Pattern Formation in Nonequilibrium Dissipative Systems-Dynamics of Dissipative Structures in Liquid Crystals

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The aim of this research project is to understand a role of system symmetries on pattern formations in nonequilibrium dissipative systems such as electrohydrodynamic instability (EHD) in nematic liquid crysals. In the EHD system, there are two different alignments ; planar and homeotropic ones. Regarding pattern formations in planar systems various new results have been obtained. Contrary to this, the study of EHD in homeotropic systems was very few, and no interesting results and no new physics were obtained so far. In the present study, we especially pay our attention to symmetries of the systems. Pattern formations in EHD strongly depend on the initial synmmetries of the systems, that is either on planar or homeotropic alignments. However the so-called chevron patterns appear independently of initial align-ments, i.e. initial symmetry of the system. Therefore we investigate at first the formation mechanism of this type of patterns. Then it is found that the chevron patterns are clas … More sified into four different types, chevron A and B, both of which are further classified into the patterns with periodic defect orientation(DMC) and defect free chevrons (DFC). DMC forms due to competitive instability between defect formation and director defomation similar to Turing instability. The mechanism of DFC in chevron A and B are unknown yet. It becomes however clear that the chevron patterns are fomed independently of boundary anchoring which always leads to no symmetry dependence in the pattern formation.Regarding EHD in a homeotropic alignment with a continuously rotational symmetry, a spatio-temporal chaos called the softmode turbulence (SMT) appears. SMT is a unique turbulence in a weakly nonlinear regime continuously connecting to a uniform stationary state via a single supercritical bifuraction and therefore expected to be understood precisely. This results from the additional Goldstone mode due to the continuously rotational symmetry, which can be suppressed by application of magnetic fields. The phase diagram has been obtained on a plane among the parameters of applied electric field intensity, its frequency and magnetic field strength. Two different STC's have been found out which depend on the symmetry of the system. Thus the small change of alignments (symmetries) leads to the big difference of pattern formations. The formation dynamics must be classified into two categories ; universal dynamics independent of symmetries and individual dynamics dependent on symmetries. Less