a Study of External Modulation of Nonlinear Systems.
Abstract
The dynamics of nonequilibrium systems are studied in two different experiments. The first investigates the effects of the external noise on the magnetic Freedericksz transition in a nematic liquid crystal. The second deals with the phase dynamics of a TaylorCouette system. In the first experiment, the effects of imposing dichotomous noise on the magnetic Freedericksz transition in the nematic liquid crystal MBBA are studied. A layer of nematic liquid crystal sample is placed in a noisy magnetic field (a DC magnetic field superimposed with a dichotomous noise). The director is initially perpendicular to the magnetic field. Various states of the nematic orientation occur as characterized by the probability density function of the rotation angle, depending on the magnitude of the DC field as well as the amplitude and correlation time of the noise component. The resultant phase diagrams are in partial agreement with the analytic results of Horsthemke, Doering, Lefever and Chi for H > H_{c } (Phys. Rev. A 31, 1123(1985)). A substantial deviation of the experimental result from computer simulations based on their model for low magnetic field(H < H_{c}) is observed. The second experiment focuses on the phase dynamics in Taylor, wavy and turbulent Taylor vortex flow in a Taylor Couette system, which has a radius ratio eta = 0.886 and aspect ratio Gamma = 70. A sinusoidal modulation along the axial direction is imposed at the upper boundary of the system and the responses of the vortices to the modulation are recorded. The results are consistent with the theoretical models proposed for each flow pattern. In the one phase variable case, the Taylor vortex flow, the perturbations at the upper boundary are found to diffuse along the axial direction and the dynamics can be described by a simple diffusion model. In the two phase variable case, wavy vortex flow, the phase dynamics are governed by coupled diffusion equations as proposed by Brand and Cross (Phys. Rev. A 27 1237(1983)). We found that the perturbations propagate as traveling waves parallel with the axis of the system when there is a strong coupling between the axial and azimuthal phase variables, and diffusively for weak coupling. Our experimental results in turbulent Taylor vortex flow show that the phase dynamics is described by a diffusion model with a diffusion coefficient a magnitude larger than the regular/laminar Taylor vortex flow.
 Publication:

Ph.D. Thesis
 Pub Date:
 1991
 Bibcode:
 1991PhDT.......187W
 Keywords:

 Physics: Fluid and Plasma