Jayaraman, A; Scheel, JD; Greenside, HS; Fischer, PF, *Characterization of the domain chaos convection state by the largest Lyapunov exponent*,
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 74 no. 1
(2006),
pp. 016209 (12 pages), American Physical Society [doi] .
**Abstract:**

*Using numerical integrations of the Boussinesq equations in rotating cylindrical domains with realistic boundary conditions, we have computed the value of the largest Lyapunov exponent λ1 for a variety of aspect ratios and driving strengths. We study in particular the domain chaos state, which bifurcates supercritically from the conducting fluid state and involves extended propagating fronts as well as point defects. We compare our results with those from Egolf, [Nature 404, 733 (2000)], who suggested that the value of λ1 for the spiral defect chaos state of a convecting fluid was determined primarily by bursts of instability arising from short-lived, spatially localized dislocation nucleation events. We also show that the quantity λ1 is not intensive for aspect ratios Γ over the range 20<Γ<40 and that the scaling exponent of λ1 near onset is consistent with the value predicted by the amplitude equation formalism. © 2006 The American Physical Society.*