Theoretical and Numerical Study in Nonlinear-Nonequilibrium Solid State Physics

外噪声作用下向列型液晶中对流模式的统计分析：外噪声作用下平面向列型液晶中对流模式的间歇出现可能存在一种新的统计规律。这是用一个带有乘性噪声的非线性随机模型来证明的。特别说明了加性噪声与模式位置变化的关系，发现对对流模式变化的统计特性的理论分析与数值模拟结果一致。各向异性Swift-Hohenberg方程中的有序过程：利用动力学模型对磁系统的非线性动力学进行了理论研究和数值模拟。结果表明，其畴壁有Nell型和Bloch型两种类型。我们推导了这些畴结构的振幅（相位）方程。两个n型壁的相互作用是吸引的，而两个b型壁的相互作用是吸引的还是排斥的，这取决于壁的手性。对两壁时间变化的数值积分表明，理论结果与数值模拟结果吻合较好。振荡磁场作用下各向异性XY自旋体系的磁壁动力学：我们绘制了各向异性XY自旋体系的动态相变相图，该相图由角频率和外力幅值组成。当几种振荡稳定存在时，我们观察到连接这些共存振荡的域结构。根据各向异性参数的不同，畴壁可分为Neel型和Bloch型两种类型。明确了n型和b型壁面的稳定区域。此外，我们还从理论上推导了墙体的临界性能。理论计算结果与数值模拟结果相吻合。少

Statistical Analysis of Convective Patterns in the Nematic Liquid Crystal under External Noise ::It was found that there might exist a new type of statistical law for the pattern evolution of intermittent emergence of convective pattern observed in the nematic liquid crystal with a planar alignment under external noise. This was shown by using a nonlinear stochastic model with a multiplicative noise. Particularly, elucidating that the additive noise is relevant to the change of pattern position, we found that the theoretical analysis on statistical characteristics of convective pattern change agrees with that of the numerical simulation.Ordering Process in the Anisotropic Swift-Hohenberg Equation :We carried out theoretical study and numerical simulation of nonlinear dynamics of magnetic system, using a dynamical model. It was found that there are two types of domain walls, Nell type and Bloch type. We derived amplitude (phase) equations for these domain structures. In contrast to that … More the interaction of two N-type walls is attractive, that for two B-type walls are either attractive or repulsive depending on the chirality of the walls. Numerical integration of the temporal change of two walls showed that the theoretical results agrees well with the numerical simulations.Dynamics of Magnetic Walls in the Anisotropic XY Spin System under Oscillating Magnetic Field :We made a phase diagram for dynamic phase transition of the anisotropic XY spin system, spanned by the angular frequency and the amplitude of the external force. When several types of oscillations stably exist, we observed the domain structures connecting these coexisting oscillations. It was found that there are two types of domain walls, Neel type and Bloch type, depending on the anisotropy parameter. We clarified the stability regions of N-type and B-type walls. Furthermore, we theoretically derived the critical behavior of the wall. The comparison of the theory turned out to be in agreement with the numerical simulation. Less