Domain wall dynamics: Growth laws, localized structures and stable droplets

Abstract.We discuss the relation between the dynamics of walls separating two equivalent domains and the existence of different kinds of localized structures in systems far from thermodynamic equilibrium. In particular we focus in systems displaying a modulational instability of a flat front where an amplitude equation for the dynamics of the curvature allows to characterize different growth regimes and to predict the existence of stable droplets, localized structures whose stability comes from nonlinear curvature effects.

[1]  W. Firth,et al.  From domain walls to localized structures in degenerate optical parametric oscillators , 1999 .

[2]  P. Colet,et al.  Stable droplets and dark-ring cavity solitons in nonlinear optical devices , 2003 .

[3]  Valery Petrov,et al.  Resonant pattern formation in achemical system , 1997, Nature.

[4]  J. Cahn,et al.  A microscopic theory for antiphase boundary motion and its application to antiphase domain coasening , 1979 .

[5]  W. Firth,et al.  Computationally determined existence and stability of transverse structures. II. Multipeaked cavity solitons. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  V. Sánchez-Morcillo,et al.  Stability of localized structures in the Swift-Hohenberg equation. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  P. Coullet,et al.  Stable static localized structures in one dimension , 2000, Physical review letters.

[8]  Kestutis Staliunas,et al.  PATTERN FORMATION AND LOCALIZED STRUCTURES IN DEGENERATE OPTICAL PARAMETRIC MIXING , 1998 .

[9]  Ouchi,et al.  Phase ordering kinetics in the Swift-Hohenberg equation. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  W. Firth,et al.  Computationally determined existence and stability of transverse structures. I. Periodic optical patterns. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Paul Mandel,et al.  Kinetics of Localized Pattern Formation in Optical Systems , 1998 .

[12]  J. S. Rowlinson,et al.  Phase Transitions and Critical Phenomena , 1972 .

[13]  A. Bray.  Theory of phase-ordering kinetics , 1994, cond-mat/9501089.

[14]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[15]  Sancho,et al.  Domain growth in binary mixtures at low temperatures. , 1992, Physical review. B, Condensed matter.

[16]  M. Berre,et al.  Kinetics of domain walls in the degenerate optical parametric oscillator , 2000 .

[17]  W. Firth,et al.  Characterization, dynamics and stabilization of diffractive domain walls and dark ring cavity solitons in parametric oscillators. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Hezi Yizhaq,et al.  Linear and nonlinear front instabilities in bistable systems , 2006 .

[19]  U. Peschel,et al.  Universal criterion and amplitude equation for a nonequilibrium Ising-Bloch transition. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  M San Miguel,et al.  Stable droplets and growth laws close to the modulational instability of a domain wall. , 2001, Physical review letters.

[21]  U. Peschel,et al.  Formation, motion, and decay of vectorial cavity solitons , 1998 .

[22]  E. Meron.  Pattern formation in excitable media , 1992 .

[23]  M. S. Miguel,et al.  Self-similar domain growth, localized structures, and labyrinthine patterns in vectorial Kerr resonators , 1999, patt-sol/9908001.

[24]  P. D. Woods,et al.  Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopft bifurcation , 1999 .

[25]  Kestutis Staliunas,et al.  Dynamics of phase domains in the Swift-Hohenberg equation☆ , 1998 .

[26]  Front dynamics in an oscillatory bistable Belousov-Zhabotinsky chemical reaction. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  M Tlidi,et al.  Phase-separation dynamics of circular domain walls in the degenerate optical parametric oscillator. , 2000, Optics letters.

[28]  Sergio Rica,et al.  Coalescence and Droplets in the Subcritical Nonlinear Schrödinger Equation , 1997 .

[29]  Kjartan Pierre Emilsson,et al.  Strong resonances of spatially distributed oscillators: a laboratory to study patterns and defects , 1992 .

[30]  P. Colet,et al.  Stable droplets and nucleation in asymmetric bistable nonlinear optical systems , 2004 .

[31]  Coullet,et al.  Breaking chirality in nonequilibrium systems. , 1990, Physical review letters.