Calculation of the Voronoi boundary for lens-shaped particles and spherocylinders

We have recently developed a mean-field theory to estimate the packing fraction of non-spherical particles [A. Baule et al., Nature Commun. (2013)]. The central quantity in this framework is the Voronoi excluded volume, which generalizes the standard hard-core excluded volume appearing in Onsager's theory. The Voronoi excluded volume is defined from an exclusion condition for the Voronoi boundary between two particles, which is usually not tractable analytically. Here, we show how the technical difficulties in calculating the Voronoi boundary can be overcome for lens-shaped particles and spherocylinders, two standard prolate and oblate shapes with rotational symmetry. By decomposing these shapes into unions and intersections of spheres analytical expressions can be obtained.Comment: 19 pages, 8 figure

Experimental measurement of an effective temperature for jammed granular materials

A densely packed granular system is an example of an out-of-equilibrium system in the jammed state. It has been a longstanding problem to determine whether this class of systems can be described by concepts arising from equilibrium statistical mechanics, such as an ``effective temperature'' and ``compactivity''. The measurement of the effective temperature is realized in the laboratory by slowly shearing a closely-packed ensemble of spherical beads confined by an external pressure in a Couette geometry. All the probe particles considered in this study, independent of their characteristic features, equilibrate at the same temperature, given by the packing density of the system.Comment: 22 pages, 7 figures, more informations at http://www.jamlab.or

Large cities are less green

We study how urban quality evolves as a result of carbon dioxide emissions as urban agglomerations grow. We employ a bottom-up approach combining two unprecedented microscopic data on population and carbon dioxide emissions in the continental US. We first aggregate settlements that are close to each other into cities using the City Clustering Algorithm (CCA) defining cities beyond the administrative boundaries. Then, we use data on $\rm{CO}_2$ emissions at a fine geographic scale to determine the total emissions of each city. We find a superlinear scaling behavior, expressed by a power-law, between $\rm{CO}_2$ emissions and city population with average allometric exponent $\beta = 1.46$ across all cities in the US. This result suggests that the high productivity of large cities is done at the expense of a proportionally larger amount of emissions compared to small cities. Furthermore, our results are substantially different from those obtained by the standard administrative definition of cities, i.e. Metropolitan Statistical Area (MSA). Specifically, MSAs display isometric scaling emissions and we argue that this discrepancy is due to the overestimation of MSA areas. The results suggest that allometric studies based on administrative boundaries to define cities may suffer from endogeneity bias

Unexpected Density Fluctuations in Jammed Disordered Sphere Packings

We computationally study jammed disordered hard-sphere packings as large as a million particles. We show that the packings are saturated and hyperuniform, i.e., that local density fluctuations grow only as a logarithmically-augmented surface area rather than the volume of the window. The structure factor shows an unusual non-analytic linear dependence near the origin, $S(k)\sim|k|$. In addition to exponentially damped oscillations seen in liquids, this implies a weak power-law tail in the total correlation function, $h(r)\sim-r^{-4}$, and a long-ranged direct correlation function.Comment: Submitted for publicatio