大学生创新实验项目:探索有机碱串联催化聚磺酸酯的合成

以有机小分子一锅法串联催化合成(聚)磺酸酯为研究项目,组建大学生创新实验团队,研究了醛的硅氰化反应和SuFEx反应中底物结构和有机碱催化剂对反应活性的影响,初步探索了将2个反应串联的可行性问题。在此过程中,通过有机合成的基本操作,培养了学生的动手能力和发现问题、分析问题、解决问题的能力。通过此次创新实验,更有利于学生深入理解有机化学、分析化学课程中的理论知识,并把各门课程知识有机结合,达到理论和实践的相辅相成。     

过阻尼谐振子的随机共振

研究了由交叉相关高斯白噪声驱动的过阻尼谐振子的随机共振,其中加法噪声被周期信号所调制,运用平稳关联函数的傅里叶变换,导出了过阻尼谐振子随机模型信噪比的精确表达式.结果揭示:在过阻尼谐振子的随机模型中存在二类随机共振.一类随机共振表现为信噪比随乘法噪声强度Q变化的曲线存在共振峰,另一类随机共振表现为信噪比随振子频率ω变化的曲线存在共振峰.大幅度改变信号频率Ω值的大小,信噪比随乘法噪声强度Q变化的曲线有单峰,一峰一谷和单调变化三种不同的形式.     

Stochastic Multiresonance for Periodically Modulated Noise in a Single—Mode Laser

Multiplicatively introducing the noise and the signM into the gain-noise model of a single-mode laser system, we detect the two forms of stochastic resonance (the single-peak form stochastic resonance and stochastic multiresonance) in the curve of the dependence of signal-to-noise ratio upon the noise correlation time. Moreover, when the correlation coefficient and the intensities of both noises are changed, the two forms of stochastic resonance alternate.     

Dynamical Properties of a Single-Mode Laser Driven by Quadratic Pump Noise

We propose a single-mode laser model driven by quadratic pump noise with cross correlation between the real and imaginary parts of the pump noise. The effect of the cross-correlation coefficient λp between the real and imaginary parts of the pump noise on dynamical properties is studied by using of the linear approximation. The theoretical expressions of intensity correlation function λ（t）, normalized intensity fluctuation λ（0） are calculated. It is found that the most conspicuous effects of λp on both the intensity correlation function and the normalized intensity fluctuation appear at ｜λP｜ = /0.5, but not at ｜λP｜ = 1.     

Stochastic resonance in a gain--noise model of a single-mode laser driven by pump noise and quantum noise with cross-correlation between real and imaginary parts under direct signal modulation

Stochastic resonance (SR) is studied in a gain--noise model of a single-mode laser driven by a coloured pump noise and a quantum noise with cross-correlation between real and imaginary parts under a direct signal modulation. By using a linear approximation method, we find that the SR appears during the variation of signal-to-noise ratio (SNR) separately with the pump noise self-correlation time \tau , the noise correlation coefficient between the real part and the imaginary part of the quantum noise \lambda_q , the attenuation coefficient \gamma and the deterministic steady-state intensity I_0 . In addition, it is found that the SR can be characterized not only by the dependence of SNR on the noise variables of \tau and \lambda_q, but also by the dependence of SNR on the laser system variables of \gamma and I₀. Thus our investigation extends the characteristic quantity of SR proposed before.     

Output power spectrum of a single-mode laser driven by coloured pump and quantum noises with coloured correlation

By using the linear approximation method, the output power spectrum is calculated for a single-mode laser driven by coloured pump and quantum noises with coloured correlation. We have observed that the configuration of the output power spectrum is complicated: that is, it can be of single peak, two peaks or three peaks. The configurations of the power spectrum can be transformed from one into another by changing the cross-correlation time, the cross-correlation coefficient between the two noises, and pump noise intensity.     

一级近似下的单模激光增益模型随机共振

把周期信号输入单模激光,对激光增益模型中的乘法噪声项取一级近似通过计算相关函数得到功率谱,发现输出信号是洛伦兹型的.信噪比随抽运噪声强度和量子噪声强度的变化均出现随机共振,但共振峰对应的噪声强度比零级近似下的小.     

信号调制色泵噪声和实虚部间关联量子噪声驱动下单模激光的随机共振现象

计算了受信号调制的色泵噪声和实虚部间关联的量子噪声驱动的单模激光损失模型的输出光强信噪比.发现信噪比R随泵噪声自关联时间τ、调制信号频率Ω和量子噪声实虚部间关联系数λq的变化均存在随机共振,这种现象扩展了“信噪比R对噪声强度的变化曲线具有极大值”的典型随机共振. 若以Ω为参数,当Ω增加时,Ｒ随τ的关系曲线经历了从同时出现共振和抑制到单峰共振,最后到单调上升的变化,呈现多种形式的随机共振．若以τ为参数,当τ增加时,Ｒ随Ω的关系曲线经历了从单调上升到同时出现共振和抑制,最后又到单调下降的变化过程．Ｒ随λq的关 关键词： 噪声 信噪比 随机共振     

THE TRANSITION RATE OF A DOUBLE WELL SYSTEM DRIVEN BY CROSS-CORRELATED NOISES

The transition rate of a double well system driven by cross-correlated noises has been investigated, in when the correlation times between the noises are nonzero. From numerical computation, we find followings: (1) The transition rate decreases as the ,λ(λ is the strength of the correlations between noises) increases. (2) The transition rate increases as the τ(τ is the correlation time between noises) increases. It imglies that τ and λ play opposite roles in the transition rate of the system (3). For the case of perfectly correlated noises (λ= 1), there is no the suppressed phenomenon in the double well system with cross-correlated noise sources.     

关联噪声对单模激光动力学性质的影响

应用线性近似方法,计算了具有指数形式关联的两白噪声驱动下的单模激光光强的关联函数、功率谱及关联时间。根据计算结果讨论了噪声间的关联程度和噪声间互联时间对以上各量的影响,并和噪声间具有δ函数关联形式的情况进行了比较