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.

NUMERICAL SIMULATION OF THE FLOW PAST WING-BODY USING EULER EQUATIONS

AbstractThis paper gives H-O type grid generation and applies finite-volume method forwing-body flow.A 3-D Euler code for wing-body has been developed. We improve in thiscode the distribution of the number of grid points over wing and body surfaces,and keepthe training edge of the wing being one of the grid lines even when the edge has sweepbackor sweep forward.The code developed can provide not only the spanwise pressure distribu-tion as usual ou cross-flow planes,but also the chordwise Pressure distributions.The com-putation for NASA TN D-712 wing-body model with the present code shows that thecomputed pressure distributions are in very good agreement with the experiment.

Numerical Simulation of Multi-Directional Random Wave Transformation in a Yacht Port

This paper extends a prediction model for multi-directional random wave transformation based on an energy balance equation by Mase with the consideration of wave shoaling, refraction, diffraction, reflection and breaking. This numerical model is improved by 1) introducing Wen's frequency spectrum and Mitsuyasu's directional function, which are more suitable to the coastal area of China; 2) considering energy dissipation caused by bottom friction, which ensures more accurate results for large-scale and shallow water areas; 3) taking into account a non-linear dispersion relation. Predictions using the extended wave model are carried out to study the feasibility of constructing the Ai Hua yacht port in Qingdao, China, with a comparison between two port layouts in design. Wave fields inside the port for different incident wave directions, water levels and return periods are simulated, and then two kinds of parameters are calculated to evaluate the wave conditions for the two layouts. Analyses show that Layout I is better than Layout II. Calculation results also show that the harbor will be calm for different wave directions under the design water level. On the contrary, the wave conditions do not wholly meet the requirements of a yacht port for ship berthing under the extreme water level. For safety consideration, the elevation of the breakwater might need to be properly increased to prevent wave overtopping under such water level. The extended numerical simulation model may provide an effective approach to computing wave heights in a harbor.

Equation oriented method for Rectisol wash modeling and analysis

Rectisol process is more efficient in comparison with other physical or chemical absorption methods for gas purification. To implement a real time simulation of Rectisol process, thermodynamic model and simulation strategy are needed. In this paper, a method of modified statistical associated fluid theory with perturbation theory is used to predict thermodynamic behavior of process. As Rectisol process is a highly heat-integrated process with many loops, a method of equation oriented strategy, sequential quadratic programming, is used as the solver and the process converges perfectly. Then analyses are conducted with this simulator.

Interaction between Topographic Conditions and Entrainment Rate in Numerical Simulations of Debris Flow

Debris flow simulations are useful for predicting the sediment supplied to watersheds from upstream areas. However, the topographic conditions upstream are more complicated than those downstream and the relationship between the topographic conditions and debris flow initiation is not well understood. This study compared the use of several entrainment rate equations in numerical simulations of debris flows to examine the effect of topographic conditions on the flow. One-dimensional numerical simulations were performed based on the shallow water equations and three entrainment rate equations were tested. These entrainment rate equations were based on the same idea that erosion and the deposition of debris flows occur via the difference between the equilibrium and current conditions of debris flows, while they differed in the expression of the concentration, channel angle, and sediment amount. The comparison was performed using a straight channel with various channel angles and a channel with a periodically undulating surface. The three entrainment rate equations gave different amounts of channel bed degradation and hydrographs for a straight channel with a channel angle greater than 21° when water was supplied from upstream at a steady rate. The difference was caused by the expression of the entrainment rate equations. For channels with little undulation, the numerical simulations gave results almost identical to those for straight channels with the same channel angle. However, for channels with large undulations, the hydrographs differed from those for straight channels with the same channel angle when the channel angle was less than 21°. Rapid erosion occurred and the hydrograph showed a significant peak, especially in cases using the entrainment equation expressed by channel angle. This was caused by the effects of the steep undulating sections, since the effect increased with the magnitude of the undulation, suggesting that a debris flow in an upstream area develops differently according to the topographic conditions. These results also inferred that numerical simulations of debris flow can differ depending on the spatial resolution of the simulation domain, as the resolution determines the reproducibility of the undulations.

A Potential Flow Based Flight Simulator for an Underwater Glider

Underwater gliders are recent innovative types of autonomous underwater vehicles （AUVs） used in ocean exploration and observation. They adjust their buoyancy to dive and to return to the ocean surface. During the change of altitude, they use the hydrodynamic forces developed by their wings to move forward. Their flights are controlled by changing the position of their centers of gravity and their buoyancy to adjust their trim and heel angles. For better flight control, the understanding of the hydrodynamic behavior and the flight mechanics of the underwater glider is necessary. A 6-DOF motion simulator is coupled with an unsteady potential flow model for this purpose. In some specific cases, the numerical study demonstrates that an inappropriate stabilizer dimension can cause counter-steering behavior. The simulator can be used to improve the automatic flight control. It can also be used for the hydrodynamic design optimization of the devices.

Numerical simulation of three-dimensional breaking waves and its interaction with a vertical circular cylinder

Wave breaking plays an important role in wave-structure interaction. A novel control volume finite element method with adaptive unstructured meshes is employed here to study 3-D breaking waves. The numerical framework consists of a ＂volume of fluid＂ type method for the interface capturing and adaptive unstructured meshes to improve computational efficiency. The numerical model is validated against experimental measurements of breaking wave over a sloping beach and is then used to study the breaking wave impact on a vertical circular cylinder on a slope. Detailed complex interfacial structures during wave impact, such as plunging jet formation and splash-up are captured in the simulation, demonstrating the capability of the present method.

BIFURCATIONS AND NEW EXACT TRAVELLING WAVE SOLUTIONS OF THE COUPLED NONLINEAR SCHRDINGER-KdV EQUATIONS

By using the method of dynamical system, the exact travelling wave solutions of the coupled nonlinear Schrdinger-KdV equations are studied. Based on this method, all phase portraits of the system in the parametric space are given. All possible bounded travelling wave solutions such as solitary wave solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, the numerical simulations are conducted for solitary wave solutions and periodic travelling wave solutions to the coupled nonlinear Schrdinger-KdV equations. The results show that the presented findings improve the related previous conclusions.

Nematic and smectic stripe phases and stripe-Sk X transformations

Based on the findings of skyrmion nature of stripes and the metastability of a state of an arbitrary number of skyrmions,precisely controlled manipulation of stripes of skyrmion number 1 in pre-designed structures and mutual transformation between helical states and skyrmion crystals(Sk Xs)are demonstrated in chiral magnetic films.As a proof of the concept,we show how to use patterned magnetic fields and spin-transfer torques(STTs)to generate nematic and smectic stripe phases,as well as“UST”mosaic from three curved stripes.Cutting one stripe into many pieces and coalescing several skyrmions into one by various external fields are good ways to transform helical states and Sk Xs from each other.

Mechanisms and Kinetics of Reaction CHCIBr＋NO2

The reaction CHClBr＋NO2 was investigated via quantum chemical methods and kinetic calculations. The reaction mechanism on the singlet potential energy surface（PES） was considered by B3LYP method, and the energies were calculated at the CCSD（T） and CASPT2 levels of theory. The rate constants and the ratios of products were obtained by utilizing VTST and RRKM methods over wide temperature and pressure ranges. Our results indicate that carbon-to-nitrogen approach via a barrierless process is preferred in the initial association of CHClBr and NO2. The dominant product is BrNO＋CHCIO（PI）, which agrees well with the experimental observation. P2（ClNO＋CHBrO） and P3（HNO＋CBrClO） may also have minor contributions to the reaction. The calculated overall rate constants are independent of pressure and consistent with the experimental data, which can be fitted with the following equation over the temperature range of 200--1500 K： k（T）=2.31 × 10^-15T^0.99exp（771/T）. Compared with reaction CH2Br＋NO2, reaction CHCIBr＋NO2 has decreased the overall rate constants.

Beam dynamics study of RFQ for CADS with a 3D space-charge-effect

The ADS（accelerator driven subcritical system） project was proposed by the Chinese Academy of Sciences.The initial proton beams delivered from an electron cyclotron resonance ion source can be effectively accelerated by 162.5 MHz 4.2 m long room temperature radio-frequency-quadrupoles（RFQ） operating in CW mode.To test the feasibility of this physical design,a new Fortran code for RFQ beam dynamics study,which is space charge dominated,was developed.This program is based on Particle-In-Cell（PIC） technique in the time domain.Using the RFQ structure designed for the CADS project,the beam dynamics behavior is performed.The well-known simulation code TRACK is used for benchmarks.The results given by these two codes show good agreements.Numerical techniques as well as the results of beam dynamics studies are presented in this paper.