Schedule Aug 19, 2003
Critical Phenomena near Bifurcations in Systems far from Equilibrium
Guenter Ahlers (UC ~ Santa Barbara)

In spatially-extended nonlinear dissipative systems far from equilibrium, bifurcations are usually discussed in terms of deterministic equations of motion. This yields a sharp bifurcation point at a critical value $R = R_c$ of the control parameter at which an exchange of stability occurs between the spatially-uniform state and the state with spatial variation. However, if the system is subjected to external (thermal) noise, then even below the bifurcation there are fluctuations of the macroscopic variables away from the uniform state and the relevant fields, although they have zero mean, have a positive (albeit small) mean square. This talk will review the measurements of the properties of these fluctuations. In the case of Rayleigh-B\'enard convection (RBC) nonlinear interaction between them yields a first-order transition as predicted by Swift and Hohenberg. The "ordered" state of convection rolls above the bifurcation exhibits thermally induced amplitude variations, roll undulations, and dislocations, as envisioned in part by Toner and Nelson. Electroconvection in nematic liquid crystals (NLC) does not belong to the same universality class as RBC, and fluctuation interactions leave the bifurcation supercritical; but the exponents are renormalized. For a Hopf bifurcation to oblique rolls in the NLC I52 experiment yields $\gamma \simeq 0.35 < \gamma_{MF} = 1/2$ for the exponent describing the fluctuation intensity, whereas a stationary bifurcation to oblique rolls in the NLC N4 gives $\gamma \simeq 0.85 > \gamma_{MF}$. Thus, as in equilibrium systems, there exist several distinct universality classes. Work done in collaboration with Michael Scherer, Jaechul Oh, and Xinliang Qiu.

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