Unstable Galaxy Models

The dynamics of collisionless galaxy can be described by the Vlasov-Poisson system. By the Jean's theorem, all the spherically symmetric steady galaxy models are given by a distribution of {\Phi}(E,L), where E is the particle energy and L the angular momentum. In a celebrated Doremus-Feix-Baumann Theorem, the galaxy model {\Phi}(E,L) is stable if the distribution {\Phi} is monotonically decreasing with respect to the particle energy E. On the other hand, the stability of {\Phi}(E,L) remains largely open otherwise. Based on a recent abstract instability criterion of Guo-Lin, we constuct examples of unstable galaxy models of f(E,L) and f(E) in which f fails to be monotone in E

Estimating the value of containment strategies in delaying the arrival time of an influenza pandemic: A case study of travel restriction and patient isolation

With a simple phenomenological metapopulation model, which characterizes the invasion process of an influenza pandemic from a source to a subpopulation at risk, we compare the efficiency of inter- and intra-population interventions in delaying the arrival of an influenza pandemic. We take travel restriction and patient isolation as examples, since in reality they are typical control measures implemented at the inter- and intra-population levels, respectively. We find that the intra-population interventions, e.g., patient isolation, perform better than the inter-population strategies such as travel restriction if the response time is small. However, intra-population strategies are sensitive to the increase of the response time, which might be inevitable due to socioeconomic reasons in practice and will largely discount the efficiency.Comment: 5 pages,3 figure

Band structure reconstruction across nematic order in high quality FeSe single crystal as revealed by optical spectroscopy study

We perform an in-plane optical spectroscopy measurement on high quality FeSe single crystals grown by a vapor transport technique. Below the structural transition at $T_{\rm s}\sim$90 K, the reflectivity spectrum clearly shows a gradual suppression around 400 cm$^{-1}$ and the conductivity spectrum shows a peak at higher frequency. The energy scale of this gap-like feature is comparable to the width of the band splitting observed by ARPES. The low-frequency conductivity consists of two Drude components and the overall plasma frequency is smaller than that of the FeAs based compounds, suggesting a lower carrier density or stronger correlation effect. The plasma frequency becomes even smaller below $T_{\rm s}$ which agrees with the very small Fermi energy estimated by other experiments. Similar to iron pnictides, a clear temperature-induced spectral weight transfer is observed for FeSe, being indicative of strong correlation effect.Comment: 6 page