Direct measurement of superdiffusive energy transport in disordered granular chains

Kim, Eun‐Ho; Martínez, Alejandro J.; Phenisee, Sean E.; Kevrekidis, P. G.; Porter, Mason A.; Yang, Jinkyu

doi:10.1038/s41467-018-03015-3

Cited by 31 publications

(36 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This assertion is supported by recent experimental results on the observation of other linear phenomena (e.g. Anderson-like localization [24] and an analogue of a Ramsauer-Townsend resonance [25]) in granular chains.…”

Section: (B) Recovering a Hofstadter Butterfly From Dynamicssupporting

confidence: 74%

“…This has yielded a wealth of insights about a diverse variety of physical phenomena, including acoustic realizations of many concepts from condensed-matter physics [21]. Most centrally for our discussion, this includes the dynamics of wave transport and localization in disordered nonlinear systems in both theoretical [22,23] and experimental [24] studies. Other phenomena (both theoretical and applied) from condensed-matter and quantum physics that have been realized in granular crystals include an analogue of a Ramsauer-Townsend resonance in the form of a square well [25], switching and rectification [26] and others.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quasiperiodic granular chains and Hofstadter butterflies

Martínez

Porter

Kevrekidis

2018

Phil. Trans. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

We study quasiperiodicity-induced localization of waves in strongly precompressed granular chains. We propose three different set-ups, inspired by the Aubry-André (AA) model, of quasiperiodic chains; and we use these models to compare the effects of on-site and off-site quasiperiodicity in nonlinear lattices. When there is purely on-site quasiperiodicity, which we implement in two different ways, we show for a chain of spherical particles that there is a localization transition (as in the original AA model). However, we observe no localization transition in a chain of cylindrical particles in which we incorporate quasiperiodicity in the distribution of contact angles between adjacent cylinders by making the angle periodicity incommensurate with that of the chain. For each of our three models, we compute the Hofstadter spectrum and the associated Minkowski-Bouligand fractal dimension, and we demonstrate that the fractal dimension decreases as one approaches the localization transition (when it exists). We also show, using the chain of cylinders as an example, how to recover the Hofstadter spectrum from the system dynamics. Finally, in a suite of numerical computations, we demonstrate localization and also that there exist regimes of ballistic, superdiffusive, diffusive and subdiffusive transport. Our models provide a flexible set of systems to study quasiperiodicity-induced analogues of Anderson phenomena in granular chains that one can tune controllably from weakly to strongly nonlinear regimes.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.

show abstract

Section: (B) Recovering a Hofstadter Butterfly From Dynamicssupporting

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Quasiperiodic granular chains and Hofstadter butterflies

Martínez

Porter

Kevrekidis

2018

Phil. Trans. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

show abstract

“…There are numerous exciting directions to pursue in this area. Experimental efforts to verify these predictions are presently underway [102]. A far more detailed understanding exists for lattice systems with on-site nonlinearities [55,105].…”

Section: Traveling Structures In Configurations Other Than Monomer Chmentioning

confidence: 99%

Nonlinear coherent structures in granular crystals

Chong

Porter

Kevrekidis

et al. 2017

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals, a type of nonlinear metamaterial, exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures -which include traveling solitary waves, dispersive shock waves, and discrete breathers -have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential engineering applications that arise from the rich dynamic response of granular crystals.

show abstract

“…1.6.2), such as Dispersion [89,90], Attenuation (Sec. 1.2), Anderson localization [87], etc. However, numerical modeling can be cumbersome if the system size is large (resulting in high computational costs).…”

Section: Modeling For Structure and Dynamic Analysesmentioning

confidence: 99%

“…Moreover, granular materials exhibit solitary wave propagation, another typical nonlinear phenomenon. It manifests under conditions of non-linear contact forces or complete lack of force (sonic vacuum with opening and closing of contacts) between particles of the particulate media [113,135,136,192]; under these nonlinear conditions, propagating localized wave packets are observed, termed as "breathers" [58,74,125,172]; these breathers are also responsible for the destruction of traditional localization [87] as they siphon the energy from the localized energy sites.…”

Section: Nonlinear Phenomenamentioning

confidence: 99%

Towards stochastic and deterministic modeling of mechanical waves in disordered media

Shrivastava¹

View full text Add to dashboard Cite

Samenvatting 159 Acknowledgments 161 Curriculum Vitae 163 • Non-destructive testing of materials for geotechnical investigations (artificial mechanical waves are sent into the material and the received response is studied using piezoelectric devices such as electronic transducers [215] or bender elements [142, 176]). A mechanical wave propagating in a disordered medium has a characteristic signature, whether the media is Earth [4] or Moon [43, 133]. The schematic illustration in Fig. 1.2 depicts the signature in time. The longitudinal mode (Pwave) arrives first, then comes the transverse mode (S-wave) and then arrive the Surface waves. Similar signatures of mechanical waves were also observed in laboratory experiments [76, 77, 93, 148, 214, 215]. However, on zooming over a particular mode of a mechanical wave in a time series profile, the me-1.5 Mesoscopic Wave Phenomena: Diffusion, Coherent Backscattering Effect & Weak Localization The diffusive transport of energy in disordered systems is a well known fact. This fact has been readily exploited to develop a diffusion model for propagation of multiply scattered mechanical waves [4, 67, 68, 147, 148, 204, 212]. However, unusual wave phenomena have been observed at intermediate or higher frequencies such as large variations in acoustic wave speed and suppression of wave propagation due to wave localization (Anderson localization [9], similar to the localization observed in ultracold atoms [23, 32, 157], microwave and light [3, 30, 31, 44, 171, 188, 213]). Amongst many definitions of Anderson localizations, two of them rely on vanishing diffusion and decay of spatially lo-1.6.2 Experimental Investigations Earthquakes are naturally occurring mechanical waves; they have been measured and recorded since a very long time; they have been quintessential in determining the internal structure of Earth, hence, their study is one of the early experimental investigations of mechanical waves in soil [55, 174]. Ultrasound experiments have become instrumental in recent years to study the unique vibrational response of granular materials [102, 103, 104, 147]. For kHz-MHz frequency signals (mechanical waves) that are sent through materials, the received signals are analyzed for identifying the internal structure of Effect of Mass Disorder on Bulk Sound Wave Speed: A Multiscale Spectral Analysis relations for disordered chains; these dispersion relations confirm the decrease in cutoff frequency and thus wave speed with increasing disorder. 1

show abstract

Direct measurement of superdiffusive energy transport in disordered granular chains

Cited by 31 publications

References 30 publications

Quasiperiodic granular chains and Hofstadter butterflies

Quasiperiodic granular chains and Hofstadter butterflies

Nonlinear coherent structures in granular crystals

Towards stochastic and deterministic modeling of mechanical waves in disordered media

Contact Info

Product

Resources

About