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ABSTRACT: We present numerical evidence and a theoretical analysis of the appearance of anticoherence resonance induced by noise, not predicted in former analysis of coherence resonance. We have found that this phenomenon occurs for very small values of the intensity of the noise acting on an excitable system, and we claim that this is a universal signature of a nonmonotonous relaxational behavior near its oscillatory regime. Moreover, we demonstrate that this new phenomenon is totally compatible with the standard situation of coherence resonance appearing at intermediate values of noise intensity. Peer Reviewed
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ABSTRACT: We consider the evaporation of periodic arrays of initially equal droplets in two-dimensional systems with open ~absorbing! boundaries. Our study is based on the numerical solution of the Cahn-Hilliard equation. We show that due to cooperative effects the droplets which are further from the boundary may evaporate earlier than those in the boundary’s vicinity. The time evolution of the overall amount of matter in the system is also studied. Peer Reviewed
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ABSTRACT: Phase separation dynamics in the presence of externally imposed stirring is stuidied. The stirring is assumed independent of the concentration and it is generated with a well-defined energy spectrum. The domain growth process is either favored or frozen depending on the intensity and correlation length of this advective flow. This behavior is explained by analytical arguments. Peer Reviewed
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ABSTRACT: A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques. Peer Reviewed
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ABSTRACT: Scroll waves, a characteristic dynamical pattern of three-dimensional excitable media, exhibit an instability under low excitability conditions. This unstable regime can be partially controlled by using random forcing in a clear manifestation of the ordering role of a stochastic external perturbation. Analytical and numerical results confirm this unexpected noise effect.
Physica A: Statistical Mechanics and its Applications.
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ABSTRACT: We present a study of the evaporation dynamics of a substance undergoing a coarsening process. The system is modeled by the Cahn-Hilliard equation with absorbing boundaries. We have found that the dynamics, although of a diffusive nature, is much slower than the usual one without coarsening. Analytical and simulation results are in reasonable agreement. Peer Reviewed
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ABSTRACT: A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.
Phys. Rev. E. 56(5).
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ABSTRACT: Dynamic morphological transitions in thin-layer electrodeposits obtained from copper sulphate solutions have been studied. The chemical composition of the electrodeposits indicates that they appear as a consequence of the competition between copper and cuprous oxide formation. In addition, the Ohmic control of the process is verified at initial stages of the deposit growth. At higher deposit developments, gravity-induced convection currents play a role in the control of the whole process and affect the position of these transitions.
Phys. Rev. E. 56(6).
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ABSTRACT: We study the problem of pattern and velocity selection of morphologically stable two-dimensional fronts propagating in a spatially modulated medium. The generic system is governed by a local equation and evolves towards a non-trivial steady state with a spatial structure which arises from non-local competition effects and does not necessarily mimic the local structure externally fixed by the modulation. The dynamical process leading to this steady state is studied both analytically and numerically.
http://dx.doi.org/10.1209/epl/i1996-00357-4.
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EPL (Europhysics Letters).
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ABSTRACT: We report a systematic study of pattern formation in a thin fluid layer driven by a simple chemical reaction. The hydrodynamic instability arises due to the increase of fluid density in the subsurface layer caused by the O<sub>2</sub> oxidation of glucose to gluconic acid with the methylene blue as a catalyst. We also report independent measurements of the kinetics of the reaction and of the increase in density which gives rise to the instability.
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ABSTRACT: We present an analytical scheme, easily implemented numerically, to generate synthetic Gaussian 2D turbulent flows by using linear stochastic partial differential equations, where the noise term acts as a random force of well-prescribed statistics. This methodology leads to a divergence-free, isotropic, stationary and homogeneous velocity field, whose characteristic parameters are well reproduced, in particular the kinematic viscosity and energy spectrum. This practical approach to tailor a turbulent flow is justified by its versatility when analizing different physical processes occurring in advectely mixed systems. Here, we focuss on an application to study the dynamics of Planktonic populations in the ocean.
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ABSTRACT: We consider diffusion of a passive substance C in a phase-separating nonmiscible binary alloy under turbulent mixing. The substance is assumed to have different diffusion coefficients in the pure phases A and B, leading to a spatially and temporarily dependent diffusion “coefficient” in the diffusion equation plus convective term. In this paper we consider especially the effects of a turbulent flow field coupled to both the Cahn-Hilliard type evolution equation of the medium and the diffusion equation (both, therefore, supplemented by a convective term). It is shown that the formerly observed prolonged anomalous diffusion [H. Lehr, F. Sagués, and J.M. Sancho, Phys. Rev. E 54, 5028 (1996)] is no longer seen if a flow of sufficient intensity is supplied.
Phys. Rev. E. 56(2).
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ABSTRACT: A pacemaker, regularly emitting chemical waves, is created out of noise when an excitable photosen-sitive Belousov-Zhabotinsky medium, strictly unable to autonomously initiate autowaves, is forced with a spatiotemporal patterned random illumination. These experimental observations are also reproduced numerically by using a set of reaction-diffusion equations for an activator-inhibitor model, and further analytically interpreted in terms of genuine coupling effects arising from parametric fluctuations. Within the same framework we also address situations of noise-sustained propagation in subexcitable media.
8754.
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ABSTRACT: The propagation of an initially planar front is studied within the framework of the photosensitive Belousov-Zhabotinsky reaction modulated by a smooth spatial variation of the local front velocity in the direction perpendicular to front propagation. Under this modulation, the wave front develops several fingers corresponding to the local maxima of the modulation function. After a transient, the wave front achieves a stationary shape that does not necessarily coincide with the one externally imposed by the modulation. Theoretical predictions for the selection criteria of fingers and steady-state velocity are experimentally validated.
Phys. Rev. E. 56(6).
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ABSTRACT: We propose a phenomenological model of fingering dynamics in the presence of an external drift, motivated by recent experiments on quasi-two-dimensional electrodeposition with hydrodynamic convection. We study the dynamical transition between a Laplacian growth regime and a weak finger competition regime. The model proposed defines a wavelength-selection problem of the finger array which is coupled in a nontrivial way to the single-finger selection problem in a channel. The wavelength-selection mechanism proposed is associated to the crossover from a diffusive to a ballistic behavior of the aggregating particles, as the coarsening spatial scale of the pattern matches the appropriate diffusion length. This yields specific predictions for the selected wavelength. The dynamics of the model are studied numerically with boundary-integral methods in the quasistatic approximation and, complementarily, using a biased random walk Monte Carlo scheme on a lattice. Results are in qualitative agreement with the theoretical predictions.
Physica D: Nonlinear Phenomena.
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ABSTRACT: We consider the evaporation of periodic arrays of initially equal droplets in two-dimensional systems with open (absorbing) boundaries. Our study is based on the numerical solution of the Cahn-Hilliard equation. We show that due to cooperative effects the droplets which are further from the boundary may evaporate earlier than those in the boundary’s vicinity. The time evolution of the overall amount of matter in the system is also studied.
Phys. Rev. E. 57(5).
