51 research outputs found
Filament bifurcations in a one-dimensional model of reacting excitable fluid flow
Recently, it has been shown that properties of excitable media stirred by
two-dimensional chaotic flows can be properly studied in a one-dimensional
framework \cite{excitablePRL,excitablePRE}, describing the transverse profile
of the filament-like structures observed in the system. Here, we perform a
bifurcation analysis of this one-dimensional approximation as a function of the
{\it Damk{\"o}hler} number, the ratio between the chemical and the strain
rates. Different branches of stable solutions are calculated, and a Hopf
bifurcation, leading to an oscillating filament, identified.Comment: 9 pages, 4 figures; elsart.cls styl
Phototactic clustering of swimming microorganisms in a turbulent velocity field
We study the distribution of swimming microorganisms advected by a two-dimensional smooth turbulent flow and attracted towards a light source through phototaxis. It is shown that particles aggregate along a dynamical attractor with fractal measure whose dimension depends on the strength of the phototaxis. Using an effective diffusion approximation for the flow, we derive an analytic expression for the increase in light exposure over the aggregate and by extension an accurate prediction for the fractal dimension based on the properties of the advection and the statistics of the attracting field
Chaotic mixing induced transitions in reaction-diffusion systems
We study the evolution of a localized perturbation in a chemical system with
multiple homogeneous steady states, in the presence of stirring by a fluid
flow. Two distinct regimes are found as the rate of stirring is varied relative
to the rate of the chemical reaction. When the stirring is fast localized
perturbations decay towards a spatially homogeneous state. When the stirring is
slow (or fast reaction) localized perturbations propagate by advection in form
of a filament with a roughly constant width and exponentially increasing
length. The width of the filament depends on the stirring rate and reaction
rate but is independent of the initial perturbation. We investigate this
problem numerically in both closed and open flow systems and explain the
results using a one-dimensional "mean-strain" model for the transverse profile
of the filament that captures the interplay between the propagation of the
reaction-diffusion front and the stretching due to chaotic advection.Comment: to appear in Chaos, special issue on Chaotic Flo
Excitable media in open and closed chaotic flows
We investigate the response of an excitable medium to a localized
perturbation in the presence of a two-dimensional smooth chaotic flow. Two
distinct types of flows are numerically considered: open and closed. For both
of them three distinct regimes are found, depending on the relative strengths
of the stirring and the rate of the excitable reaction. In order to clarify and
understand the role of the many competing mechanisms present, simplified models
of the process are introduced. They are one-dimensional baker-map models for
the flow and a one-dimensional approximation for the transverse profile of the
filaments.Comment: 14 pages, 16 figure
Aggregation of chemotactic organisms in a differential flow
We study the effect of advection on the aggregation and pattern formation in
chemotactic systems described by Keller-Segel type models. The evolution of
small perturbations is studied analytically in the linear regime complemented
by numerical simulations. We show that a uniform differential flow can
significantly alter the spatial structure and dynamics of the chemotactic
system. The flow leads to the formation of anisotropic aggregates that move
following the direction of the flow, even when the chemotactic organisms are
not directly advected by the flow. Sufficiently strong advection can stop the
aggregation and coarsening process that is then restricted to the direction
perpendicular to the flow
Synchronization and oscillator death in oscillatory media with stirring
The effect of stirring in an inhomogeneous oscillatory medium is
investigated. We show that the stirring rate can control the macroscopic
behavior of the system producing collective oscillations (synchronization) or
complete quenching of the oscillations (oscillator death). We interpret the
homogenization rate due to mixing as a measure of global coupling and compare
the phase diagrams of stirred oscillatory media and of populations of globally
coupled oscillators.Comment: to appear in Phys. Rev. Let
Noise-sustained coherent oscillation of excitable media in a chaotic flow.
Constructive effects of noise in spatially extended systems have been well studied in static reaction-diffusion media. We study a noisy two-dimensional Fitz Hugh-Nagumo excitable model under the stirring of a chaotic flow. We find a regime where a noisy excitation can induce a coherent global excitation of the medium and a noise-sustained oscillation. Outside this regime, noisy excitation is either diluted into homogeneous background by strong stirring or develops into noncoherent patterns at weak stirring. These results explain some experimental findings of stirring effects in chemical reactions and are relevant for understanding the effects of natural variability in oceanic plankton bloom
Influence of turbulent advection on a phytoplankton ecosystem with nonuniform carrying capacity
In this work we study a plankton ecosystem model in a turbulent flow. The plankton model we consider contains logistic growth with a spatially varying background carrying capacity and the flow dynamics are generated using the two-dimensional (2D) Navier-Stokes equations. We characterize the system in terms of a dimensionless parameter, γ TB / TF, which is the ratio of the ecosystem biological time scales TB and the flow time scales TF. We integrate this system numerically for different values of γ until the mean plankton reaches a statistically stationary state and examine how the steady-state mean and variance of plankton depends on γ. Overall we find that advection in the presence of a nonuniform background carrying capacity can lead to very different plankton distributions depending on the time scale ratio γ. For small γ the plankton distribution is very similar to the background carrying capacity field and has a mean concentration close to the mean carrying capacity. As γ increases the plankton concentration is more influenced by the advection processes. In the largest γ cases there is a homogenization of the plankton concentration and the mean plankton concentration approaches the harmonic mean, 1/K -1. We derive asymptotic approximations for the cases of small and large γ. We also look at the dependence of the power spectra exponent, β, on γ where the power spectrum of plankton is k-β. We find that the power spectra exponent closely obeys β=1+2/γ as predicted by earlier studies using simple models of chaotic advection
Reaction front propagation in a turbulent flow
The propagation of reaction fronts was studied by direct numerical simulations. The velocity field was obtained by integrating the Navier-Stokes equation. The structure of the reaction front and the enhancement of the front propagation speed were investigated. The ratio of eddy turnover times and of the characteristic chemical time scale was determined
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