Computing Optimal Experimental Designs via Interior Point Method

In this paper, we study optimal experimental design problems with a broad class of smooth convex optimality criteria, including the classical A-, D- and p th mean criterion. In particular, we propose an interior point (IP) method for them and establish its global convergence. Furthermore, by exploiting the structure of the Hessian matrix of the aforementioned optimality criteria, we derive an explicit formula for computing its rank. Using this result, we then show that the Newton direction arising in the IP method can be computed efficiently via Sherman-Morrison-Woodbury formula when the size of the moment matrix is small relative to the sample size. Finally, we compare our IP method with the widely used multiplicative algorithm introduced by Silvey et al. [29]. The computational results show that the IP method generally outperforms the multiplicative algorithm both in speed and solution quality

Diffraction of a pulse by a three-dimensional corner

Three dimensional diffraction of sonic booms by corners of structure

Progressive amorphization of GeSbTe phase-change material under electron beam irradiation

Fast and reversible phase transitions in chalcogenide phase-change materials (PCMs), in particular, Ge-Sb-Te compounds, are not only of fundamental interests, but also make PCMs based random access memory (PRAM) a leading candidate for non-volatile memory and neuromorphic computing devices. To RESET the memory cell, crystalline Ge-Sb-Te has to undergo phase transitions firstly to a liquid state and then to an amorphous state, corresponding to an abrupt change in electrical resistance. In this work, we demonstrate a progressive amorphization process in GeSb2Te4 thin films under electron beam irradiation on transmission electron microscope (TEM). Melting is shown to be completely absent by the in situ TEM experiments. The progressive amorphization process resembles closely the cumulative crystallization process that accompanies a continuous change in electrical resistance. Our work suggests that if displacement forces can be implemented properly, it should be possible to emulate symmetric neuronal dynamics by using PCMs