Phase transition of holographic entanglement entropy in massive gravity

The phase structure of holographic entanglement entropy is studied in massive gravity for the quantum systems with finite and infinite volumes, which in the bulk is dual to calculate the minimal surface area for a black hole and black brane respectively. In the entanglement entropy$-$temperature plane, we find for both the black hole and black brane there is a Van der Waals-like phase transition as the case in thermal entropy$-$temperature plane. That is, there is a first order phase transition for the small charge and a second order phase transition at the critical charge. For the first order phase transition, the equal area law is checked and for the second order phase transition, the critical exponent of the heat capacity is obtained. All the results show that the phase structure of holographic entanglement entropy is the same as that of thermal entropy regardless of the volume of the spacetime on the boundary.Comment: 15 pages, many figures, some statments are adde

Soft Consistency Reconstruction: A Robust 1-bit Compressive Sensing Algorithm

A class of recovering algorithms for 1-bit compressive sensing (CS) named Soft Consistency Reconstructions (SCRs) are proposed. Recognizing that CS recovery is essentially an optimization problem, we endeavor to improve the characteristics of the objective function under noisy environments. With a family of re-designed consistency criteria, SCRs achieve remarkable counter-noise performance gain over the existing counterparts, thus acquiring the desired robustness in many real-world applications. The benefits of soft decisions are exemplified through structural analysis of the objective function, with intuition described for better understanding. As expected, through comparisons with existing methods in simulations, SCRs demonstrate preferable robustness against noise in low signal-to-noise ratio (SNR) regime, while maintaining comparable performance in high SNR regime

Unconventional Quantum Hall Effect and Tunable Spin Hall Effect in MoS2 Trilayers

We analyze the Landau level (LL) structure and spin Hall effect in a MoS2 trilayer. Due to orbital asymmetry, the low-energy Dirac fermions become heavily massive and the LL energies grow linearly with $B$, rather than with $\sqrt{B}$. Spin-orbital couplings break spin and valley degenerate LL's into two time reversal invariant groups, with LL crossing effects present in the valence bands. We find a field-dependent unconventional Hall plateau sequence $\nu=...$ $-2M-6$, $-2M-4$, $-2M-2$, $-2M-1$, ..., -5, -3, -1, 0, 2, 4 .... In a p-n junction, spin-resolved fractionally quantized conductance appears in two-terminal measurements with a controllable spin-polarized current that can be probed at the interface. We also show the tunability of zero-field spin Hall conductivity.Comment: 5 pages, 4 figure

Contributions of natural and human factors to increases in vegetation productivity in China

Increasing trends in vegetation productivity have been identified for the last three decades for many regions in the northern hemisphere including China. Multiple natural and human factors are possibly responsible for the increases in vegetation productivity, while their relative contributions remain unclear. Here we analyzed the long-term trends in vegetation productivity in China using the satellite-derived normalized difference vegetation index (NDVI) and assessed the relationships of NDVI with a suite of natural (air temperature, precipitation, photosynthetically active radiation (PAR), atmospheric carbon dioxide (CO2) concentrations, and nitrogen (N) deposition) and human (afforestation and improved agricultural management practices) factors. Overall, China exhibited an increasing trend in vegetation productivity with an increase of 2.7%. At the provincial scale, eleven provinces exhibited significant increases in vegetation productivity, and the majority of these provinces are located within the northern half of the country. At the national scale, annual air temperature was most closely related to NDVI and explained 36.8% of the variance in NDVI, followed by afforestation (25.5%) and crop yield (15.8%). Altogether, temperature, total forest plantation area, and crop yield explained 78.1% of the variance in vegetation productivity at the national scale, while precipitation, PAR, atmospheric CO2 concentrations, and N deposition made no significant contribution to the increases in vegetation productivity. At the provincial scale, each factor explained a part of the variance in NDVI for some provinces, and the increases in NDVI for many provinces could be attributed to the combined effects of multiple factors. Crop yield and PAR were correlated with NDVI for more provinces than were other factors, indicating that both elevated crop yield resulting from improved agricultural management practices and increasing diffuse radiation were more important than other factors in increasing vegetation productivity at the provincial scale. The relative effects of the natural and human factors on vegetation productivity varied with spatial scale. The true contributions of multiple factors can be obscured by the correlation among these variables, and it is essential to examine the contribution of each factor while controlling for other factors. Future changes in climate and human activities will likely have larger influences on vegetation productivity in China

An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation

In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional. For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.Comment: This paper has been accepted for publication in SCIENCE CHINA Mathematic