Penta-Hepta Defect Chaos in a Model for Rotating Hexagonal Convection

Abstract

In a model for rotating non-Boussinesq convection with mean flow we identify a regime of spatiotemporal chaos that is based on a hexagonal planform and is sustained by the induced nucleation of dislocations by penta-hepta defects. The probability distribution function for the number of defects deviates substantially from the usually observed Poisson-type distribution. It implies strong correlations between the defects in the form of density-dependent creation and annihilation rates of defects. We extract these rates from the distribution function and also directly from the defect dynamics.

Statistics of defect trajectories in spatio-temporal chaos in inclined layer convection and the complex Ginzburg–Landau equation

“…2,3 In other situations, spatiotemporal chaos coexists with stable ordered states and finiteamplitude perturbations are needed to take the system from one attractor to the other. 7,8 In a Swift-Hohenberg model for hexagonal patterns under the influence of rotation, penta-hepta defect chaos can be main-tained by the ''induced nucleation'' of defects, in which penta-hepta defects trigger the nucleation of further defects, while regular hexagon patterns are actually linearly stable. 5 A similar situation occurs also in the CGL in certain Benjamin-Feir-stable regimes.…”

“…A striking example of this situation is spiral-defect chaos 4 in thermal convection in gases, which occurs despite the fact that straight-roll states are stable for the same values of the system parameters. 7 In rotating non-Boussinesq convection, numerical simulations have identified a regime in which a chaotic state is maintained through the interplay between defects in the hexagon pattern and whirling activity of the convection cells. 6 Recently, such bistability has also been identified in hexagonal patterns in the presence of rotation.…”

Geometric diagnostics of complex patterns: Spiral defect chaos

“…20 Many complex patterns exhibit striking, isolated objects like point defects, e.g., dislocations, 21,22 disclinations, 23 or penta-hepta defects. 24,25 Dislocations often take on the form of spirals, as is the case for points of vanishing oscillation amplitude in spatially extended oscillations. 26,27 Similar spirals also arise in excitable systems.…”

Approximate time-dependent solution of a master equation with full linear birth-death rates

“…There are growing interests on dynamics of phase-singularities (PSs) in complex systems such as ventricular fibrillation [1,2,[4][5][6], defect dynamics in fluids [7,8] and liquid crystals [9], living creatures [10], quantum vortex dynamics [11] and so on. A master equation approach on the number n of PS for studying birth-death dynamics of PSs in a 2D Complex Ginzburg-Landau equation is invented first by Gil, Lega and Meunier [12].…”

“…A master equation approach on the number n of PS for studying birth-death dynamics of PSs in a 2D Complex Ginzburg-Landau equation is invented first by Gil, Lega and Meunier [12]. Although the method is applied in various real systems [7,8,13], it can be utilized to get only the equilibrium distribution of PSs, P s (n). To catch the true dynamical features of PSs, it is necessary to get the information on (i) the PS number distribution, (ii) the waiting time (lifetime) distribution, (iii) the velocity distribution of PS.…”