## Posts Tagged ‘order’

### Symmetry, shape and order, and the predictive powers of h-index

December 4, 2007

A couple of interesting papers in the latest issue of PNAS:

• Symmetry, shape and order by Trovato et al:

Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low-temperature phases of matter. In celebrated work, Kepler conjectured that the densest packing of spheres is realized by stacking variants of the face-centered-cubic lattice and has a packing fraction of $\pi/(3 \sqrt{2}) \approx 0.7405$. Much more recently, an unusually high-density packing of $\approx 0.770732$ was achieved for congruent ellipsoids. Such studies are relevant for understanding the structure of crystals, glasses, the storage and jamming of granular materials, ceramics, and the assembly of viral capsid structures. Here, we carry out analytical studies of the stacking of close-packed planar layers of systems made up of truncated cones possessing uniaxial symmetry. We present examples of high-density packing whose order is characterized by a broken symmetry arising from the shape of the constituent objects. We find a biaxial arrangement of solid cones with a packing fraction of $\pi/4$. For truncated cones, there are two distinct regimes, characterized by different packing arrangements, depending on the ratio c of the base radii of the truncated cones with a transition at $c^{\star} = \sqrt{2} - 1$.

• Does the h index have predictive power? by J E Hirsch:

Bibliometric measures of individual scientific achievement are of particular interest if they can be used to predict future achievement. Here we report results of an empirical study of the predictive power of the h index compared with other indicators. Our findings indicate that the h index is better than other indicators considered (total citation count, citations per paper, and total paper count) in predicting future scientific achievement. We discuss reasons for the superiority of the h index.