Inverse‐Opal Conducting Polymer Monoliths in Microfluidic Channels

Inverse opal monolithic flow‐through structures of conducting polymer (CP) were achieved in microfluidic channels for lab‐on‐a‐chip (LOC) applications. In order to achieve the uniformly porous monolith, polystyrene (PS) colloidal crystal (CC) templates were fabricated in microfluidic channels. Consequently, an inverse opal polyaniline (PANI) structure was achieved on‐chip, through a two‐step process involving the electrochemical growth of PANI and subsequent removal of the template. In this work the effect of CP electropolymerisation time on these structures is discussed. It was found that growth time is critical in achieving an ordered structure with well‐defined flow‐through pores. This is significant as these optimised porous structures will allow for maximising the surface area of the monolith and will also result in well‐defined flow profiles through the microchannel.     

Preparation and properties of Nafion/SiO2 composite membrane derived via in situ sol–gel reaction: size controlling and size effects of SiO2 nano‐particles

A novel technique in controlling the size of SiO₂ nano‐particles in the preparation of Nafion/SiO₂ composite membranes via in situ sol–gel method, as well as the effects of nano‐particle size on membrane properties and cell performance, is reported in this paper. Nafion/SiO₂ composite membranes containing SiO₂ nano‐particles with four different diameters (5 ± 0.5, 7 ± 0.5, 10 ± 1, and 15 ± 2 nm) are fabricated by altering the reactant concentrations during in situ sol–gel reaction. Sequentially, size effects of SiO₂ nano‐particles on membrane properties and cell performance are investigated by SEM/EDAX, TEM, TGA, mechanical tensile, and single cell tests, etc. The results suggest that 10 nm is a critical diameter for SiO₂ incorporated into Nafion matrix, exhibiting desirable physico‐chemical properties for operation at elevated temperature and low humidity. At 110°C and 59% RH, the output voltage of the cell equipped with Nafion/SiO₂ (10 nm) obtains an output voltage of 0.625 V at 600 mA/cm², which is 50 mV higher than that of unmodified Nafion. Copyright © 2010 John Wiley & Sons, Ltd.     

Matrix‐assisted laser ablation production of gold cluster ions from Au‐coated photonic crystals

A new strategy was explored to generate pure gold cluster ions, Au_n^+/?, from gold films deposited on solid substrates via a matrix‐assisted laser ablation technique. The gold films deposited on SiO₂‐particle‐assembled photonic crystals were demonstrated to be the most ideal compared with the films deposited on various glass slides. Dropped with a matrix of 2‐(4‐hydroxyphenylazo) benzoic acid and bombarded by nitrogen pulse laser (355 nm), they could release a series of Au_n⁺ with n more than 110 or Au_n^? with n more than 60 according to the data obtained by inline time‐of‐flight mass spectrometry. The gold‐deposited photonic crystal substrates could be stored at room temperature for at least 6 months. The method is hence steady and convenient in use. Copyright © 2012 John Wiley & Sons, Ltd.     

On the existence of tori in Asada’s two-regional model

A two-regional five-dimensional model describing the development of income, capital stock and money stock, which was introduced by Asada in (2004) [2] is analysed. Sufficient conditions for the existence of two pairs of purely imaginary eigenvalues and the last one being negative in the linear approximation matrix of the model are found. Formulae for the calculation of the coefficients in the bifurcation equation of the model are derived. The theorem on the existence of invariant tori is presented. A numerical example illustrating the gained results is given.     

Equations of the shallow water model on a rotating attracting sphere. 1. Derivation and general properties

A shallow water model on a rotating attracting sphere is proposed to describe large-scale motions of the gas in planetary atmospheres and of the liquid in the world ocean. The equations of the model coincide with the equations of gas-dynamic of a polytropic gas in the case of spherical gas motions on the surface of a rotating sphere. The range of applicability of the model is discussed, and the conservation of potential vorticity along the trajectories is proved. The equations of stationary shallow water motions are presented in the form of Bernoulli and potential vorticity integrals, which relate the liquid depth to the stream function. The simplest stationary solutions that describe the equilibrium state differing from the spherically symmetric state and the zonal flows along the parallels are found. It is demonstrated that the stationary equations of the model admit the infinitely dimensional Lie group of equivalence. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 24–36, March–April, 2009.     

A numerical approach based on the meshless collocation method in elastodynamics

In this paper, a collocation technique with the modified equilibrium on line method （ELM） for imposition of Neumann （natural） boundary conditions is presented for solving the two-dimensional problems of linear elastic body vibrations. In the modified ELM, equilibrium over the lines on the natural boundary is satisfied as Neumann boundary condition equations. In other words, the natural boundary conditions are satisfied naturally by using the weak formulation. The performance of the modified version of the ELM is studied for collocation methods based on two different ways to construct meshless shape functions： moving least squares approximation and radial basis point interpolation. Numerical examples of two-dimensional free and forced vibration analyses show that by using the modified ELM, more stable and accurate results would be obtained in comparison with the direct collocation method.     

Stochastic modeling of unresolved scales in complex systems

Model uncertainties or simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., ‘unresolved’) due to a lack in our understanding of these mechanisms or limitations in computational power. The impact of these unresolved scales on the resolved scales needs to be parameterized or taken into account. A stochastic scheme is devised to take the effects of unresolved scales into account, in the context of solving nonlinear partial differential equations. An example is presented to demonstrate this strategy. Dedicated to Professor Peter E. Kloeden on the occasion of his 60th birthday     

自重体积力作用下坡体张应力及坡面位移的变化规律

为了提高对边坡体力学行为的认识,借助于FLAC有限差分软件的数值模拟,并结和相似理论的推导验证,研究了在仅有自重体积力作用的条件下,线弹性边坡体的一些力学特征及其与相关变量或物理力学参数的相关关系。没有外载荷影响时边坡地表最大主应力和最小主应力分别平行和垂直于地表,当深度增加时,主应力的取向逐渐变成竖直和水平两个方向,坡面处既有张应力区也有拉应力区,坡脚处亦存在较大的张应力,这是自重体积力作用下边坡体应力分布的一般性特征,在本文和前人的研究中都能体现。本文还重点揭露了：坡角线性增加时坡顶最大张应力的变化速率表现为：快——慢——快; 沿坡顶面竖直向下张应力随深度增加线性减小; 小变形条件下边坡应力场与弹性模量无关; 最后验证了满足相似理论的坡体,坡面对应点的位移比是其几何尺寸比的平方倍。本文不仅是对既有研究成果的进一步补充,而且为以后研究复杂条件下边坡体的力学特征奠定了基础,对于理论和实践都有一定的启发意义。