9 research outputs found
Biscale Chaos in Propagating Fronts
The propagating chemical fronts found in cubic autocatalytic
reaction-diffusion processes are studied. Simulations of the reaction-diffusion
equation near to and far from the onset of the front instability are performed
and the structure and dynamics of chemical fronts are studied. Qualitatively
different front dynamics are observed in these two regimes. Close to onset the
front dynamics can be characterized by a single length scale and described by
the Kuramoto-Sivashinsky equation. Far from onset the front dynamics exhibits
two characteristic lengths and cannot be modeled by this amplitude equation. An
amplitude equation is proposed for this biscale chaos. The reduction of the
cubic autocatalysis reaction-diffusion equation to the Kuramoto-Sivashinsky
equation is explicitly carried out. The critical diffusion ratio delta, where
the planar front loses its stability to transverse perturbations, is determined
and found to be delta=2.300.Comment: Typeset using RevTeX, fig.1 and fig.4 are not available, mpeg
simulations are at
http://www.chem.utoronto.ca/staff/REK/Videos/front/front.htm
Diffusion of passive scalars under stochastic convection
The diffusion of passive scalars convected by turbulent flows is addressed here. A practical procedure to obtain stochastic velocity fields with wellÂżdefined energy spectrum functions is also presented. Analytical results are derived, based on the use of stochastic differential equations, where the basic hypothesis involved refers to a rapidly decaying turbulence. These predictions are favorable compared with direct computer simulations of stochastic differential equations containing multiplicative spaceÂżtime correlated noise
Multiplicative noise effects on relaxations from marginal states
Relaxational processes in bistable potentials close to marginal conditions are studied under the combined effect of additive and multiplicative fluctuations. Characteristic time scales associated with the first-passage-time-distribution are analytically obtained. Multiplicative noise introduces large effects on the characteristic decay times, which is particularly significant when relaxations are mediated by fluctuations, i.e., below marginality and for small noise intensity. The relevance of our approach with respect to realistic chemical bistable systems experimentally operated under external noise influences is mentioned
Stochastic generation of homogeneous isotropic turbulence with well-defined-spectra
A precise and simple computational model to generate well-behaved two-dimensional turbulent flows is presented. The whole approach rests on the use of stochastic differential equations and is general enough to reproduce a variety of energy spectra and spatiotemporal correlation functions. Analytical expressions for both the continuous and the discrete versions, together with simulation algorithms, are derived. Results for two relevant spectra, covering distinct ranges of wave numbers, are given
Stochastic generation of homogeneous isotropic turbulence with well-defined-spectra
A precise and simple computational model to generate well-behaved two-dimensional turbulent flows is presented. The whole approach rests on the use of stochastic differential equations and is general enough to reproduce a variety of energy spectra and spatiotemporal correlation functions. Analytical expressions for both the continuous and the discrete versions, together with simulation algorithms, are derived. Results for two relevant spectra, covering distinct ranges of wave numbers, are given
Diffusion of passive scalars under stochastic convection
The diffusion of passive scalars convected by turbulent flows is addressed here. A practical procedure to obtain stochastic velocity fields with wellÂżdefined energy spectrum functions is also presented. Analytical results are derived, based on the use of stochastic differential equations, where the basic hypothesis involved refers to a rapidly decaying turbulence. These predictions are favorable compared with direct computer simulations of stochastic differential equations containing multiplicative spaceÂżtime correlated noise
Effective diffusion in a stochastic velocity field
Analytical results are derived for the effective dispersion of a passive scalar in a
stochastic velocity field evolving in a fast time scale. These results are favorably
compared with direct computer simulation of stochastic differential equations
containing multiplicative space-time correlated noisePeer Reviewe
Effective diffusion in a stochastic velocity field
Analytical results are derived for the effective dispersion of a passive scalar in a
stochastic velocity field evolving in a fast time scale. These results are favorably
compared with direct computer simulation of stochastic differential equations
containing multiplicative space-time correlated noisePeer ReviewedPostprint (published version
Effective diffusion in a stochastic velocity field
Analytical results are derived for the effective dispersion of a passive scalar in a
stochastic velocity field evolving in a fast time scale. These results are favorably
compared with direct computer simulation of stochastic differential equations
containing multiplicative space-time correlated noisePeer Reviewe