Traveling waves and spatial variation in the convection of a binary mixture

Heinrichs, Richard; Ahlers, Guenter; Cannell, David S.

doi:10.1103/physreva.35.2761

Cited by 209 publications

(61 citation statements)

References 14 publications

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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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confidence: 99%

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

Clerc

Petrossian²,

Residori³

2005

Phys. Rev. E

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“…During the last two decades, spatial pattern formation has been largely studied, leading to the identification of various types of spatiotemporal instabilities and symmetry selection processes in the general frameworks of dynamical systems and bifurcation theory [2,3]. Localized structures, that is, patterns extended over a restricted spatial domain, have received, in particular, a large interest, and from the early observations of magnetic domains in ferromagnetic materials [4], localized states have been successively observed in such different systems as liquid crystals [5], plasmas [6], chemical reactions [7], fluid surface waves [8], granular media [9,10], and thermal convection [11,12]. In nonlinear optics localized structures were first predicted as solitary waves in bistable optical cavities [13], and successively also explained in terms of diffractive auto-solitons [14].…”

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confidence: 99%

Localized States in Bi‐Pattern Systems

Bortolozzo

Clerc

Haudin

et al. 2009

International Journal of Optics

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We present a unifying description of localized states observed in systems with coexistence of two spatially periodic states, called bi-pattern systems. Localized states are pinned over an underlying lattice that is either a self-organized pattern spontaneously generated by the system itself, or a periodic grid created by a spatial forcing. We show that localized states are generic and require only the coexistence of two spatially periodic states. Experimentally, these states have been observed in a nonlinear optical system. At the onset of the spatial bifurcation, a forced one-dimensional amplitude equation is derived for the critical modes, which accounts for the appearance of localized states. By numerical simulations, we show that localized structures persist on twodimensional systems and exhibit different shapes depending on the symmetry of the supporting patterns.

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“…During the last years emerging localized structures in dissipative systems 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], localized 2D states in fluid surface waves [5], oscillons in granular media [6], isolated states in thermal convection [7], solitary waves in nonlinear optics [8], just to mention a few. In one-dimensional systems, localized patterns can be described as homoclinic orbits passing close to a spatially oscillatory state and converging to an homogeneous state [9,10], whereas domains are seen as heteroclinic trajectories joining the fixed points of the corresponding dynamical system [11].…”

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Localized States in Bistable Pattern-Forming Systems

Bortolozzo

Clerc²,

Falcón³

et al. 2006

Phys. Rev. Lett.

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We present an unifying description close to a spatial bifurcation of localized states, appearing as large amplitude peaks nucleating over a pattern of lower amplitude. Localized states are pinned over a lattice spontaneously generated by the system itself. We show that the phenomenon is generic and requires only the coexistence of two spatially periodic states. At the onset of the spatial bifurcation, a forced amplitude equation is derived for the critical modes, which accounts for the appearance of localized peaks. In one-dimensional systems, localized patterns can be described as homoclinic orbits passing close to a spatially oscillatory state and converging to an homogeneous state [9,10], whereas domains are seen as heteroclinic trajectories joining the fixed points of the corresponding dynamical system [11]. Recently, in a nematic liquid crystal light valve with optical feedback it has been found experimentally a different type of localized states, appearing as a large amplitude peaks nucleating over a lower amplitude pattern and therefore called localized peaks [12]. Similar observations have been reported in a Newtonian fluid when non linear surface waves are parametrically excited with two frequencies [13] and in numerical simulations of an atomic vapor with optical feedback [14]. Recently, longitudinal modes with localized peaks over a spatially modulated background have been shown in numerical simulations of Maxwell-Bloch equations for a semiconductor laser [15].All these different types of localized states appear over a patterned background and thus constitute a different class of structures with respect to the ones appearing over an uniform background. The aim of this manuscript is to show that localized peaks are a generic class of localized states, appearing whenever a pattern forming system exhibits coexistence of two spatially periodic states. The mechanisms that originate this circumstances are more than a few, for instance, one can consider a multi-stable system, which shows two consecutive spatial bifurcations to different states when one parameter is changed. There is a large number of physical systems that display this kind of behavior, therefore there is a vast number of possible models. In order to derive an unifying and simple description of localized peaks, we develop a theoretical model for one-dimensional spatially extended systems close to a spatial bifurcation. The model, which shows coexistence between different patterns and stable front solutions between them, is based on an amplitude equation that includes a spatial parametric forcing. This extension with respect to conventional amplitude equations, allows to describe localized patterns and to account for the main properties of these solutions. The model includes the interaction of the slowly varying envelope with the small scale of the underlying pattern solution [16], well-known as the non-adiabatic effect [17,18].

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Traveling waves and spatial variation in the convection of a binary mixture

Cited by 209 publications

References 14 publications

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

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

Localized States in Bi‐Pattern Systems

Localized States in Bistable Pattern-Forming Systems

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