Spatial asymmetries of resonant oscillations in periodically forced heterogeneous media

Edri, Yuval; Meron, Ehud; Yochelis, Arik

doi:10.1016/j.physd.2020.132501

Cited by 9 publications

(6 citation statements)

References 62 publications

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“…We believe this is the reason why such drift has not been observed in previous studies, which have been mainly focused on homogeneously driven systems. The role of heterogeneities is increasingly becoming an important factor in many nonlinear systems in different areas of physics [13,[26][27][28]. Our findings validate the use of non-local terms, such as those naturally appearing in Eq.…”

Section: Discussionsupporting

confidence: 74%

Drift instabilities in localised Faraday patterns

Marín¹,

Ávila²,

Coulibaly³

et al. 2021

Preprint

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Nature is intrinsically heterogeneous, and remarkable phenomena can only be observed in the presence of intrinsically nonlinear heterogeneities. Spontaneous pattern formation in nature has fascinated humankind for centuries, and the understanding of the underlying symmetry-breaking instabilities has been of longstanding scientific interest. In this article, we provide theoretical and experimental evidence that heterogeneities can generate convection (drift instabilities) in the amplitude of localised patterns. We derive a minimal theoretical model describing the growth of localised Faraday patterns under heterogeneous parametric drive, unveiling the presence of symmetry-breaking nonlinear gradients. The model reveals new dynamics in the phase of the underlying patterns, exhibiting convective instabilities when the system crosses a secondary bifurcation point. We discuss the impact of our results in the understanding of convective instabilities induced by heterogeneities in generic nonlinear extended systems far from equilibrium.

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Section: Discussionsupporting

confidence: 74%

Drift instabilities in localised Faraday patterns

Marín¹,

Ávila²,

Coulibaly³

et al. 2021

Preprint

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“…However, this minimum

, i.e., the weakest physical coupling, signifies the strongest mode coupling [ 15 , 17 ]. Generally speaking, large

leads to the synchronization and small

leads to the (mode) localization [ 58 ].…”

Section: Resultsmentioning

confidence: 99%

Mode Localization and Eigenfrequency Curve Veerings of Two Overhanged Beams

2021

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Overhang provides a simple but effective way of coupling (sub)structures, which has been widely adopted in the applications of optomechanics, electromechanics, mass sensing resonators, etc. Despite its simplicity, an overhanging structure demonstrates rich and complex dynamics such as mode splitting, localization and eigenfrequency veering. When an eigenfrequency veering occurs, two eigenfrequencies are very close to each other, and the error associated with the numerical discretization procedure can lead to wrong and unphysical computational results. A method of computing the eigenfrequency of two overhanging beams, which involves no numerical discretization procedure, is analytically derived. Based on the method, the mode localization and eigenfrequency veering of the overhanging beams are systematically studied and their variation patterns are summarized. The effects of the overhang geometry and beam mechanical properties on the eigenfrequency veering are also identified.

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“…We believe this is the reason why such drift has not been reported in previous studies, which have been focused on uniformly accelerated systems. Recently, the role of spatial nonuniformity has often been identified as an important factor in nonlinear systems 21,[44][45][46][47] . Our theoretical insights on the underlying instabilities of localised patterns may be relevant in understanding other wandering localised structures observed in one and two-dimensional heterogeneous nonequilibrium systems.…”

Section: Discussionmentioning

confidence: 99%

Drifting Faraday patterns under localised driving

et al. 2023

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Physical systems undergoing spontaneous pattern formation are governed by intrinsic length scales that may compete with extrinsic ones, resulting in exceptional spatiotemporal behaviour. In this work, we report experimental and theoretical evidence that spatial nonuniformity sets Faraday-wave patterns in motion, which are noticeable in the zigzag and drift dynamics exhibited by their wave crests. We provide a minimal theoretical model that succeeds in characterising the growth of localised patterns under nonuniform parametric driving. Furthermore, the derivation accounts for symmetry-breaking nonlinear gradients that we show are the source of the drift mechanism, which comes into play right after the system has crossed a secondary bifurcation point. Numerical solutions of the governing equations match our experimental findings and theoretical predictions. Our results advance the understanding of pattern behaviour induced by nonuniformity in generic nonlinear extended systems far from equilibrium.

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Spatial asymmetries of resonant oscillations in periodically forced heterogeneous media

Cited by 9 publications

References 62 publications

Drift instabilities in localised Faraday patterns

Drift instabilities in localised Faraday patterns

Mode Localization and Eigenfrequency Curve Veerings of Two Overhanged Beams

Drifting Faraday patterns under localised driving

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