Numerical solution of Navier–Stokes equations using multiquadric radial basis function networks

A numerical method based on radial basis function networks (RBFNs) for solving steady incompressible viscous flow problems (including Boussinesq materials) is presented in this paper. The method uses a ‘universal approximator’ based on neural network methodology to represent the solutions. The method is easy to implement and does not require any kind of ‘finite element‐type’ discretization of the domain and its boundary. Instead, two sets of random points distributed throughout the domain and on the boundary are required. The first set defines the centres of the RBFNs and the second defines the collocation points. The two sets of points can be different; however, experience shows that if the two sets are the same better results are obtained. In this work the two sets are identical and hence commonly referred to as the set of centres. Planar Poiseuille, driven cavity and natural convection flows are simulated to verify the method. The numerical solutions obtained using only relatively low densities of centres are in good agreement with analytical and benchmark solutions available in the literature. With uniformly distributed centres, the method achieves Reynolds number Re = 100 000 for the Poiseuille flow (assuming that laminar flow can be maintained) using the density of , Re = 400 for the driven cavity flow with a density of and Rayleigh number Ra = 1 000 000 for the natural convection flow with a density of . Copyright © 2001 John Wiley & Sons, Ltd.     

轴对称薄壁结构自由振动的边界元分析

采用双互易法分析薄壁轴对称结构自由振动的特征频率以及特征模态.首先,采用径向基函数插值域积分里的位移,利用双互易法将域积分转化为子午面边界的积分.然后,将边界物理量、基本解和特解展开为傅里叶级数,沿环向积分后得到的边界积分方程可用于轴对称结构带体积力问题和受非对称载荷的动力学分析,其积分域为轴对称结构子午面边界上的线积分,进一步降低了问题的维度和离散的难度.文章详细探讨了源点处于对称轴的特殊情况,根据基本解和特解的退化形式,针对无体积力和有体积力分别给出了处理奇异矩阵的方案.对于薄壁结构,采用双曲正弦变换处理近奇异积分有效提高积分精度.最后将双互易法和双曲正弦变化应用于薄壁轴对称结构带体积力的静力学和自由振动分析.数值结果表明,文章提出的处理奇异矩阵的方法能够有效处理源点处于对称轴的情况;当圆筒厚高比为$10^{-3}$,边界元计算的特征频率的相对误差为$10^{-3}$,且优于有限元的结果.      

Numerical analysis of funnel formation during unsteady fluid outflow from a rotating cylindrical vessel

The main features of the unsteady outflow of a fluid from a cylindrical vessel rotating together with it at a constant angular velocity through a central drain hole in the bottom are studied. The software package STAR-CD tested on the results of experiments with water in the absence of rotation is used. Certain important features of the phenomenon under consideration related with the formation of vortex funnels in the fluid are established. The effect of the main control parameters of the problem, namely, angular velocity, viscosity, initial depth, etc., is analyzed.     

完全变换法在无网格伽辽金方法中的应用

由于移动最小二乘形函数一般不具有常规有限元或边界元形函数所具有的插值特征，本质边界条件的处理成为无网格伽辽金法实施中的一个难点。本文通过建立节点位移和广义位移之间的关系对移动最小二乘形函数进行修正，给出了修正的移动最小二乘形函数；以二维问题为例，对完全交换法在无网格伽辽金方法中的应用进行了研究，实现了本质边界条件在节点处的精确施加。数值计算结果表明该方法不仅简单合理，而且具有较高的精度、收敛性和稳定性。     

Finite difference method for 2-D and 3-D nonlinear free surface wave problems

A finite difference method is developed for the numerical modelling of the 2-D and 3-D unsteady potential flow generated by transient disturbances on the free surface, on which the nonlinear boundary conditions are fully satisfied. The unknown function is computed with an iteration scheme processing in a transformed time-invariant space. After the velocity is calculated, the location of the free surface is renewed and so is the value of velocity on it. The boundary-value problem of the governing equation is then solved at the next time step. The present method incorporates the FFT. Consequently, a tri-diagonal equation system is obtained which could be readily solved. The feasibility of this method has been demonstrated by 2-D and 3-D examples corresponding to different initial disturbances. This work is supported by the science foundation of Academia Sinica. The paper had been accepted by the XVIth International Congress of IUTAM, Lyngby, Denmark, August, 1984.     

Numerical analysis of free vibrations of a beam with oscillators

The problem of free vibrations of a beam with free ends of variable cross section and mass, from which point masses (oscillators) are suspended by bars, is considered. It is shown that parametric resonances can occur in this oscillating system. Numerical examples showing the efficiency of the calculation method proposed are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 135–144, July–August, 2006.     

On the Role of the Electronic Structure of the Heteronuclear Oxide Cluster [Ga2Mg2O5].+ in the Thermal Activation of Methane and Ethane: An Unusual Doping Effect

The reactivity of the heteronuclear oxide cluster [Ga₂Mg₂O₅]^.+, bearing an unpaired electron at a bridging oxygen atom (O_b^.?), towards methane and ethane has been studied using Fourier transform ion cyclotron resonance mass spectrometry (FT‐ICR‐MS). Hydrogen‐atom transfer (HAT) from both methane and ethane to the cluster ion is identified experimentally. The reaction mechanisms of these reactions are elucidated by state‐of‐the‐art quantum chemical calculations. The roles of spin density and charge distributions in HAT processes, as revealed by theory, not only deepen our mechanistic understanding of C? H bond activation but also provide important guidance for the rational design of catalysts by pointing to the particular role of doping effects.     

Radical Compatibility with Nonaqueous Electrolytes and Its Impact on an All‐Organic Redox Flow Battery

Nonaqueous redox flow batteries hold the promise of achieving higher energy density because of the broader voltage window than aqueous systems, but their current performance is limited by low redox material concentration, cell efficiency, cycling stability, and current density. We report a new nonaqueous all‐organic flow battery based on high concentrations of redox materials, which shows significant, comprehensive improvement in flow battery performance. A mechanistic electron spin resonance study reveals that the choice of supporting electrolytes greatly affects the chemical stability of the charged radical species especially the negative side radical anion, which dominates the cycling stability of these flow cells. This finding not only increases our fundamental understanding of performance degradation in flow batteries using radical‐based redox species, but also offers insights toward rational electrolyte optimization for improving the cycling stability of these flow batteries.     

Optical Absorption and Magnetic Field Effect Based Imaging of Transient Radicals

Short‐lived radicals generated in the photoexcitation of flavin adenine dinucleotide (FAD) in aqueous solution at low pH are detected with high sensitivity and spatial resolution using a newly developed transient optical absorption detection (TOAD) imaging microscope. Radicals can be studied under both flash photolysis and continuous irradiation conditions, providing a means of directly probing potential biological magnetoreception within sub‐cellular structures. Direct spatial imaging of magnetic field effects (MFEs) by magnetic intensity modulation (MIM) imaging is demonstrated along with transfer and inversion of the magnetic field sensitivity of the flavin semiquinone radical concentration to that of the ground state of the flavin under strongly pumped reaction cycling conditions. A low field effect (LFE) on the flavin semiquinone–adenine radical pair is resolved for the first time, with important implications for biological magnetoreception through the radical pair mechanism.     

A Triphenylamine with Two Phenoxy Radicals Having Unusual Bonding Patterns and a Closed‐Shell Electronic State

Reported herein is the structure and the electronic properties of a novel triphenylamine derivative having two phenoxy radicals appended to the amino nitrogen atom. X‐ray single crystal analysis and the magnetic resonance measurements demonstrates the unexpected closed‐shell electronic structure, even at room temperature, of the molecule and two unusual C? N bonds with multiple‐bond character. The theoretical calculations support the experimentally determined molecular geometry with the closed‐shell electronic structure, and predicted a small HOMO–LUMO gap originating from the nonbonding character of the HOMO. The optical and electrochemical measurements show that the molecule has a remarkably small HOMO–LUMO gap compared with its triphenylamine precursor.