Highly nonlinear solitary waves in chains of hollow spherical particles

Ngo, Tuan; Griffiths, Stéphane; Khatri, Devvrath; Daraio, Chiara

doi:10.1007/s10035-012-0377-5

Cited by 28 publications

(20 citation statements)

References 31 publications

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“…A nonlinear index n = 1.98 outputs 12 3 La  , consistent with the simulation result in Figure 5 where waves are localized within a width of 4 consecutive GNSs as propagation. In Figure 5, the particle velocities of all GNSs are extracted at three instants, i.e.…”

Section: Resultssupporting

confidence: 86%

Mechanical wave propagation within nanogold granular crystals

Zheng

2017

Extreme Mechanics Letters

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We computationally investigate the wave propagation characteristics of nanoscopic granular crystals composed of one-dimensionally arrayed gold nanoparticles using molecular dynamics simulation. We examine two basic configurations, i.e. homogeneous lattices and diatomic lattices with mass-mismatch.We discover that homogeneous lattices of gold nanospheres support weakly dissipative and highly localized solitary wave at 300 K, while diatomic lattices have a good tuning ability of transmittance and wave speed. We establish a validated nonlinear spring contact model with the consideration of complex interactions between gold nanospheres which reveals the physical nature of wave behaviors at nanoscale. This work sheds light on the application of nanogold as a novel mechanical wave tuner, qualitatively and fundamentally different from its counterpart granular materials at meso-and macroscale.

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Section: Resultssupporting

confidence: 86%

Mechanical wave propagation within nanogold granular crystals

Zheng

2017

Extreme Mechanics Letters

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“…This limiting procedure is a first step towards the rigorous justification of previous formal continuum approximations [17,26,13]. Moreover, it is interesting to note that the case p ≈ 2 is physically sound in the context of granular chain models [16,27,19].…”

Section: Theorem 1 the Stationary Dps Equationmentioning

confidence: 94%

Breather Solutions of the Discrete p-Schrödinger Equation

James

Starosvetsky

2013

Nonlinear Systems and Complexity

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Summary. We consider the discrete p-Schrödinger (DpS) equation, which approximates small amplitude oscillations in chains of oscillators with fully-nonlinear nearest-neighbors interactions of order α = p − 1 > 1. Using a mapping approach, we prove the existence of breather solutions of the DpS equation with even-or oddparity reflectional symmetries. We derive in addition analytical approximations for the breather profiles and the corresponding intersecting stable and unstable manifolds, valid on a whole range of nonlinearity orders α. In the limit of weak nonlinearity (α → 1 + ), we introduce a continuum limit connecting the stationary DpS and logarithmic nonlinear Schrödinger equations. In this limit, breathers correspond asymptotically to Gaussian homoclinic solutions. We numerically analyze the stability properties of breather solutions depending on their even-or odd-parity symmetry. A perturbation of an unstable breather generally results in a translational motion (traveling breather) when α is close to unity, whereas pinning becomes predominant for larger values of α.

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“…This may make it possible for us to observe nonlinear wave propagation through hollow spherical shells, as shown in Ref. 24.…”

Section: Discussionmentioning

confidence: 95%

Porogranular materials composed of elastic Helmholtz resonators for acoustic wave absorption

Griffiths

Nennig

Job

2017

The Journal of the Acoustical Society of America

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We present a theoretical and experimental study of the acoustic absorption of granular porous media made of non-cohesive piles of spherical shells. These shells are either rigid or elastic, possibly drilled with a neck (Helmholtz resonators), and either porous or impervious. A description is given of acoustic propagation through these media using the effective medium models proposed by Johnson (rigid particles) and Boutin (rigid Helmholtz resonators), which we extend to the configurations studied in this work. A solution is given for the local equation of elasticity of a shell coupled to the viscous flow of air through the neck and the micropores. The models and our simulations are compared to absorption spectra measured in reflection in an impedance tube. The effective medium models and our measurements show excellent agreement for configurations made of rigid particles and rigid Helmholtz resonators that induce an additional peak of absorption at low frequency. A shift of the Helmholtz resonance toward low frequencies, due to the softness of the shells is revealed by our experiments for elastic shells made of soft elastomer and is well reproduced by our simulations. We show that microporous shells enhance and broaden acoustic absorption compared to stiff or elastic resonators.

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Highly nonlinear solitary waves in chains of hollow spherical particles

Cited by 28 publications

References 31 publications

Mechanical wave propagation within nanogold granular crystals

Mechanical wave propagation within nanogold granular crystals

Breather Solutions of the Discrete p-Schrödinger Equation

Porogranular materials composed of elastic Helmholtz resonators for acoustic wave absorption

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