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Codimension-two points in annular electroconvection as a function of aspect ratio
V B Deyirmenjian1, Zahir A Daya, Stephen W Morris
1Department of Physics, University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
Summary
Researchers derived a Landau amplitude equation for electrically driven convection in liquid crystals. The study reveals how geometric and material properties influence the system
Area of Science:
- Physics
- Fluid Dynamics
- Materials Science
Background:
- Electrically driven convection in thin liquid crystal films is a complex phenomenon.
- Understanding the primary bifurcation is crucial for predicting system behavior.
Purpose of the Study:
- To derive the Landau amplitude equation from first principles for electrically driven convection.
- To investigate the dependence of the nonlinear coefficient 'g' on geometrical (radius ratio alpha) and material (dimensionless number P) parameters.
Main Methods:
- First-principles derivation of the generic Landau amplitude equation.
- Explicit calculation of the leading cubic nonlinearity coefficient 'g'.
- Systematic study of 'g' as a function of alpha and P.
Main Results:
- 'g' decreases with decreasing P, becoming nearly constant for P >= 1.
- 'g' approaches infinity as P approaches 0.
- 'g' exhibits a nontrivial and discontinuous dependence on the radius ratio alpha.
- Discontinuities in 'g' occur at codimension-two points identified by varying alpha.
Conclusions:
- The derived Landau amplitude equation accurately models the experimental system.
- The study elucidates the critical role of geometric and material parameters in electrically driven convection.
- Codimension-two bifurcations are identified through the discontinuous behavior of 'g' with respect to alpha.
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