Pattern formation its multiplicative stochastic processes

向列相液晶电流体动力学不稳定性(END)中对流模式的生长过程基本上可分为三个演化阶段：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性质在早期被实验观察到，但在后期和末期都不成立。关联时间N和噪声强度Q是控制EHD不稳定性乘性随机过程分叉的关键参数。随着噪声强度的增加，第一次失稳开始的阈值发生了剧烈的变化。我们观察到阈值产生的曲率随着一个人的移动而变化，例如从Williams域(WD)的开始到GP的开始。这一结果反映了从WD到GP的流动结构的转变和动态散射…更多运行模式(DSM：湍流)。随着噪声强度的进一步增加，第一次失稳的发生变得更加复杂。还详细研究了WD到波动WD(FWD)区的缺陷运动、图样选择、向混沌的转变以及这些磁场效应。在有限长宽比条件下，通过无缺陷的规则卷曲状态，缺陷混沌(FWD)可能会出现在阈值以上。在这种状态下，缺陷永远不会消失，缺陷的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。外加电场引起EHD开始的阈值上移，在磁场中增大。磁场可以将滚动轴的方向改变为垂直于其磁场的方向。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。较少

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