Nanosize pattern formation in overdamped stochastic reaction-diffusion systems with interacting adsorbate (original) (raw)
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2011
We study nano-pattern formation in a stochastic model for adsorption-desorption processes with interacting adsorbate and hyperbolic transport caused by memory effects. It is shown that at early stages the system manifests pattern selection processes. Stationary stable patterns of nano-size are analyzed. It was found that multiplicative noise satisfying fluctuation-dissipation relation can induce re-entrant pattern formation related to non-equilibrium transitions. According
Interplay between noise and boundary conditions in pattern formation in adsorbed substances
Physical review. E, Statistical, nonlinear, and soft matter physics, 2005
We have studied the interplay between noise and boundary conditions on the possibility of noise induced pattern formation. With this aim, we have exploited a deterministic model for pattern formation in adsorbed substances-including the effect of lateral interactions-used to describe the phenomenon of adsorption in surfaces, where a multiplicative noise fulfilling a fluctuation-dissipation relation was added. We have found solutions for different boundary conditions, particularly corresponding to two stable and one unstable patterns, where one of the stable and the unstable one, are purely induced by the multiplicative noise. In the case of albedo boundary conditions we have found a transition from monostable to a noise induced bistable behavior as the albedo parameter is varied.
Dichotomous-noise-induced pattern formation in a reaction-diffusion system
Physical Review E, 2013
We consider a generic reaction-diffusion system in which one of the parameters is subjected to dichotomous noise by controlling the flow of one of the reacting species in a continuous-flow-stirred-tank reactor (CSTR)-membrane reactor. The linear stability analysis in an extended phase space is carried out by invoking Furutzu-Novikov procedure for exponentially correlated multiplicative noise to derive the instability condition in the plane of the noise parameters (correlation time and strength of the noise). We demonstrate that depending on the correlation time an optimal strength of noise governs the self-organization. Our theoretical analysis is corroborated by numerical simulations on pattern formation in a chlorine-dioxide-iodine-malonic acid reaction-diffusion system.
Relating chaos to deterministic diffusion of a molecule adsorbed on a surface
Journal of Physics: Condensed Matter, 2009
Chaotic internal degrees of freedom of a molecule can act as noise and affect the diffusion of the molecule on a substrate. A separation of time scales between the fast internal dynamics and the slow motion of the centre of mass on the substrate makes it possible to directly link chaos to diffusion. We discuss the conditions under which this is possible, and show that in simple atomistic models with pair-wise harmonic potentials, strong chaos can arise through the geometry. Using molecular-dynamics simulations, we demonstrate that a realistic model of benzene is indeed chaotic, and that the internal chaos affects the diffusion on a graphite substrate.
Phase-field modeling of epitaxial growth in stochastic systems with interacting adsorbate
Physica Scripta, 2011
We study the epitaxial growth of pyramidal patterns in stochastic systems with interacting adsorbate within the framework of the phase-field approach based on the Burton-Cabrera-Frank model. Considering the statistical criteria of pattern formation, it is shown that the system dynamics is governed by the interaction strength of adatoms and the noise intensity of the total flux fluctuations. We have shown that the noise action can crucially change the processes of pyramidal pattern formation. The scaling behavior of the height-height correlation function is discussed.
Spatiotemporal patterns driven by autocatalytic internal reaction noise
The Journal of Chemical Physics, 2005
The influence that intrinsic local density fluctuations can have on solutions of mean-field reactiondiffusion models is investigated numerically by means of the spatial patterns arising from two species that react and diffuse in the presence of strong internal reaction noise. The dynamics of the Gray-Scott (GS) model with constant external source is first cast in terms of a continuum field theory representing the corresponding master equation. We then derive a Langevin description of the field theory and use these stochastic differential equations in our simulations. The nature of the multiplicative noise is specified exactly without recourse to assumptions and turns out to be of the same order as the reaction itself, and thus cannot be treated as a small perturbation. Many of the complex patterns obtained in the absence of noise for the GS model are completely obliterated by these strong internal fluctuations, but we find novel spatial patterns induced by this reaction noise in regions of parameter space that otherwise correspond to homogeneous solutions when fluctuations are not included.
Adaptation of autocatalytic fluctuations to diffusive noise
Physical Review E, 2001
Evolution of a system of diffusing and proliferating mortal reactants is analyzed in the presence of randomly moving catalysts. While the continuum description of the problem predicts reactant extinction as the average growth rate becomes negative, growth rate fluctuations induced by the discrete nature of the agents are shown to allow for an active phase, where reactants proliferate as their spatial configuration adapts to the fluctuations of the catalyst density. The model is explored by employing field theoretical techniques, numerical simulations, and strong coupling analysis. For dр2, the system is shown to exhibits an active phase at any growth rate, while for dϾ2 a kinetic phase transition is predicted. The applicability of this model as a prototype for a host of phenomena that exhibit self-organization is discussed.
Journal of Physical Studies
We present study concerns a generalization of the model for extended stochastic systems with a field-dependent kinetic coefficient and a noise source satisfying fluctuation-dissipation relation. Phase transitions with entropy driven mechanism are investigated in systems with conserved and nonconserved dynamics. It is found that in stochastic systems with a relaxational flow and a symmetric local potential reentrant phase transitions can be observed. We have studied the entropy-driven mechanism leading to stationary patterns formation in stochastic systems of reaction diffusion kind. It is shown that a multiplicative noise fulfilling a fluctuation-dissipation relation is able to induce and sustain stationary structures. Our mean-field results are verified by computer simulations.