Phenomenology and origin of growth oscillations: A simple stochastic model

Morphology of amorphous layers ballistically deposited on a planar substrate

“…Their conclusion was that in many models quasiperiodic irrational-frequency density fluctuations should be present, with density fluctuating on scales larger than the underlying particle-size "clock" length, 1 in our reduced units (2.2). It should be emphasized that fluctuations in density and other quantities (see Section 5) found in our work are not the "bulk" effect described in [12]. In fact, what we are observing is the "clock" particle-size fluctuations with underlying periodicity 1.…”

“…These fluctuations fade away for distances over 5-6 particle diameters from the wall. Therefore, the irrational-frequency fluctuations [12] cannot be present in the model considered here. Indeed, far from the wall even the basic particle-size periodicity is not preserved; the deposit is truly amorphous.…”

“…where x 1 is the first-moment displacement, Note that relations (4.3)-(4.5) for the density are recursive along the chains which are anyway approximate objects. In a series of papers [12], Savit and coworkers con--13 -sidered approximate recursive relations in time, for particle adhesion probability distribution within the growing kinetically-roughened interface. Their conclusion was that in many models quasiperiodic irrational-frequency density fluctuations should be present, with density fluctuating on scales larger than the underlying particle-size "clock" length, 1 in our reduced units (2.2).…”

Growth oscillations in ballistic aggregation

“…This is indeed the case, and is related to a conjecture concerning the generic relationship between growth oscillations and random fractal growth. See [ l ] and [2] for more details.…”

“…The oscillations, which may have wavelengths up to orders of magntidue larger than atomic distances, occur as a result of the beating between two length scales. The first is a static length scale characterising the size of the accreting material, and the second is a suitably defined, dynamically generated length scale, related, for example, to the velocity of the moving interface [ 1,2]. While the size of the effects we describe is typically rather small, they should be observable in carefully controlled experiments using recently developed techniques of growth and observation such as molecular beam epitaxy and scanning tunnelling microscopy.…”