From surface scum to fractal swirls.Flecks of soapy scum floating on the surface of water draining out of a bathtub sometimes gather into intricate patterns. The geometry of the resulting patterns provides a snapshot of currents within the draining water. These convoluted flows cause local upwelling up·well·ing
1. The act or an instance of rising up from or as if from a lower source: an upwelling of emotion.
2. in some locations and downwelling Downwelling is the process of accumulation and sinking of higher density material beneath lower density material, such as cold or saline water beneath warmer or fresher water or cold air beneath warm air. It is the sinking limb of a convection cell. --where floating particles tend to collect - in others.
Two physicists have now applied this phenomenon to demonstrate a direct link between the complicated motion of a fluid and the resulting fractal pattern displayed by an aggregate of floating particles. Fractals are complex shapes that look roughly the same whether greatly magnified or viewed from a distance.
Researchers have noted fractal patterns in the shapes of clouds, the branching of blood vessels Blood vessels
Tubular channels for blood transport, of which there are three principal types: arteries, capillaries, and veins. Only the larger arteries and veins in the body bear distinct names. , the jaggedness of coastlines, and the roughness of fractured rocks. But there has been no obvious connection between such patterns and the physical processes responsible for creating them.
"[Our] research may be a first step on the road to understanding why fractals exist in nature,' says John C. Sommerer of the Johns Hopkins University Johns Hopkins University, mainly at Baltimore, Md. Johns Hopkins in 1867 had a group of his associates incorporated as the trustees of a university and a hospital, endowing each with $3.5 million. Daniel C. Applied Physics Laboratory The Johns Hopkins University Applied Physics Laboratory (APL), located in Laurel, Maryland, is a not-for-profit, university-affiliated research center employing 4,000 people. in Laurel, Md. Sommerer and Edward Ott of the University of Maryland University of Maryland can refer to:
The researchers' apparatus - their scum machine - consists of a cylindrical tub sitting inside a larger, taller cylindrical tub. Both are filled with a thick syrup. A pump forces the syrup upward between the inner and outer cylinders. The flowing syrup crosses over the inner cylinder's lip, then moves downward to drain out of a central spout. Tiny plastic spheres that fluoresce fluo·resce
intr.v. fluo·resced, fluo·resc·ing, fluo·resc·es
To undergo, produce, or show fluorescence.
[Back-formation from fluorescence. in ultraviolet light float on the liquid's surface.
With steady pumping and under perfectly symmetrical conditions, these tracer particles would simply converge on the exit. But a sequence of pumping pulses produces a complicated, unstable flow, and the particles gather wherever the flow is downward.
By photographing the tracer particles under ultraviolet light, the researchers obtain images from which they can derive the Lyapunov exponent, which indicates how rapidly the paths of nearby particles spread apart. They can also measure the fractal dimension - the intricacy in·tri·ca·cy
n. pl. in·tri·ca·cies
1. The condition or quality of being intricate; complexity.
2. Something intricate: the intricacies of a census form.
Noun 1. - of the resulting pattern.
The results show that the fractal characteristics of the patterned surface quantitatively mirror the physical process that created the pattern, as characterized by its Lyapunov exponent.
"This establishes that a fractal's dimension is related in some way to the set of forces that produce it," Sommerer says. "In our experiment, we have a fractal, and we know where it comes from."