Oscillon-type structures and their interaction in a Swift–Hohenberg model

Crawford, Catherine H.; Riecke, Hermann

doi:10.1016/s0167-2789(98)00280-2

Cited by 72 publications

(68 citation statements)

References 26 publications

(44 reference statements)

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“…This often requires modifications to be introduced into the generic models. This approach was taken by Aranson and Tsimring (1998); Aranson et al (1999a); Crawford and Riecke (1999); Tsimring and Aranson (1997); Venkataramani and Ott (1998) in order to describe patterns in a vibrated granular layer. Details of these approaches can be found in Sec.…”

Section: B Phenomenological Modelsmentioning

confidence: 99%

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Patterns and collective behavior in granular media: Theoretical concepts

2006

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Granular materials are ubiquitous in our daily lives. While they have been a subject of intensive engineering research for centuries, in the last decade granular matter attracted significant attention of physicists. Yet despite a major efforts by many groups, the theoretical description of granular systems remains largely a plethora of different, often contradicting concepts and approaches. Authors give an overview of various theoretical models emerged in the physics of granular matter, with the focus on the onset of collective behavior and pattern formation. Their aim is two-fold: to identify general principles common for granular systems and other complex non-equilibrium systems, and to elucidate important distinctions between collective behavior in granular and continuum pattern-forming systems.

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Section: B Phenomenological Modelsmentioning

confidence: 99%

“…Another description of the primary pattern-forming bifurcation was done by Crawford and Riecke (1999) in the framework of the generalized Swift-Hohenberg equation…”

Section: Fig 20mentioning

confidence: 99%

Patterns and collective behavior in granular media: Theoretical concepts

2006

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“…Such models have been widely used to address general questions regarding the dynamics of patterns (e.g. [17,19,12,[21][22][23]). If the patterns arise from a long-wave instability equations of the Swift-Hohenberg type can be derived systematically in a long-wave analysis.…”

Section: Introductionmentioning

confidence: 99%

Instabilities and spatio-temporal chaos in hexagon patterns with rotation

Sain

Riecke

2000

Physica D: Nonlinear Phenomena

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The dynamics of hexagon patterns in rotating systems are investigated within the framework of modified Swift-Hohenberg equations that can be considered as simple models for rotating convection with broken up-down symmetry, e.g. non-Boussinesq Rayleigh-Bénard or Marangoni convection. In the weakly nonlinear regime a linear stability analysis of the hexagons reveals long-and short-wave instabilities, which can be steady or oscillatory. The oscillatory short-wave instabilities can lead to stable hexagon patterns that are periodically modulated in space and time, or to a state of spatio-temporal chaos with a Fourier spectrum that precesses on average in time. The chaotic state can exhibit bistability with the steady hexagon pattern. There exist regimes in which the steady hexagon patterns are unstable at all wavenumbers.

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“…In addition, the combined effect of temporal forcing and dispersion has been investigated. With the inclusion of weak dispersion, the interaction between fronts can be described qualitatively by a single equation combining the two interaction terms (25). It was found that in the dispersive regime forcing can lead to the creation of new pulses or the destruction of pulses depending on system parameters.…”

Section: Discussionmentioning

confidence: 99%

Tunable front interaction and localization of periodically forced waves

Crawford

Riecke

2002

Phys. Rev. E

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In systems that exhibit a bistability between nonlinear traveling waves and the basic state, pairs of fronts connecting these two states can form localized wave pulses whose stability depends on the interaction between the fronts. We investigate wave pulses within the framework of coupled GinzburgLandau equations describing the traveling-wave amplitudes. We find that the introduction of resonant temporal forcing results in a new, tunable mechanism for stabilizing such wave pulses. In contrast to other localization mechanisms the temporal forcing can achieve localization by a repulsive as well as by an attractive interaction between the fronts. Systems for which the results are expected to be relevant include binary-mixture convection and electroconvection in nematic liquid crystals.

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Oscillon-type structures and their interaction in a Swift–Hohenberg model

Cited by 72 publications

References 26 publications

Patterns and collective behavior in granular media: Theoretical concepts

Patterns and collective behavior in granular media: Theoretical concepts

Instabilities and spatio-temporal chaos in hexagon patterns with rotation

Tunable front interaction and localization of periodically forced waves

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