Abstract
The usual deterministic description of spatially-extended nonlinear dissipative systems far from equilibrium yields a sharp bifurcation point at a crtical value R=Rc of the control parameter where the system makes a transition from the spatially uniform ground state to a state with spatial variation. However, when the effect of thermal noise is considered, 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 mean square. Here we review measurements of the properties of these fluctuations. In the case of Rayleigh–Bénard convection (RBC) in common fluids, fluctuation amplitudes are small and the exponent of the powerlaw which describes their mean square has its classical (mean-field) value γMF=1/2 in experimentally accessible parameter ranges. However, for RBC of a fluid near its liquid-gas critical point fluctuation amplitudes are much larger and nonlinear interactions between them yield a first-order transition as predicted by Swift and Hohenberg. 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 critical behavior is renormalized.
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