2006
DOI: 10.1016/j.physd.2006.08.005
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Cluster–cluster aggregation as an analogue of a turbulent cascade: Kolmogorov phenomenology, scaling laws and the breakdown of self-similarity

Abstract: We present a detailed study of the statistical properties of a system of diffusing aggregating particles in the presence of a steady source of monomers. We emphasise the case of low spatial dimensions where strong diffusive fluctuations invalidate the mean-field description provided by standard Smoluchowski kinetic theory. The presence of a source of monomers allows the system to reach a statistically stationary state at large times. This state is characterised by a constant flux of mass directed from small to… Show more

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Cited by 27 publications
(27 citation statements)
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“…For 0, the scaling h ÿ3 ÿ is already established. It is trivially true for d > 2 where mean field holds, in d 2 due to cancellation of logarithmic corrections [6] and in d < 2 by an exact solution [21]. The scaling of the flux correlation function mCm m ÿ3ÿ agrees with general CFR, Eq.…”
mentioning
confidence: 59%
“…For 0, the scaling h ÿ3 ÿ is already established. It is trivially true for d > 2 where mean field holds, in d 2 due to cancellation of logarithmic corrections [6] and in d < 2 by an exact solution [21]. The scaling of the flux correlation function mCm m ÿ3ÿ agrees with general CFR, Eq.…”
mentioning
confidence: 59%
“…The analogy turns out to be useful in both directions however. For a discussion of stochastic aggregation from the point of view of turbulence theory, see [12,13].…”
Section: Formulation Of the Isotropic 3-wave Kinetic Equation As mentioning
confidence: 99%
“…A huge amount is known about the average mass density in the mean-field case [9] from exact analyses [10] and extensive numerical simulations of the Smoluchowski equation. Relatively less is known about the mass density in the diffusion limited regime but several models have been solved exactly or treated approximately by field-theoretic methods [11,12]. Almost nothing is known about higher order correlation functions in the diffusion-limited regime, despite the fact that they encode the details of the fluctuations which dominate the dynamics.…”
Section: Introductionmentioning
confidence: 99%