70 research outputs found

    Smoluchowski's equation for cluster exogenous growth

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    We introduce an extended Smoluchowski equation describing coagulation processes for which clusters of mass s grow between collisions with ds/dt=Asβds/dt=As^\beta. A physical example, dropwise condensation is provided, and its collision kernel K is derived. In the general case, the gelation criterion is determined. Exact solutions are found and scaling solutions are investigated. Finally we show how these results apply to nucleation of discs on a planeComment: Revtex, 4 pages (multicol.sty), 1 eps figures (uses epsfig

    Persistence exponent in a superantiferromagnetic quenching

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    We measure the persistence exponent in a phase separating two-dimensional spin system with non-conserved dynamics quenched in a region with four coexisting stripe phases. The system is an Ising model with nearest neighbor, next-to-the-nearest neighbor and plaquette interactions. Due the particular nature of the ground states, the order parameter is defined in terms of blocks of spins. Our estimate of the persistence exponent, θ=0.42\theta=0.42, differs from those of the two-dimensional Ising and four state Potts models. Our procedure allows the study of persistence properties also at finite temperature TT: our results are compatible with the hypothesis that θ\theta does not depend on TT below the critical point.Comment: LaTeX file with postscript figure

    Comment on ``Phase ordering in chaotic map lattices with conserved dynamics''

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    Angelini, Pellicoro, and Stramaglia [Phys. Rev. E {\bf 60}, R5021 (1999), cond-mat/9907149] (APS) claim that the phase ordering of two-dimensional systems of sequentially-updated chaotic maps with conserved ``order parameter'' does not belong, for large regions of parameter space, to the expected universality class. We show here that these results are due to a slow crossover and that a careful treatment of the data yields normal dynamical scaling. Moreover, we construct better models, i.e. synchronously-updated coupled map lattices, which are exempt from these crossover effects, and allow for the first precise estimates of persistence exponents in this case.Comment: 3 pages, to be published in Phys. Rev.

    Coarsening and persistence in a class of stochastic processes interpolating between the Ising and voter models

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    We study the dynamics of a class of two dimensional stochastic processes, depending on two parameters, which may be interpreted as two different temperatures, respectively associated to interfacial and to bulk noise. Special lines in the plane of parameters correspond to the Ising model, voter model and majority vote model. The dynamics of this class of models may be described formally in terms of reaction diffusion processes for a set of coalescing, annihilating, and branching random walkers. We use the freedom allowed by the space of parameters to measure, by numerical simulations, the persistence probability of a generic model in the low temperature phase, where the system coarsens. This probability is found to decay at large times as a power law with a seemingly constant exponent θ0.22\theta\approx 0.22. We also discuss the connection between persistence and the nature of the interfaces between domains.Comment: Late

    Persistence in systems with conserved order parameter

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    We consider the low-temperature coarsening dynamics of a one-dimensional Ising ferromagnet with conserved Kawasaki-like dynamics in the domain representation. Domains diffuse with size-dependent diffusion constant, D(l)lγD(l) \propto l^\gamma with γ=1\gamma = -1. We generalize this model to arbitrary γ\gamma, and derive an expression for the domain density, N(t)tϕN(t) \sim t^{-\phi} with ϕ=1/(2γ)\phi=1/(2-\gamma), using a scaling argument. We also investigate numerically the persistence exponent θ\theta characterizing the power-law decay of the number, Np(t)N_p(t), of persistent (unflipped) spins at time tt, and find Np(t)tθN_{p}(t)\sim t^{-\theta} where θ\theta depends on γ\gamma. We show how the results for ϕ\phi and θ\theta are related to similar calculations in diffusion-limited cluster-cluster aggregation (DLCA) where clusters with size-dependent diffusion constant diffuse through an immobile `empty' phase and aggregate irreversibly on impact. Simulations show that, while ϕ\phi is the same in both models, θ\theta is different except for γ=0\gamma=0. We also investigate models that interpolate between symmetric domain diffusion and DLCA.Comment: 9 pages, minor revision

    Analytical results for generalized persistence properties of smooth processes

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    We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the diffusion equation evolving from random initial conditions, one of the simplest coarsening systems. Exact results are obtained in certain limits, and rely on a new method to deal with constrained multiplicative processes. An excellent agreement of our analytical predictions with direct numerical simulations of the diffusion equation is found.Comment: 21 pages, 4 figures, to appear in Journal of Physics

    Analytical results for random walk persistence

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    In this paper, we present the detailed calculation of the persistence exponent θ\theta for a nearly-Markovian Gaussian process X(t)X(t), a problem initially introduced in [Phys. Rev. Lett. 77, 1420 (1996)], describing the probability that the walker never crosses the origin. New resummed perturbative and non-perturbative expressions for θ\theta are obtained, which suggest a connection with the result of the alternative independent interval approximation (IIA). The perturbation theory is extended to the calculation of θ\theta for non-Gaussian processes, by making a strong connection between the problem of persistence and the calculation of the energy eigenfunctions of a quantum mechanical problem. Finally, we give perturbative and non-perturbative expressions for the persistence exponent θ(X0)\theta(X_0), describing the probability that the process remains bigger than X0X_0\sqrt{}.Comment: 23 pages; accepted for publication to Phys. Rev. E (Dec. 98

    Anisotropic Coarsening: Grain Shapes and Nonuniversal Persistence

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    We solve a coarsening system with small but arbitrary anisotropic surface tension and interface mobility. The resulting size-dependent growth shapes are significantly different from equilibrium microcrystallites, and have a distribution of grain sizes different from isotropic theories. As an application of our results, we show that the persistence decay exponent depends on anisotropy and hence is nonuniversal.Comment: 4 pages (revtex), 2 eps figure

    Dynamic Scaling in One-Dimensional Cluster-Cluster Aggregation

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    We study the dynamic scaling properties of an aggregation model in which particles obey both diffusive and driven ballistic dynamics. The diffusion constant and the velocity of a cluster of size ss follow D(s)sγD(s) \sim s^\gamma and v(s)sδv(s) \sim s^\delta, respectively. We determine the dynamic exponent and the phase diagram for the asymptotic aggregation behavior in one dimension in the presence of mixed dynamics. The asymptotic dynamics is dominated by the process that has the largest dynamic exponent with a crossover that is located at δ=γ1\delta = \gamma - 1. The cluster size distributions scale similarly in all cases but the scaling function depends continuously on γ\gamma and δ\delta. For the purely diffusive case the scaling function has a transition from exponential to algebraic behavior at small argument values as γ\gamma changes sign whereas in the drift dominated case the scaling function decays always exponentially.Comment: 6 pages, 6 figures, RevTeX, submitted to Phys. Rev.

    Persistence exponents in a 3D symmetric binary fluid mixture

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    The persistence exponent, theta, is defined by N_F sim t^theta, where t is the time since the start of the coarsening process and the "no-flip fraction", N_F, is the number of points that have not seen a change of "color" since t=0. Here we investigate numerically the persistence exponent for a binary fluid system where the coarsening is dominated by hydrodynamic transport. We find that N_F follows a power law decay (as opposed to exponential) with the value of theta somewhat dependent on the domain growth rate (L sim t^alpha, where L is the average domain size), in the range theta=1.23 +-0.1 (alpha = 2/3) to theta=1.37 +-0.2 (alpha=1). These alpha values correspond to the inertial and viscous hydrodynamic regimes respectively.Comment: 9 pages RevTex, 9 figures included as eps files on last 3 pages, submitted to Phys Rev
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