基于平面度的燃料电池电化学性能模拟

 固体氧化物燃料电池的翘曲会影响电极-盖板界面的接触情况，从而影响电化学性能，对相关制造工艺提出了很大的挑战．为了分析燃料电池平面度对放电过程的影响，揭示其潜在的风险，我们建立了两个基于有限元法的仿真模型，对考虑平面度缺陷的燃料电池封装和放电进行分析．在对固体氧化物燃料电池进行平面度测量的基础上，首先建立了具有真实燃料电池翘曲特性的几何模型，分析封装过程中接触压力的分布情况．然后将接触电阻的仿真结果导入到三维多物理场耦合模型中，模拟具有平面度缺陷的燃料电池电化学性能．计算结果展示了燃料电池两侧封装过程中接触压力的分布情况．通过对比有接触电阻和无接触电阻的燃料电池电流密度，分析了电池与盖板的接触对放电过程的影响．结果表明，燃料电池的凹陷面较难达到满意的接触状态，需要比凸起面更大的封装压力．燃料电池表面接触电阻的变化将引起电流传导路径的变化，产生局部高电流或低电流．这项工作强调了在燃料电池中保持均匀分布的接触电阻的重要性，为今后的优化工作奠定了基础．     

Stochastic sensitivity analysis of coupled acoustic-structural systems under non-stationary random excitations

This paper presents a new sensitivity analysis method for coupled acoustic–structural systems subjected to non-stationary random excitations. The integral of the response power spectrum density (PSD) of the coupled system is taken as the objective function. The thickness of each structural element is used as a design variable. A time-domain algorithm integrating the pseudo excitation method (PEM), direct differentiation method (DDM) and high precision direct (HPD) integration method is proposed for the sensitivity analysis of the objective function with respect to design variables. Firstly, the PEM is adopted to transform the sensitivity analysis under non-stationary random excitations into the sensitivity analysis under pseudo transient excitations. Then, the sensitivity analysis equation of the coupled system under pseudo transient excitations is derived based on the DDM. Moreover, the HPD integration method is used to efficiently solve the sensitivity analysis equation under pseudo transient excitations in a reduced-order modal space. Numerical examples are presented to demonstrate the validity of the proposed method.     

A note on 3‐partite graphs without 4‐cycles

Let $C_4$ be a cycle of order 4. Write $ex\left(n,n,n,C_4\right)$ for the maximum number of edges in a balanced 3‐partite graph whose vertex set consists of three parts, each has $n$ vertices that have no subgraph isomorphic to $C_4$. In this paper, we show that $ex\left(n,n,n,C_4\right)\ge \frac{3}{2}n\left(p+1\right)$, where $n=\frac{p\left(p?1\right)}{2}$ and $p$ is a prime number. Note that $ex\left(n,n,n,C_4\right)\le \left(\frac{3\sqrt{2}}{2}+o\left(1\right)\right)n^{\frac{3}{2}}$ from Tait and Timmons's works. Since for every integer $m$, one can find a prime $p$ such that $m\le p\le \left(1+o\left(1\right)\right)m$, we obtain that $\underset{n\to \infty }{\lim }\frac{ex\left(n,n,n,C_4\right)}{\frac{3\sqrt{2}}{2}{n}^{\frac{3}{2}}}=1$.     

Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ_∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.     

Assessment of the nature of interactions of cations with cycloheptatriene derivatives using change in the aromaticity: Comparison with electron density and NBO results

ABSTRACT

Interactions of cycloheptatriene derivatives, C₇H₆X, (X?=?NH, PH, AsH, O, S, Se) with the cations H⁺, CH₃⁺, Cu⁺, Al⁺, Li⁺, Na⁺, and K⁺ are studied using B3LYP functional and 6-311++G(d,p) basis set. The calculated gas-phase cation affinities (CA) and cation basicities (CB) for all molecules decrease as H⁺ > CH₃⁺ > Cu⁺ > Al⁺ > Li⁺ > Na⁺ > K⁺. We used the induced aromaticity in the 7-membered ring of C₇H₆X upon interaction with the cations, M⁺, as a measure of C₇H₆X/M⁺ interaction. Nucleus-independent chemical shift (NICS) and harmonic oscillator model of aromaticity (HOMA) were used as two indices of aromaticity. The highest and lowest induced aromaticities were observed for interactions of H⁺ and K⁺, respectively. Also, the aromaticity induced by interaction with a cation in C₇H₆AsH and C₇H₆PH was larger than that in C₇H₆NH and C₇H₆O. Hence, the aromaticity was considered as a measure of covalency for the C₇H₆X/M⁺ interactions showing a rational dependence on both the molecule and cation. The nature of the interactions was also assessed using electron density, charge distribution analysis and NBO calculations. The results of the aromaticity indices, NICS and HOMA, were compared with the electron density and NBO results.     

安培环路定理的拓扑学描述

近年来拓扑学在量子力学中得到了广泛的运用.本文将安培环路定理积分式重新表达为一矢量场在轮胎参数面上的第一类陈数积分.数值模拟展示了该积分值为一整数即第一陈数,其代表矢量场的整体性质:当经历连续变换时,矢量场的局部数值发生改变但整体积分值即陈数仍保持不变;若陈数发生改变,则表明矢量场变换的连续性条件发生破坏,矢量场出现奇点.进一步通过高斯映射将该矢量场从参数轮胎面映射到单位球面上,并给出了第一陈数的直观几何意义.理论和数值结果揭示了安培环路定理的拓扑学本质,表明拓扑概念在经典物理学中也会有广泛应用.     

Flow induced oscillation of two rigid rectangular plates in a side-by-side configuration

The present work is an experimental study of two oscillating rigid plates placed in side-by-side configuration, hinged at their leading edges, subjected to low subsonic flow. This problem is investigated using smoke-wire flow visualization, hot-wire anemometry, and time resolved particle image velocimetry. It is found that beyond a critical Reynolds number, the plates set into oscillatory motion. This critical Reynolds number depends on the gap between the plates. It is also seen that this value of Reynolds number, at lower values of gap to thickness ratio (<7) is significantly higher than that of the single plate configuration value. The frequency and amplitude of the oscillating plates at various gaps and Reynolds numbers have been studied and compared with the characteristics of an oscillating single plate. It is also found that depending on the gap and acceleration of the free-stream, there exist two modes of oscillation - (i) in-phase and (ii) out-of-phase. For gap to thickness ratio less than 10, only in-phase oscillations take place for all values of free-stream velocity considered in the present work, whereas, when this ratio is greater than 10, the mode of oscillation depends on the initial conditions up to a certain free-stream velocity, beyond which the plates switch to in-phase mode. Smoke wire flow visualization technique along with time resolved particle image velocimetry reveal that the vorticity distributions around the plates are responsible for the initiation of the two modes of oscillations.