Statistics of defect motion in spatiotemporal chaos in inclined layer convection

Abstract

We report experiments on defect-tracking in the state of undulation chaos observed in thermal convection of an inclined fluid layer. We characterize the ensemble of defect trajectories according to their velocities, relative positions, diffusion, and gain and loss rates. In particular, the defects exhibit incidents of rapid transverse motion which result in power law distributions for a number of quantitative measures. We examine connections between this behavior and Lévy flights and anomalous diffusion. In addition, we describe time-reversal and system size invariance for defect creation and annihilation rates. Topological defects within patterns are observed in many systems to move in a spatiotemporally chaotic fashion. We examine the motion of such defects within a defect-turbulent state observed in thermal convection of an inclined fluid layer. We characterize the trajectories of the defects both by analogy to fluid turbulence -velocity distributions, diffusion, and power spectra -and by properties dependent upon the topological characteristics of the defects: pair creation/annihilation and interactions.

Anomalous velocity fluctuation in one-dimensional defect turbulence

“…In order to reduce the influence of the spatiotemporal resolutions on the trajectories, we replaced the hole positions with their weighted average. The weighting function for a hole position Xj at time /,■ affected [32]. From the smoothed trajectory with coordinates i,-= ]TL WjjXj, we obtained the hole velocity at each time step at every position using the local linear regression.…”

Superstatistics: theory and applications

“…They have a well-defined position and velocity, they are created and annihilated (in pairs of course), and one can even formally attribute a 'charge' to them: There are positive and negative defects. For more details, see [7,24] and references therein.…”

“…For large enough temperature differences, interesting convection patterns start to evolve. An inclined layer convection experiment [7,24] is a kind of Raleigh-Benard experiment where the apparatus is tilted by an angle (say 30 degrees), moreover the liquid is confined between two very narrow plates. For large enough temperature differences, the convection rolls evolve chaotically.…”

Superstatistics and System Identification for a Class of Generalized Cauchy Processes

“…Real world examples which give the generalized Cauchy distribution are listed below: (i) return rate in economic time series (Kiyono et al, 2006) [18]; (ii) velocity fluctuation in thermal convection (Daniels et al, 2004) [23,24]; (iii) phase-velocity of neutron fluctuation in a power reactor (Konno et al, 1998) [25]; (iv) phasevelocity of EEG fluctuation in human brain (Konno et al, 2005) [26]; (v) RR interval fluctuation of heart beat (Kiyono et al, 2009) [22].…”