Coefficients C₃ of hyperfine levels of excited states|6²P_3/2 F> (F=2, 3, 4, 5) of ¹³³Cs atom are calculated with irreducible tensor method and van der Waals (vdW) interaction between alkali atoms and perfect surface of a metal. C₃ of|6²P_3/2F>(F=2, 3, 4, 5) we obtained are 4.3385 kHz·μm³, 4.3619 kHz·μm³, 4.3680 kHz·μm³, and 4.3467 kHz·μm³. Our data are compared with other theoretical data and experimental data. It shows that they are reliable.

A mathematical model for numerical simulation of 2D water-oil phase reservoir concerning start-up pressure gradient is solved with full implicit finite difference scheme. A reduced-order model is established by projecting original model in low dimension space formed by basis functions, which is produced from collected snapshots; CVT-Lloyd algorithm is employed in cluster analysis to tackle with flaws from collecting snapshots of same time interval. Computational results show that reduced-order model established based on POD is able to approximate the original model effectively. With cluster analysis, data reduction is eliminated, which could create uniform snapshots in space resulting in enhanced accuracy of reduce-order model. On the other hand, extremely limited clustering groups may lead to loss of information and thus impairing accuracy of reduced-order model.

Based on interconnection transmission differential equation,transform voltage and current expressions are derived by incorporating appropriate boundary conditions for interconnect energy analysis.We considered a practical transmission line with driver and load to find out relation between transform input and output voltage and current responses.Interconnection energy distribution is obtained,which considers non-ideal step stimulation.In 65 nm CMOS process,the non-uniform interconnect analytic model enables to estimate energy within 5% compared with Hspice simulations.The method has high accuracy.The analytic model can be applied to front end optimizing design and analysis of high performance global interconnection.

A three-dimensional analytical heat transfer model for stacked chips is developed, which takes into account horizontal heat transfer effect in three-dimensional integrated circuits (3D ICs) with through silicon via (TSV). Effects of horizontal heat transfer is analyzed with number of strata, TSV density, TSV diameter and thickness of BEOL layer under specific process and thermal parameters. It indicated that temperature rise simulated by the model is lower compared with result not considering horizontal heat transfer effect. Difference of temperature rise can be above 10%. Effect of horizontal heat transfer on thermal management of 3D ICs is more obvious with increasing of integrated level. The model conforms to actual situation. It is more accurate in analyzing temperatures of stacked chips in 3D ICs.

Nematic droplets are studied with Monte Carlo simulations with a modified Gruhn-Hess pair potential. The potential is spatially anisotropic and potential parameters are related to elastic constants K₁₁ ,K₂₂ ,K₃₃ and surface-like elastic constant K₁₃. It is assumed that nematic droplet surface is a free surface. Second order parameters and introrse intensity, which describes quantitatively intrinsic anchoring induced by surface at low temperatures, are calculated with a modified Gruhn-Hess pair potential and are compared with those in Gruhn-Hess model I. It is shown that the modified model with K₁₃ induces intrinsic anchoring near droplet surface, orientation and intrinsic anchoring strength depend strongly on K₁₃, and introrse intensity is related to K₃₃/K₁₁. Order degree of nematic droplet is lower from inner shell to outer shell due to incomplete anisotropic nematic-nematic interactions.

An expression of thermal resistance matrix is given.Transient temperature characteristics of three-dimensional chip-muhiprocessors(3D-CMP) are studied.Effect of heat capacity,thermal resistance and power consumption on temperature is analyzed. It shows that steady temperature of 3D-CMP is limited effectively by reducing thermal resistance and power consumption.Heat capacity influences rise time of temperature.It does not affect steady temperature.

Convective-type boundary conditions at interface of vessel walls are used in simulating convective heat transfer in blood vessels. To study feasibility of the method, convective heat transfer between blood and tissue in a simple furcated vessel system is computed with finite element analysis. Mean Nusselt number on cross-section along the vessel is obtained at various flow velocities or vessel radii. It shows that the mean Nueselt number in the branching vessel varies within a narrow range, and shows fast convergence rate. A tongue with a simple vascular tree is simulated as an example. Conjugated numerical method, and a approximate method are used to calculate 3-D velocity and temperature of the tongue. Distributions of temperature calculated are similar and quantitative difference between temperatures obtained by two methods is less than 0.2℃.

Nematic droplets are studied with Monte Carlo simulation in a spatially anisotropic molecular pair potential model. The potential is based on a lattice model and dependent on elastic constants of liquid crystals. We assume that nematic droplet surface is a free surface and introduce tangent-introrse intensity to quantitatively describe intrinsic anchoring induced by surface. The tangent-introrse intensity and the second order parameters in different regions of droplets at low temperature are calculated by two schemes with spatially anisotropic potential and are compared with those in Lebwohl-Lasher model. Only one scheme can give intrinsic easy axis near droplets surface and introrse intensity is related to K₃₃/K₁₁. The degree of nematic order in the vicinity of droplet surface becomes lower from inner shell to outer shell due to incomplete anisotropic nematic-nematic interactions.

In a condensate gas reservoir welhest model of Xu & Lee, error function express of wellbore phase redistribution is adopted and a mathematical model of variable wellbore storage in triple porosity condensate gas reservoir is shown. With Laplace transformation and Stehfest inversion, effects of pressure parameters on pressure and differential of pressure are analyzed. Typical pressure curves are given.

We describe an unsteady flow model of blood in arterioles of normal and tumor tissues,and show effect of external magnetic field on flow field of blood considering coupling of magnetic field and flow. Traditional single-phase model is modified by a discrete method,and dynamical simulation with a finite element route is used to investigate transmission of magnetic nano-drug in arteriole.The result indicates that the capture of nano-drug by magnetic field is entirely different from that of microdrug by magnetic field.The trajectoriy of nano-drug is primarily coincident with the streamline of blood flow.However,the effect of magnetic field on the blood flow is obvious due to the presence of magnetic nano-drug.Several whirlpools are formed near the magnet.In tumor arteriole these whirlpools stay for a long time and the magnetic nano-drug is efficiently captured by external magnetic field.

A sort of birth-death process is investigated.We calculate eigenvalue,eigenvectors of the main matrix for the birth-death process differential equation and get a similar decomposition of the main matrix.Using the technique of matrix decomposition,we obtain the solution of the birth-death process differential equation and study the heavy element abundance of the slow neutron capture process(s-process) in the solar system.A full calculation of heavy element abundance of s-process in solar system is carried out.The result agrees well with astrophysical measurement.

In this paper, Finite element method (FEM) coupled with Element free Galerkin method (EFGM), is developed it, not only takes advantage of FEM, but also gives EFGM local technique and element-free character. Both make it has more advantages in calculating. The paper introduces EFGM in details, and meantime dedues discrete equations of consolidation. It gives two examples of calculating and analyzing, the results of calculating point out that the implementation will achieve more accurate in the deformation of consolidation, another discovery is that an accurate solution of fluid flux can be obtained. In particularly, combining with FEM the results is more effective, in conclusion, EFGM is powerful complementary of FEM.

DV-X_α method,is applied for calculating the Electronic structure and Magnetic properties of YFe₁₂,which is an ideal structure of ThMn₁₂.The result shows that this method has satisfactory advantages on the theoretic of magnetic material.