Generic occurrence of rings in rotating systems

In rotating scattering systems, the generic saddle-center scenario leads to stable islands in phase space. Non-interacting particles whose initial conditions are defined in such islands will be trapped and form rotating rings. This result is generic and also holds for systems quite different from planetary rings.Comment: 10 pages, 5 ps figures; uses elsart.sty and epsfig.sty Accepted in Phys. Lett.

Volume growth, eigenvalue and compactness for self-shrinkers

In this paper, we show an optimal volume growth for self-shrinkers, and estimate a lower bound of the first eigenvalue of $\mathcal{L}$ operator on self-shrinkers, inspired by the first eigenvalue conjecture on minimal hypersurfaces in the unit sphere by Yau \cite{SY}. By the eigenvalue estimates, we can prove a compactness theorem on a class of compact self-shrinkers in \ir{3} obtained by Colding-Minicozzi under weaker conditions.Comment: 17 page

Filtration and transport of heavy metals in graphene oxide enabled sand columns

A fixed-bed sand column with graphene oxide (GO) layer was used to remove heavy metals (Cu(II) and Pb(II)) from an aqueous solution injected under steady flow. Due to the time constrained kinetic process of heavy metal sorption to GO, removal efficiency was affected by the injection flow rate. When injection flow rate changed from 1 to 5 mL min−1, the removal efficiency of the two metals decreased from 15.3% to 10.3% and from 26.7% to 19.0% for Cu(II) and Pb(II), respectively. Provided a fixed concentration of heavy metals in the injected flow, an increase in GO in column from 10 to 30 mg resulted in an sharp increase in the removal efficiency of Pb(II) from 26.7% to 40.5%. When Cu(II) and Pb(II) were applied simultaneously, the removal efficiency of the two metals was lower than when applied by individually. GO-sand column performance was much better for the removal of Pb(II) than for Cu(II) in each corresponding treatment. When breakthrough curve (BTC) data were simulated by the convection-dispersion-reaction (CDER) model, the fittings for Cu in every treatment were better than that of Pb in corresponding treatment. Considering the small amount of GO used to enable the sand columns that resulted in a great increase in k value, compared to the GO-free sand columns, the authors propose GO as an effective adsorption media in filters and reactive barriers to remove Pb(II) from flowing water

Entanglement Entropy and Mutual Information in Bose-Einstein Condensates

In this paper we study the entanglement properties of free {\em non-relativistic} Bose gases. At zero temperature, we calculate the bipartite block entanglement entropy of the system, and find it diverges logarithmically with the particle number in the subsystem. For finite temperatures, we study the mutual information between the two blocks. We first analytically study an infinite-range hopping model, then numerically study a set of long-range hopping models in one-deimension that exhibit Bose-Einstein condensation. In both cases we find that a Bose-Einstein condensate, if present, makes a divergent contribution to the mutual information which is proportional to the logarithm of the number of particles in the condensate in the subsystem. The prefactor of the logarithmic divergent term is model dependent.Comment: 12 pages, 6 figure

Fully Bayesian Penalized Regression with a Generalized Bridge Prior

We consider penalized regression models under a unified framework. The particular method is determined by the form of the penalty term, which is typically chosen by cross validation. We introduce a fully Bayesian approach that incorporates both sparse and dense settings and show how to use a type of model averaging approach to eliminate the nuisance penalty parameters and perform inference through the marginal posterior distribution of the regression coefficients. We establish tail robustness of the resulting estimator as well as conditional and marginal posterior consistency for the Bayesian model. We develop a component-wise Markov chain Monte Carlo algorithm for sampling. Numerical results show that the method tends to select the optimal penalty and performs well in both variable selection and prediction and is comparable to, and often better than alternative methods. Both simulated and real data examples are provided

Superconducting gap symmetry of Ba0.6K0.4Fe2As2 studied by angle-resolved photoemission spectroscopy

We have performed high-resolution angle-resolved photoemission spectroscopy on the optimally-doped Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ compound and determined the accurate momentum dependence of the superconducting (SC) gap in four Fermi-surface sheets including a newly discovered outer electron pocket at the M point. The SC gap on this pocket is nearly isotropic and its magnitude is comparable ($\Delta$ $\sim$ 11 meV) to that of the inner electron and hole pockets ($\sim$12 meV), although it is substantially larger than that of the outer hole pocket ($\sim$6 meV). The Fermi-surface dependence of the SC gap value is basically consistent with $\Delta$($k$) = $\Delta$$_0$cos$k_x$cos$k_y$ formula expected for the extended s-wave symmetry. The observed finite deviation from the simple formula suggests the importance of multi-orbital effects.Comment: 4 pages, 3 figures, 1 tabl