Deviations from Linear Theory for Fluctuations below the Supercritical Primary Bifurcation to Electroconvection

2000/05/05 by Michael Scherer, Michael A. Scherer, Guenter Ahlers +3 · 3 citations
Agricultural and Biological Sciences · Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Plant and animal studies #Theoretical and Computational Physics #cond-mat

paper · pdf · doi:10.1103/physrevlett.85.3754

4 pages, 5 figures, submitted to Phys. Rev. Lett

arxiv created 2000/05/05 · openalex publication_date 2000/10/30 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Over two decades ago it was predicted that nonlinear interactions between thermally driven fluctuations in dissipative nonlinear nonequilibrium systems lead to deviations from mean-field theory. Here we report experimental observations of such deviations as a supercritical primary bifurcation is approached. We measured the mean-square director-angle fluctuations 〈\ensuremathθ²〉 below the bifurcation to electroconvection of two different nematic liquid crystals. For \ensuremathε_mf\ensuremath≡V²/V_c,mf²\ensuremath-1\ensuremath\lesssim\ensuremath-0.1 ( V is the applied voltage) we find 〈\ensuremathθ²〉\ensuremath∝|\ensuremathε_mf|^\ensuremath-\ensuremathγ with \ensuremathγ given by linear theory (LT). Closer to the bifurcation there are deviations from LT with a smaller \ensuremathγ and with V_c²>V_c,mf².

Citations

• Hydrodynamic fluctuations at the convective instability
• Pattern formation outside of equilibrium

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