Dynamics characteristics of two bubbles in a quiescent fluid were simulated with three-dimensional lattice Boltzmann model. Eight-point and eighteen-point difference schemes were used to calculate the first and the second order derivative ▽ φ and ▽²φ in order to avoid numerical instability caused by large density ratios. It shows that for two rising bubbles with same size, the leading bubble rises like an isolated bubble, and the trailing bubble is influenced by the wake of the leading bubble. For two rising bubbles with different sizes, however, the larger bubble always strongly affects the smaller one in any initial sizes and locations.

In view of structural evolution difficulty caused by integer variables in heat exchanger network with fixed investment cost, a fixed investment cost relaxation strategy is proposed. It simplifies mathematical model of the problem by relaxing fixed investment cost. As heat exchanger is very small, fixed investment cost is almost zero. With increase of heat exchanger, fixed investment cost is gradually increased with a certain slope, and finally equals to the actual value. Controlling the change slope by the relaxation strength coefficient, on the basis of ensuring reliability of optimization results, heat exchangers with structural evolutionary obstacles are guided to generate or eliminate. The strategy is used to two cases in the literature, and effect of this strategy on generation or elimination of heat exchanger under different relaxation strength is investigated. Finally, a random walk algorithm with compulsive evolution based on fixed investment cost relaxation strategy is proposed. The algorithm is applied to a heat transfer network case. The result is superior to existing literature.

As a high-temperature phase of Pu, δ-Pu doped with little Ga can stay to room temperature. Crystal structure and electronic structure of systems with different contents of Ga are calculated with density functional theory (DFT) method. Calculations mainly include lattice constant, density, formation energy, density of states(DOS), electron density and Mulliken population. It shows that within studied doping scope, lattice constant of systems decrease and density of systems increase with increase of content of Ga, while stability of system with 6.25% content of Ga is superior to that with 3.125% and 12.5% content of Ga. Ga-doping enhanced locality and strengthens bonding ability of electrons, which, to some degree, reveals electronic mechanism of Ga stabilizing δ-Pu. Character of Pu-Ga bond is metallic state, and interaction is mainly contributed by Pu 7s, 6p, 6d and Ga 4s, 4p orbital electrons. While interaction is relatively weak, doped systems maintain fine mechanical properties and machining performance. Contribution of Ga to stability of δ-Pu lies mainly in its improvement on bonding performance of Pu, instead of its immediate bonding effect with Pu.

Density functional theory with B3LYP functionals was used to study generating phenanthrene derivatives mechanism of acetylenic-keton intramolecular cyclization reaction catalyzed by AuCl₃. It shows that the reaction can occur through [2+2] and [2+6] reaction pathways with and without AuCl₃ catalyst. Without catalyst, energy barrier of rate determining step of [2+2] pathway is lower than that of [2+6] pathway by 32.01 kJ·mol^-1. Reaction mainly occurs through [2+2] pathway. With AuCl₃ catalyst, dominent reaction pathway is still [2+2] pathway with an energy barrier of rate determining step of 137.05 kJ·mol^-1. Energy barrier of rate determining step of four-membered ring pathway with AuCl₃ catalyst is 102.72 kJ·mol^-1 lower than that of reaction without catalyst. This difference indicates that AuCl₃ is an efficient catalyst which can raise reaction rate and moderate reaction condition.

Optimization in random walking algorithm with compulsive evolution (RWCE) for heat exchanger network synthesis (HENS) turns to slow down in late evolution as heat load of all heat exchangers are optimized simultaneously. A random walk algorithm with compulsive evolution combined with restrictive-evolution strategy for heat unit (RS-RWCE) is proposed, in which number of evolved heat units in HEN is restricted in each random walk evolution to keep fast convergence of total annual cost in early evolution process and fine search in late evolution process. Specific examples are applied to verify high computational efficiency and accuracy of the strategy. It gives consideration to integer variable and continuous variable. The results are encouraging.

To deeply understand mechanism of shock wave interacting with a flame,a numerical study on a planar incident shock wave and reflected wave interacting with a spherical flame was carried out with two-dimensional Navier-Stokes equations coupled with chemical reaction. Okubo-Weiss function are proved appropriate for compressible flow by analyzing characteristic equation of velocity gradient tensor. Emphasis was placed on two-dimensional flow topology characteristics of flame zone. It shows that integral of Okubo-Weiss function conserves within flame zone after passages of shock waves. However,inner and surface of flame zone display completely different flow status. Flow compressibility basically has no effect on evolution of flame. Besides,flow topology of flame zone is mainly controlled by foci and saddle,which means deformation is dominant in flow field.

Under the frame of time-dependent density functional theory( TDDFT) and molecular dynamics,we studied microscopic electronic-ionic association dynamics in collision between hydroxyl and proton which moves toward molecular axis of hydroxyl with 15 eV initial kinetic energy. Energies of projectile and target,electron and vibration excitations of target and real time distribution of electron density are identified. It is found that proton captures electrons of hydroxyl in collision and it rebounds from the target with loss of 26.7% of initial kinetic energy. While the kinetic energy of hydroxyl increases and hydroxyl moves toward to numerical boundary accompanied with stretch oscillation. Hydroxyl loses 1% electrons and exists as neutral and ＋1 valence forms with 93% and 7%probabilities respectively.

With computational fluid dynamics method, effect of embankment inclining angle on aerodynamic characteristics of high speed train under crosswinds is explored. It shows that as inclining angle of embankment is increased, side force coefficient on head train is increased a little and then decreased. Side force coefficient on middle train is gradually decreased. Side force coefficient on rear train is decreased a little and then increased as the angle reaches 47.5°. Negative lifting force coefficient on middle train is increased and lifting force coefficient on rear train is sensitive to inclining angle of embankment. The flow field around train is transformed as the inclining angle of embankment is changed and aerodynamic force or moment is changed consequently.

With time-dependent density functional theory and molecular dynamics excitations of linear and rhombic C₄ in intense laser field are explored.It is found that electrons of 1incar C₄ obtain mote enelrgy while ions of rhombic C₄ get more from the 1aser filed. Ionization is enhanced as C₄ owns 8 linear structure. As laser polarization is along the x axis there is only D_x excitation of a linear C₄ while dipole oscillations of a rhombic C₄ in x and y directions are excited.

A rotating black hole is supposed to lie in a standard acc.retion disk.Imaging of the black hole shadow in an accretion disk are drawn as accretion disk inner boundary is equal to the last stable orbit.With qualitative and quantitative analysis of shape and position of a black hole,it is found that the size and shape of a black hole shadow for black holes with same mass are relevant to black hole spin.Shape and position of n rotating black hole shadow are asymmetrical relative to its rotating axis.The center of mass and rotation parameters of a black hole are determinated with position between rotating axis and black hole shadow.

Numerical radiograph using Monte Carlo method is used to study fidelity of density reconstruction in high. energy X-ray radiography.A density reconstruction method for a polyenergetic X-ray source and an object composed of different materials is proposed.The method includes energy spectrum,angular spectrum and spot size of photon source. And it indudes mass absorption coefficients explicitly in density reconstruction as well.A constrained conjugate gradient algorithm and variation regularization are applied to determine material edges and density reconstruction of a French test object.It shows that the method is valid for density reconstruction and energy spectrum of imaging photons is important in obtaining accurate material densities in high-energy X-ray radiography.

A three-dimensional simulation on deformation and instability of low-density spherical bubble induced by incident and reflected shock waves is performed with Navier-Stokes equations.A computational model validated by experiments is used to study deformation of bubbles,formation and three-dimensional instability of vortex rings.It is found that low.density spherical bubbles can deform and form vortex rings with different rotating directions along streamwise direction induced by incident and reflected shock waves. Baroclinic effect is the main reason for formation of vortex rings.Vortex rings move due to self-induced effect and flow field velocity. And azimuthal instability OCCURS due to disturbance.Finally.vortex rings may induce turbulent flow a8 they form a complicated structure dominated by small-scale streamwise vortices.

A boundary element method (BEM) for Burton-Miller boundary integral equation is accelerated efficiently with Graphics Processing Units (GPUs).Conventional BEM formulations are reformulated so that they can be handled efficiently in GPU.Singularity extraction and local correction techniques are used to evaluate singular integrals,including strong-and hyper-singular ones.Numerical results show that:(1)The proposed method obtains unique and correct solutions at fictitious frequencies;(2)Accuracy of the method is almost the same as that of conventional BEM;(3)Computational time and memory consumptions of the proposed method are much lower than reported results.It shows that GPU-accelerated BEM based on Burton-Miller equation is a fast,efficient and simple method for medium-or large-scale acoustic problems in engineering.

A variable-density stochastic vortex model is used in simulating H₂/O₂/N₂ turbulent jet diffusion flames,in which turbulence is modeled by vortex sample,vortex suppression and vortex turnover.A large-vortex suppression mechanism for variable density reacting flows is presented and effects of parameters in model prediction are discussed in detail.It shows that the modified model can predict reasonably H₂/O₂/N₂ jet flame structures,and reflect characteristics of turbulent vortices.It also reveals that various parameters in vortex sample and vortex suppression affect results of the model.

Electromagnetic scattering of conducting targets located above lossy half-space is analyzed with multilevel fast multipole algorithm (MLFMA).In order to expand half space Green's functions with addition theorem,a high order approximation method is proposed for evaluation of reflection term of half-space Green's functions with far interactions.A careful investigation is presented to confirm accuracy of the Green's function analysis.Accuracy and efficiency of the proposed method is examined by several numerical applications.It demonstrates that the proposed method has merit of low memory requirement and simple operation.

Electromagnetic scattering of arbitrarily shaped 3-D homogenous dielectric objects located above a lossy half space is investigated.With spatial domain half-space Green's functions surface integral equations are studied to reduce iterations and to enhance efficiency of the method of moment(MoM).An integral equation called JMCFIE is extended to half-space to realize accurate and fast solution.This formulation leads to a well-conditioned matrix equation with RWG basis functions and Galerkin's method.Numerical results demonstrate accuracy and efficiency of the proposed method.

We study orderd structures of binary mixtures with mobile particles under Gaussian noise with Monte Carlo method. It shows that interaction between particle and component decides position of particles and motion of particle can break up isotropy of the system. As this interaction is large, tilted strip pattern formation is observed with a particular external C, aussian noise and particle concentration. Furthermore, an optimal noise frequency region(p=0.005~0.02)exists, in which the system quickly forms high-oriented tilted strip pattern.

Complex microstructures assembled with ABC amphiphilic nanoperticle-coil macromolecules are investigated with an extending serfconsistent field theory (SCFT) and density functional theory (DFT). The tail of macromolecule is an AB dibiock copolymer, and the attached "head" is a nanoparticle in dilute solution. Serf-assembly morphologies of ABC "tadpole" are different from aggregate morphologies of linear ABC triblock copolymers. As nanoparticle is hydrophilic, spherelike micelles are observed in a weak segregation state. While interaction between different species of "tadpole" increases to a strong segregation state, aggregate morphologies of tadpole transform from spherelike micelles to quadrangle or triangle micelles with increasing of hydrophobic property of blocks A and B. In this case, block B is distributed in corners of quadrangle or triangle micelles. As block A is hydrophilic, hydrophobic nanoparticle assembles into parallel rods or squares in spherelike micelles.

With an improved Numerov algorithm, continuum state wave functions and its normalization are investigated. Cowan' s normalization is discussed and a more precise and effective calculation is offered. We calculate the Thomas-Reiche-Kuhn(TRK) sum of several hydrogen atomic states (l=0~3). The least-squared method is used to generate infinite asymptotical forms of TRK. The residues are approximately calculated with an integral processing.

The shock compression of condensed matter can be effe ctively dealt with by molecular dynamics,and has been applied to many fields of science.However,there is large scale computation in molecular dynamics,so it is very important to develop the parallel and optimizing algorithm.An approach to the parallelization and optimization is proposed on the NOW (Network of Workstation),and has got the satisfactory result.

Using symbolic capabilities of MATHEMATICA software,a package(VCE 1.0) is developed to use for variational cumulant expansion study in lattice models with neiboring interaction.Enumerating high order connected diagrams and analytical expansions of free energy and so on can be obtained by this package.This package can also be used to study some models of lattice gauge theory and statistical physics.