Unified description of long-time tails and long-range correlation functions for sheared granular liquids

Unified description on the long-time tail of velocity autocorrelation function and the long-range correlation for the equal-time spatial correlation functions is developed based on the generalized fluctuating hydrodynamics. The cross-over of the long-time tail from $t^{-3/2}$ to $t^{-5/2}$ is predicted independent of the density, and the equal-time spatial density correlation function and the equal-time spatial velocity correlation function respectively satisfy $r^{-11/3}$ and $r^{-5/3}$ for large $r$ limit.Comment: 10 pages. to be published in Euro. Phys. J.

What\u27s Average and What\u27s Not AboutAttractive Faces

We reported in this journal (Langlois & Roggman, 1990) findings showing that attractive faces are those that represent the mathematical average of faces in a population. These findings were intriguing because they provided a parsimonious definition of facial attractiveness and because they supported explanations of attractiveness from the point of view of both evolutionary and cognitive-prototype theory. Since our 1990 report, several alternative explanations of our findings have been offered. In this article, we show that none of these alternatives explains our results adequately