Convergence of Adaptive Finite Element Approximations for Nonlinear Eigenvalue Problems

In this paper, we study an adaptive finite element method for a class of a nonlinear eigenvalue problems that may be of nonconvex energy functional and consider its applications to quantum chemistry. We prove the convergence of adaptive finite element approximations and present several numerical examples of micro-structure of matter calculations that support our theory.Comment: 24 pages, 12 figure

Energy-Conserving Lattice Boltzmann Thermal Model in Two Dimensions

A discrete velocity model is presented for lattice Boltzmann thermal fluid dynamics. This model is implemented and tested in two dimensions with a finite difference scheme. Comparison with analytical solutions shows an excellent agreement even for wide temperature differences. An alternative approximate approach is then presented for traditional lattice transport schemes

First-principles study of native point defects in Bi2Se3

Using first-principles method within the framework of the density functional theory, we study the influence of native point defect on the structural and electronic properties of Bi$_2$Se$_3$. Se vacancy in Bi$_2$Se$_3$ is a double donor, and Bi vacancy is a triple acceptor. Se antisite (Se$_{Bi}$) is always an active donor in the system because its donor level ($\varepsilon$(+1/0)) enters into the conduction band. Interestingly, Bi antisite(Bi$_{Se1}$) in Bi$_2$Se$_3$ is an amphoteric dopant, acting as a donor when $\mu$$_e$$<$0.119eV (the material is typical p-type) and as an acceptor when $\mu$$_e$$>$0.251eV (the material is typical n-type). The formation energies under different growth environments (such as Bi-rich or Se-rich) indicate that under Se-rich condition, Se$_{Bi}$ is the most stable native defect independent of electron chemical potential $\mu$$_e$. Under Bi-rich condition, Se vacancy is the most stable native defect except for under the growth window as $\mu$$_e$$>$0.262eV (the material is typical n-type) and $\Delta$$\mu$$_{Se}$$<$-0.459eV(Bi-rich), under such growth windows one negative charged Bi$_{Se1}$ is the most stable one.Comment: 7 pages, 4 figure

Partially linear censored quantile regression

Censored regression quantile (CRQ) methods provide a powerful and flexible approach to the analysis of censored survival data when standard linear models are felt to be appropriate. In many cases however, greater flexibility is desired to go beyond the usual multiple regression paradigm. One area of common interest is that of partially linear models: one (or more) of the explanatory covariates are assumed to act on the response through a non-linear function. Here the CRQ approach of Portnoy (J Am Stat Assoc 98:1001–1012, 2003) is extended to this partially linear setting. Basic consistency results are presented. A simulation experiment and unemployment example justify the value of the partially linear approach over methods based on the Cox proportional hazards model and on methods not permitting nonlinearity