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Stable droplets and growth laws close to the modulational instability of a domain wall

Gomila, Damià and Colet, Pere and Oppo, Gian-Luca and San Miguel, Maxi (2001) Stable droplets and growth laws close to the modulational instability of a domain wall. Physical Review Letters, 87 (19). 194101/1-194101/4. ISSN 0031-9007

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Abstract

We consider the curvature driven dynamics of a domain wall separating two equivalent states in systems displaying a modulational instability of a flat front. An amplitude equation for the dynamics of the curvature close to the bifurcation point from growing to shrinking circular droplets is derived. We predict the existence of stable droplets with a radius R that diverges at the bifurcation point, where a curvature driven growth law R(t)≈t1/4 is obtained. Our general analytical predictions, which are valid for a wide variety of systems including models of nonlinear optical cavities and reaction-diffusion systems, are illustrated in the parametrically driven complex Ginzburg-Landau equation.