Apparent horizon and gravitational thermodynamics of Universe in the Eddington-Born-Infeld theory

The thermodynamics of Universe in the Eddington-Born-Infeld (EBI) theory was restudied by utilizing the holographic-style gravitational equations that dominate the dynamics of the cosmical apparent horizon $\Upsilon_{A}$ and the evolution of Universe. We started in rewriting the EBI action of the Palatini approach into the Bigravity-type action with an extra metric $q_{\mu\nu}$. With the help of the holographic-style dynamical equations, we discussed the property of the cosmical apparent horizon $\Upsilon_{A}$ including timelike, spacelike and null characters, which depends on the value of the parameter of state $w_{m}$ in EBI Universe. The unified first law for the gravitational thermodynamics and the total energy differential for the open system enveloped by $\Upsilon_{A}$ in EBI Universe were obtained. Finally, applying the positive-heat-out sign convention, we derived the generalized second law of gravitational thermodynamics in EBI universe.Comment: 23 pages, 0 figure

Efficient Numerical Evaluation of Feynman Integral

Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with $\mathcal{O}(10^{-3})$ accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass.Comment: 8 pages, 5 figures, published in Chinese Physics

(3,6-Dibromo-o-phenyl­ene)dimethanol

The title compound, C8H8Br2O2, was synthesized from the hydrolysis of 1,4-dibromo-2,3-bis­(bromo­meth­yl)benzene. One intra­molecular O—H⋯O and two intra­molecular C—H⋯Br inter­actions occur. In the crystal, mol­ecules are linked into a chain running parallel to [010]. Adjacent chains are linked into a two-dimensional layer by a combination of inter­molecular O—H⋯O hydrogen bonds and C—H⋯π inter­actions