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Bifurcation to worms in electroconvection
1Department of Physics and Center for Nonlinear Science, University of California at Santa Barbara, Santa Barbara, California 93106, USA.
Summary
This study reveals that electroconvection in liquid crystals can exhibit a subcritical bifurcation, forming localized "worms" below the stability limit. The bifurcation transitions to supercritical at higher conductivities, with implications for understanding pattern formation.
Area of Science:
- Nonlinear Dynamics
- Soft Matter Physics
- Liquid Crystal Physics
Background:
- Electroconvection in liquid crystals can lead to pattern formation.
- Localized convection rolls, termed "worms," appear in certain liquid crystal systems.
- The nature of the bifurcation to worm formation (supercritical vs. subcritical) was previously undetermined.
Purpose of the Study:
- To experimentally determine whether the bifurcation to electroconvection worms in a specific liquid crystal (I52) is supercritical or subcritical.
- To investigate the influence of fluid conductivity on the bifurcation type.
- To characterize the voltage-dependent behavior and stability limits of the conduction and worm states.
Main Methods:
- Estimating the critical voltage V(c) by extrapolating thermal fluctuation amplitudes below onset.
- Measuring the lifetime of the conduction state to determine the saddle-node voltage V(s).
- Systematically varying fluid conductance (sigma) to observe changes in bifurcation behavior.
Main Results:
- The bifurcation to worm formation was found to be subcritical at low conductivities.
- Worm structures were observed to appear below the stability limit of the conduction state.
- At higher conductivities (sigma > 1.2 x 10^-8 Omega^-1 m^-1), the bifurcation transitioned to supercritical.
- A parameter epsilon(s) = V(s)^2/V(c)^2 - 1 was found to approach zero from negative values near this transition.
Conclusions:
- The study experimentally confirms a subcritical bifurcation to electroconvection worms in liquid crystals at low conductivities.
- The bifurcation nature shifts to supercritical with increasing conductivity, indicating a complex phase diagram.
- Further investigation is needed to clarify the transition mechanism between subcritical and supercritical bifurcations, potentially involving tricritical points or disconnected bifurcation lines.