Growth oscillations in ballistic aggregation

Abstract

We demonstrate the existence of growth oscillations in single clusters of particles grown stochastically according to a synchronous (finite density) version of ballistic aggregation, which is a model of relevance to a variety of experimental situations. We find clear evidence for these unexpected dynamically induced oscillations both in the propagation of the interface and in the resulting density of the cluster. We describe the general features of the spectra of the oscillations, and briefly discuss possible experimental systems in which growth oscillations might be observed.

Quasiperiodic behaviour in growth oscillations

“…For irrational U, ( 7 ) shows a dense point spectrum with varying weights, which is qualitatively the feature of the spectra obtained in [4]. This is the quasiperiodic behaviour we seek.…”

“…clearly a reasonable assumption. Furthermore, its validity, at least as a semiquantitative guide to the effects of discreteness, is well supported by our study of several stochastic and deterministic models [2,4].…”

“…Letter to the Editor L99 1 should be a common occurrence in these power spectra. Indeed, this peak doubling has been observed in computer simulations of ballistic aggregation [4].…”

“…(If ( 4) is not obeyed, then this heuristic picture requires some modifications which involve, in the main, extracting a suitably defined average growth velocity to replace the parameter v in (4). See [4] for an example. )…”

Hierarchical deposition and scale-free networks: A visibility algorithm approach

“…Here, we will consider the hierarchical deposition model (HDM) that was introduced in Ref. [11], which assumes that particles are deposited according to a power law as a function of their size in a synchronous fashion, where particles of the same size are all deposited simultaneously in "generations", analogous to a finite density aggregation process where the incoming particle flux can be controlled [12][13][14]. Similar studies on systems with power-law particle distributions investigated sequential deposition by including a power-law distributed noise, resulting in rare-event dominated fluctuations [15,16].…”