Early Tracking Behavior in Small-field Quintessence Models

We study several quintessence models which are singular at Q=0, and use a simple initial constraint $Q_i\ge H_{inflation}/2\pi$ to see when they enter tracking regime, disregarding the details of inflation. We find it can give strong constraints for the inverse power-law potential $V=V_0Q^{-\alpha}$, which has to enter tracking regime for ${\rm ln}z \sim 10$. While for the supergravity model $V=V_0Q^{-\alpha}{\rm exp}(kQ^2/2)$, the constraint is much weakened. For another kind inverse power-law potential $V=V_0{\rm exp}(\lambda/Q)$, it exhibits no constraints.Comment: 11 pages,5 figures. Improved versio

Spatiotemporal Analysis of Groundwater Recharge Trends and Variability in Northern Taiwan

In this study, the base flow estimation method was used to assess long‐term changes of groundwater recharge in Northern Taiwan. The Mann‐Kendall test was used to examine the characteristics of the trends. This was followed by trend slope calculation and change‐point analysis. The annual groundwater recharge was found to exhibit a significant upward trend for the Fushan and Hengxi stations (Tamsui river basin). On the other hand, the Ximen Bridge station (Lanyang river basin) recorded a significant downward trend. Calculations showed that the rate of change for the Fengshan and Touqian river basins was small (less than 10%). However, that for the following stations was greater than 30%: Fushan, Hengxi, Ximen Bridge, and Niudou (also in the Lanyang river basin). The results of the change‐point analysis further indicated a significant change‐point for the annual recharge at Fushan, Hengxi, and Ximen Bridge stations in 1999, 1983, and 2001, respectively. The findings can be used for regional hydrological studies and as reference for water resource planning

Social clustering in epidemic spread on coevolving networks

Even though transitivity is a central structural feature of social networks, its influence on epidemic spread on coevolving networks has remained relatively unexplored. Here we introduce and study an adaptive susceptible- infected-susceptible (SIS) epidemic model wherein the infection and network coevolve with nontrivial proba- bility to close triangles during edge rewiring, leading to substantial reinforcement of network transitivity. This model provides an opportunity to study the role of transitivity in altering the SIS dynamics on a coevolving network. Using numerical simulations and approximate master equations (AMEs), we identify and examine a rich set of dynamical features in the model. In many cases, AMEs including transitivity reinforcement provide accurate predictions of stationary-state disease prevalence and network degree distributions. Furthermore, for some parameter settings, the AMEs accurately trace the temporal evolution of the system. We show that higher transitivity reinforcement in the model leads to lower levels of infective individuals in the population, when closing a triangle is the dominant rewiring mechanism. These methods and results may be useful in developing ideas and modeling strategies for controlling SIS-type epidemics