SUMMARY OF ELECTROCONVECTION EXPERIMENTS
WORK HAS BEEN FUNDED PRIMARILY BY: NSF award DMR 9975479
Nematic liquid crystals are long rod-like molecules that tend to align with each other. The direction of the average alignment is referred to as the director. For the study of electroconvection, the nematic liquid crystal is confined between two glass plates with a thickness of 25 - 100 microns. The glass is treated so the that the director is aligned in a uniform directions parallel to the plates. The glass also is coated with transparent conductors, and an ac voltage is applied perpendicular to the plates. Above a critical value of the voltage, a periodic distortion of the director and an associated flow in the form of convection rolls develops. This is referred to as a pattern. The pattern is imaged from above using a microscope (see photograph on the left) and generally consists of a single set of stripes or a superposition of a small number of stripe with different orientations. In electroconvection, the director selects out a direction, so it is possible to have oblique rolls. These are patterns where the wavevector of the pattern forms a nonzero angle with respect to the director. An example of such a pattern is show in the image on the right.
useful for studying a number of interesting nonlinear and pattern forming
Domain growth deals with the study of systems after a sudden change in an external parameter. In the case of electronvection, one can make a sudden change in the driving voltage from below the critical voltage to above the critical voltage. If the steady state consists of oblique rolls, a pattern of small domains of zig and zag rolls forms. As a function of time, these domains grow in size, that is the pattern "coarsens". We study the scaling behavior of the growth of these domains and the dynamics of the defects that control the coarsening. Studies of this system may have implications for other systems in which domain growth in a periodic systems is important, such as crystalline materials. For examples of coarsening, see the movie page.
Spatiotemporal chaos refers to
deterministic patterns with unpredictable, non-periodic spatial and temporal
variations (the image at the right is a single snapshot in time that
highlights the non-periodic spatial behavior of the amplitude of a set of
convection rolls). Spatio-temporal chaos occurs in a wide variety of systems
where spatial degrees of freedom contribute to the dynamics, such as
population dynamics, traffic flow, chemical reaction/diffusion systems, and
arrays of Josephson junctions. Some aspects of spatio-temporal chaos that we
study using electroconvection include:
· the dynamics as a function of system size in order to elucidate the role of the spatial degrees of freedom.
· resonace effects and
regularization of spatiotemporal chaos using temporal and spatial modulations
of the driving force.
Our work has focused on using modulations of the control parameter to stabilize regular dynamics. Movies of the impact of resonant modulation can be found at the picture page. These movies illustrate the establishment of regular standing wave patterns from irregular traveling waves. This work has been published in Temporal Modulation of the Control Parameter in Electroconvection in the Nematic Liquid Crystal I52, M. Dennin, Phys. Rev. E 62, 7842 (2000).
We have also used modulation to study the dynamics of localized states, known as worms. This work has appeared in Phys. Rev. E.