A universal scaling law for the evolution of granular gases

Dry, freely evolving granular materials in a dilute gaseous state coalesce into dense clusters only due to dissipative interactions. This clustering transition is important for a number of problems ranging from geophysics to cosmology. Here we show that the evolution of a dilute, freely cooling granular gas is determined in a universal way by the ratio of inertial flow and thermal velocities, that is, the Mach number. Theoretical calculations and direct numerical simulations of the granular Navier--Stokes equations show that irrespective of the coefficient of restitution, density or initial velocity distribution, the density fluctuations follow a universal quadratic dependence on the system's Mach number. We find that the clustering exhibits a scale-free dynamics but the clustered state becomes observable when the Mach number is approximately of $\mathcal{O}(1)$. Our results provide a method to determine the age of a granular gas and predict the macroscopic appearance of clusters

Enhancement of the Electron Spin Resonance of Single-Walled Carbon Nanotubes by Oxygen Removal

We have observed a nearly fourfold increase in the electron spin resonance (ESR) signal from an ensemble of single-walled carbon nanotubes (SWCNTs) due to oxygen desorption. By performing temperature-dependent ESR spectroscopy both before and after thermal annealing, we found that the ESR in SWCNTs can be reversibly altered via the molecular oxygen content in the samples. Independent of the presence of adsorbed oxygen, a Curie-law (spin susceptibility $\propto 1/T$) is seen from $\sim$4 K to 300 K, indicating that the probed spins are finite-level species. For both the pre-annealed and post-annealed sample conditions, the ESR linewidth decreased as the temperature was increased, a phenomenon we identify as motional narrowing. From the temperature dependence of the linewidth, we extracted an estimate of the intertube hopping frequency; for both sample conditions, we found this hopping frequency to be $\sim$100 GHz. Since the spin hopping frequency changes only slightly when oxygen is desorbed, we conclude that only the spin susceptibility, not spin transport, is affected by the presence of physisorbed molecular oxygen in SWCNT ensembles. Surprisingly, no linewidth change is observed when the amount of oxygen in the SWCNT sample is altered, contrary to other carbonaceous systems and certain 1D conducting polymers. We hypothesize that physisorbed molecular oxygen acts as an acceptor ($p$-type), compensating the donor-like ($n$-type) defects that are responsible for the ESR signal in bulk SWCNTs.Comment: 14 pages, 7 figure