Defect turbulence and generalized statistical mechanics

Abstract

We present experimental evidence that the motion of point defects in thermal convection patterns in an inclined fluid layer is well-described by Tsallis statistics with an entropic index $q\approx 1.5$. The dynamical properties of the defects (anomalous diffusion, shape of velocity distributions, power law decay of correlations) are in good agreement with typical predictions of nonextensive models, over a range of driving parameters.

References in corpus (14)

• Superstatistics
• Anomalous diffusion in the presence of external forces: exact time-dependent solutions and entropy
• Dynamical foundations of nonextensive statistical mechanics
• Measurement of Particle Accelerations in Fully Developed Turbulence
• Option Pricing Formulas based on a non-Gaussian Stock Price Model
• A nonextensive thermodynamical equilibrium approach in $e^{+}{e}^{-}\to hadrons$
• Constructing a statistical mechanics for Beck-Cohen superstatistics
• Measuring non-extensitivity parameters in a turbulent Couette-Taylor flow
• Non-extensive statistical mechanics and particle spectra in elementary interactions
• Non-extensive statistics, fluctuations and correlations in high energy nuclear collisions
• Defect turbulence in inclined layer convection
• On the small-scale statistics of Lagrangian turbulence
• Penta-hepta defect chaos in a model for rotating hexagonal convection
• Statistics of defect motion in spatiotemporal chaos in inclined layer convection

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