Numerical simulation of Richtmyer-Meshkov instability

The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms=1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock     

寿命服从对数正态分布、有置信度时概率疲劳S-N曲线的合理重构

当概率疲劳S-N曲线以特定存活概率(P)和置信度(C)的方式给出并无法重做试验时,除特定P-C外无法做其它概率水平的可靠性分析.因此,需要广泛适用的曲线模型.建立了疲劳寿命服从对数正态分布时疲劳试验S-N数据及广义曲线的Monte Carlo模拟重构方法.为了避免现有人为放大样本到数千给出偏危险评价,从实际试验情况出发,采用了材料小试样每组样本7至20、结构试样每组样本至多10个、还原统计参量误差小于5%的模拟策略.然后,依据模拟数据利用回归法重建了可实现任意P-C水平可靠性分析的P-C-S-N曲线.铁路60Si2Mn高强度弹簧钢概率曲线的重构实践说明了方法的有效性与适用性.     

Atom-transfer radical polymerization of styrene with bifunctional and monofunctional initiators: Experimental and mathematical modeling results

Bulk atom transfer radical polymerization (ATRP) of styrene was carried out at 110 °C using benzal bromide as bifunctional initiator and 1-bromoethyl benzene as monofunctional initiator. CuBr/2,2′-bipyridyl was used as the ATRP catalyst. The polymerization kinetic data for styrene with both initiators was measured and compared with a mathematical model based on the method of moments and another one using Monte Carlo simulation. An empirical correlation was incorporated into the model to account for diffusion-controlled termination reactions. Both models can predict monomer conversion, polymer molecular weight averages, and polydispersity index. In addition, the Monte Carlo model can also predict the full molecular weight distribution of the polymer. Our experimental results agree with our model predictions that bifunctional initiators can produce polymers with higher molecular weights and narrower molecular weight distributions than monofunctional initiators. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2212–2224, 2007     

多分散高浓度介质偏振光后向扩散散射的Monte Carlo仿真

建立了针对多分散高浓度介质偏振光后向扩散散射的Monte Carlo仿真模型，导出了多分散 系统的有效自由程分布函数. 给出了半径为50nm与550nm及其三种不同体积浓度比混合的聚 苯乙烯微球作为散射粒子的高浓度介质的仿真结果. 定性地分析了多分散介质偏振光后向扩 散散射的光强空间分布特征与粒子的体积浓度比的关系. 关键词： 后向扩散散射 偏振光 多分散高浓度介质 Monte Carlo仿真     

Mathematical modelling and computational analysis of enzymatic degradation of xenobiotic polymers

We study the enzymatic degradation of xenobiotic polymers mathematically. As a mathematical model, we derive a linear second-order hyperbolic partial differential equation which governs the evolution of the weight distribution with respect to the molecular weight. Given an initial weight distribution and a final weight distribution, we formulate a problem to determine a degradation rate. We establish a necessary and sufficient condition for which the problem has a local solution. We also introduce a numerical technique based on our analysis, and present a numerical result that we obtained applying weight distributions before and after enzymatic degradation of polyvinyl alcohol.     

The effect of three-body interactions on thermal desorption spectra

Thermal desorption spectra are calculated for a one-dimensional chain and for a two-dimensional square lattice using the transfer-matrix technique and Monte Carlo simulations. Lateral interactions of adsorbed particles cause a splitting of spectra. The repulsive three-body interactions are shown to lead to an inequality of the integral intensities of the thermal desorption peaks.     

Dynamics of gold clusters on amorphous carbon films induced by annealing in a transmission electron microscope

The change of the size distribution of Au clusters induced by annealing was studied in situ by transmission electron microscopy. Starting from statistically distributed Au clusters on a thin amorphous carbon film, “islands” are formed within a few months storage at room temperature, which consist of Au clusters with sizes <4 nm embedded in a thin Au film. These islands cover originally areas with sizes around 25 × 70 nm². If the temperature is increased in the transmission electron microscope two different processes can be clearly distinguished that lead to the coarsening of the cluster size distribution: cluster coalescence and (contactless) Ostwald ripening. The degree and rate of the coarsening are found to depend on the underlying surface (Au film or amorphous carbon) and the exposure to the high-flux high-energy electron beam, which can be estimated to lead to high-temperature excursions in a cluster on a 10⁻¹² s time scale. The experimental findings are confirmed by Monte-Carlo simulations using the many-body Gupta potentials in order to calculate the Au/Au interaction. Moreover, the results of MC simulations suggest an electron-beam induced formation of a “quasi-two-dimensional gas” of small highly mobile Au species on the Au film, which promotes Ostwald ripening.     

喷动床内纳米颗粒气固两相流动的数值模拟

采用欧拉-欧拉双流体模型,颗粒动理学理论模拟颗粒相流动,采用周涛和李洪钟(1999)的力平衡模型预测纳米颗粒聚团尺寸,对喷动床内纳米颗粒聚团流化过程进行了数值模拟,得到了喷动床内纳米颗粒聚团的流化过程,获得喷射区和环隙区内颗粒相速度和浓度分布。分析了喷动床结构和进口气体速度等对纳米颗粒聚团流化特性的影响。由于纳米颗粒的特殊性质,不易形成喷泉区。适当的喷动床结构和进口气体速度有助于形成稳定喷动。     

Ar-buffer-assisted deposition of Cu13 on Cu(1 1 1) surfaces

In this paper, the deposition of Cu₁₃ onto Cu(1 1 1) surface through argon buffer layers was investigated by molecular dynamics (MD) simulations. The interactions between Cu-Cu, Cu-Ar, and Ar-Ar were described by Finnis-Sinclair (FS) tight-binding potential and L-J potential, respectively. The impact energy was chosen to be 2-6 eV/atom in order to compare with experimental results. It was observed that with Ar-buffer layers, the Cu cluster deposited on the surface may retain its free cluster symmetry (I_h). Whereas, on originally bare Cu surface, the deposited Cu cluster lost its original symmetry completely and was recrystalized to have the same fcc structure as the substrate. The Ar-buffer dissipates most of the translational energy of the incident cluster. Therefore, it prevents the cluster from being overheated upon impinging. Furthermore, the interaction between Ar and Cu benefits the confinement of the cluster structure. Our study shows that with Ar-buffer layers, the lateral spread of deposited clusters is 20% smaller than that on the bare Cu surface. This is consistent with the experimental findings.     

Numerical simulation of the unsteady aerodynamic interaction of two plane airfoil cascades

A method for the calculation of unsteady aerodynamic interaction of two plane airfoil cascades that are in relative motion in a subsonic flow of ideal gas is developed. This interaction provides a two-dimensional approximation of the flow in a stage of an axial turbomachine. The method is based on the reduction of the problem to the calculation of the unsteady flow in a single interblade passage of each of the cascades. The calculation uses generalized space-time periodicity relations corresponding to the unsteady process of interest. The calculation is based on the direct numerical integration of the non-stationary gas dynamics equations with the use of the finite difference Godunov-Kolgan-Rodionov scheme of the second approximation order with respect to time and space. The calculation procedure includes the determination of the acoustic fields that are generated by the stage in the incident flow and in the flow behind it. The results of the calculations that illustrate the accuracy of the numerical solution and the capabilities of the method are presented.