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

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

Research output: Contribution to journalArticle

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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

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domain wall
curvature
Landau-Ginzburg equations
cavities
radii
predictions

Keywords

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

Cite this

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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.",
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Stable droplets and growth laws close to the modulational instability of a domain wall. / Gomila, Damià; Colet, Pere; Oppo, Gian-Luca; San Miguel, Maxi.

In: Physical Review Letters, Vol. 87, No. 19, 194101 , 17.10.2001.

Research output: Contribution to journalArticle

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T1 - Stable droplets and growth laws close to the modulational instability of a domain wall

AU - Gomila, Damià

AU - Colet, Pere

AU - Oppo, Gian-Luca

AU - San Miguel, Maxi

PY - 2001/10/17

Y1 - 2001/10/17

N2 - 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.

AB - 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.

KW - domain wall

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KW - optics

KW - Ginzburg-Landau equation

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