Stochastic phase lockings in a relaxation oscillator forced by a periodic input with additive noise: A first-passage-time approach

Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a transition of an input phase density after one cycle of the oscillator. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator.     

Limit cycle analysis of a class of strongly nonlinear oscillation equations

The limit cycle of a class of strongly nonlinear oscillation equations of the form % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqadwhagaWaaiabgUcaRmXvP5wqonvsaeHbbjxAHXgiofMCY92D% aGqbciab-DgaNjab-HcaOiaadwhacqWFPaqkcqWF9aqpcqaH1oqzca% WGMbGaaiikaiaadwhacaGGSaGabmyDayaacaGaaiykaaaa!50B8!\[\ddot u + g(u) = \varepsilon f(u,\dot u)\] is investigated by means of a modified version of the KBM method, where is a positive small parameter. The advantage of our method is its straightforwardness and effectiveness, which is suitable for the above equation, where g(u) need not be restricted to an odd function of u, provided that the reduced equation, corresponding to =0, has a periodic solution. A specific example is presented to demonstrate the validity and accuracy of our 09 method by comparing our results with numerical ones, which are in good agreement with each other even for relatively large .     

盐水振荡研究的新发现

在对化学振荡的研究中,无论是溶液均相氧化还原形成的振荡反应,还是界面扩散受阻形成的界面振荡,都普遍采取各种电极法来监测。前文[1,2]研究了各种不同电极监测液膜振荡的变化,本文将讨论不同的电极方法在监测盐水振荡现象过程中的新发现。1970年,地球物理学家Martin[3]发现把     

电沉积AuInSe2半导体薄膜上的电化学振荡现象

研究了电沉积制得的ＡｕＩｎＳｅ２半导体薄膜上过氧化氢阴极还原过程中产生的电化学振荡行为，对影响该振荡行为的一些因素如半导体薄膜的后处理、溶液组成、传质、光照、化学浸渍作用等进行了分析，同时采用外界周期性光照和外接小幅度正弦波电位来调节振荡频率，为金铟硒半导体薄膜发展成为光电传感器件提供了一定的理论与实践基础．     

葡萄糖、半乳糖和乙醇恒电流氧化过程电位振荡的EQCM研究

采用电化学石英晶体微天平(EQCM)研究了0.5 mol•L^-1 NaOH水溶液中铂电极上葡萄糖、半乳糖和乙醇恒电流氧化过程中伴随的电位振荡行为. 两个糖体系的电位振荡过程伴随EQCM频率的同步振荡响应, 而乙醇体系中相应的频率响应却非常小；三个体系振荡过程的同步动态电阻响应均很小, 表明振荡过程频率响应主要为质量效应. 虽然葡萄糖和半乳糖结构相似, 电位和频率振荡的幅度相当, 但频率波数和周期明显不同, 表明电位振荡行为对两者呈现良好的分子识别能力. 本文也讨论了相关振荡机理和NaOH浓度效应及碱性介质中铂电极电化学过程, 提出了所形成的铂氧化物主要是PtO₂-3H₂O_ad以及两糖体系振荡过程中糖酸根阴离子伴随着高/低电位在铂电极上吸/脱附的新观点.     

Reverse permeation of sodium ions driven by pH difference across a liquid membrane: time dependencies of membrane resistance and membrane potential in a reverse permeation system

The diffusional flux of sodium ions across a liquid membrane was observed as a reverse permeation phenomenon: sodium ions were transported across the membrane against their own concentration difference. A supported liquid membrane having stearic acid as an ionic carrier was used. The internal aqueous phase contained NaCl and HCl and the external aqueous phase contained NaOH of the same initial concentration as NaCl in the internal aqueous phase. The reverse permeation occurred with a long time delay. During the delay, sodium ions flowed from the acidic to alkaline solution. The diffusion coefficient of sodium ion estimated from the flux equation taking into account the Donnan equilibrium at the interface was found to be much greater than that in the membrane solvent, 1-octanol. In the same membrane system as for the flux measurement, the membrane conductance and the membrane potential were measured as a function of time. The time dependence of the membrane potential in the presteady state showed a biphasic behavior. The initial rapid phase could be attributed to the change in the phase boundary potential and the subsequent slow step to the change in the diffusion potential within the membrane. Before the steady membrane potential had been reached, the reverse permeation of sodium ions against their own concentration difference was not observed. During the slow relaxation process of the membrane potential, the membrane resistance decreased to approach the steady state. Moreover, the oscillation of membrane potential abruptly started at a time in the slow step of the potential change and continued during the steady state. It was suggested that, at the presteady state, the increase in the amount of water in the membrane would drive a drastic change in the state of the liquid membrane in the filter pore, e.g. an inverted micellar structure making.     

苯乙烯－马来酸酐共聚物单分子膜的静、动态性质

对不同分子量的苯乙烯－马来酸酐共聚物（PSM）单分子膜的π－A等温线、微 分曲线进行了研究，讨论了PSM单分子膜成膜过程及分子量对膜相变的影响，并用 动态膜障振动法测定了PSM单分子膜的动态弹性，结果表明，分子链的相互作用（ 如卷曲和缠结）在膜的形成中起着重要的作用，并影响膜的静、动态性质，单分子 膜的动态弹性曲线有双峰，且前者比后者小，随分子量增大，膜的凝聚性、刚性和 稳定性都增强，动态弹性都增大；且分子链的相互作用对PSM单分子性质影响增大 ，压缩过程中单分子膜的相变更明显。     

8,10-二炔廿五碳酸LB膜的周期结构

合成了8,10-二炔廿五碳酸,在玻璃片、石英片和镀金片上沉积了它的LB膜,X-射线衍射研究了LB膜的周期结构和聚合对它的影响。在2θ=1°—15°范围内观察到了多达7个布拉格衍射峰。由此计算了等同周期和分子在基片上的倾斜角。用分子模型计算了衍射峰强度,得到了与实验结果相符合的衍射峰强度奇偶起伏现象。     

一种新的ⅥA族化学反应振荡器：Na_2S_2O_8－KSCN－CuSO_4体系

一种新的ⅥＡ族化学反应振荡器：Ｎａ_２Ｓ_２Ｏ_８－ＫＳＣＮ－ＣｕＳＯ_４体系林娟娟，高庆宇，宋浩，黄振炎，赵学庄（南开大学化学系，天津，３０００７１）关键词化学振荡，非线性化学反应，过硫酸盐，硫氰酸盐自经典的均相ＢＺ化学振荡反应体系的发现及提出耗散结构...     

Fluctuating hydrodynamics and principal oscillation pattern analysis

Principal oscillation pattern (POP) analysis was recently introduced into climatology to analyze multivariate time series x_i(t) produced by systems whose dynamics are described by a linear Markov process x=Bx + . The matrixB gives the deterministic feedback and is a white noise vector with covariances (t) _j (t*Q _ij (t–t. The POP method is applied to data from a direct simulation Monte Carlo program. The system is a dilute gas with 50,000 particles in a Rayleigh-Bénard configuration. The POP analysis correctly reproduces the linearized Navier-Stokes equations (in the matrixB) and the stochastic fluxes (in the matrixQ) as given by Landau-Lifschitz fluctuating hydrodynamics. Using this method, we find the Landau-Lifschitz theory to be valid both in equilibrium and near the critical point of Rayleigh-Bénard convection.