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

Damià Gomila, Pere Colet, Gian-Luca Oppo, Maxi San Miguel

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50 Citations (Scopus)
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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.
Original languageEnglish
Article number194101
Number of pages4
JournalPhysical Review Letters
Volume87
Issue number19
DOIs
Publication statusPublished - 17 Oct 2001

Keywords

  • domain wall
  • curvature driven growth law
  • nonlinear physics
  • optics
  • Ginzburg-Landau equation

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