Orthogonal arrays: An introduction and their application in optimizing underrelaxation factors in ‘simple’-based algorithm

The primary aim of this paper is to demonstrate how the ‘design-of-experiments’ techniques which are successful in physical experiments could also be adapted to a numerical simulation code. As an example this technique is applied to a general finite difference code used for predicting three-dimensional turbulent recirculating flows. Here the equations for velocities and continuity are solved using the algorithm called SIMPLE, which stands for semi-implicit method for pressure-linked equations. Physical modelling of turbulence is taken care of by means of kinetic energy and turbulence dissipation rate equations. The objective is to optimize the underrelaxation factors of primary and secondary flow variables so that the number of iterations required for convergence is minimum. This is done by the orthogonal array technique (a particular type of design-of-experiment technique). The geometry considered for this purpose is that of a simple gas turbine can combustor and the study is restricted to the isothermal non-reacting condition. Tests are carried out on three different grid configurations. In each case the underrelaxation factor for velocities contributed most to speed up the rate of convergence. Also, for each grid configuration the underrelaxation factor settings for minimum iterations for convergence was found to be same. Hence it is proposed that when doing grid independence tests for any similar flow situation, all the underrelaxation factors could be optimized on coarse grids.     

Selective and Sequential Re‐Assembly of Patterned Block Copolymer Thin Film for Fabricating Polymeric,Inorganic, and Their Composite Nanostructured Arrays

We report that the nanostructures of poly(styrene‐block‐4‐vinylpyridine) block copolymer (PS‐b‐P4VP) thin film on a wafer substrate can be re‐assembled by sequential vapor treatment using selected solvents. Metal or other inorganic nanoparticles that were randomly pre‐loaded inside or on the surface of PS‐b‐P4VP thin film could be pulled to the rim of PS and P4VP along with the movements of PS and P4VP blocks during the treatment. As a result, the patterned polymeric or inorganic/polymer composite nanoisland and nanoring arrays were fabricated.

     

Microphase Separation of a Diblock Copolymer Dispersed in Nanorod Arrays Grafted on a Plate: A Monte Carlo Study

The microstructure of a diblock copolymer dispersed in nanorod arrays grafted on a plate are investigated via annealing MC simulation. The confinement in nanorod arrays provides a complex confined space which leads to complicated microphase separation structures. Different morphologies of top and bottom of the film in the nanorod arrays are observed by varying the inducing height of nanorod and its grafting density in the bottom. Due to a short inducing range by the nanorods, the top structures are therefore mainly dominated by the competition between the absolute height of off‐induced layer on the top and the nature of block copolymer itself; while the bottom structures are affected by the symmetry of block copolymer and the gap among rods.

     

海面波浪坡度场光学测量装置的光源设计(英文)

在海面波浪坡度场光学测量系统中,光源是一个非常重要的照明元件。合理的设计和选用光源,是保证系统精度和布局的重要因素之一。比较传统光源短弧氙灯的明显优势,如低能耗,寿命长,更好的安全性和稳定性等,本文提出了采用LED作为本系统光源的设想,确定了所需LED个数和LED阵列方式,并经过计算和光学软件模拟,验证了本设想的可行性。     

Light propagation in nonuniform plasmonic subwavelength waveguide arrays

We study light propagation in nanoscale periodic structures composed of dielectric and metal in the visible range. We demonstrate that diffraction curves of nonuniform waveguide arrays can be tailored by varying the geometric and dielectric features of the waveguides. The results obtained from a proper formulation of coupled mode theory for nonuniform arrays are validated through numerical solution of Maxwell equations in frequency domain.     

Efficient one-pot synthesis of Ag nanoparticles loaded on N-doped multiphase TiO2 hollow nanorod arrays with enhanced photocatalytic activity

The simultaneous Ag loaded and N-doped TiO₂ hollow nanorod arrays with various contents of silver (Ag/N-THNAs) were successfully synthesized on glass substrates by one-pot liquid phase deposition (LPD) method using ZnO nanorod arrays as template. The catalysts were characterized by Raman spectrum, field-emission scanning electron microscopy (FESEM), high-resolution transmission electron microscope (HRTEM), ultraviolet-vis (UV-vis) absorption spectrum and X-ray photoelectron spectroscopy (XPS). The results suggest that AgNO₃ additive in the precursor solutions not only can promote the anatase-to-rutile phase transition, but also influence the amount of N doping in the samples. The photocatalytic activity of all the samples was evaluated by photodegradation of methylene blue (MB) in aqueous solution. The sample exhibited the highest photocatalytic activity under UV light illumination when the AgNO₃ concentration in the precursor solution was 0.03 M, due to Ag nanoparticles acting as electron sinks; When the AgNO₃ concentration was 0.07 M, the sample performed best under visible light illumination, attributed to the synergetic effects of Ag loading, N doping, and the multiphase structure (anatase/rutile).     

A symbolic treatment of Riordan arrays

We approach Riordan arrays and their generalizations via umbral symbolic methods. This new approach allows us to derive fundamental aspects of the theory of Riordan arrays as immediate consequences of the umbral version of the classical Abel?s identity for polynomials. In particular, we obtain a novel non-recursive formula for Riordan arrays and derive, from this new formula, some known recurrences and a new recurrence relation for Riordan arrays.     

Uni-mode uniqueness conditions for CANDECOMP/PARAFAC decomposition of n-way arrays with linearly dependent loadings

Guo, Miron, Brie and Stegeman [X. Guo, S. Miron, D. Brie, A. Stegeman, Uni-mode and partial uniqueness conditions for CANDECOMP/PARAFAC of three-way arrays with linearly dependent loadings, SIAM J. Matrix Anal. Appl. 33 (2012) 111–129] give three sufficient conditions for the three-way CANDECOMP/PARAFAC (CP) model which ensure uniqueness in one of the three modes (“uni-mode-uniqueness”). In this paper, we generalize these uniqueness conditions to n?3$n?3$. Based on these conditions, a partial uniqueness condition is given which allows collinear loadings in only one mode.     

正交平衡区组设计统计模型中的方差分析

正交平衡区组设计(或广义正交表)的数据分析类似于正交拉丁方(或正交表)的数据分析.利用类似于正交表数据分析中的投影矩阵的正交分解技术,研究正交平衡区组设计的统计分析模型,给出了方差分析中的二次型以及各因子的二次型的分布性质,从而给出正交平衡区组设计统计模型中的方差分析方法.