Monte-Carlo simulation of a stochastic differential equation

For solving higher dimensional diffusion equations with an inhomogeneous diffusion coefficient,Monte Carlo（MC） techniques are considered to be more effective than other algorithms, such as finite element method or finite difference method. The inhomogeneity of diffusion coefficient strongly limits the use of different numerical techniques. For better convergence, methods with higher orders have been kept forward to allow MC codes with large step size. The main focus of this work is to look for operators that can produce converging results for large step sizes. As a first step, our comparative analysis has been applied to a general stochastic problem.Subsequently, our formulization is applied to the problem of pitch angle scattering resulting from Coulomb collisions of charge particles in the toroidal devices.

Simulating Deposition of Aerosol Particles on Single Fiber Surface

The stochastic simulation method, based on the concept of control window and the numerical solution of the Langevin equation, is applied to solve the deposition problem of particles from the flowing suspensions onto a fiber collector. Using the Kuwabara model to characterize the flow field, the effects of Stokes number, interception parameter, packing density, particle size distribution on the collection efficioncy, and the deposition morphology of particles onto a collector are i examined. The morphology of deposit obtained in the simulated results agrees Well with experimental observations. The estimation of the initial coUection efficiency through the simulations considers that the deposited particles are in good agreement with published experimental data. In addition, the collection efficiency of particles increases in a wider particle size distribution region.

Characterization on jointed rock masses based on PFC2D

Geometrical parameters of discontinuities,such as spacing,length,dip and fault throw between joints have a great influence on the mechanical behavior of jointed rock masses.Accurate characterization for discontinuities is important for investigate the stability of rock masses.In this paper,the PFC2D is combined with joint network generation method to examine the mechanical behaviors of jointed mass.Taking Miaogou Open-pit Mine as an example,the information and statistical distributions of discontinuities of the slope rock masses are measured by ShapeMetriX3D measuring tool.Then,the automatic generation algorithm of random joints network based on the Monte-Carlo method is proposed using the programming language(FISH)embedded within PFC2D.This algorithm could represent the discontinuities compared with the geological surveys.In simulating the compression test of a jointed rock sample,the mechanical behavior and crack propagation were investigated.The results reveal that the failure mode and crack propagation of the jointed rock are dominated by the distribution of joints in addition to the intact rock properties.The simulation result shows the feasibility of the joints generating method in application to jointed rock mass.