Null geodesics and gravitational lensing in a nonsingular spacetime

In this paper, the null geodesics and gravitational lensing in a nonsingular spacetime are investigated. According to the nature of the null geodesics, the spacetime is divided into several cases. In the weak deflection limit, we find the influence of the nonsingularity parameter $q$ on the positions and magnifications of the images is negligible. In the strong deflection limit, the coefficients and observables for the gravitational lensing in a nonsingular black hole background and a weakly nonsingular spacetime are obtained. Comparing these results, we find that, in a weakly nonsingular spacetime, the relativistic images have smaller angular position and relative magnification, but larger angular separation than that of a nonsingular black hole. These results might offer a way to probe the spacetime nonsingularity parameter and put a bound on it by the astronomical instruments in the near future.Comment: 15 pages, 5 figures, 1 tabl

Gravity Localization and Effective Newtonian Potential for Bent Thick Branes

In this letter, we first investigate the gravity localization and mass spectrum of gravity KK modes on de Sitter and Anti-de Sitter thick branes. Then, the effective Newtonian gravitational potentials for these bent branes are discussed by the two typical examples. The corrections of the Newtonian potential turns out to be $\Delta U(r)\sim 1/r^{2}$ at small $r$ for both cases. These corrections are very different from that of the Randall-Sundrum brane model $\Delta U(r)\sim 1/r^{3}$.Comment: 6 pages, 2 figure

Geometric curvatures of plane symmetry black hole

In this paper, we study the properties and thermodynamic stability of the plane symmetry black hole from the viewpoint of geometry. Weinhold metric and Ruppeiner metric are obtained, respectively. The Weinhold curvature gives phase transition points, which correspond to the first-order phase transition only at N=1, where $N$ is a parameter in the plane symmetry black hole. While the Ruppeiner one shows first-order phase transition points for arbitrary $N\neq 1$. Both of which give no any information about the second-order phase transition. Considering the Legendre invariant proposed by Quevedo et. al., we obtain a unified geometry metric, which gives a correctly the behavior of the thermodynamic interactions and phase transitions. The geometry is also found to be curved and the scalar curvature goes to negative infinity at the Davies' phase transition points when the logarithmic correction is included.Comment: 16 pages, 6 figure

Chemical freeze-out parameters via functional renormalization group approach

We study the freeze-out parameters in a QCD-assisted effective theory that accurately captures the quantum and in-medium effects of QCD at low energies. Functional renormalization group approach is implemented in our work to incorporate the non-perturbative quantum, thermal and density fluctuations. By analyzing the calculated baryon number susceptibility ratios $\chi_{2}^{B}/\chi_{1}^{B}$ and $\chi_{3}^{B}/\chi_{2}^{B}$, we determine the chemical freeze-out temperatures and baryon chemical potentials in cases of hard thermal or dense loop improved $\mu$-dependent glue potential and $\mu$-independent glue potential. We calculate the ${\chi_{4}^{B}}/{\chi_{2}^{B}}\, (\kappa \sigma^{2})$ and ${\chi_{6}^{B}}/{\chi_{2}^{B}}$ along the freeze-out line for both cases. It's found that $\kappa \sigma^{2}$ exhibits a nonmonotonic behavior in low collision energy region and approach to one for lower collision energy. ${\chi_{6}^{B}}/{\chi_{2}^{B}}$ shows a similar complicated behavior in our calculation.Comment: 14 pages, 11 figures, 7 table

Adaptive evolution of the spike gene of SARS coronavirus: changes in positively selected sites in different epidemic groups

BACKGROUND: It is believed that animal-to-human transmission of severe acute respiratory syndrome (SARS) coronavirus (CoV) is the cause of the SARS outbreak worldwide. The spike (S) protein is one of the best characterized proteins of SARS-CoV, which plays a key role in SARS-CoV overcoming species barrier and accomplishing interspecies transmission from animals to humans, suggesting that it may be the major target of selective pressure. However, the process of adaptive evolution of S protein and the exact positively selected sites associated with this process remain unknown. RESULTS: By investigating the adaptive evolution of S protein, we identified twelve amino acid sites (75, 239, 244, 311, 479, 609, 613, 743, 765, 778, 1148, and 1163) in the S protein under positive selective pressure. Based on phylogenetic tree and epidemiological investigation, SARS outbreak was divided into three epidemic groups: 02–04 interspecies, 03-early-mid, and 03-late epidemic groups in the present study. Positive selection was detected in the first two groups, which represent the course of SARS-CoV interspecies transmission and of viral adaptation to human host, respectively. In contrast, purifying selection was detected in 03-late group. These indicate that S protein experiences variable positive selective pressures before reaching stabilization. A total of 25 sites in 02–04 interspecies epidemic group and 16 sites in 03-early-mid epidemic group were identified under positive selection. The identified sites were different between these two groups except for site 239, which suggests that positively selected sites are changeable between groups. Moreover, it was showed that a larger proportion (24%) of positively selected sites was located in receptor-binding domain (RBD) than in heptad repeat (HR)1-HR2 region in 02–04 interspecies epidemic group (p = 0.0208), and a greater percentage (25%) of these sites occurred in HR1–HR2 region than in RBD in 03-early-mid epidemic group (p = 0.0721). These suggest that functionally different domains of S protein may not experience same positive selection in each epidemic group. In addition, three specific replacements (F360S, T487S and L665S) were only found between 03-human SARS-CoVs and strains from 02–04 interspecies epidemic group, which reveals that selective sweep may also force the evolution of S genes before the jump of SARS-CoVs into human hosts. Since certain residues at these positively selected sites are associated with receptor recognition and/or membrane fusion, they are likely to be the crucial residues for animal-to-human transmission of SARS-CoVs, and subsequent adaptation to human hosts. CONCLUSION: The variation of positive selective pressures and positively selected sites are likely to contribute to the adaptive evolution of S protein from animals to humans