A 2D numerical simulation program is developed for nonlinear evolution of magneto-Rayleigh-Taylor instability(MRTI). Based on an ideal magnetohydrodynamic model, a 5th WENO scheme is employed to calculate MHD equations and a projection scheme is used to clean spurious magnetic field divergence. The method is validated with MRTI compared with theory of linear stability. It is shown that the vertical magnetic field suppresses evidently MRTI in both linear and nonlinear stages. The parallel magnetic field has weak effect on MRTI in linear stage. However, it reduces remarkably Kelvin-Helmholtz instability and overall instability in nonlinear regime. High order harmonic occurs in the nonlinear evolution of single mode, and many modes except fundamental modes and harmonic occur in the evolution of double modes. In MRT evolution of multi-mode seeds inverse cascade occur, which means that perturbations evolve from short wavelength to long wavelength in the nonlinear stage.

With immersed boundary-lattice Boltzmann method, inertial migration behavior and rotational dynamics of an ellipsoidal particle in an infinite square cross-section microchannel were numerically studied. Two main motion states were found for ellipsoidal particles migrating in a microchannel, i.e., tumbling and log-rolling. It shows that for particles in flow with relatively low Re (Re=10), rotational behavior varied from different initial orientation. However, for particles in flow with higher Re (50≤Re≤200), they perform same rotational behavior and reach the same equilibrium position. As Re number increases, equilibrium position of the ellipsoidal particle moves firstly towards the wall then the center of the channel. At higher Re numbers (Re>300), the particles do not retain stable inertial focusing. Finally, the phenomena were analyzed from flow field around the particles. In addition, mechanism of transition of motion states of particles is explained from fluid and particle inertia.

Based on geometric model of metal fiber sintering nodes, with Caputo fractional differential equations, a time fractional surface diffusion model is established. Numerical solution by finite difference method is made. Numerical simulation of metal fiber sintering process is realized. Numerical simulation of sintering process and variation of neck length as fractional order varies from 0 to 1 are obtained. As the order is fixed at 0.9, sintering process at initial included angles of 0°, 30°, 60° and 90° are simulated. It shows that as the order is equal to 1 the result is consistent with integer order diffusion model. Neck radius with integer order and fractional order grows rapidly in initial stage of sintering. With progress of sintering, fractional simulation of sintering neck length appears local fluctuation, and finally grows at an increase rate greater than the integer order. As the order is fixed, the smaller the initial angle, the greater the rate of growth. The fractional order surface diffusion model describes well the complex change of sintering node during fiber sintering process than the integer order surface diffusion model.

A scheme of convolutional perfectly matched layer (CPML) absorbing boundary condition (ABC) is proposed, which is used to truncate finite-difference time-domain (FDTD) method modeling transient electromagnetic (TEM) response. It derives specially CPML formulation dealing explicitly with divergence of magnetic induction and conceives an algorithm calculating convolutional term of z component. Then, the scheme is validated by numerical modeling of a homogeneous half-space model. The results indicate that efficient calculation of TEM is achieved.

Lattice dynamics,electronic and lattice contributions to dielectric and piezoelectric responses of BaTiO₃/SrTiO₃(1:1)(BTO/STO 1:1) 10-atom superlattice with Ba/Sr [110] and [111] ordering were investigated with first-principles calculations. We explored ground structure from the highest phase by successively freezing in unstable polar modes. We found that ground structure are in Pm and R3m symmetry,respectively. Lattice contributions to dielectric and piezoelectric tensor coming from individual atoms and individual modes were explored. O and Ti atoms provide extraordinary great contribution to lattice dielectric and piezoelectric responses. On the other hand,great dielectric and piezoelectric tensor are mainly due to low frequency phonons. Especially,for BTO/STO(1:1)superlattice with Ba/Sr [110] ordering,ε₁₁is mainly due to A' phonons with ω_λ=49 cm^-1.

Disturbance equations of velocity and temperature fields are built based on Boussinesq approximation,in which second order and higher-order disturbance of Bénard convection are ignored. Transcendental equations controlling Bénard convection are obtained with non-dimensional treatment of variables. Specific parameters of Bénard convection are obtained,which provide reference and guidance for Bénard convection experiments.

A shock-pinned random projection method( SRPM) is proposed. To overcome difficulty of multidirectional propagation,local random projection is applied by introducing a shock indicator along with proper rules for choosing local projection zones around shocks in each reaction step. Numerical experiments are presented. It shows that SRPM is appropriate for detonation waves with multi-directional propagation,which is high-efficient in solving stiff reactive equations and extensible to 3D situations.

We introduce figure repair technology based on partial differential equation into seismic data digital processing, and put forward seismic data repair technology based on diffusion filtering method. The technology diffuses undamaged area's data to data to be repaired using diffusion filtering method with a certain diffusion function. In each iteration, only the data to be repaired is updated, and undamaged area' s data is remained unchanged. Final iteration termination condition can be ensured by comparing difference with threshold before and after iterations. Two application examples of seismic data interpolation processing and seismic data local repair processing show that the technology can achieve the purpose of repairing seismic data. It recovers effectively lost seismic wave field information. Therefore, it can be used in practical seismic data digital processing.

From PM equation we derive muhi-dimensionay diffusion filtering equation discrete formula and its stable condition. We construct multi-scale decomposition and reconstruction method based on diffusion filtering, and provide two specific implementation plans. Application in practical seismic data shows that the method is reasonable and reliable. In the first plan 2D Fourier wave-number spectrum main energy is away from spectrum center with increase of scale, and residual signal acts at high wave numbers, which shows perfect application in random noise suppression. In the second plan 2D Fourier wave-number spectrum energy is close to spectrum center with increase of scale, and residual signal acts at low wave numbers, which shows perfect application in low-frequency reverse time migration noise suppression. The method computation is simple and easy to implement. It provides a multi-scale decomposition and reconstruction method for signal processing. It may has great application in seismic signal processing.

We present an equivalent dual elastic wave separation equation, which simulates particle-velocity, pressure, divergence and curl fields in pure P- and S- modes. The method is used in full elastic wave numerical simulations. We give complete derivations of explicit high-order staggered-grid finite difference discrete equations, together with stability condition, dispersion relation and perfectly matched layer (PML) absorbing boundary condition. Theoretical analysis and numerical simulations show that pare P-waves and S-waves in final numerical results are completely separated in the method. Effect of absorbing boundary is perfect. Storage and computing time requirements are greatly reduced compared with previous works.

To study non-linear relations between field emission current density and temperature at top surface of a cathode microprotrusion, thermal effects on cathode microprotrusion are investigated numerically at various applied electric fields. Enhancement factor of electric field at top surface of microprotrusion is different as ratio of top radius to bottom radius is changed. It leads to obvious difference in temperature distribution in microprotrusion when temperature at microprotrusion peak reaches melting point of cathode material. At a given applied electric field, the smaller the ratio of top radius to bottom radius of microprotrusion, the shorter the time delay of explosive emission. Time delay of explosive emission increases exponentially with decrease of applied electric field.

Two-mode phase-field-crystal (PFC) method is used to simulate coherent boundary of nano-twins.It shows that atomic arrangement in coherent twin-grain boundary is not in good order as sphere grains grow and run into each other to form dislocations.Atomic arrangement in coherent twin-grain boundary as band-shape grains colliding each other is more tidy.For designing and controlling numbers of atomic layer in nano-twins,PFC model can be used to realize manipulation for coherent nano-twins structure.It is significant for guiding experiment and revealing nano-twins structure and properties.

Based on a mathematical model of non-Darcy unsteady seepage flows in low-permeability porous media with moving boundary conditions,a differential equation of propagation velocity for moving boundary was deduced.It indicates that propagation velocity of a moving boundary is proportional to the second derivative of formation pressure with respect to radial distance on the moving boundary.And with Lagrange three-point interpolation formula,finite difference scheme of governing equation near a moving boundary was obtained.Exact position of a moving boundary is able to be tracked.Numerical results show that the front tracking method describes propagation behaviors of moving boundary of non.Darcy unsteady seepage flows in low-permeability porous media well.

Threshold gain of laser mode in terahertz quantum cascade laser is calculated with finite element method. It shows that contact layer thickness and doping density have far greater impact on threshold gain than waveguide width and lasing wavelength. As thickness and density becoming smaller (greater), threshold gain of TM₁ (TM₀) mode becomes smaller. Far-field characteristics of the beam are analyzed using vector diffraction theory. The beam spot is basically elliptical. With increase of waveguide width or lasing wavelength, far-field divergence angles at x direction decrease or increase linearly. Though the contact layer thickness and doping density for TM₀ mode are different from that for TM₁, their far-field divergence angles at x direction are same. Moreover, far-field divergence angles at y direction are unaffected by waveguide width, and less affected by lasing wavelength. In terms of threshold gain and beam quality, TM₁ is more desirable than TM₀ mode.

Magnetic field molding is a key technique in obtaining hish-performance permanent magnetic materials from strontium ferrite,Based on a mathematical model,we focus on effect of domain center and material geometrical center's relative position on magnetic properties of strontium ferrite.It shows that the external magnetic field atcts on magnetic domain center more obviously as the center shifts downward;as the sample is flat and the external magnetic field vertically acts on the sample absolutely.the effect is the greatest,and strontium ferrite in shape anisotropy can be obtained.

With Fokker-Plank equation of pitch-angle diffusion,a numerical method for atmospheric diffusion loss of radiation belt trapped electrons is shown.Flux and energy spectrum are calculated as atmospheric scattering of fission β spectrum electrons injected in radiation belt by high altitude nuclear detonation.Diffusion due to atmospheric scattering is remarkable as L < 1.3.Low energy electrons are removed more rapidly than those with high energy.Electron flux decays rapidly at an initial phase and then decays gradually as an exponential function of time.

A semi-microscopic proton optical potential with parameters is constructed for analyzing elastic scattering data.It's real part is given by a folding model incorporated with one-body density matrix of shell model with Woods-Saxon potential,and the imaginary part is taken consistently with that of Koning-Delaroche(K-D) global optical potential.Potential parameters are obtained by fitting proton elastic scattering data up to 200 MeV in a range of mass number A=28~90.Compared with measurements of elastic scattering angular distributions and analyzing powers it is overall better than those of K-D global optical potential.

The atmosphere is a kind of non-uniform media,whose density drops rapidly with the increase of height.In order to simulate transport of gamma ray in high-altitude atmosphere,the media is divided into many uniform layers with different densities.To eliminate error,the number of layers should be as many as possible,which results in a large amount of computation.We propose a method without layering.It samples mass distance to replace step length of particles.The results agree well with those calculated directly by MCNP code.The method increases speed of computation considerably.

Specific acoustic impedance of transparent liquid, sound transmitting distance of laser induced sound and laser beam waist radius are analyzed. It shows that the peak pressure, dominant frequency and energy of laser induced sound increase as specific acoustic impedance increases. The dominant frequency quickly drops in a short distance and then becomes a constant at a larger distance. Under the condition of optical breakdown, a high ratio of laser to sound energy conversion can be obtained with a large laser beam waist radius.

Charge transfer in He⁺-H^- collisions is investigated using two-center atomic orbital close-coupling(TC-AOCC) method.All bound states of He⁺ (nl) with n≤7,as well as 1s bound states and ns(n=2~6) quasi-continuum states of H^- are included in the AOCC basis.Energies of bound states calculated are in good agreement with NIST data and theoretical results.The total and state-selective cross sections are calculated within a range of energy from 4 to 400 keV.For low-energy collisions,dominant capturing channels are those with quantum numbers n=3-5.With increasing incident energies,transfer of charge to n=2 becomes the dominant reaction.Moreover,for low-energy collisions,cross sections for electrons capture to higher-l states are bigger than that to lower l states.For high-energy collisions,dominant channel is to l=1 states.Charge exchange spectrum due to electron captured to excited states is calculated.Importance of cascade effects is found.

We develop a general-purpose two-dimensional semiconductor simulator (GSS),by which the drift-diffusion model and hydrodynamic model are calculated.It calculates steady-state and transient responses of the devices with different materials structures and is applied to an NPN transistor and MESFET.IV curves,electron density distribution and temperature variation are obtained.

A no-line-search parallel nonlinear conjugate gradient method(NLS-PNCG) for unconstrained optimization is proposed. In this method the step length is evaluated by a fixed formula. It is shown that the NLS-PNCG requires less computation and its performance is superior to those with line search on Deep Comp 6800.

A novel body fitted numerical method with Cartesian coordinates for solving incompressible viscous fluid flow problems is studied.This method takes advantage of Cartesian coordinat and reserves irregular control volumes near boundaries,so this scheme is full body fitted method.It is different from all other Cartesian grid methods.To test the accuracy of this approach,it is applied to two benchmark cases.Agreement is found with analytical,numerical benchmark,and STAR-CD results.The flow field around a 2-D blunt body is simulated which is quite similar to that of STAR-CD.All these show that this method is validated and can also be used for simulating complex flow phenomena.

The inverse scattering problem is converted to an operator equation F(Γ)=f, which consists of the far field operator F, the measured far field data f and the shape Γ of the unknown obstacle. Using the Levenberg-Marquardt method and the derivative of F on Γ, in-troduced by A. Kirsh, this equation is solved and the shape Γ is determined. The numerical results show that this algorithm is practical and efficient.

A modified method is presented to calculate the vector potential for the two-dimensional transient scattering.In the conventional method,the vector potential is expressed in terms of three dimensional Green function,in which the time delay between the source and field points in the same patch is always neglected for the selfterm.This time delay is introduced.Numerical experiments show that this modified method can provide stable solutions to the EFIE for the transient scattering from the open structures.

The numerical computation is often used to predict or study pool fires.The fluid flow,heat and mass transfer,chemical reaction and their interaction in the burning process are studied by formulating and solving a set of governing equations.The treatment of oil surface is given in details also.Many results of pool fires under various wind speeds are gained,and computational results are obtained.

High order accurate, non-oscillating finite volume schemes using spline interpolation for solving conservation laws in arbitrary curvilinear coordinate are analyzed and three different flux splitting schemes are compared. Numerical experiment indicates that these schemes are of high resolution to shock and contact discontinuities.

It is shown that there are partial TVD regions after analyzing Lax Wendroff and Warming Beam schemes from the TVD conditions of hyperbolic equation. Based on which, new second order accurate TVD schemes of three or four grids in space are constructed in order to keep second order accuracy near the extreme points. Finally a comparative study is presented to solve linear hyperbolic equation by the new and old TVD schemes.

Physical property parameters of oil gas reservoir(i.e.reservoir parameters) are important in reservoir description. Considering both the complexity of finding reservoir parameters by seismic data and the shortages of the nonlinear mapping of BP network which needs complete sample information and is the low effciency of learning.This paper presents a method combining Complete Utilization of Sample Information (CUSI) with genetic algorithm(GA) to calculate these parameters.

A numerical approach is presented for simulating the stability of harmonic resonance overvoltage in power systems and the relationship is discussed between the stability of harmonic solutions and the change of parameters of system by using the methods of Galerkin and Runge Kutta.It can be used for describing further bifurcation phenomenon in power systems.