Kosterlitz-Thouless phase transition and reentrance in an anisotropic 3-state Potts model on the generalized Kagome lattice

The unusual reentrant phenomenon is observed in the anisotropic 3-state Potts model on a gen- eralized Kagome lattice. By employing the linearized tensor renormalization group method, we find that the reentrance can appear in the region not only under a partial ordered phase as commonly known but also a phase without a local order parameter, which is uncovered to fall into the uni- versality of the Kosterlitz-Thouless (KT) type. The region of the reentrance depends strongly on the ratios of the next nearest couplings {\alpha} = J2 /|J1 | and {\beta} = J3 /|J1 |. The phase diagrams in the plane of temperature versus {\beta} for different {\alpha} are obtained. Through massive calculations, it is also revealed that the quasi-entanglement entropy can be used to accurately detect the KT transition temperature

Numerical Research on The Nozzle Damping Effect by A Wave Attenuation Method

AbstractNozzle damping is one of the most important factors in the suppression of combustion instability in solid rocket motors. For an engineering solid rocket motor that experiences combustion instability at the end of burning, a wave attenuation method is proposed to assess the nozzle damping characteristics numerically. In this method, a periodic pressure oscillation signal which frequency equals to the first acoustic mode is superimposed on a steady flow at the head end of the chamber. When the pressure oscillation is turned off, the decay rate of the pressure can be used to determine the nozzle attenuation constant. The damping characteristics of three other nozzle geometries are numerically studied with this method under the same operating condition. The results show that the convex nozzle provides more damping than the conical nozzle which in turn provides more damping than the concave nozzle. All the three nozzles have better damping effect than that of basic nozzle geometry. At last, the phase difference in the chamber is analyzed, and the numerical pressure distribution satisfies well with theoretical distribution

Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics

We introduce the extension of local polynomial fitting to the linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to nonparametric technique of local polynomial estimation, we do not need to know the heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we focus on comparison of parameters and reach an optimal fitting. Besides, we verify the asymptotic normality of parameters based on numerical simulations. Finally, this approach is applied to a case of economics, and it indicates that our method is surely effective in finite-sample situations