Saturday, June 30, 2012

Rose-petal accumulation dynamics

Contrary to the hypothesis suggested in the previous post, I suspect that non-aerodynamic factors are dominant in the formation of at least two of the pictured rose-petal accumulations.

In the case at the top here, it seems likely that the spider webs (just discernible against the black background) formed sticky nucleation points, trapping an initial collection of petals, which then accreted further layers, in much the same way that a crystal precipitates from solution.

Meanwhile, with respect to the largest pool of petals, adjacent to the slatted gate, the original hypothesis suggested some influence from the chair positioned at the exit of the passageway. This hypothesis was tested by removing the chair. No change was observed in the petal distribution, hence the hypothesis was refuted.

Closer inspection indicates that this accumulation occupies a shallow depression in the paving slabs (across which a thriving population of red insects hurries to and fro on inscrutable entomological errands). Given the occurrence of rain showers in the days preceding the petal pattern formation, it seems likely that this region became damper than its surroundings, increasing the local coefficient of friction, and nucleating the pool of petals.

These petal distribution inhomogeneities, then, are a consequence of positive feedback processes operating on small existing background inhomogeneities.

Did you never wonder as a child what was responsible for the small knots in a wooden fence? Or question why the knots were of different shapes and sizes, and why there was a knot here, and (k)not somewhere else? And why, for that matter, is one cloud shaped differently from another?

All these questions are special cases of a more general and profound question:

Why is the universe not exactly homogeneous?

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