The gravitational heat conduction and the hierarchical structure in solar interior

With the assumption of local Tsallis equilibrium, the newly defined gravitational temperature is calculated in the solar interior, whose distribution curve can be divided into three parts, the solar core region, radiation region and convection region, in excellent agreement with the solar hierarchical structure. By generalizing the Fourier law, one new mechanism of heat conduction, based on the gradient of the gravitational temperature, is introduced into the astrophysical system. This mechanism is related to the self-gravity of such self-gravitating system whose characteristic scale is large enough. It perhaps plays an important role in the astrophysical system which, in the solar interior, leads to the heat accumulation at the bottom of the convection layer and then motivates the convection motion.Comment: 8 pages, 2 figures, 1 table, 19 reference

The limit behavior of the evolution of Tsallis entropy in self-gravitating systems

In this letter, we study the limit behavior of the evolution of Tsallis entropy in self-gravitating systems. The study is carried out under two different situations, drawing the same conclusion. No matter in the energy transfer process or in the mass transfer process inside the system, when nonextensive parameter q is more than unity, the total entropy is bounded; on the contrary, when this parameter is less than unity, the total entropy is unbounded. There are proofs in both theory and observation that the q is always more than unity. So the Tsallis entropy in self-gravitating system generally exhibits a bounded property. This indicates the existence of global maximum of Tsallis entropy. It is possible for self-gravitating systems to evolve to thermodynamically stable states

Two physical explanations of the nonextensive parameter in a self-gravitating system

We present two possible physical explanations of the nonextensive parameter in a self-gravitating system. One is related to the detailed balance in such system. With the detailed balance, the statistical balance of molecular energy is reached, under which the radiation energy "stored" in the molecules becomes important. Then the relation between the nonextensive parameter and the storage coefficient which measures the ability of molecules to store the radiation energy is constructed. The other explanation is from one dimensionless quantity called (logarithmic) temperature gradient defined in the stellar physics. In view of this, we find that in order to keep the nuclear reactions alive inside the Sun, the ratio of radiation pressure to the total pressure in the core must be more than 0.2833.Comment: 10 pages, 2 figure

Sound field separation method for motorcycle coherent sound sources

To solve the problem of main noise sources of motorcycles running at high speed, especially restoring the free sound field information of the target sound source in the non-free sound field, direct separation method with single holographic surface is proposed. According to the transfer function relationship between the theoretical and the measured sound pressure on the holographic surface based on the wave superposition algorithm, the individual radiation information of the target sound source in the coherent sound field is obtained. Through numerical simulation, it is found that the method could effectively separate the coherent sources. The radiation sound of motorcycles engine speed at 6000 r/min is measured, and the results show that the direct sound field separation method can effectively separate the coherent sound sources and intake noise radiate the higher pressure amplitude