2,304 research outputs found
Noise-Driven Mechanism for Pattern Formation
We extend the mechanism for noise-induced phase transitions proposed by
Ibanes et al. [Phys. Rev. Lett. 87, 020601-1 (2001)] to pattern formation
phenomena. In contrast with known mechanisms for pure noise-induced pattern
formation, this mechanism is not driven by a short-time instability amplified
by collective effects. The phenomenon is analyzed by means of a modulated mean
field approximation and numerical simulations
Comprehensive study of phase transitions in relaxational systems with field-dependent coefficients
We present a comprehensive study of phase transitions in single-field systems
that relax to a non-equilibrium global steady state. The mechanism we focus on
is not the so-called Stratonovich drift combined with collective effects, but
is instead similar to the one associated with noise-induced transitions a la
Horsthemke-Lefever in zero-dimensional systems. As a consequence, the noise
interpretation (e.g., Ito vs Stratonvich) merely shifts the phase boundaries.
With the help of a mean-field approximation, we present a broad qualitative
picture of the various phase diagrams that can be found in these systems. To
complement the theoretical analysis we present numerical simulations that
confirm the findings of the mean-field theory
Spatial Patterns Induced Purely by Dichotomous Disorder
We study conditions under which spatially extended systems with coupling a la
Swift-Hohenberg exhibit spatial patterns induced purely by the presence of
quenched dichotomous disorder. Complementing the theoretical results based on a
generalized mean-field approximation, we also present numerical simulations of
particular dynamical systems that exhibit the proposed phenomenology
Dissipative collapse of the adiabatic piston
An adiabatic piston, separating two granular gases prepared in the same
macroscopic state, is found to eventually collapse to one of the sides. This
new instability is explained by a simple macroscopic theory which is
furthermore in qualitative agreement with hard disk molecular dynamics.Comment: 7 pages, 5 figure
Critical Behaviour of Non-Equilibrium Phase Transitions to Magnetically Ordered States
We describe non-equilibrium phase transitions in arrays of dynamical systems
with cubic nonlinearity driven by multiplicative Gaussian white noise.
Depending on the sign of the spatial coupling we observe transitions to
ferromagnetic or antiferromagnetic ordered states. We discuss the phase
diagram, the order of the transitions, and the critical behaviour. For global
coupling we show analytically that the critical exponent of the magnetization
exhibits a transition from the value 1/2 to a non-universal behaviour depending
on the ratio of noise strength to the magnitude of the spatial coupling.Comment: 4 pages, 5 figure
Stochastic Stokes' drift of a flexible dumbbell
We consider the stochastic Stokes drift of a flexible dumbbell. The dumbbell
consists of two isotropic Brownian particles connected by a linear spring with
zero natural length, and is advected by a sinusoidal wave. We find an
asymptotic approximation for the Stokes drift in the limit of a weak wave, and
find good agreement with the results of a Monte Carlo simulation. We show that
it is possible to use this effect to sort particles by their flexibility even
when all the particles have the same diffusivity.Comment: 12 pages, 1 figur
Natural hybridization between Populus nigra L. and P. x canadensis Moench. Hybrid offspring competes for niches along the Rhine river in the Netherlands
Black poplar (Populus nigra L.) is a major species for European riparian forests but its abundance has decreased over the decades due to human influences. For restoration of floodplain woodlands, the remaining black poplar stands may act as source population. A potential problem is that P. nigra and Populus deltoides have contributed to many interspecific hybrids, which have been planted in large numbers. As these Populus x canadensis clones have the possibility to intercross with wild P. nigra trees, their offspring could establish themselves along European rivers. In this study, we have sampled 44 poplar seedlings and young trees that occurred spontaneously along the Rhine river and its tributaries in the Netherlands. Along these rivers, only a few native P. nigra L. populations exist in combination with many planted cultivated P. x canadensis trees. By comparison to reference material from P. nigra, P. deltoides and P. x canadensis, species-specific AFLP bands and microsatellite alleles indicated that nearly half of the sampled trees were not pure P. nigra but progeny of natural hybridisation that had colonised the Rhine river banks. The posterior probability method as implemented in NewHybrids using microsatellite data was the superior method in establishing the most likely parentage. The results of this study indicate that offspring of hybrid cultivated poplars compete for the same ecological niche as native black poplars
Macroscopic limit cycle via pure noise-induced phase transition
Bistability generated via a pure noise-induced phase transition is reexamined
from the view of bifurcations in macroscopic cumulant dynamics. It allows an
analytical study of the phase diagram in more general cases than previous
methods. In addition using this approach we investigate patially-extended
systems with two degrees of freedom per site. For this system, the analytic
solution of the stationary Fokker-Planck equation is not available and a
standard mean field approach cannot be used to find noise induced phase
transitions. A new approach based on cumulant dynamics predicts a noise-induced
phase transition through a Hopf bifurcation leading to a macroscopic limit
cycle motion, which is confirmed by numerical simulation.Comment: 8 pages, 8 figure
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