Elastic properties of a cellular dissipative structure
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Transition towards spatio-temporal chaos in one-dimensional interfacial patterns often involves two degrees of freedom: drift and out-of-phase oscillations of cells, respectively associated to parity breaking and vacillating-breathing secondary bifurcations. In this paper, the interaction between these two modes is investigated in the case of a single domain propagating along a circular array of liquid jets. As observed by Michalland and Rabaud for the printer’s instability , the velocity V g of a constant width domain is linked to the angular frequency \(\omega\) of oscillations and to the spacing between columns \(\lambda_0\) by the relationship \(V_g = \alpha \lambda_0 \omega\). We show by a simple geometrical argument that \(\alpha\) should be close to \(1/ \pi\) instead of the initial value \(\alpha = 1/2\) deduced from their analogy with phonons. This fact is in quantitative agreement with our data, with a slight deviation increasing with flow rate.
KeywordsElastic Property Angular Frequency Velocity Versus Single Domain Quantitative Agreement
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