受迫薛罗格双匣化学反应模型的随机共振

为了在理论上揭示高斯白噪声激励的薛罗格双匣化学反应模型对弱周期扰动的线性与非线性响应 ,分四态近似和两态近似两种情形 ,基于绝热近似与速率方程方法 ,解析导出线性的和非线性的敏感性以及信噪比的表达式 ,并与数值模拟结果进行比较 ,在一次谐波的意义上得到了解析结果与数值模拟结果的定量一致性 .理论上讲 ,该模型只能表现出奇次谐波的随机共振 ,但数值模拟结果也出现了二次谐波的随机共振 ,其原因可能归结为在数值模拟中有限频率的截断引入了误差 ,也可能归结为信号的高次谐波与背景噪声难以区分所致 .     

Triarylaminium salt facilitated Friedel–Crafts reaction of indoles with enamides and vinyl ethers

Commercially available stable radical cation triarylaminium salt can be used as an efficient initiator for Friedel–Crafts reaction of indoles with enamides to regioselectively construct complex indole derivatives and for double Friedel–Crafts reaction of indoles with vinyl ethers to offer 3,3′-Bis(indolyl)alkane derivatives. The ready availability of the starting materials and the usefulness of the products make this strategy attractive.     

受迫薛罗格双匣化学反应模型的随机共振

In order to theoretically disclose the linear and nonlinear responses of the Gaussian white noise driven Schrodinger Model of Two Boxes in chemical reaction to a weak periodic perturbation, the rate equation method is used to derive the analytical expression of linear and nonlinear susceptibilities and the signal-to noise ratio according to quadrustable or bistable adiabatic approximations with in different parameter ranges.The analytically approximate result is also compared with that from numerical simulation. For the parameters under concern, the qualitative agreement is observed between the analytic and the numerical first order resonant structures when the noise intensity is not in zero limit. Moreover, the analytic results show that the resonant behavior can occur only in the odd-order harmonic of the model, but the numerical simulation also shows the second-order harmonic resonance, which might be induced by the finite frequency truncations on the Gaussian white noiseor by the indistinguish ability between high-order harmonics and background noise.