Nonextensive Statistical Mechanics

7.1 Physics 229Fig. 7.7 Example shadowgraph image of undulation chaos in fluid (compressed CO 2 with Prandtlnumber Pr = ν/κ ≃ 1, where ν is the kinematic viscosity and κ is the coefficient of thermal expansion)heated from below and cooled from above, inclined by an angle of 30 o . The dimensionlessdriving parameter is ɛ = 0.08. The black (white) box encloses a positive (negative) defect. Theconvection cell has a thickness d = (388 ± 2) m and dimensions 100d × 203d, of which only acentral 51d × 63d region was used for analysis (from [427]).the distribution of velocities is, along six decades, a q-Gaussian with q ≃ 1.5, asillustrated in Fig. 7.8. Furthermore, superdiffusion was observed with a diffusionexponent α ≃ 4/3, as illustrated in Fig. 7.9. These values satisfy the prediction(4.16) (with the notation change μ ≡ α). Similar results are to be expected [427]for phenomena such as electroconvection in liquid crystals, nonlinear optics, andauto-catalytic chemical reactions.Fig. 7.8 Transverse velocity (v x ) distributions for ɛ = 0.08 (a) andɛ = 0.17 (b) for positive andnegative defects, rescaled to unit variance. Solid lines are q-Gaussian fittings (q being the onlyfitting parameter) for positive defects. Dashed lines represent a unit variance Gaussian. Insets:Relative errors [p experiment − p theory ]/p theory for positive defects (from [427]).