Control of droplet size of polymer–diluent blends through thermally induced phase separation

The effects of process conditions and molecular structure of polymer and diluent on the droplet size of membranes formed by thermally induced phase separatiom (TIPS) process were examined. The observed upper critical solution temperature–type phase boundaries of nylon‐12 blended with poly(ethylene glycol) (PEG) and nylon 12 diluted with poly(ethylene glycol) dimethyl ether (PEGDE) and their interaction energy densities calculated using the Flory–Huggins theory suggest that the nylon‐12/PEGDE blends are less stable than the nylon‐12–PEG blends. Infrared spectra confirmed that the difference in phase stability might come from specific interactions of the hydroxyl terminal groups of PEG with the amide groups from nylon‐12, which are not be feasible in the nylon‐12–PEGDE blends. The phase stability of diluent PEG blended with various nylons that are different in the number of methyl groups in the repeat unit was ranked in the order of: nylon‐6–PEG blend < nylon‐12–PEG blend < nylon‐11–PEG blend. We also noted that the phase‐separated droplets grew by both coalescence and the Oswald ripening process after the onset of phase separation. As a result, the cubic exponent of average droplet radius (R³) plotted against time satisfied the linear relationship. As the blends became less stable, the droplet growth rate increased and larger equilibrium droplets formed at a constant quenching depth. The TIPS membranes with desired pore structure could be prepared by controlling the molecular structure of components as well as by varying processing conditions such as quenching depth and annealing time. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3042–3052, 2000     

Simulations of multiphase flows with multiple length scales using moving mesh interface tracking with adaptive meshing

In multiphase flows, the length scales of thin regions, such as thin films between nearly touching drops and thin threads formed during the interface pinch-off, are usually several orders of magnitude smaller than the size of the drops. In this paper, a number of extra length criteria for adaptive meshes are developed and implemented in the moving mesh interface tracking method to solve these multiple-length-scale problems with high fidelity. A nominal length scale based on the solutions of Laplace’s equations with the unit normal vectors of surfaces as the boundary conditions is proposed for the adaptive mesh refinement in the thin regions. For almost flat interfaces/boundaries which are near to the thin regions, the averaged length of the interior edges sharing the two nodes with the boundary edge is introduced for the mesh adaptation. The averaged length of the interfacial edges is used for the interior elements near the interfaces but outside of the thin regions. For the interior mesh away from the interfaces/boundaries, different averaged length scales based on the initial mesh are employed for the adaptive mesh refining and coarsening. Numerous cases are simulated to demonstrate the capability of the proposed schemes in handling multiple length scales, which include the relaxation and necking of an elongated droplet, droplet–droplet head-on approaching, droplet-wall interactions, and a droplet pair in a shear flow. The smallest length resolved for the thin regions is three orders of magnitude smaller than the largest characteristic length of the problem.     

Final bubble lengths for aqueous foam coarsened in a horizontal cylinder

We report on length statistics measured for bubbles in the equilibrium bamboo state, achieved by the coarsening of aqueous foam in long cylindrical tubes, such that the soap films are all flat and perpendicular to the axis of the tube. The average bubble length is found to be 0.88 times the tube diameter, independent of variation of the liquid filling fraction by a factor of nearly three. The actual distribution is well-approximated by a shifted Rayleigh form, with a minimum bubble size of 0.28 tube diameters. And, perhaps surprisingly, no correlations are found in the lengths of neighboring bubbles. The observed length distribution agrees with that of Fortes et al. for short bubbles, but not for long bubbles.     

Modelling of austenite grain growth kinetics in a microalloyed steel (30MSV6) in the presence of carbonitride precipitates

Austenite grain growth kinetics in the presence of secondary precipitates of a microalloyed steel (30MSV6) was studied employing quantitative metallographic techniques. Austenitizing experiments were carried out at 1,000, 1,100 and 1,200?°C. According to the experimental data, abnormal grain growth behaviour is observed at 1,100?°C while it is normal at 1,000 and 1,200?°C. TEM observation represents multicomponent carbonitride precipitate, (Ti,V)(C,N), in the as-received steel with a mean radius of 35?nm. A mathematical model is proposed considering austenite grain growth along with dissolution and coarsening kinetics of the multicomponent precipitates. The austenite grain growth model for short-term non-isothermal and subsequent long-term isothermal heating stages was developed using a statistical approach. The model includes an algorithm to estimate the size distribution of austenite grains. Precipitate mean field dissolution and Lifshitz–Slyozov–Wagner coarsening models were integrated in the proposed model to calculate the pinning pressure retarding the grain boundary movement. The mean austenite grain size and the grain size distribution (normal and abnormal) calculated by the model are in good agreement with experimental data.     

Coulomb sink effect on coarsening of metal nanostructures on surfaces

We discuss Coulomb effects on the coarsening of metal nanostructures on surfaces. We have proposed a new concept of a “Coulomb sink” [Phys. Rev. Lett., 2004, 93: 106102] to elucidate the effect of Coulomb charging on the coarsening of metal mesas grown on semiconductor surfaces. A charged mesa, due to its reduced chemical potential, acts as a Coulomb sink and grows at the expense of neighboring neutral mesas. The Coulomb sink provides a potentially useful method for the controlled fabrication of metal nanostructures. In this article, we will describe in detail the proposed physical models, which can explain qualitatively the most salient features of coarsening of charged Pb mesas on the Si(111) surface, as observed by scanning tunneling microscopy (STM). We will also describe a method of precisely fabricating large-scale nanocrystals with well-defined shape and size. By using the Coulomb sink effect, the artificial center-full-hollowed or half-hollowed nanowells can be created.      

不等长相移效应滤波器的快速调试方法

提出一种基于渐进空间映射算法（ASM）与遗传算法（GA）相结合的I/O端口不等长相移效应的滤波器快速调试方法。渐进空间映射算法能够准确预测精细模型的调试方向与幅度,遗传算法能够准确快速得到I/O端口的相移效应,并且通过柯西法提取粗糙模型。基于有限元的全波电磁仿真软件HFSS, 建立精细模型,粗糙模型参数即等效电路参数, 则由去除I/O端口处相移效应后的S参数获得。利用该方法对六阶交叉耦合滤波器进行调试,经过几步迭代即可使滤波器满足所要求的响应指标,验证了该调试方法的正确性和有效性。     

An algebraic multigrid-based algorithm for circuit clustering

Digital circuits have grown exponentially in their sizes over the past decades. To be able to automate the design of these circuits, efficient algorithms are needed. One of the challenging stages of circuit design is the physical design where the physical locations of the components of a circuit are determined. Coarsening or clustering algorithms have become popular with physical designers due to their ability to reduce circuit sizes in the intermediate design steps such that the design can be performed faster and with higher quality. In this paper, a new clustering algorithm based on the algebraic multigrid (AMG) technique is presented. In the proposed algorithm, AMG is used to assign weights to connections between cells of a circuit and find cells that are best suited to become the initial cells for clusters, seed cells. The seed cells and the weights between them and the other cells are then used to cluster the cells of a circuit. The analysis of the proposed algorithm proves linear-time complexity, O(N), where N is the number of pins in a circuit. The numerical experiments demonstrate that AMG-based clustering can achieve high quality clusters and improve circuit placement designs with low computational cost.     

An improved convergence analysis of smoothed aggregation algebraic multigrid

We present an improved analysis of the smoothed aggregation algebraic multigrid method extending the original proof in [Numer. Math. 2001; 88 :559–579] and its modification in [Multilevel Block Factorization Preconditioners. Matrix‐based Analysis and Algorithms for Solving Finite Element Equations. Springer: New York, 2008]. The new result imposes fewer restrictions on the aggregates that makes it easier to verify in practice. Also, we extend a result in [Appl. Math. 2011] that allows us to use aggressive coarsening at all levels. This is due to the properties of the special polynomial smoother that we use and analyze. In particular, we obtain bounds in the multilevel convergence estimates that are independent of the coarsening ratio. Numerical illustration is also provided. Copyright © 2011 John Wiley & Sons, Ltd.     

二维非线性抛物方程广义差分法/有限体积法的自适应计算

给出三角网上二维非线性抛物方程广义差分法(有限体积法)的一种基于残量估计的后验误差估计,并在此基础上设计了自适应计算方案,以适应物理解在时空的大梯度变化.提出了适合发展方程自适应计算的三角网数据结构(不是树状结构)和灵活的局部粗化算法.     

Algebraic interface‐based coarsening AMG preconditioner for multi‐scale sparse matrices with applications to radiation hydrodynamics computation

Coarsening is a crucial component of algebraic multigrid (AMG) methods for iteratively solving sparse linear systems arising from scientific and engineering applications. Its application largely determines the complexity of the AMG iteration operator. Usually, high operator complexities lead to fast convergence of the AMG method; however, they require additional memory and as such do not scale as well in parallel computation. In contrast, although low operator complexities improve parallel scalability, they often lead to deterioration in convergence. This study introduces a new type of coarsening strategy called algebraic interface‐based coarsening that yields a better balance between convergence and complexity for a class of multi‐scale sparse matrices. Numerical results for various model‐type problems and a radiation hydrodynamics practical application are provided to show the effectiveness of the proposed AMG solver.