With molecular dynamics study,we investigate microstructure of liquid Al₂O₃ at 2663 K and 2223 K.The first and second nearest-neighbor distances are in good agreement with results of Ansell et al.Analysis on coordination numbers and angle-distribution functions show that the microstructure of liquid aluminum oxide mostly consists of three-fold coordination of oxygen,four-fold and five-fold coordination of aluminum.Evidence of liquid-liquid phase transition due to separation of high and low coordinate species is not found.

Differential algebra is a new mathematical method and a promising tool in charged particle optics. As a kind of automatic differentiation techniques, it is based on the nonstandard analysis and normal power series theory. It presents a straightforward method for the study of arbitrary order property of nonlinear systems, with accuracy limited only by the computer. The differential algebraic method is widely applicable, and it is an effective and elegant tool for the tracking, analysis and correction of high-order aberrations, sensitivity analysis and optimization of structure design, etc., of the charged particle optical systems. The principle and virtues of differential algebra are summarized. The application of differential algebra method in charged particle optics and its implementation in various computer languages are analysed. Some new research subjects in this field are discussed.