Random packing of spheres.The familiar arrangement evident in piles of neatly stacked oranges at a supermarket represents the tightest possible packing of identical spheres (SN: 8/15/98, p. 103). The ordered spheres occupy 74 percent of the total space available. The fraction of space typically filled by randomly packed spheres--whether peas poured into a bag or ball bearings ball bearings n → roulement m à billes into a tin--has proved much more difficult to pin down. Now, chemist Salvatore Torquato and his coworkers at Princeton University Princeton University, at Princeton, N.J.; coeducational; chartered 1746, opened 1747, rechartered 1748, called the College of New Jersey until 1896. Schools and Research Facilities argue that traditional, empirical methods Empirical method is generally taken to mean the collection of data on which to base a theory or derive a conclusion in science. It is part of the scientific method, but is often mistakenly assumed to be synonymous with the experimental method. of achieving random packings--pouring followed by shaking for a sufficiently long time, for example--fail to give consistent results. The pouring rate and the amplitude and frequency of vibration can readily affect the final answer, they contend. Computer simulations of random packings reveal similar problems. To make the notion of random packing more consistent and mathematically precise, Torquato and his colleagues have introduced the concept of what they call a "maximally random jammed" state. A given sphere is jammed if it can't move when all the other spheres are fixed. The researchers focus on the most disordered arrangement in which all spheres are immobilized. The packing fraction packing fraction n. The quotient of the algebraic difference between the isotopic mass and the mass number of a nuclide, divided by its mass number, often interpreted as a measure of stability. for this state is about 64 percent. The researchers report their findings in the March 6 PHYSICAL REVIEW LETTERS Physical Review Letters is one of the most prestigious journals in physics.[1] Since 1958, it has been published by the American Physical Society as an outgrowth of The Physical Review. . |
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