The entropy evolution of a noncommutative black hole under Hawking radiation

By calculating the entropy of a scalar field in the interior volume of noncommutative black holes and considering an infinitesimal process of Hawking radiation, a proportion function is constructed that reflects the evolution relation between the scalar field entropy and Bekenstein–Hawking entropy under Hawking radiation. Comparing with the case of Schwarzschild black holes, the new physics of this research can be expanded to the later stage of Hawking radiation. From the result, we find that the proportion function is still a constant in the earlier stage of Hawking radiation, which is identical to the case of Schwarzschild black holes. As Hawking radiation goes into the later stage, the behavior of the function will be dominated by the noncommutative effect. In this circumstance, the proportion function is no longer a constant and decreases with the evaporation process. When the noncommutative black hole evolves into its final state with Hawking radiation, the interior volume will converge to a certain value, which implies that the loss of information of the black hole during the evaporation process will finally be stored in the limited interior volume.

Derivation Method for the Foundation Boundaries of Hydraulic Numerical Simulation Models Based on the Elastic Boussinesq Solution

The foundation boundaries of numerical simulation models of hydraulic structures dominated by a vertical load are investigated. The method used is based on the stress formula for fundamental solutions to semi-infinite space body elastic mechanics under a vertical concentrated force. The limit method is introduced into the original formula, which is then partitioned and analyzed according to the direction of the depth extension of the foundation. The point load will be changed to a linear load with a length of2a. Inverse proportion function assumptions are proposed at parameteraand depthlof the calculation points to solve the singularity questions of elastic stress in a semi-infinite space near the ground. Compared with the original formula, changing the point load to a linear load with a length of2ais more reasonable. Finally, the boundary depth criterion of a hydraulic numerical simulation model is derived and applied to determine the depth boundary formula for gravity dam numerical simulations.