Nonlocal absorption of gold and silver nanostructures is studied with ADE-FDTD method. A Drude-Lorentz model of metal material is discretized and iterative coefficients are deduced in detail. Absorption characteristics of one-, two- and three-dimensional gold and silver nanostructures are studied. It shows that the nonlocal layered films conforms to the equivalent medium theory. In one- and two-dimensional cases, nonlocal absorption peaks are related to the nano scale and have no relation with the material. The nonlocal absorption properties of three-dimensional nanostructures are related to nanoscale, and to material as well. Nonlocal effect of three-dimensional nano structures is the strongest, and the blue shift of the absorption peak is larger. Therefore, three-dimensional gold and silver nano structures are expected to play a role in nano devices.

Fourier property of nonlinear weights and limiters in wave-space are analyzed. Firstly, a statistical method is designed to analyze Fourier property of nonlinear weights. Secondly, averaged values and deviations of nonlinear weights are shown, and values with change of wave-number are analyzed. It is helpful to comprehension of nonlinear schemes. The method is a guidance for designing shock-capture schemes.

Based on density functional perturbation theory, phonon properties and electron-phonon interaction in Bi₄Se₃ film system are studied with first-principles calculations. It shows that dynamic of Bi₄Se₃ film system for two terminations is stable. There exists mismatch in projected phonon density of states between Bi₂ bilayer and Bi₂Se₃quintuple layer. It prevents part phonons to transport in Bi₄Se₃ film, which leads to thermal conductivity reduce and improves thermoelectric performance of material. Besides, electron-phonon coupling constant of Bi₄Se₃ film in two kinds of termination are small (about 0.278), which is in favour of electronic device in room temperature.

Most of current corrected panel methods failed to correct out-of-phase part of distributed unsteady pressure. A method combining traditional downwash weighting method and successive kernel expansion is developed. Precision of the method is verified with an example on ONERA M6 wing. Based on modified aerodynamics,flutter boundary of wing is calculated which predicts well nonlinear flutter of wing in transonic regime.

Geometries of Mg_xAl_yN (x,y=1-5) clusters are studied by using hybrid density functional theory (B3LYP) with 6-311+G^* basis sets. For lowest-energy structures of Mg_xAl_yN clusters, stabilities and electronic properties are investigated. It shows that planar structures are dominant structures of Mg_xAl_yN (x+y≤4) clusters. The lowest-lying Mg_xAl_yN clusters mostly derived from ground-state structures of Al_nN or Mg_x-1Al_y+1N clusters. Mg_xAl_yN clusters are stable with respect to fragmentation into atoms or smaller clusters. Compared with neighboring clusters, MgAl₃N and Mg₃Al₃N clusters own higher stability. For all Mg_xAl_yN clusters studied, we found co-existence of covalent, ionic, and metallic bonding characteristics. Furthermore, ionization potential and electron affinity exhibit weak oscillations as increasing cluster size. Ro general pattern is observed.

Structure and elastic property of ZrV₂ under high pressure are investigated with first-principles calculations based on plane-wave pseudo-potetial in the framework of density functional theory within generalized gradient approximation (GGA). With a quasi-harmonic Debye model, in which phonon effects are considered, we calculated thermodynamic properties of ZrV₂ in a pressure range from 0 to 20 GPa and temperature range from 0 to 1200 K. Pressure dependence of elastic constants, bulk modulus and heat capacity, and thermal expansion with pressure and temperature are presented. It shows that calculated lattice parameters of ZrV₂ are in good agreement with existing experimental data and other theoretical results. Elastic constants, Debye temperature and bulk modulus increases with increasing pressure. Relative volume, heat capacity decreases with increasing pressure. Temperature effect is weaker than pressure effect in thermal expansion of ZrV₂ under high pressures.

To keep interface fixed.we derive formula of smoothing parameter in level set re-initialization equation and form a implicit re-initialization method.It was proved that as the developed method is used to reinitialize the level set function for ensuring sign of level set function on nodes near interlace the time step need only to satisfy the original CFL condition.Finally,the improved method is combined with the original method to make an accurate and fast implicit re-initialization method. Numerical examples illustrate effectiveness of the methods.

For a Fibonacci chain constructed recursively with S_m+1={S_m|S_m-1}, in a tight-binding model of single electron, we investigate numerically density of electronic states and electronic energy band structure with negative eigenvalue theory and three diagonally symmetric matrixes. Trifurcating structure of energy band of the system is demonstrated. With renormalization-group method and scattering theory, we study localization length and transmission coefficients of electronic states in a chain. At particular eigen-energies, extend states with localization lengths greater than size of the system are found and transmission coefficient is equal nearly to 1. At most eigen-energies, corresponding electronic states are localized states due to short localization length. In addition, relations between transmission coefficients and parameters of Fibonacci chain are qualitatively investigated.

We propose a one-dimensional sandpile model with avalanche probability.The simulation is performed with the cellular automata method.As the local slope closes to the critical slope sands avalanche with a probability.The avalanche size and the average local slope are studied at different avalanche probabilities. The self-organized critical (SOC) behavior is studied at critical exponent α=1.50±0.02 as the avalanche probability is between 0.05 and 0.98.The average local slope descends with the increase of collapse probability.A sharp transition occurs between the trival behavior and SOC behavior in this model.The SOC phenomenon in one-demensional rice-pile experiment is well explained.

A sort of birth-death process is investigated.We calculate eigenvalue,eigenvectors of the main matrix for the birth-death process differential equation and get a similar decomposition of the main matrix.Using the technique of matrix decomposition,we obtain the solution of the birth-death process differential equation and study the heavy element abundance of the slow neutron capture process(s-process) in the solar system.A full calculation of heavy element abundance of s-process in solar system is carried out.The result agrees well with astrophysical measurement.

A concrete algorithm of selecting delay time in the state space reconstruction in the mutual information method is introduced. A simple and practical program algorithm based on a reticulate layer is established. An analysis on calculated result shows that the mutual information needs to be computed to a certain reticulate layer in selecting delay time. Therefore, the algorithm is simplified significantly. The Lyapunov exponents calculation of attractors(Rossler and Lorenz) verifies the validity of this algorithm.

The motion of a neutral particle with magnetic moment,μ antiparallel to the field of an Ioffe trap is studied are obtained. With interaction between the magnetic moment of the particle and the magnetic field, classical motion equations of neutral particles in an Ioffe trap are abtained. With limited conditions we derive concise form of the motion equations using a perturbative method. They are Mathieu equations. With proper parameters the Mathieu equations are solved with traditional WKBJ method. As an attempt, we study periodic solutions, i.e., Floquet solutions of the Mathieu equation. It is necessary that parameters (λ and q) in the Mathieu equation satisfy special relations. With appropriate Ioffe trap parameters and initial condition of the particle, we present several periodic solutions.

The densities of electronic states (DOS) of quasi-one-dimensional disordered systems with three parallel chains are computed with thirty thousand sites based on the negative eigenvalue theory. Compared with one-dimensional and quasi-one-dimensional disordered systems under conditions as diagonal disordered system and non-diagonal disordered system, the electronic structure, the localization of electrons, the distribution of the system energy and the dimensional effects are discussed. The results show that the diagonal disorder causes increasing of the number of localized electrons, and the non-diagonal disorder leads to changing of the distribution of the system energy. Comparing the electronic structure of one-dimensional system and quasi-one-dimensional system with three chains, we find that the peak number of the DOS increase, and the bandgap energy of zero DOS decreases.The dimensional effect of system under the same condition is shown.

Asymptotic boundary conditions of one-dimensional atomic model in intense laser field are derived using Fourier transformation.Errors of the three asymptotic boundary conditions are analyzed.The probability distribution and the average energy for one-dimensional hydrogen atom in the intense laser field are numerically computed using the first boundary condition and the symplectic method for the linear inhomogeneous canonical equations.The results are compared with theoretic analyses.

In a quantum system,when the Hamiltonian operator is time-dependent,"artificial" variables are introduced to construct the symplectic integrators with arbitrary high order accuracy.As an example,the time-evolution of an electron in the infinite deep potential well interacting with an animated laser field is investigated.The computed results coincide with the theory and can preserve the norm,which show that the methods are reasonable.

For an intense field model, the time-dependent Schrødinger equation with initial and boundary conditions can be discretized into the inhomogeneous linear canonical equation by substituting the symmetric difference quotient for the partial derivative. As the general solution of its homogeneous equation and the particular solution of the inhomogeneous equation can be generalized by the symplectic transformation, it is a reasonable numerical method to use the symplectic scheme. To prove its utility, a simple example is described using the symplectic scheme and RK method, and compared with the exact solution. The results show that the solution using the symplectic scheme can preserve the intrinsic properties of the equations after a long evolution, but RK method cannot.

Construction of discretization schemes, convergence principle, strongly convergent scheme and weakly convergent scheme for stochastic differential equations as well as computing method of jump stochastic differential equation are presented. Related partial differential equations are solved by probability method. Finally several examples in application are given.

A charge conservation statistics enhancement method used in semiconductor divice Monte Carlo simulation is approached,which smoothes the charge fluctuation caused by the statistics enhancement, and keeps the continuation of cross edge charge flow. As an example, Schottky barrier diode characteristics is simulated using this method.

The symplectic algorithm in the complex symplectic space is the algorithm that preserves the Wronskian.The Wronskian calculated by using the symplectic scheme keeps unchanged which is in good agreement with theoretical analyses after a long distance of computation.The numerical solutions of the one dimensional model of strong laser field are calculated by using the Wronskian preserving and symplectic scheme.

This paper presents a pathwisely jump-adapted approximation of the Poisson driven Markov processes governed by stochastic differential equations.Any trajectory of the processes is divided into continuous phases. Within each phase, the corresponding ODEs are established and solved by the Runge Kutta schemes.The method is applied to investigate the Langevin equation as well as the Duffing-Van der Poloscillator.

The paper gives a necessary condition of asymptotic mean square stability for the implicit Milstein scheme for linear complex-valued stochastic jump-diffusion equations and shows how the stability depends on the implicitness of the scheme.

In this paper, the well-testing analysis is made, based on the finite element method, for a naturally fractured reservoir with two intersection boundaries. Covergence of the numerical solution is proved and some typical theoretical curves of the pressure are presented in the cases of different location of the well position, different types of boundary conditions, and different intersection angles of the boundaries.