Electronic structures of unsaturated and H saturated GaN nanowires with diameters of 9.5Å, 15.9Å and 22.5Å are studied with generalized gradient approximation (GGA) of density functional theory (DFT). Results show that unsaturated and H saturated GaN nanowires have direct band gaps. Band gaps of unsaturated GaN nanowires decrease with the increase of nanowire diameter, but not significantly. Band gaps of H saturated GaN nanowires decrease with the increase of nanowire diameter as well. They are more apparent than unsaturated ones. 2p electrons of N atoms in surface of unsaturated GaN nanowires locate at top of valence band, and 4p electrons of Ga atoms in surface locate at bottom of conduction band. These two kinds of electrons are local which decide the band gap. Surface effect of surface atoms can be eliminated by saturating with hydrogen atoms.

Interfacial heat transfer coefficient (IHTC) between casting and mould is an essential boundary condition in simulation of metal solidification. We present an inverse method based on Tikhonov regularization theory. A regularized functional is established and regularization parameters are deduced with Arcangeli criterion and Morozov discrepancy principle. The functional is solved by sensitivity coefficients and Newton-Raphson iteration method. The regularization method ensures stability and accuracy of determination and overcomes ill-pesedness of inverse heat conduction problems (IHCP). It shows better accuracy especially with increasing error of measurement temperature.

Penning trap is an advanced equipment of microplasmas. To find its electrostatic field,a general "degenerated analogy method" is presented. As an application of this method, the electrostatic field is simply solved by structural analysis programs. The numerical result is consistent with the experimental result. The structural analysis programs are widely implemented by engineers and researchers. The users can simply extend their function to solve the engineering field problems not belonging to structural mechanics.