Theoretical and Numerical Study in Nonlinear-Nonequilibrium Solid State Physics

非线性非平衡固体物理的理论与数值研究

基本信息

批准号：
15540369
负责人：
FUJISAKA Hirokazu
金额：
$ 2.24万
依托单位：
Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

项目摘要

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

外部噪声下向列液晶对流模式的统计分析::发现在外部噪声下平面排列向列液晶中观察到的对流模式间歇性出现的模式演化可能存在一种新型统计规律这是通过使用具有乘性噪声的非线性随机模型来证明的，特别是，阐明了加性噪声与图案位置的变化有关，我们发现对噪声的统计特性进行了理论分析。对流模式的变化与数值模拟的一致。各向异性Swift-Hohenberg方程的排序过程：我们使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，发现有两种类型。磁畴壁、内尔型和布洛赫型。与此相反，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或排斥的。取决于两个壁的时间变化的数值积分表明理论结果与数值模拟吻合良好。振荡磁场下各向异性 XY 自旋系统中磁壁的动力学：我们制作了动态相图。各向异性 XY 自旋系统的相变，由角频率和外力振幅组成。当多种类型的振荡稳定存在时，我们观察到连接这些共存的域结构。发现根据各向异性参数的不同，有两种类型的畴壁：Neel 型和 Bloch 型，我们阐明了 N 型和 B 型壁的稳定区域。此外，我们从理论上推导了的临界行为。理论的比较结果与数值模拟一致。