6533b86cfe1ef96bd12c8135

RESEARCH PRODUCT

Kinetics of growth process controlled by convective fluctuations

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A model of the spherical (compact) growth process controlled by a fluctuating local convective velocity field of the fluid particles is introduced. It is assumed that the particle velocity fluctuations are purely noisy, Gaussian, of zero mean, and of various correlations: Dirac delta, exponential, and algebraic (power law). It is shown that for a large class of the velocity fluctuations, the long-time asymptotics of the growth kinetics is universal (i.e., it does not depend on the details of the statistics of fluctuations) and displays the power-law time dependence with the classical exponent $1/2$ resembling the diffusion limited growth. For very slow decay of algebraic correlations of fluctuations asymptotically like ${t}^{\ensuremath{-}\ensuremath{\gamma}},$ $\ensuremath{\gamma}\ensuremath{\in}(0,1]),$ kinetics is anomalous and depends strongly on the exponent $\ensuremath{\gamma}.$ For the averaged radius of the crystal $〈R(t)〉\ensuremath{\sim}{t}^{1\ensuremath{-}\ensuremath{\gamma}/2}$ for $0l\ensuremath{\gamma}l1$ or $〈R(t)〉\ensuremath{\sim}(t\mathrm{ln}{t)}^{1/2}$ for $\ensuremath{\gamma}=1.$