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.

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.

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.

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.

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.

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 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 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.