We combine group velocity formula and phase velocity formula in tilted transverse isotropy (TTI) media with elastic matrix theory in anisotropic media,and design a model in transversely isotropic (TTI) strata with inclined symmetry axis. According to the model,velocity of TTI coal bed phase velocity changes gently with the change of anisotropic parameter while group velocity change fiercely. Therefore, group velocity determines the wave field shape of anisotropic media; Within a certain range, group and phase velocity for qP wave are greater with increasing ε; Group and phase velocity for qSV wave are greater with increasing δ; Group and phase velocity for qSH wave are greater with increasing γ.

We computed equations of state of hydrogen in warm dense matter regime by using DPIMC method. In large part of the regime, pressure difference between DPIMC and RPIMC is less than 10%. In low temperature regime, some difference beyond 20%. We pointed out two clerical errors in pressure of RPIMC. In dissociation and ionization regime, pressures of DPIMC lie between results of TF and TFC model. In dissociation regime, the largest pressure difference between DPIMC and RPIMC is 15%. In ionization regime, pressures of DPIMC are agree with RPIMC. In low density regime, internal energies of DPIMC are close to those of RPIMC, less than those of QMD and those of IG model. In high density regime, pressures of DPIMC lie between results of TFC and IG model, internal energies of DPIMC less than those of IG model.

Application of simulated annealing method in chemical free energy model to search for chemical composition of equilibrium state is proposed. Due to the random "thermal" fluctuations introduced by simulated annealing method, the difficulty associated with sensitivity of result to initial values is removed. Moreover, in the regime of first order phase transition where stable state and meta-stable state coexist, the stable state can always be obtained. As an example, chemical free energy model improved by simulated annealing method is applied to the equation of state for fluid helium, which demonstrates the plasma phase transition induced by pressure ionization.

Dynamical behavior of a class of 4D memristive chaotic circuits was discussed, and attracting domain of multi-stability was studied. In order to guarantee efficiency and accuracy of calculation results, CPU+GPU large-scale computing power were introduced and more than 128 decimal places of precision GMP library and MPFR library were applied to calculate domain of corresponding attractor. Finally, existence of hyperchaos was proved by using method of topological horseshoe theory and constructing memristive analog circuit.

Equation of state of detonation products for HMX explosive is calculated. Detonation velocity and detonation pressure at CJ point are calculated as initial density of HMX explosive is 1.90 g·cm^-3. It shows satisfactory agreement with experimental data. Mole numbers of various detonation products are predicted and compared with results of BKW and LJD. Pressure, γ and mole numbers of detonation products along CJ adiabatic expansion path are given. They are helpful for understanding phenomenon of detonation.

It is hard to apply topological horseshoe in 3D maps due to high dimension and complex structure since dimension of a chaotic attractor is often lower than its state space. We fit a surface with attractor near a selected unstable periodic orbit, and present a "dimension reduction" method to find topological horseshoes with one-directional expansion in 3D space. It is realized with a MATLAB toolbox. Compass walking model is shown to verify effectiveness, and illustrates detailed procedure for finding a topological horseshoe. It successfully verifys existence of chaotic gait and analyzes chaotic invariant set with horseshoe.

With potential energy surface constructed in 2003, we study stereodynamics of reaction Li+HF→LiF+H using quasiclassical trajectory (QCT) method. Polarization dependent differential cross sections (PDDCSs) and P(θ_r,φ_r) distributions describing k-k'-j' correlation related to collision energies. Vibrational states and rotational states are discussed at 1.15 kcal·mol^-1-5.0 kcal·mol^-1. Furthermore, cross sections are compared with that of other calculations and experiments. It indicates that vibrational and rotational excitations have stronger impacts on PDDCSs and P(θ_r,φ_r) than collision energy. Backscattering polarization of product rotational angular momentum is positive correlated with collision energy. Cross sections agree well with results of other theories and experiments in the range of calculation collision energies.

A model to calculate stress sensitivity is established based on theory of accumulation of geology, geomechanics and theory of flow through porous media. Compared with experimental results, the model is accurate and reliable. Distribution range of tight oil reservoir in Daqing Field is narrower than that of Changqing Field. It results in that stress sensitivity of Daqing Field is severer than that of Chaingqing Field. And productivity of Daqing Field is lower than that of Changqing Field. We make a quantitative description on mechanism of stress sensitivity in tight oil reservoirs.

To solve unsteady laminar flow problems,a method of velocity-stress-pressure formulation instead of velocity-vorticitypressure formulation is developed.With Newton's linearized method to linearize convective terms and preconditioned conjugate gradient method to solve equations,unsteady stress formulation of Navier-Stokes equations is solved.Comparison between numerical and experimental results of cavity laminar flow shows that result of stress formulation fits experiment better and has higher accuracy than vorticity formulation.The stress formulation can deal with subgrid stress with least squares finite element method.Comparison with experimental results of cavity turbulent flow reveals feasibility of the method.It lays a firm foundation for large eddy simulation computation.

An atomic-based finite element method is developed,spanning from atomic scale to macroscopic one. With theoretical deduction dispersion relation and dynamic scattering behavior are calculated. For spurious reflection caused by non-uniform grid,lowpass filter boundary condition is designed to effectively eliminate the reflection of high-frequency phonons,while keeping low-frequency ones transparent. These schemes are demonstrated with numerically calculating reflection and transmission coefficients in onedimensional modeling.

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.

We use Jordan-Wigner transform and Bogoliubov theory to study specific heat of triangular chains. In the absence of external magnetic field,it shows that doublet-peak structure disappears gradually as specific heat of a frustration system increases,which is due to antiferromagenetic excitation of spins in dimer state. As frustration is set 0.2 and applied external magenetic field,disappearence of specific heat double structure is due to occurrence of long-range magnetic order.

Based on Reissner-Mindlin plate theory,a meshless Kriging interpolation method (MKIM) is developed for bending of moderately thick plate.Corresponding discrete equations are derived.Approximation function in the method is built on a group of scattered nodes and therefore it can eliminate effectively complex meshing and disadvantage of mesh distortion.Compared with moving least squares (MLS) approximation widely used in meshless methods,shape functions constructed by moving Kriging interpolation method possess Kronecker delta property,which facilitates imposition of essential boundary conditions.High efficiency,good accuracy and easy implementation of the method in bending of moderately thick plate problem are demonstrated with numerical examples.

Lattice Boltzmann multiphase method based on Shan-Chen model is used to a systematic study on dynamics of two-phase fluid flows in a lid-driven square cavity.Effects of Reynolds (Re),Capillary number (Ca) and surface wettability on flowing and mixing are investigated in details.It shows that the greater the Re and Ca,the longer pength of two phase fluid mixing interface in the cavity.In addition,the length of mixing interface increases with surface hydrophobicity.However,for a highly hydrophilic surface,the length of mixing interface tends to a constant finally.

A mathematical model is established to describe convective heat transfer in magnetic microencapsulated phase change material slurry (MMPCMS) flows in a circular tube under an external magnetic field. Influences of magnetic field strength, volume fraction of magnetic phase change materials (MMPCM), mass flow rate, and heat flux on convective heat transfer are analyzed. It shows that convective heat transfer of slurries is obviously enhanced by external magnetic field. Since distributions of MMPCM volume fraction and slurry temperature are changed clue to magnetic force on MMPCM.

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.

A hybrid method is proposed to study microcosmic characteristics of nanofluid mulfiphase flows in a lattice Boltzmann approach. Multicomponent lattice Boltzmann model on fine mesh is used in regions where physical parameters, such as density and velocity change tempestuously, otherwise a single component one on coarse mesh is used. In order to keep continuity of physical information (physical parameters) in overlapping regions, principle of mass and momentum conservation is used. It shows that in the model microcosmic characteristics of nanofluid flow can be obtained. Computational efficiency is improved observably compared with a multicomponent method.

A lattice Bohzmann model is established to describe liquid-vapor phase transitions using a model proposed by Shan instead of the R-K model. Evaporation from a higher density phase to a lower density phase is simulated. The model improves calculation efficiency and obtains good results. The model is also used to simulate phase transitions in porous media with a pore scale to demonstrate feasibility of the model for complicate phase transition problems.

With analysis of water balance in elements controlled by nodes,a stable computational scheme is proposed similar to FEM of Galerkin.It holds mass conservation automatically.A nonlinear phreatic water problem is solved conveniently by this scheme.Numerical calculation provides good result in solving a Theis problem.

The Navier-Stokes equations are solved with the second-order LU-SGS-τTS implicit time-stepping method. The sixth-order symmetric TVD scheme with fifth-order WENO interpolation based on Roe is applied to the convection terms. A boundary layer flow around a flat plate, a low speed flow around the Aerospatial A-profile at high incidence and a transonic flow with shock/boundary interaction around RAE2822 airfoil are computed by Baldwin-Lomax and Spalart-Allmaras models with the transition criterion, respectively. The results show that the approaches capture the transition automatically.

A practical and efficient computation method for stable and unstable manifolds is proposed.Pictures of unstable (stable) manifolds are obtained easily.Thus one can investigate geometrically dynamics of a dynamical system and features of stability regions.The algorithm consists of two steps:Firstly,calculate on well distributed points in the unstable manifold by means of integration so that details of the unstable manifold are shown.Secondly,draw a picture of the manifold with these points by means of triangle partition.

A high accuracy and resolution finite difference method is first used to simulate numerically the compressible wake shear layers induced by flat plates with different thicknesses. The new method is named the Fu-Ma UCD5-SCD6 hybrid compact scheme. The fully two-dimensional compressible Navier-Stokes equations are directly solved. Based on the Steger-Warming flux-splitting technique, the convective terms are discretized by using the fifth-order upwind compact difference method, while the dissipative terms are discretized by using sixth-order symmetric compact difference method. A third-order Rung-Kutta method is selected for time marching. At convective Mach number M_c=0.3, four flat plate thicknesses and three upper incoming Mach numbers are considered. In all cases, the self-excited large scale vortex coherent structures are captured successfully, and their spatial evolution such as eddy rollup and pairing is investigated. Results show that the flat plate thickness can obviously affect the coherent structures. Increasing the flat plate thickness can accelerate the vortex rollup and enhance mixing. Moreover, for the same convective Mach number, increasing incoming Mach number can delay the vortex rollup and damp the vortex pairing. This can somehow be attributed to the well-known compressibility effect.

A lattice Boltzmann model is proposed for the double diffusive natural convection system.The flow in a square cavity driven by a temperature gradient and a concentration gradient is then simulated using the present model.The influence of the concentration field on the flow patterns is investigated,and some quantitative comparisons with other studies are made.It is shown that the present LB model can predict the flow characteristics correctly.

A newly developed gas-kinetic BGK scheme is further simplified. Numerical tests show that the new simplification not only keeps the advantages of the old scheme, such as its robustness and automatic satisfaction of the entropy condition but also makes the scheme simpler and more efficient.

Mo-algorithm is applied for electric network design, and faster convergent rate and higher precision results are obtained.

A boundary correction method is proposed for the numerical solution of the degenerate four-wave mixing in photorefractive crystals. The present method can easily deal with the problem of split boundary conditions. Results from the present method shows that the incidence angles of and ratio of pump beam intensity in the PCR lead to a significant improvement; The line absorption of the interacting beams by the crystals is nonlinear in the PCR.