Dynamics and scaling of noise-induced domain growth

Ibañes, Marta; García-Ojalvo, Jordi; Toral, Raúl; Sancho, J. M.

doi:10.1007/s100510070015

Cited by 19 publications

(20 citation statements)

References 25 publications

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“…In this section we are concerned with the growth of these noise-induced domains. Although the mechanism that induces the phase transition is different from those that have been reported before, we can expect that, once the domains have appeared, their dynamics has the same characteristics as those of the domain growth following the quench of a system below its order-disorder transition temperature, as happens in the Ginzburg-Landau model [19]. For non-conserved order parameter models, one of the domains grows until it fills the whole system.…”

Section: Domain Growth Dynamicsmentioning

confidence: 79%

Intrinsic noise-induced phase transitions: Beyond the noise interpretation

et al. 2003

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We discuss intrinsic noise effects in stochastic multiplicative-noise partial differential equations, which are qualitatively independent of the noise interpretation ͑Itô vs Stratonovich͒, in particular in the context of noise-induced ordering phase transitions. We study a model which, contrary to all cases known so far, exhibits such ordering transitions when the noise is interpreted not only according to Stratonovich, but also to Itô. The main feature of this model is the absence of a linear instability at the transition point. The dynamical properties of the resulting noise-induced growth processes are studied and compared in the two interpretations and with a reference Ginzburg-Landau-type model. A detailed discussion of a different numerical algorithm valid for both interpretations is also presented.

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Section: Domain Growth Dynamicsmentioning

confidence: 79%

Intrinsic noise-induced phase transitions: Beyond the noise interpretation

et al. 2003

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“…There are ample instances in the literature where a naive discretisation of both the momentum [4] and order parameter [5,6,28] equations have led to FDT violations on the lattice. An important question, then, is how best FDTs, derived in the continuum with respect to appropriate conservation laws, can be implemented in discrete space and time.…”

Section: Discretisation and Fdt Violationmentioning

confidence: 99%

“…To verify the above analysis, we perform simulations using the method proposed by Petschek and Metiu [5] and used, for example, in [6] and [28]. Their method is essentially the one outlined above, with specific choices of the gradient and Laplacian.…”

Section: Discretisation and Fdt Violationmentioning

confidence: 99%

Lattice-Boltzmann-Langevin simulations of binary mixtures

2011

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We report a hybrid numerical method for the solution of the model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes are solved using the stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretisation of the order parameter equation. Special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattice level in both cases. The methods are benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytical and numerical results. The Galilean invariance of the model is tested and found to be satisfactory. Thermally induced capillary fluctuations of the interface are captured accurately, indicating that the model can be used to study nonlinear fluctuations.

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“…The Cahn-Hilliard equation describes the process of phase separation, such as when the two components of a binary fluid spontaneously separate. A number of studies have been published that solve the stochastic Cahn-Hilliard composition equations, decoupled from the continuity, momentum and energy equations (e.g., [9,11,[28][29][30]36,61]). In these studies, the stochastic forcing is obtained from the fluctuationdissipation theorem, however, it has not been determined that the resulting concentration fluctuations are consistent with statistical mechanics expectations (aside from structure factors and pair correlation functions - Figure 6.…”

Section: Future Workmentioning

confidence: 99%

Computational fluctuating fluid dynamics

Bell

Garcia²,

Williams

2010

ESAIM: M2AN

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Abstract. This paper describes the extension of a recently developed numerical solver for the LandauLifshitz Navier-Stokes (LLNS) equations to binary mixtures in three dimensions. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by using white-noise fluxes. These stochastic PDEs are more complicated in three dimensions due to the tensorial form of the correlations for the stochastic fluxes and in mixtures due to couplings of energy and concentration fluxes (e.g., Soret effect). We present various numerical tests of systems in and out of equilibrium, including timedependent systems, and demonstrate good agreement with theoretical results and molecular simulation.Mathematics Subject Classification. 35R60, 60H10, 60H35, 82C31, 82C80.

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Dynamics and scaling of noise-induced domain growth

Cited by 19 publications

References 25 publications

Intrinsic noise-induced phase transitions: Beyond the noise interpretation

Intrinsic noise-induced phase transitions: Beyond the noise interpretation

Lattice-Boltzmann-Langevin simulations of binary mixtures

Computational fluctuating fluid dynamics

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