A driven two-dimensional granular gas with Coulomb friction

We study a homogeneously driven granular gas of inelastic hard particles with rough surfaces subject to Coulomb friction. The stationary state as well as the full dynamic evolution of the translational and rotational granular temperatures are investigated as a function of the three parameters of the friction model. Four levels of approximation to the (velocity-dependent) tangential restitution are introduced and used to calculate translational and rotational temperatures in a mean field theory. When comparing these theoretical results to numerical simulations of a randomly driven mono-layer of particles subject to Coulomb friction, we find that already the simplest model leads to qualitative agreement, but only the full Coulomb friction model is able to reproduce/predict the simulation results quantitatively for all magnitudes of friction. In addition, the theory predicts two relaxation times for the decay to the stationary state. One of them corresponds to the equilibration between the translational and rotational degrees of freedom. The other one, which is slower in most cases, is the inverse of the common relaxation rate of translational and rotational temperatures.Comment: 23 pages, 17 figure

Anthropogenic ²³⁶U in the North Sea – A Closer Look into a Source Region

In this study we present new seawater data of ²³⁶U and ²³⁸U sampled in the North Sea in 2010. The North Sea has been and is still receiving a considerable input of anthropogenic radionuclides from nuclear reprocessing facilities located in La Hague (France) and Sellafield (Great Britain). It therefore represents an important source region for oceanographic tracer studies using the transient signal of anthropogenic ²³⁶U. A proper knowledge of the sources of ²³⁶U is an essential prerequisite for such tracer studies. The ²³⁶U data set presented in this study covers the transition regions of the North Sea to the Atlantic Ocean, to the Baltic Sea, and upstream the Elbe River. It is discussed in the context of available ²³⁶U data from the literature. Our results show that both ²³⁶U concentrations and ²³⁶U/²³⁸U ratios in surface waters of the North Sea can be explained by simple binary mixing models implying that ²³⁶U behaves conservatively in seawater. We further show that the input of ²³⁶U by the Elbe River is negligible, while there might be a maximum input of 12 g/yr via the Baltic Sea. The results of the mixing models suggest that this still unidentified ²³⁶U contamination could be supplied by fresh water input