Number 857, February 28, 2008 by Phillip F. Schewe and Jason S. Bardi
Fractals Through Time
A new theoretical study looks at what fractal things look like not just when you magnify them in space (they are scale invariant: they look the same even at finer and finer size scales) but also when you magnify them in time---that is, when you look at them over finer and finer time intervals. Fractals are those geometrical shapes so tortuously indented as to take on extra dimensionality. For example, a nominally one-dimensional curve can, with enough switchbacks, begin to be characterized by a dimension somewhere between 1 and 2. In other words the curve starts to take on the properties of a surface. Similarly a two dimensional surface can be so dimpled as to acquire some “volume.” This fractal geometry is especially interesting to consider for minerals and for certain living things (such as tumors) where highly non-Euclidean interfaces are important.
In a new paper, Carlos Escudero of the Institute for Mathematics and Fundamental Physics in Madrid performs calculations of the dynamic scaling (how a surface changes in space and over time at several different scales) of growing structures, such as the kind of semiconductor films used in the microchip industry where, even under the most carefully controlled of conditions, rough (non-Euclidean) geometries can exist. He found that the moment-by-moment behavior of the surfaces are strongly effected by the fractal geometry. Escudero (34- 915616800, cel@imaff.cfmac.csic.es) will soon be testing his theories with colleagues in several practical areas of research, including the growth of tumor-like tissues in plants and the growth of semiconductor films. ( Physical Review Letters upcoming article)
More Spacecraft Velocity Anomalies
A new look at the trajectories for various spacecraft as they fly past the Earth finds in each case a tiny amount of surplus velocity. For craft that pursue a path mostly symmetrical with respect to the equator, the effect is minimal. For craft that pursue a more unsymmetrical path, the effect is larger. In the case of the NEAR asteroid rendevous craft (<http://near.jhuapl.edu/>), for instance, the velocity anomaly amounts to 13 mm/sec. Although this is only one-millionth of the total velocity, the precision of the velocity measurements, carried out by looking at the Doppler shift in radio waves bounced off the craft, is 0.1 mm/sec, and this suggests that the anomaly represents a real effect, one needing an explanation.
Some ten years ago another anomaly was identified for the Pioneer 10 spacecraft (see http://www.aip.org/pnu/1998/split/pnu391-1.htm) and a certain amount of controversy has clung to the subject since then. One of the researchers on that earlier measurement is part of the new study, conducted by Jet Propulsion Lab scientists. John D. Anderson (jdandy@earthlink.net, 626-449-0102) says that the JPL scientists are now working with German colleagues to search for possible velocity anomalies in the recent flyby of the Rosetta spacecraft. (Anderson et al., Physical Review Letters, upcoming article; designated as an editor’s suggested articlePhysical Review Letters)
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