具有无穷边界值的二次非线性奇摄动边值问题的双边界层

研究了具有无穷边界值的二次非线性奇摄动边值问题的双边界层,利用边界层校正函数,构造其渐近解,并利用微分不等式理论,给出了一致有效渐近估计.最后给出算例验证了相关结论的正确性.     

First-principle investigation on the thermodynamics of X_2N_2O(X = C,Si, Ge) compounds

The structures under different pressures, elastic properties, electronic structures and lattice vibrations of the X_2N_2O(X = C, Si, Ge) compounds are investigated by using the first-principle method. Based on the phonon density of state,the thermodynamic properties of the present compounds are studied under different pressures and at different temperatures. The structural parameters including the bond lengths and bond angles are in agreement with available experimental measurements and theoretical calculations. We employ the elastic theory to calculate the nine independent elastic constants(C_(ij)) and the derived elastic moduli(B, G, E, v). Results indicate that these X_2N_2O(X = C, Si, Ge) compounds are mechanically stable and show the brittle behaviors. The electronic properties of the present compounds are analyzed by using the band structure and density of states. The phonon dispersion calculations imply that the present compounds are dynamically stable. Based on the quasi-harmonic approximation, the calculations of the specific heat indicate that the temperature in a range of 0 K–1500 K and pressure in a range of 0 GPa–40 GPa have a large effect on the thermal quantities of Ge_2N_2O,compared with on those of the C_2N_2O and Si_2N_2O compounds.