Molecular dynamics simulation is used to simulate response of nonlinear sinusoidal alternation flow of helium gas oscillation in a pulse tube. Formation of axial pressure wave and temperature field inducted by gas oscillation was studied.Influence of length to diameter ratio on temperature difference and phase of cold and hot ends of the pulse tube is shown. It shows that the pressure wave,speed wave and mass flow wave accompanying by driving force are similar to a sinusoidal function while the temperature wave is similar to a half-sinusoidal function. The oscillation period is shortened with increase of the diameter of the tube and prolonged with increase of the length of the tube. The maximum temperature difference between hot end and cold end increases with the length of the tube but independent of diameter. It is predicted that there is an optimal aspect ratio and oscillation period for pulse tube with different diameter, which increases with increasing of the diameter. It provides a theoretical basis for optimizing efficiency of pulse tube.

Electronic properties of graphene nanoribbons (GNRs) doped with rhombus boron nitride segments are investigated by using first-principles method based on density functional theory. It is shown that band gaps of AGNRs increase owing to doping, and band gaps of AGNRs vary slightly as doped at different positions. In nonmagnetic states, ZGNRs are metal whether or not it is doped. In ferromagnetic states, ZGNRs change from metal to semiconductor due to doping. In antiferromagnetic states, ZGNRs are semiconductor whether or not it is doped, but band gaps are changed owing to doping. Structures of doped AGNRs and ZGNRs are stable, and ground state of doped ZGNRs is antiferromagnetic. It suggests that rhombus boron nitride segments doping controls effectively properties of GNRs, which is positive on future graphene nanoelectronic devices.

For energy deposition of fast electrons in high density plasma, a relativistic Fokker-Planck equation in three-dimensional momentum space is introduced. It includes both binary collision and contribution from plasma collective response. Numerical method as well as kinetic code of the equation is developed. Typical energy deposition cases are presented with comparison with stopping power model. Energy deposition of fast electrons with energy from 0.5 MeV to 3.5 MeV in 300 g·cm^-3 DT plasma are simulated. It shows that scattering angle ϕ plays minor role on range and penetration depth of energy deposition of fast electrons.

We study numerical method for relativistic Vlasov equation and present a scheme for computing Vlasov equation based on Cartesian-spherical coordinate system, which can be used to reduce number of numerical grid for momentum space. Furthermore, a 4th order non-splitting finite volume scheme is proposed in order to solve momentum parts of relativistic Vlasov equation. In test problems, especially relativistic Landau problem, laser-plasma interaction are solved by using the scheme. We confirm the scheme with theoretically analysis as well as numerical comparison with results of PIC method.

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.

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.

Based on analyses of SAGD field production data and numerical simulations,SAGD production process in thin heavy oil reservoirs was divided into periods: steam chamber horizontal expansion period and steam chamber downwards migration period. A model was built,which includes mass conservation equation,energy conservation equation and heat loss equation. A comprehensive mathematical expression was obtained to describe steam chamber development process. The expression is a typical Volterra integral function of the second kind,which could be solved by Laplace transformation. Comparisons were made between the model and CMG Stars'. A small relative error,less than 5% for the whole SAGD production process,was found. The model provides an accurate and quick method for determination of limited reservoir properties and proper production parameters for SAGD production.

Modeling of generalized perfectly matched layer (GPML) absorbing boundary conditions in ground penetrating radar (GPR) simulation is discussed. Maxwell's equations are discretized by finite-difference time domain (FDTD) method,and Mur super absorbing boundary conditions and GPML absorbing boundary conditions are adopted to simulate GPR sections of a water-filled karst. GPR images of a multi-cylinder model and an inclined interface model are obtained by FDTD method with GPML absorbing boundary conditions. It shows that as an absorbing boundary condition GPML absorbs outgoing wave effectively. Its absorbing effect is better than that of Mur super absorbing boundary conditions. It can be applied to GPR simulations.

In a FENE bead-spring chain model,a parallel algorithm for Brownian configuration fields with finite volume method is used to simulate pressure driven pipe nows, velocity-pressure driven pipe nows with same and opposite directions. Validity of the algorithm is verified with numerical examples. Velocity,stress and stretch of molecular chain of pipe nows are obtained. It shows that the proposed algorithm overcomes shortcomings of huge computation and time-consuming for Brownian configuration fields. And it has excellent expansibility. Parallel efficiency is over 85% as number of beads is greater than two. It also shows that the time of now to reach steady state is shorter with increasing number of chain segments.

An improved time-delayed dual model for internet congestion control is investigated.Normal form theory,center manifold theorem and Hopf bifurcation theory are used for analysis.Bifurcation and stability analysis are mainly decided by communication time delay.As the delay passes through a critical value,Hopf bifurcation forms,which leads to a large oscillation of link price function.In addition,bifurcation direction and bifurcation periodic solution are derived,which provide model design with theoretical foundations.This work is summarized as two theorems verified by numerical simulations.

A fractal theory for double porous media reservoir is introduced. An effective well radius mathematical model is used to calculate pressure of non-stesdy flow in a complex intluent system considering wellbore storage, skin factor and phase redistribution. With Douglus-Jones predictor-correcter method we obtain numerical solution of infinitely large system with constant rate production. Entire drawdown curve of the complex influent system includes 4 periods. Effects of phase redistribution parameters, double porous media parameters and fractal parameters on drawdown are shown in typical pressure curves.

For boundary conditions with functions changing rapidly,especially in charged conductors,we combine compact feature of wavelet functions and high accuracy of RBF in a coupled method and solve ground metal trough/box problems. Rectangular,ridge and round waveguides are analyzed with RBF and FEM methods.Numerical experiments show that RBF method is efficient in solving electromagnetic boundary and eigenvalue problems.RBF method is easier and more accurate with less nodes.

For a magnetic tunneling junction with ferromagnetic metal/magnetic potential barrier layer/ferromagnetic metal structure, tunneling conductance, spin polarization and tunneling magneto resistance rate under zero bias voltage are calculated in a quasi-free electron model. The impact of potential barrier, molecular field strength and molecular field orientation, etc. on tunneling of electrons is analyzed. It exhibits useful instructions for the design of spin electronic devices.

An iterative physical optics(IPO) method combined with multilevel fast multipole algorithm(MLFMA) is used to solve electromagnetic scattering by a three-dimensional complex cavity efficiently and rapidly.The iterative formulations of hybrid algorithm are derived.For slow bending cavities in engineering,a proper subsection structured grouping method is provided to avoid the shelter of facets between two groups.A generalized reciprocity integral(GRI) method is applied to cavities with complex termination.The methods obtain accurate results and improve computing speed.

The TVD conditions of finite difference schemes are interpreted on geometrical views for hyperbolic equations,and from it the non-oscillatory conditions are derived for conventional second-order schemes.A mainly third-order non-oscillatory scheme (NOS) is developed.Numerical experiments show high order,non-oscillation,simplicity and symmetric diffusion of the scheme.

Based on the stream function-vorticity expression a discrete procedure is employed to approximate the imcompressible fluid with zero viscosity,in which the vorticity is approximated by finite difference along its streamline,the velocity field and the stream function are approximated simultaneously by a mixed finite element.The analysis shows that the procedure possesses both high accuracy and good stability which are not shared by standard methods.

Taking into account of various factors which effect the reconstruction precision of EAS events and selecting some suitable optimum algorithn (such as simplex method algorithm, DFS algorithm). A new software EAS-FIT is made, which is of wider use and described briefly with some applications. This new software was been used to analyse the EAS raw data of Beijing Huairou array. The results show that it can improve overall precision of the array and greatly increse the speed of off line reconstruction (20-120 times faster than the old one). In addition, some important physics results can be obtained such as energy spectrum at the ‘keen’ region and so on.

A Monte Carlo simulation code has been written for heavy-ion induced fission at sub-barrier energies with a simple model. The final properties of the heavy fragmemts such as mass, charge, energy, angular distribution and angular correlation have been simulated for complete fusion-fission and transfer-fission. The angles and velocities of the fragments relative to the recoil direction are given in the laboratory system. Consideration covers the combined kinematic effects of the distributions in mass energy and angular for the heavy fragments and pre-scission, post-scission neutron emission. The code can be used as a tool for experiment planning and analysis.

In the essay, the finite element algebraic equations by element assembling is replaced by node assembling, and the right term is dealt with by the idea of lumped mass, and the most compactly-stored finite element method is obtained.Thus, the total matrix elements are reduced to less than three times of unknown node, and the stored-units are even less than which the rectangle grid finite-difference method needs. The program structure is more rational and simpler, meanwhile the calculation quantity is reduced and the computational effciency is improded. All these become more obvious in process of solving nonlinear problems.