Tenuous structures from disorderly growth processes

Colloidal aggregation and other random growth processes produce structures that behave differently from ordinary bulk matter. Much of this behavior can be described in terms of the invariance of the aggregates under changes of spatial length scale: they appear to be fractals. There are two types of basic mechanisms for producing fractal aggregates. Those in which aggregation proceeds cluster by cluster can be understood qualitatively in terms of a solvable schematic model. The diffusion-limited aggregation or deposition of individual particles to make a large cluster is not as well understood. It is closely related to several irreversible processes in other areas of physics, such as two-fluid displacement in porous materials and the dielectric breakdown of insulators. More generally, disorderly growth mechanisms provide structures having unique properties, many of which can be understood by using simple statistical principles.     

Periodicity in tree rings from the corn belt

Previous tree-ring studies indicated that the total area affected by drought in the western United States has rhythmically expanded and contracted over the past 300 years, with a period near the 18.6-year lunar nodal and 22-year double-sunspot cycles. Recently collected tree-ring data from the U.S. Corn Belt for the years 1680 to 1980 were examined for evidence of either of these cycles on a regional scale. Spectral analysis indicated no periodicity in the eastern part of the Corn Belt, but a significant 18.33-year period in the western part. The period length changed from 17.60 to 20.95 years between the first 150 years and the last 151. High-resolution frequency analysis showed that the structure of the 18.33-year spectral peak was complex, with contributions from several frequencies near both the lunar nodal and double-sunspot periods. A t-test of difference of means in reconstructed annual precipitation weakly corroborated a previous finding of an association between drought area and the phase of the double-sunspot cycle. Both the high-resolution frequency analysis and the t-test results indicate that the periodic component of drought near 20 years is too weak and irregular to be of use in drought forecasting for the Corn Belt.