一种特殊的Θ-method求解比例尺方程的收敛性分析(英文)

介绍了用偏序的概念去研究用一种特殊的Θ-method求解比例尺方程的数值解和解析解的收敛性,然后证明了使用该种特殊的Θ-method求解该比例尺方程的数值解和解析解的收敛性.对这类研究的目前状况做一个简短的研究.

非线性比例尺微分方程组的稳定性分析及数值处理(英文)

主要研究了多延时非线性比例尺方程理论解及数值解的稳定性质y′(t)=f(t,y(t),y(λ1t),…,y(λdt)),其中f:×N×…×N→N,y:→N,0<λd<…<λ1<1.获得了比例尺微分方程稳定及渐近稳定的充分条件,同时研究了隐式欧拉方法的稳定性质.

Indentation size effect of germanium single crystal with different crystal orientations

In order to study the indentation size effect(ISE)of germanium single crystals,nano-indentation experiments were carried out on the(100),(110)and(111)plane-orientated germanium single crystals.The true hardness of each crystal plane of germanium single crystals was calculated based on the Meyer equation,proportional sample resistance(PSR)model and Nix-Gao model,and the indentation size effect(ISE)factor of each crystal plane was calculated.Results show that,the germanium single crystals experience elastic deformation,plastic deformation and brittle fracture during the loading process,and the three crystal planes all show obvious ISE phenomenon.All three models can effectively describe the ISE of germanium single crystals,and the calculated value of Nix-Gao model is the most accurate.Compared with the other two crystal planes,Ge(110)has the highest size effect factor m and the highest hardness,which indicates that Ge(110)has the worst plasticity.