A new meshless method, named collocation method with barycentric Lagrange interpolation (BLIC), is presented for analyzing steady-state heat conduction in two-dimensional functionally graded materials(FGMs). Two-variable barycentric Lagrange interpolation function and its partial derivatives at Chebyshev nodes are derived. Then, based on a collocation method, it is directly introduced into controlling equations and boundary conditions of GEMs to obtain a linear discretijed equation. The method is a truly meshless method and takes advantages of both barycentric Lagrange interpolation and collocation method such as low computational cost, stable, accurate and easy to numerical implementation. Temperature fields of exponential, quadratic and trigonometrical FGMs models are simulated. It shows that the method is accurate and efficient, and is not sensitive to the change of material gradient parameters. It can be extended to solve transient heat conduction and thermal stress analysis of FGMs.

Electronic structures and optical properties of ZnO, Bi-ZnO and 2Bi-ZnO are investigated with first-principles of plane wave ultra-soft pseudo-potential method based on density functional theory. It shows that variation trends of band gap of ZnO doped with different number of Bi atoms are not consistent. After doping, imaginary part of dielectric function peaks are broaden, and exhibit a red shift in the direction of low energy. Absorption peak, reflection peak and energy loss in high energy region decrease gradually as dopant atoms increased, which enhances transmission. Besides, absorption coefficient and reflection coefficient in visible and ultraviolet increase, which promotes the use of ZnO materials in visible light.

For mesh generation of a two-parameter surface, anisotropic and non-uniform node placement method with bubble simulation is applied to optimize node distribution in parameter area. Then the parameter area is meshed with constrained Delaunay triangulation. Finally, according to the mapping method, two-parametric surface mesh is obtained. A second order Riemann metric tensor determines distribution of nodes in the parameter area. It could be co-generated with a three-dimensional surface metric tensor and gradient of surface functions. Numerical examples show that the node placement method with bubble simulation can generate node set meeting requirements of Riemann metric in parameter area. Nodes are meshed and mapped back into the surface. A high quality surface mesh is obtained.

With numerical solution of full Maxwell-Bloch equations obtained by finite-difference time-domain method and iterative predictor-corrector method,spatial distributions of pulse and populations of few-cycle laser pulse propagates in a ladder-type three-level atomic medium are investigated.It shows that,spatial distributions changes evidently with pulse area.As the pulse area is smallr,the pulse shape is irregular and oscillation time increases.As the pulse area is large,the pulse shape becomes relatively regular and oscillation times decreases evidently.With increasing of pulse area,amplitude and group velocity of pulse increase progressively,oscillation times of populations increase gradually and variation of spatial distributions of the pulse and populations at different moments decreases considerably.Moreover,spatial distribution of populations correlates closely to spatial distribution of the pulse.

A 4-layer sphere model of human head is built for the forward problem of magnetic induction tomography.The layers represent the brain,the CFS,the skull,and the scalp respectively.Taking vector magnetic potential as a variable,Helmholtz equation in a spherical coordinates is constructed as a control equation of the forward problem.A variables separation method is used to solve the equations with boundary and interface conditions.Distribution of the magnetic vector potential and eddy current in the model are obtained.Equi-potential lines of the eddy current are given.Influence of frequency and magnitude of the exciting current on the induced voltage is analyzed.The algorithm is validated by solving a forward problem of magnetic induction tomography.It can be used as a fast algorithm to generate sensitivity matrix in an inverse problem.

Full Maxwell-Bloch equations are solved with PC-FDTD method to investigate population evolution of dense V-type three-level medium in few-cycle laser pulses.It is shown that the ratio of transition dipole moments(γ) has strong influence on appearing time and oscillation frequency of population inversion.As γ=1 population inversion with LFC appears later than that without LFC and near dipole-dipole(NDD) interaction delays population inversion.As γ>1,appearing with LFC is earlier than that without LFC and NDD interaction accelerates the population inversion.The number of population inversion with unequal transition dipole moments is more than that with equal transition dipole moments.Moreover,evolution of populations in a dense medium is quite different from that in a dilute medium.At input surface,in a dilute medium,population inversion appears with time evolution.With increasing of medium density,populations show quasi-periodicity oscillation and oscillation frequencies of populations with LFC are less than that without LFC.