Regular black holes with sub-Planckian curvature

We construct a sort of regular black holes with a sub-Planckian Kretschmann scalar curvature. The metric of this sort of regular black holes is characterized by an exponentially suppressing gravity potential as well as an asymptotically Minkowski core. In particular, with different choices of the potential form, they can reproduce the metric of Bardeen/Hayward/Frolov black hole at large scales. The heuristical derivation of this sort of black holes is performed based on the generalized uncertainty principle over curved spacetime which includes the effects of tidal force on any object with finite size which is bounded below by the minimal length.Comment: 22 pages, 12 figure

Changes in plant species richness distribution in Tibetan alpine grasslands under different precipitation scenarios

Species richness is the core of biodiversity-ecosystem functioning (BEF) research. Nevertheless, it is difficult to accurately predict changes in plant species richness under different climate scenarios, especially in alpine biomes. In this study, we surveyed plant species richness from 2009 to 2017 in 75 alpine meadows (AM), 199 alpine steppes (AS), and 71 desert steppes (DS) in the Tibetan Autonomous Region, China. Along with 20 environmental factors relevant to species settlement, development, and survival, we first simulated the spatial pattern of plant species richness under current climate conditions using random forest modelling. Our results showed that simulated species richness matched well with observed values in the field, showing an evident decrease from meadows to steppes and then to deserts. Summer precipitation, which ranked first among the 20 environmental factors, was further confirmed to be the most critical driver of species richness distribution. Next, we simulated and compared species richness patterns under four different precipitation scenarios, increasing and decreasing summer precipitation by 20% and 10%, relative to the current species richness pattern. Our findings showed that species richness in response to altered precipitation was grassland-type specific, with meadows being sensitive to decreasing precipitation, steppes being sensitive to increasing precipitation, and deserts remaining resistant. In addition, species richness at low elevations was more sensitive to decreasing precipitation than to increasing precipitation, implying that droughts might have stronger influences than wetting on species composition. In contrast, species richness at high elevations (also in deserts) changed slightly under different precipitation scenarios, likely due to harsh physical conditions and small species pools for plant recruitment and survival. Finally, we suggest that policymakers and herdsmen pay more attention to alpine grasslands in central Tibet and at low elevations where species richness is sensitive to precipitation changes

The commensurate state and lock-in in a holographic model

We study a holographic model in which the striped structure of charge density is spontaneously formed over an ionic lattice which breaks the translational symmetry explicitly. The effect of commensurate lock-in between the spontaneous stripes and the ionic lattice is observed when the lattice amplitude is large enough. We investigate the optical conductivity as a function of frequency in commensurate state and compare its characteristics during the phase transition from metallic phase to insulating phase. Notably, we find that the DC resistivity in lock-in state increases algebraically with lowering temperature, which is in line with the phenomenon observed in the holographic model for simulating the experimental behavior of Mott insulator in [Nature Phys. 14, no.10, 1049-1055 (2018)]. Moreover, in unlock-in state we find that the system may undergo a transient unstable process in which the real part of the conductivity exhibits a behavior with small negative values, while in lock-in state we find this phenomenon disappears. In addition, at lower temperature the pseudogap is observed for both unlock-in and lock-in states. This holographic model successfully demonstrates the commensurate lock-in signatures, and provides more information for understanding the interplay between ionic lattices and electronic lattices by holography.Comment: 25pages, 11 figure