and by patterns of phase-locked motion. When disorder is
introduced into the system by additive or multiplicative Gaussian noise, we
observe a non-monotonic dependence of the degree of order in the system as a
function of the noise intensity: intervals of noise intensity with low
synchronization between the oscillators alternate with intervals where more
oscillators are synchronized. In the latter case, noise induces a higher degree
of order in the sense of a larger number of nearly coinciding phases. This
order-by-disorder effect is reminiscent to the analogous phenomenon known from
spin systems. Surprisingly, this non-monotonic evolution of the degree of order
is found not only for a single interval of intermediate noise strength, but
repeatedly as a function of increasing noise intensity. We observe noise-driven
migration of oscillator phases in a rough potential landscape.Comment: 12 pages, 13 figures; comments are welcom
Stochastic Description of a Bistable Frustrated Unit
Mixed positive and negative feedback loops are often found in biological
systems which support oscillations. In this work we consider a prototype of
such systems, which has been recently found at the core of many genetic
circuits showing oscillatory behaviour. Our model consists of two interacting
species A and B, where A activates not only its own production, but also that
of its repressor B. While the self-activation of A leads already to a bistable
unit, the coupling with a negative feedback loop via B makes the unit
frustrated. In the deterministic limit of infinitely many molecules, such a
bistable frustrated unit is known to show excitable and oscillatory dynamics,
depending on the maximum production rate of A which acts as a control
parameter. We study this model in its fully stochastic version and we find
oscillations even for parameters which in the deterministic limit are deeply in
the fixed-point regime. The deeper we go into this regime, the more irregular
these oscillations are, becoming finally random excitations whenever
fluctuations allow the system to overcome the barrier for a large excursion in
phase space. The fluctuations can no longer be fully treated as a perturbation.
The smaller the system size (the number of molecules), the more frequent are
these excitations. Therefore, stochasticity caused by demographic noise makes
this unit even more flexible with respect to its oscillatory behaviour.Comment: 28 pages, 17 figure