Pattern formation its multiplicative stochastic processes

向列相液晶电流体动力不稳定性（END）中对流模式的生长过程基本分为三个演化机制；1)早期阶段（幅度动力学），2)后期阶段（相位动力学）和3)最后阶段（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实验上观察到在早期阶段，但在后期和最终阶段都不成立。在EHD不稳定的乘性随机过程中，相关时间_N和噪声强度Q是控制分岔的关键参数。随着噪声强度的增加，第一次不稳定发生的阈值急剧变化。我们观察到，阈值产生的曲率随着人们从威廉姆斯域（WD）的开始到GP的开始而变化。这一结果反映了气流结构从WD向GP的转变和动力散射模态（DSM：湍流）。随着噪声强度的进一步增大，第一次失稳的发生变得更加复杂。并对缺陷运动、模式选择、向混沌的跃迁以及磁场效应进行了详细研究。在有限宽高比条件下，在无缺陷的正常轧辊状态下，会产生略高于阈值的缺陷混沌（FWD）。在这种状态下，缺陷永远不会消失，缺陷的数量总是随时间发生非周期性的变化。该数时间变化的功率谱为l/f型谱。磁场可以抑制缺陷混沌，稳定系统。外加电场诱发EHD的阈值在磁场中呈递增趋势向上移动。磁场可以改变滚轴的方向，使之与磁场垂直。磁场和倍增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