A finite difference method is used for high-order numerical solution of two-dimensional unsteady semilinear diffusion reaction equation. The spatial derivative term is discretized by a fourth-order compact difference formula, and the time derivative term is discretized by a fourth-order backward Euler formula. An unconditionally stable high-order five-level fully implicit scheme is proposed. Truncation error of the scheme is O(τ⁴+τ²h²+h⁴), that is, the time and space have fourth-order accuracy. In calculation of start-up steps, the first, second and third time levels are discretized by Crank-Nicolson method. Richardson extrapolation formula was used to extrapolate startup time accuracy to the fourth-order. A multigrid method based on the scheme is established, which accelerates convergence speed of the algebraic equations on each time level and improves computational efficiency. Finally, accuracy, stability and efficiency of the scheme and multigrid approach are verified with numerical experiments.

Based on maximum principle analysis together with definitions of restriction position and restriction stencil, a unification of multidimensional limiter construction process for unstructured mesh was presented. To enhance flow resolution, a new type of multidimensional limiter was developed. It was compared with several conventional limiters. It shows that due to less restriction in gradient reconstruction process, the new limiter is less dissipative and has better resolution for complex flow with shock and contact discontinuity interaction.

Three-dimensional adjoint transport calculation module was integrated into S_N transport code ARES in which automated variance reduction parameters are generated based on consistent adjoint driven importance sampling method to accelerate calculation of MCNP5. It shows that automated variance reduction parameters are effective to improve MC calculational efficiency and to produce unbiased statistical results. Automated variance reduction technique with S_N function estimates particle importance more economically and accurately. It avoids obstacles of manual estimation and could be applied for MC simulation of large-scale, complicated shielding problems.

Heat transfer distribution is analyzed on a rough wall in high speed turbulent compressible flow via computational fluid dynamics(CFD) method and analytical correlations, focusing on heat transfer with different roughness number and roughness element shape. It shows that, in all cases, heat flux augmentation predicted with CFD increases with reduction of roughness element density and levels off after roughness shape density is small, which differs with data of three analytical correlations. Predicted heat fluxes are same if same roughness element density and equivalent height are imposed on analytical correlations distinguishing from tendency of CFD results, which changes with roughness element shapes.

In large eddy simulations (LES), a flat ground model and rough wedge ground models with different wedge heights were adopted to investigate near-surface wind field characteristics under condition of time-varying upstream inflows. In both flat ground model and rough wedge ground models, simulated results show that there is downdraft in peak period of gusty wind and updraft in valley period, respectively. Intensity of downdraft/updraft flows are related to ground roughness in upwind areas and amplitude of inflows. It follows that wind velocity and direction in atmospheric boundary layer always change over time in time-varying upstream inflows, which enhances transportation of mass and energy in actual atmospheric boundary layer.

Inverse mode problem of a horizontal bar structure, a single branch structure of a rod-beam-rod system, is investigated. Sign-oscillatory properties of inherent vibration stiffness matrix of discrete horizontal bar structure are shown mathematically. In addition, qualitative properties of frequencies and modes are introduced. Physical parameters of horizontal bar structure are constructed from two sets of displacement or strain modes and corresponding circular frequencies. Several numerical examples are given. A particular inverse mode problem is discussed, where structure parameters of horizontal bar are symmetrical for geometrical symmetry axis. It shows that formulation of inverse problems is reasonable and solution method is validated.

Inverse mixed problems of a discrete system for a rod are studied, i.e., stiffness and mass matrices of discrete system of a rod are reconstructed from some frequency data and part of mode data. Three inverse mixed problems are formulated. Solving methods for these problems are given. And conditions of existing solutions for these inverse problems are discussed. Numerical examples are also shown. Potential worth for this type of inverse problems is analysed.

Electronic structure and magnetic structures of BaTi₂Bi₂O are studied with first-principles calculations.In nonmagnetic state,density of states at Fermi level are mostly derived from d_z²,d_x²-y² and d_xy orbitals.Fermi surface (FS) consists of three sheets.The third FS sheet (along X-R line) nests with the first FS sheet (along M-A line) by q-vector q₁=(π/a,0,0) or q₂=(0,π/a,0) shift.Calculated bare susceptibility χ₀(q) peaked at X-point,rather than at M-point in Fe As-based superconductors.Such peaked susceptibility induces spin density wave (SDW).Magnetic ground state is nearly two degenerate antiferromagnetism of bi-collinear antiferromagnetism (AF3) and blocked checkerboard antiferromagnetism (AF4).Peak of susceptibility χ₀(q) is obviously suppressed and becomes slightly in-commensurate with hole doping,but increased with electron doping.As spin fluctuation is suppressed superconductivity appears.It explains that superconductivity appears only in hole-doped compounds,and not in electron-doped ones.

We illustrate a technique of ray tracing by shooting method and analyze rules of ray in VTI coal. With mixed-language programming of VC ++ and Fortran, ray tracing in VTI coal with a complex velocity model is realized. It demonstrates necessaries of anisotropic ray tracing in VTI coal by comparison of ray tracing in VTI coal and isotropic media. By contrast of calculation time, it indicates that this method is efficient to meet needs of seismic records forward. The technique can be used in multi-wave ray tracing in anisotropic coal as giving responding formulae and parameters.

Conditions and method for constructing stiffness distribution function of various parameters symmetric simple supported beams with a symmetric or anti-symmetric mode and specified polynomial density distributing function are discussed. It is shown that the constructed stiffness distribution functions are positive functions in case with different density distributing. Two numeral examples are given. And two problems correlated are explained.

A high efficiency finite difference time-domain method based on high order compact scheme is shown.It not only improves accuracy,but also has the advantages of fewer grid nodes,lower memory consumes and CPU time.Numerical simulations of electromagnetic wave propagation in a lossless waveguide and photonic crystals fibers are realized.They prove efficiency and accuracy of the algorithm.

Support vector machine and neural network theory and internal network training differences of them are studied.Root mean square height and correlation length of Gauss rough surface are inversed by support vector machine and neural network,respectively.Simulation results and inversing errors show that in the case of small numbers of rough surface sample inversion of support vector machine are better than that of neural network,while in the case of sufficient numbers of rough surface samples inversion accuracy of neural network increases and time of inversion by neural network is much less than that of support vector machine.

With transport characteristics and experiment about molecular motor,an impact force model is established,which conforms Langevin equation.Kinetics of molecular motor transport is analyzed.Molecular motors could take stable stepping motion and effective transport in right impact force combined with noise intensity.Direction of motion of molecular motor is adjusted by direction of impulse force.Though average speed is not zero at different noise intensity,efficient transport of molecular motor ensemble indicates that the system is selective on noise intensity.Average speed of molecular motor ensemble decreases with increasing of load force,the motion even changes its direction as load force is great enough.

We analyze numerically thermalization process of atoms sputtered from a cathode in N2/Ti micro-hollow cathode discharge plasma by using Monte Carlo method.PIC/MC model is used to simulate nitrogen ion(N₂⁺,N⁺) bombarding cathode surface.Thermalization process,density distribution and average energy of Ti atoms are calculated.It shows that initial energy sputtered to all directions from 90 percent of Ti metal atoms is less than 30 eV.Its scattering angle is mainly between 30 and 60 degrees.And thermalization maximum of sputtering Ti atoms is appeared at a distance of about 0.04mm from the hollow cathode wall.

A scalable parallel algorithm for three-dimensional semiconductor device simulation on unstructured tetrahedral meshes using drift-diffusion model is proposed,which is characterized by finite volume discretization,fully coupled Newton iterations for discretized nonlinear equations,and GMRES iterations using algebraic multigrid(AMG) preconditioner for linear equations in Newton iterations.The algorithm was implemented using a parallel adaptive finite element toolbox PHG.Large scale parallel numerical experiments with several problems,including PN diode and MOSFET,were carried out.In numerical simulations the largest mesh size are 500 million elements and the largest number of MPI processes used are 1 024.It shows that the proposed algorithm is efficient,robust and highly scalable.

A PIC/MC model is developed for electrons,atomic ions N⁺ and molecular ions N₂⁺ in a capacitively coupled rf glow discharge.Modeling results are compared with those in a dc glow discharge at similar conditions.It reveals that the mean densities of particles(e,N₂⁺,N⁺) in rf discharge are nearly ten times greater than those in dc discharge,the mean energy near a rf electrode is about three times less than that near a cathode in dc discharge;the ions N⁺ have higher energy near two electrodes,the ions N₂⁺ have higher density,and the density of N₂⁺ is about six times the density of N⁺.The simulated electron energy probability distributions agree with measured results.

Hartree-Fock and hybrid DFT and Hartree-Fock methods am used to calculate Young modulus of carbon nanotubos on the basis of ab-initio theory with program Crystal03.Calculated result with Hartree-Fock approximation agrees with other theoretical and experimental ones-Result with hybrid DFT and Hartree-Fock is smaller.Young's modulus of C nanotube depends on geometric structure and electronic structure as well.

With a combination of mean cross section and Mott model,differential cross section,total cross section and angular distribution of electron elastic scattering in liquid water with energy below 10 keV are calculated and systematically compared with those of Rutherford model and experiment.Elastic scattering of low-energy electrons in liquid water is simulated.The method is reliable and can be applied conveniently to the simulation of track structure of low-energy electrons in liquid water.

Mode inverse problem for a beam with overhangs is discussed.Flexural rigidity and density of beam with overhangs are solved with two groups of displacement modes or two groups of strain modes and corresponding frequency.Necessary and sufficient conditions for unique existence of solution of the problem are discussed.An algorithm is proposed and numerical calculations are carried out.Two examples show that better results can be attained if strain modes instead of displacement mode are employed.

Molecular dynamics simulation is made to study configuration and total energy of 0.5 mol%,2.1mol%,3.8mol% VB transition metal ions (V⁵⁺,Nb⁵⁺,Ta⁵⁺)/TiO₂ in rutile at 300K and 101 325 Pa.As 2.1mol% Ti⁴⁺ is substituted by dopants,configuration remains well with less mean-square displacements (MSDs),distinct planes of atoms and higher stability.Nb⁵⁺ incorporates into TiO₆ octahedra well and shows a large solubility in TiO₂ compared with V⁵⁺ or Ta⁵⁺ due to comparable valence and ionic radius between Nb⁵⁺ and Ti⁴⁺.

By the grand canonical Monte Carlo method,physisorption of hydrogen storage in single-walled boron nitride nanotube arrays(SWBNNTA) at moderate pressure with normal temperature is studied.The influences of tube diameter,distance between tubes and pressure on hydrogen physisorption in SWBNNTA are investigated.It indicates that at normal temperature and moderate pressure the hydrogen storage capacity(mass percent) of SWBNNTA is obviously greater than that of single-walled carbon nanotube arrays,and exceeds the commercial standard presented by U.S.Department of Energy.Corresponding theoretical explanation is given.

A general Godunov finite difference scheme—WENO(Weighted Essentially Non-Oscillatory) scheme with fifth-order accuracy is used to calculate 2-dimensional axis symmetrical laser-supported plasma flow field under laser ablated solid target,considering ionization degree of plasma and the interaction and coupling between laser beam and plasma.Evolution of the ablation plasma due to the interaction between laser and solid target is obtained.The simulation shows that the laser beam is strong absorbed by plasma on target surface,and the velocity of LSD(Laser Supported Detonation) wave is half of the ideal LSD derived with C-J detonation theory.

We present a method for electromagnetic scattering with obliquely incident pulse plane wave using BOR-FDTD(body of revolution finite-difference time-domain) method.The obliquely incident pulse plane wave is expanded in a cylindrical coordinate and a total-field/scattered-field formulation is introduced as excitation.The method is validated by comparing with the method of moments.It shows good agreement.

Based on the Warren-Root model,introducing fractal parameter and deformable coefficient and considering the effect of pressure on permeability and porosity,we construct a seepage flow model for pressure-sensitive deformable double media fractal gas reservoirs.A finite element method which has advantages in numerical solution of partial differences equations is used.The effect of parameters on pressure and importance in pressure-sensitive deformable double media fractal gas reservoirs are analyzed in detail.

A lattice kinetic Monte Carlo model for nano-crystal growth is presented and discussed in detail. As an example, we performed case studies of thin film growth. The result shows that an alteration of three-dimensional (3D) Ehrlich-Schwoebel (ES)barrier leads to shape transition of islands with multiple atomic layers in thin film growth.

We examine the super compact symmetric finite difference scheme (SCSFD) and compare it with traditional difference methods and compact difference methods. The result shows high efficiency of SCSFD. According to the characteristics of the algorithm, a parallel algorithm named block pipelined method for three-dimensional compressible Navier-Stokes equations using SCSFD is designed and its parallel performance is analysed. Numerical experiments are carried out.

We present a parallel bisection mesh refinement algorithm based on ALBERT (Adaptive multi-Level finite element toolbox using Bisection refinement and Error control by Residual Techniques). The goal is to develop a parallel adaptive finite element code suitable for distributed memory parallel computers or PC clusters. An overview on the basic strategy for the parallelization of ALBERT is given. Issues on the parallel mesh refinement are addressed. A modified mesh refinement algorithm, which can be implemented efficiently on distributed memory parallel computers, is proposed and its properties are discussed. Numerical experiments with parallel bisection mesh refinement algorithm are shown.

Grand canonical Monte Carlo (GCMC) method is adopted to investigate the dependence of hydrogen storage capacity on the diameter of a single-walled carbon nanotube (SWCNT), the distance between walls and the shell number of a multi-walled carbon nanotube (MWCNT),as well as the inter-tube distance and configuration of SWCNT array (SWCNTA),at 298K and 10MPa.The calculated results show that when the diameter of SWCNT approaches 6 nm the average number density (n_AV) of hydrogen within the tube reaches its maximum.When the difference between the internal radius and the external radius increases from 0.34 to 0.61 or 0.88 nm the hydrogen storage capacity is improved effectively.As the inter-tube distance of SWCNTA approaches 1.7 nm n_AV within the interstitial space of SWCNTA reaches its maximum and a square array is better than a triangular array for hydrogen physisorption.It is also found that n_AV within the interstitial space is larger than that within the tube whether for a square array or a triangular array,only if inter-tube distance is larger than 0.6 nm.The hydrogen storage capacity could be effciently increased by the reasonable choice of the diameter of SWCNT,the distance between walls of MWCNT,the inter-tube distance and configuration of SWCNTA.Conclusions are discussed and explained.

Based on the high accuracy compact difference scheme and the alternating group explicit (AGE) iterative method which has obvious property of parallelism,an AGE iterative method with the fourth-order compact scheme is established for the steady convection-diffusion equation.Numerical solutions are obtained for the model problem of natural convection in a square cavity with large Rayleigh number of physical interest and small Prandtl numbers attempted.Some results of the present are compared with the referenced paper.

Doping of moderate elements Sb,Te,Ag,Cu can greatly improve the thermoelectric properties of Mg₂Si. For explaning the experimental result,a calculable model is presented.It applies DV-Xα quantum chemistry computation to reveal the micro-structure information, such as the covalent bond grade and the density of state. The calculated results imply that the covalent bond grade of Mg-Si are decreased and the forbidden gaps become narrower after doping. This results appears to be consistent with the experiments.