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Number 403, November 20, 1998 by Phillip F. Schewe and Ben Stein
CLUSTERING AND COLLAPSE IN GRANULAR MATERIAL. Collections of grains (salt, sand, sugar, seeds, steel balls, etc.) represent a sort of 4th state of matter. Granular materials share some properties with solids (they bear loads), liquids (they pour), and ideal gases (they constitute collections of non-cohesive particles), but they also have peculiar properties of their own. For one thing temperature is not important. Freezing or baking grains doesn't make them flow any better. The thermal energy of a grain is a trillion times less than the energy it takes to lift one grain on top of another. In an effort to explore the differences and similarities between granular materials and other types of matter, scientists often tumble and shake grains in various containers. In one experiment at Georgetown University (Jeffrey Olafsen, 202- 687-6004, olafsen@physics.georgetown.edu) a layer of thousands of tiny steel balls on a tray is vertically shaken. This agitated system can be "cooled" by decreasing the amplitude of the shaking. Below a certain "granular temperature" the balls start to cluster together. In a still cooler state, many of the balls collapse (one might say crystallize) into a condensate which remains at rest even as other balls continue to move about. Besides wanting to apply knowledge about granular materials in a variety of industrial settings (foodstuffs, paint mixing, pharmaceuticals, agriculture), researchers hope to find more relations among the many things in the universe that clump and condense (atoms, bacteria, galaxies). Olafsen will report these findings next week at the 1998 Meeting of the APS Division of Fluid Dynamics in Philadelphia. (See also Olafsen and Urbach, Physical Review Letters, 16 Nov 1998 and Pouliquen et al., Physical Review Letters, 10 Nov 1997; see figure at Physics News Graphics.)
DOES CHAOS AFFECT THE COURSE OF AN ARMS RACE? Yes, it may, particularly when great disparities exist between two nations' economies (as is the case with the US and Iraq), according to a new mathematical model developed by researchers in Japan (Mitsuo Kono, Chuo University, kono@fps.chuo-u.ac.jp, 011-81-426-74-4161). In an attempt to mathematically model the feedback between two adversarial nations as each builds up arms stocks, British scientist Lewis F. Richardson published in 1949 a well-known set of equations with variables describing such things as a nation's military spending levels and parameters quantifying factors such as a nation's internal pressure against military spending. This model suffered from shortcomings, most notably that its linear equations provided all too predictable results; critics noted that many arms races spiral unpredictably out of control. In the Japanese researchers' model a nation's reaction to an enemy's weapons buildup is not automatically to build more weapons but is instead a function of the difference in weapons and military spending between two nations. This approach leads to more realistic nonlinear differential equations which quantify concepts normally unknown to physics, concepts such as fear, threat, grievance, and fatigue. Their model shows an arms race can progress in a mathematically chaotic fashion when the economic situation of the two countries is different, but is more predictable when the economies are more comparable (Tomochi and Kono in the journal Chaos, December 1998.)
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