By the statistical entropy of the Dirac field of the static spherically symmetric black hole, the result is obtained that the radiation energy flux of the black hole is proportional to the quartic of the temperature of its event horizon. That is, the thermal radiation of the black hole always satisfies the generalised Stenfan-Boltzmann law. The derived generalised Stenfan-Boltzmann coefficient is no longer a constant. When the cut-off distance and the thin film thickness are both fixed, it is a proportional coefficient related to the space-time metric near the event horizon and the average radial effusion velocity of the radiation particles from the thin film. Finally, the radiation energy fluxes and the radiation powers of the Schwarzschild black hole and the Reissner-NordstrSm black hole are derived, separately.
The spin-weighted spheroidal equation in the case of s = 1/2 is thoroughly studied by using the perturbation method from the supersymmetric quantum mechanics. The first-five terms of the superpotential in the series of parameter β are given. The general form for the n-th term of the superpotential is also obtained, which could also be derived from the previous terms Wk, k 〈 n. From these results, it is easy to obtain the ground eigenfunction of the equation. Furthermore, the shape-invariance property in the series of parameter β is investigated and is proven to be kept. This nice property guarantees that the excited eigenfunctions in the series form can be obtained from the ground eigenfunction by using the method from the supersymmetric quantum mechanics. We show the perturbation method in supersymmetric quantum mechanics could completely solve the spin-weight spheroidal wave equations in the series form of the small parameter β.
A systematic study has been performed to investigate the flow and thermal patterns of vertical rotating Thomas Swan MOCVD reactor at low pressure,using 2-D dynamic modeling.By varying and calculating the several important process parameters of the reactor,the optimized conditions of the uniform distributions of velocity and temperature profiles in steady state have been obtained.Then,time-dependent models with the step response perturbation of the total gas rate can help identify the visual transient behavior inside the reactor and analyze the mechanism of delay time,relaxation oscillation and pulsative oscillation.These results are beneficial to the process parameter optimization and geometrical configuration design of the MOCVD reactor.
ZHONG ShuQuan REN XiaoMin HUANG YongQing WANG Qi HUANG Hui
