179 research outputs found
Moment Equations for a Spatially Extended System of Two Competing Species
The dynamics of a spatially extended system of two competing species in the
presence of two noise sources is studied. A correlated dichotomous noise acts
on the interaction parameter and a multiplicative white noise affects directly
the dynamics of the two species. To describe the spatial distribution of the
species we use a model based on Lotka-Volterra (LV) equations. By writing them
in a mean field form, the corresponding moment equations for the species
concentrations are obtained in Gaussian approximation. In this formalism the
system dynamics is analyzed for different values of the multiplicative noise
intensity. Finally by comparing these results with those obtained by direct
simulations of the time discrete version of LV equations, that is coupled map
lattice (CML) model, we conclude that the anticorrelated oscillations of the
species densities are strictly related to non-overlapping spatial patterns.Comment: 10 pages, 3 figure
Nonlinear response of a linear chain to weak driving
We study the escape of a chain of coupled units over the barrier of a
metastable potential. It is demonstrated that a very weak external driving
field with suitably chosen frequency suffices to accomplish speedy escape. The
latter requires the passage through a transition state the formation of which
is triggered by permanent feeding of energy from a phonon background into humps
of localised energy and elastic interaction of the arising breather solutions.
In fact, cooperativity between the units of the chain entailing coordinated
energy transfer is shown to be crucial for enhancing the rate of escape in an
extremely effective and low-energy cost way where the effect of entropic
localisation and breather coalescence conspire
Moment equations in a Lotka-Volterra extended system with time correlated noise
A spatially extended Lotka-Volterra system of two competing species in the
presence of two correlated noise sources is analyzed: (i) an external
multiplicative time correlated noise, which mimics the interaction between the
system and the environment; (ii) a dichotomous stochastic process, whose jump
rate is a periodic function, which represents the interaction parameter between
the species. The moment equations for the species densities are derived in
Gaussian approximation, using a mean field approach. Within this formalism we
study the effect of the external time correlated noise on the ecosystem
dynamics. We find that the time behavior of the order moments are
independent on the multiplicative noise source. However the behavior of the
order moments is strongly affected both by the intensity and the
correlation time of the multiplicative noise. Finally we compare our results
with those obtained studying the system dynamics by a coupled map lattice
model.Comment: 12 pages, 7 figures, to appear in Acta Phys. Pol.
Giant enhancement of hydrodynamically enforced entropic trapping in thin channels
Using our generalized Fick-Jacobs approach [Martens et al., PRL 110, 010601
(2013); Martens et al., Eur. Phys. J. Spec. Topics 222, 2453-2463 (2013)] and
extensive Brownian dynamics simulations, we study particle transport through
three-dimensional periodic channels of different height. Directed motion is
caused by the interplay of constant bias acting along the channel axis and a
pressure-driven flow. The tremendous change of the flow profile shape in
channel direction with the channel height is reflected in a crucial dependence
of the mean particle velocity and the effective diffusion coefficient on the
channel height. In particular, we observe a giant suppression of the effective
diffusivity in thin channels; four orders of magnitude compared to the bulk
value.Comment: 16 pages, 8 figure
Hydrodynamically enforced entropic trapping of Brownian particles
We study the transport of Brownian particles through a corrugated channel
caused by a force field containing curl-free (scalar potential) and
divergence-free (vector potential) parts. We develop a generalized Fick-Jacobs
approach leading to an effective one-dimensional description involving the
potential of mean force. As an application, the interplay of a pressure-driven
flow and an oppositely oriented constant bias is considered. We show that for
certain parameters, the particle diffusion is significantly suppressed via the
property of hyrodynamically enforced entropic particle trapping.Comment: 5 pages, 4 figures, in press with Physical Review Letter
Quasi-deterministic transport of Brownian particles in an oscillating periodic potential
We consider overdamped Brownian dynamics in a periodic potential with
temporally oscillating amplitude. We analyze the transport which shows
effective diffusion enhanced by the oscillations and derive approximate
expressions for the diffusion coefficient. Furthermore we analyze the effect of
the oscillating potential on the transport if additionally a constant force is
applied. We show the existence of synchronization regimes at which the
deterministic dynamics is in resonance with the potential oscillations giving
rise to transport with extremely low dispersion. We distinguish slow and fast
oscillatory driving and give analytical expressions for the mean velocity and
effective diffusion.Comment: submitted: Feb 12th, 201
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