CASTEP program based on density functional theory was employed to study adsorbing of Fe on N doping carbon nanotube rings under deformation. It shows that bonding energy of new construction is negative, which satisfying energy conditions of stable existence. Adsorbing energies of Fe are enhanced since activities of doping system are increased to form Fe-N covalent bonds easily. Increasing stretch and compression deformations linearly, adsorbing energies of Fe reduce rapidly in parabola shape. They are more sensitive to stretch deformations.

Atom module of α-Fe [100](010) edge dislocation is built in metallic matrix of ductile cast iron. Density functional theory CASTEP method is employed to calculate energy parameters of carbon doping edge dislocation system including atom embedded energy,affinity energy and Mulliken population. It shows that there exist C_2v symmetry group in structure of α-Fe [100](010) edge dislocation and localized effect of dislocation happens in limited range. Energy valley attracts light impurity carbon which forms atom clusters in dislocation corn. Interaction between C and Fe atoms is strengthened with charge transportation between C-4s and Fe-2p obtains which pins dislocation slipping. Mulliken population of Fe atom and C atom is high. Length is short. Iron carbide could be produced. Binding energy and PDOS of carbon doping cementite system show that silicon promotes cementite decomposing and nicalon becomes corn of graphite ball,which improve impact toughness of ductile cast iron.

With Langevin equation of particle motion,PDF equations in two levels are obtained in which the fluid fluctuation velocity is expanded in dimension and one-dimensional colored noise is transformed into two-dimensional white noise.They are two-phase PDF transport equation of turbulence and particle-phase PDF transport equation.With particle motion equations and assumption of Gaussian distribution,a closure problem of PDF equation is solved and a second-order-moment model is obtained.It is simplified into an algebra stress model [ASM].A finite analytic numerical method for convective diffusion equation is applied to solve the two-order moment model of two-phase flows.A wall-jet-flow loaded with solid particles is studied in the ASM by finite analytic numerical method.Numerical results are compared with experimental results.

Based on a colored noise model with general Gaussian process,by functional derivation and small correlation time expansion,high-dimensional colored noises are calculated approximately and an effective Fokker-Planck equation(FPE) is derived.The effective FPE is applied to obtain probability density function transport equations of particles in two-phase flows and a second order moment model of two-phase flows.It is simplified into an algebra stress model(ASM).The finite analytic numerical method used in convective diffusion equation is applied to the second-order moment model.A wall-jet-flow loaded with solid particles is calculated with ASM and finite analytic numerical method.Numerical results are compared with experimental results.