Formation of Clusters of Localized States in a Gas Discharge System via a Self-Completion Scenario

Astrov, Yu. A.; Logvin, Yu. A.

doi:10.1103/physrevlett.79.2983

Cited by 131 publications

(97 citation statements)

References 19 publications

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“…In the last decade localized patterns or localized structures have been observed in different experiments: liquid crystals [3], gas discharge systems [4], chemical reactions [5], fluids [6], granular media [7], and nonlinear optics [8,9]. One can understand these localized patterns as patterns extend only over a small portion of the spatial homogeneous systems.…”

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confidence: 99%

Localized patterns and hole solutions in one-dimensional extended systems

Clerc

Falcón

2005

Physica A: Statistical Mechanics and its Applications

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The existence, stability properties, and bifurcation diagrams of localized patterns and hole solutions in one-dimensional extended systems is studied from the point of view of front interactions. An adequate envelope equation is derived from a prototype model that exhibits these particle-type solutions. This equation allow us to obtain an analytical expression for the front interaction, which is in good agreement with numerical simulations. , and nonlinear optics [8,9]. One can understand these localized patterns as patterns extend only over a small portion of the spatial homogeneous systems. From the dynamic point of view, localized patterns in one-dimensional spatial systems are the homoclinic connection for the stationary dynamical system. Recently, from a geometrical point of view, the existence, stability properties, and bifurcation diagrams of localized patterns in one-dimensional extended systems have been studied [10].The aim of this manuscript is to describe how one-dimensional localized patterns and hole solutions arise from front interactions. From a prototype model that exhibits localized patterns and hole solutions, the subcritical Swift-Hohenberg equation, we deduce an adequate equation for the envelope of these particle type solutions. This model has a front solution that connects a stable homogeneous state with an also stable but spatially periodic one. Due to the

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confidence: 99%

Localized patterns and hole solutions in one-dimensional extended systems

Clerc

Falcón

2005

Physica A: Statistical Mechanics and its Applications

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“…Pacs: 05.45.-a, 42.65.Sf, 47.54.+r During the last years localized structures have been observed in different fields, such as domains in magnetic materials [1], chiral bubbles in liquid crystals [2], current filaments in gas discharge experiments [3], spots in chemical reactions [4], pulses [5], kinks [6] and localized 2D states [7] in fluid surface waves, oscillons in granular media [8], isolated states in thermal convection [9,10], solitary waves in nonlinear optics [11,12,13] and cavity solitons in lasers [14]. Localized states are patterns which extend only over a small portion of a spatially extended and homogeneous system [15].…”

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confidence: 99%

Bouncing localized structures in a liquid-crystal light-valve experiment

Clerc

Petrossian²,

Residori³

2005

Phys. Rev. E

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Experimental evidence of bouncing localized structures in a nonlinear optical system is reported. Oscillations in the position of the localized states are described by a consistent amplitude equation, which we call the Lifshitz normal form equation, in analogy with phase transitions. Localized structures are shown to arise close to the Lifshtiz point, where non-variational terms drive the dynamics into complex and oscillatory behaviors. [11,12,13] and cavity solitons in lasers [14]. Localized states are patterns which extend only over a small portion of a spatially extended and homogeneous system [15]. Different mechanisms leading to stable localization have been proposed [16]. Among these, two main classes of localized structures have to be distinguished, namely those localized structures arising as solutions of a quintic Swift-Hohenberg like equation [16] and those that are stabilized by nonvariational terms in the subcritical Ginzburg-Landau equation [17]. The main difference between the two cases is that the first-type localized structures have a characteristic size which is fixed by the pinning mechanism over the underlying pattern or by spatial damped oscillations between homogenous states [16,18], whereas the second-type ones have no intrinsic spatial length, their size being selected by non-variational effects and going to infinity when dissipation goes to zero. In both cases, non-variational effects may lead to dynamical behaviors of localized structures [19]. Variational models based on a generalized Swift-Hohenberg equation have been proposed to describe the appearance of localized structures in nonlinear optics [20]. However, a generalization including non-variational terms is generically expected to apply even in optics, as happens, for instance, in semiconductor laser instabilities [21], giving rise to dynamical behaviors of localized structures, such as propagation and oscillations of their positions [22]. PacsWe report here an experimental evidence of localized structures dynamics in a Liquid-Crystal-Light-Valve (LCLV) with optical feedback. It is already known that, in the simultaneous presence of bistability and pattern forming diffractive feedback, the LCLV system shows localized structures [12,23,24,25]. Recently, rotation of localized structures along concentric rings have been reported in the case of a rotation angle introduced in the feedback loop [26]. Here, we fix a zero rotation angle and we show a new dynamical behavior, the bouncing of two adjacent localized structures, that is not related to imposed boundary conditions but is instead a direct consequence of the non-variational character of the system under study. Theoretically, we show that the LCLV system has several branches of bistability connecting an homogeneous state to a patterned one and we derive an amplitude equation accounting for the appearance of localized structures. This is a one-dimensional model, that we call the Lifshitz normal form equation [22], characterizing the dynamics of localized structures close to each po...

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“…An interesting series of experiments has been performed on such glow discharges with wide lateral extension [2][3][4][5][6][7][8][9][10][11][12][13] where the formed patterns were explored very systematically. The observed structures (stripes, hexagons, spirals, spots, homogeneous oscillations, etc.)…”

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confidence: 99%

“…In comparison to the other systems, the glow discharge system has the advantage of particular convenient experimental handling and time scales [14]. In addition to structures familiar from other physical systems, glow discharges continue to exhibit new structures that might be specific for this system [2][3][4][5][6][7][8][9][10][11][12][13]. We will focus on the experiment in Ref.…”

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confidence: 99%