Universal Non-Debye Scaling in the Density of States of Amorphous Solids.

At the jamming transition, amorphous packings are known to display anomalous vibrational modes with a density of states (DOS) that remains constant at low frequency. The scaling of the DOS at higher packing fractions remains, however, unclear. One might expect to find a simple Debye scaling, but recent results from effective medium theory and the exact solution of mean-field models both predict an anomalous, non-Debye scaling. Being mean-field in nature, however, these solutions are only strictly valid in the limit of infinite spatial dimension, and it is unclear what value they have for finite-dimensional systems. Here, we study packings of soft spheres in dimensions 3 through 7 and find, away from jamming, a universal non-Debye scaling of the DOS that is consistent with the mean-field predictions. We also consider how the soft mode participation ratio evolves as dimension increases.

Internal carotid arterial canal size and scaling in Euarchonta: Re-assessing implications for arterial patency and phylogenetic relationships in early fossil primates.

Primate species typically differ from other mammals in having bony canals that enclose the branches of the internal carotid artery (ICA) as they pass through the middle ear. The presence and relative size of these canals varies among major primate clades. As a result, differences in the anatomy of the canals for the promontorial and stapedial branches of the ICA have been cited as evidence of either haplorhine or strepsirrhine affinities among otherwise enigmatic early fossil euprimates. Here we use micro X-ray computed tomography to compile the largest quantitative dataset on ICA canal sizes. The data suggest greater variation of the ICA canals within some groups than has been previously appreciated. For example, Lepilemur and Avahi differ from most other lemuriforms in having a larger promontorial canal than stapedial canal. Furthermore, various lemurids are intraspecifically variable in relative canal size, with the promontorial canal being larger than the stapedial canal in some individuals but not others. In species where the promontorial artery supplies the brain with blood, the size of the promontorial canal is significantly correlated with endocranial volume (ECV). Among species with alternate routes of encephalic blood supply, the promontorial canal is highly reduced relative to ECV, and correlated with both ECV and cranium size. Ancestral state reconstructions incorporating data from fossils suggest that the last common ancestor of living primates had promontorial and stapedial canals that were similar to each other in size and large relative to ECV. We conclude that the plesiomorphic condition for crown primates is to have a patent promontorial artery supplying the brain and a patent stapedial artery for various non-encephalic structures. This inferred ancestral condition is exhibited by treeshrews and most early fossil euprimates, while extant primates exhibit reduction in one canal or another. The only early fossils deviating from this plesiomorphic condition are Adapis parisiensis with a reduced promontorial canal, and Rooneyia and Mahgarita with reduced stapedial canals.