Pattern formation its multiplicative stochastic processes

双折射液晶电流体动力学不稳定性（END）中对流斑图的发展过程基本上分为三个演化阶段：1）早期（振幅动力学），2）晚期（相动力学）和3）末期（缺陷动力学）。基于噪声朗道方程的振幅和方差的标度特性在早期阶段被实验观察到，但在后期和最终阶段都不成立。在EHD不稳定性的乘性随机过程中，噪声的关联时间N和强度Q是控制分岔的关键参数。随着噪声强度的增加，第一不稳定性开始的阈值急剧变化。我们观察到，阈值产生的曲率随着例如从威廉姆斯域（WD）的开始到GP的开始而变化。这一结果反映了流场结构从WD向GP的转变以及动力散射的变化 ...更多信息 湍流模式（DSM：湍流）。随着噪声强度的进一步增加，第一不稳定性的开始变得更加复杂。详细研究了缺陷运动、模式选择、向混沌的转变以及这些磁场效应在WD到波动WD（FWD）区域中的变化。当高宽比为有限时，缺陷混沌（FWD）可以通过规则的无缺陷轧辊状态在略高于阈值的情况下发生。在这种状态下，缺陷永远不会消失，其数量总是随时间非周期性地变化。该数随时间变化的功率谱呈l/f型谱。磁场可以抑制缺陷混沌，使系统稳定。在外加电场中，EHD发生的阈值向上移动，在磁场中增加。磁场可以将滚动轴的方向改变为垂直于其场的方向。磁场和乘性噪声效应的定量动力学研究有待于进一步研究。少

The growth process of the convective pattern in the electrohydrodynamic instability(END) of nematic liquid crystals is basically devided into three evolution regimes; 1) the early stage(amplitude dynamics), 2)the late stage(phase dynamics) and 3)the final stage (defect dynamics). The scaling properties based on the noisy Landau equation for the amplitude and for the variances are experimentally observed in the early stage but not hold in both a late and a final stages. Both the correlation time _N and the intensity Q of the noise are the crucial parameters to control the bifurcation in multiplicative stochastic processes of EHD instability. With increasing a noise intensity the threshold for the onset of the first instability changes drastically. We observe that the curvature arising for the threshold changes as one is going e.g. from the onset of the williams domains(WD) to the onset of the GP. This result reflects the transition in the flow structure from WD to GP and dynamical scatt … More ering mode (DSM:turbulence). As the intensity of noise is increased further, the onset of the first instability becomes more complex. Defect motions, pattern selections, transition to chaos and these magnetic-field effect are also studied detailedly in WD to the fluctuating WD(FWD) regimes. The defect chaos(FWD) could occur slightly above the threshold, via the state with regular rolls without any defect for finite aspect ratio. In this state, defects never disappear whose number always changes nonperiodically in time. The power spectrum of the temporal change of this number shows l/f type-spectrum. A magnetic field can suppress a defect chaos and stabilized the system. The threshold of an applied electric field for the onset of EHD shifts upward increasing in a magnetic field. The magnetic field could change the direction of a roll axis into the direction perpendicular to its field. The quantitative dynamical studies on magnetic field and multiplicative noise effects are left to be investigated in future. Less