Pairing State with a time-reversal symmetry breaking in FeAs based superconductors

We investigate the competition between the extended $s_{\pm}$-wave and $d_{x^2-y^2}$-wave pairing order parameters in the iron-based superconductors. Because of the frustrating pairing interactions among the electron and the hole fermi pockets, a time reversal symmetry breaking $s+id$ pairing state could be favored. We analyze this pairing state within the Ginzburg-Landau theory, and explore the experimental consequences. In such a state, spatial inhomogeneity induces supercurrent near a non-magnetic impurity and the corners of a square sample. The resonance mode between the $s_{\pm}$ and $d_{x^2-y^2}$-wave order parameters can be detected through the $B_{1g}$-Raman spectroscopy.Comment: 4 pages, 4 figures, new references adde

Tracing the Attention of Moving Citizens

With the widespread use of mobile computing devices in contemporary society, our trajectories in the physical space and virtual world are increasingly closely connected. Using the anonymous smartphone data of $1 \times 10^5$ users in 30 days, we constructed the mobility network and the attention network to study the correlations between online and offline human behaviours. In the mobility network, nodes are physical locations and edges represent the movements between locations, and in the attention network, nodes are websites and edges represent the switch of users between websites. We apply the box-covering method to renormalise the networks. The investigated network properties include the size of box $l_B$ and the number of boxes $N(l_B)$. We find two universal classes of behaviours: the mobility network is featured by a small-world property, $N(l_B) \simeq e^{-l_B}$, whereas the attention network is characterised by a self-similar property $N(l_B) \simeq l_B^{-\gamma}$. In particular, with the increasing of the length of box $l_B$, the degree correlation of the network changes from positive to negative which indicates that there are two layers of structure in the mobility network. We use the results of network renormalisation to detect the community and map the structure of the mobility network. Further, we located the most relevant websites visited in these communities, and identified three typical location-based behaviours, including the shopping, dating, and taxi-calling. Finally, we offered a revised geometric network model to explain our findings in the perspective of spatial-constrained attachment.Comment: 15 pages, 8 figure

A Fractional Lie Group Method For Anomalous Diffusion Equations

Lie group method provides an efficient tool to solve a differential equation. This paper suggests a fractional partner for fractional partial differential equations using a fractional characteristic method. A space-time fractional diffusion equation is used as an example to illustrate the effectiveness of the Lie group method.Comment: 5 pages,in pres