Theoretical and Numerical Study in Nonlinear-Nonequilibrium Solid State Physics

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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