二维广义非齐次KdV-Burgers方程的反周期行波解

讨论了二维广义非齐次KdV-Burgers方程{ut (f(u)x auxx βuxxx}x δuyy=g t≥0,x,y∈R的反周期行波解的连续依赖性、解的有界性以及估计式。     

Burgers方程的指数型差分格式

Burgers方程可以作为描述许多物理现象的数学模型.对Burgers方程的初边值问题进行了研究,构造了该方程的指数型有限差分格式,数值结果表明所构造的差分格式具有较高的精度,适用于小扩散系数,可以采用较大的时间步长进行计算.     

基于蠕变试验及Burgers模型参数分析的三趾马红土长期强度确定

为了确定重塑三趾马红土的长期强度,首先利用改进的直剪蠕变仪,对甘肃陇东地区三趾马红土进行了剪切蠕变试验,得到了三组固结压力下蠕变曲线。在对各级固结压力蠕变曲线的Burgers模型拟合参数分析的基础上,提出了利用Burgers模型参数中的Maxwell体的黏滞系数与相应的剪应力加载等级之间曲线的最大曲率点确定三趾马红土的长期强度的方法,得到了三趾马红土的长期强度。通过与过渡蠕变法及等时曲线法确定的长期强度值对比,表明基于Burgers拟合参数分析的三趾马红土的长期强度确定方法较为合理。提出的长期强度确定方法及试验结果可对黄土地区受三趾马红土层控制的滑坡的稳定性评价及工程防治提供参考。     

非线性发展方程的新精确行波解

应用(G/G′)展开法成功获得了(1+1)维改进的BBM方程和(1+1)维Burgers方程以及(2+1)维Zakharov-Kuznetsov(ZK)方程的精确行波解,同时也获得了一些含有参数的新解.结果表明,该方法是求解非线性发展方程精确行波解的一种有效工具.而且也可以用来求解数学物理领域中其它非线性偏微分方程.     

半空间上Burgers方程改进的Legendre有理谱逼近

用改进的Legendre有理谱方法对半无限空间上Burgers方程构造了一种具有守恒性质的逼近格式,并用误差估计方法证明了格式的收敛性。     

Further mechanism of α/β interphase boundary evolution and dynamic globularization of Ti–5Al–2Sn–2Zr–4Mo–4Cr at elevated temperature deformation

The evolution characterization of the α/β interphase boundaries of the isothermally compressed Ti–5Al–2Sn–2Zr–4Mo–4Cr with lamellar microstructure was carried out via electron backscatter diffraction (EBSD) and transmission electron microscope (TEM). The effect of the α/β interphase boundary evolution on the dynamic globularization was discussed, and the nucleation model for the β recrystallized grain at the cusp of α lath in the late stage of deformation in terms of the classic nucleation theory was established. The mean α/β interface deviation angle from Burgers orientation relationship (BOR) increased continuously up to 18.9° with the increasing strain from 0.1 to 0.5, which was dominated by the continuous dynamic recrystallization. Restoration of BOR between α and β phases at the strains of 0.7 and 0.9 occurred due to the occurrence of recrystallized α and β grains following BOR, which was rationalized by a nucleation model considering the stored energy of deformation provided the driving force for nucleation at the cusp of α lath. Loss of coherency of α/β interphase boundaries at a strain about 0.3 was responsible for accelerating the dynamic globularization of α lamellae since the energy of α/β interphase boundaries increased up to the maximum value when the non-coherent α/β interphase boundaries were formed. Restoration of coherency of α/β interphase boundaries due to the recrystallization nucleation in the late stage of deformation did not substantially affect the dynamic globularization since the α/α intraphase high-angle boundaries (HAGBs) were formed and the most α/β interphase boundaries were non-coherent.