Nonlocal Elasticity near Jamming in Frictionless Soft Spheres

Baumgarten, Karsten; Vågberg, Daniel; Tighe, Brian P.

doi:10.1103/physrevlett.118.098001

Cited by 25 publications

(40 citation statements)

References 53 publications

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“…We first look at the continuum limit of phonon transport, which is measured with respect to the wavelength at Ω = ω ex0 , λ α0 ≡ 2πc α0 /ω ex0 : [47] studied the wavelengths at Ω = ω * , which follow the same scaling laws as those of λ T 0 and λ L0 . λ T 0 and λ L0 are naturally expected to correspond to the continuum limit of elastic response that has been studied in previous works [71,[85][86][87]. In particular, Ref.…”

Section: F Length Scales In the Amorphous Solidmentioning

confidence: 75%

Phonon transport and vibrational excitations in amorphous solids

2018

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One of the long-standing issues concerning the thermal properties of amorphous solids is the complex pattern of phonon transport. Recent advances in experiments and computer simulations have indicated a crossover from Rayleigh scattering to Ω 2 law (where Ω is the propagation frequency). A number of theories have been proposed, yet critical tests are missing and the validity of these theories is unclear. In particular, the precise location of the crossover frequency remains controversial, and more critically, even the validity of the Rayleigh scattering itself has been seriously questioned. To settle these issues, we focus on a model amorphous solid, whose vibrational eigenmodes were recently clarified over a wide frequency regime: a mixture of phonon modes and soft localized modes in the continuum limit and disordered and extended modes in the boson peak regime. The present work demonstrates that Rayleigh scattering occurs in the continuum limit and Ω 2 damping occurs in the boson peak regime, and these behaviors are therefore linked to the underlying eigenmodes in the corresponding frequency regimes. Our results unambiguously determine the crossover frequency. Furthermore, we establish characteristic scaling laws of phonon transport near the jamming transition, which are consistent with the prediction of the mean-field theory at higher frequencies but inconsistent in the low-frequency, Rayleigh scattering regime. Our results therefore reveal crucial issues to be solved with regard to the current theory.

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Section: F Length Scales In the Amorphous Solidmentioning

confidence: 75%

Phonon transport and vibrational excitations in amorphous solids

2018

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“…As commonly practiced in the field of unjamming [6,21,32], we calculated some of the observables in a shadow system for which the forces − ∂ϕ ∂r were set to zero. The shadow systems can be considered as relaxed elastic spring networks (i.e., in which all springs reside at their respective rest lengths) whose stiffnesses are given by the original pairwise potential stiffnesses…”

Section: E Observablesmentioning

confidence: 99%

“…This is typically achieved in soft spheres or disks by decompressing the system such that their packing fraction φ is reduced towards the random close packing fraction φ c or in elastic networks by removing interactions from the network. It is now well established that approaching the unjamming point is accompanied by the emergence of an excess of low-frequency vibrational modes [1,2], diverging correlation [3] and response [4][5][6] length scales, and the vanishing of elastic moduli [7]. Several claims have been made that the unjamming constitutes a nonequilibrium phase transition between disordered-solid and fluid phases of matter [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Unjamming in models with analytic pairwise potentials

Kooij

Lerner

2017

Phys. Rev. E

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Canonical models for studying the unjamming scenario in systems of soft repulsive particles assume pairwise potentials with a sharp cutoff in the interaction range. The sharp cutoff renders the potential nonanalytic but makes it possible to describe many properties of the solid in terms of the coordination number z, which has an unambiguous definition in these cases. Pairwise potentials without a sharp cutoff in the interaction range have not been studied in this context, but should in fact be considered to understand the relevance of the unjamming phenomenology in systems where such a cutoff is not present. In this work we explore two systems with such interactions: an inverse power law and an exponentially decaying pairwise potential, with the control parameters being the exponent (of the inverse power law) for the former and the number density for the latter. Both systems are shown to exhibit the characteristic features of the unjamming transition, among which are the vanishing of the shear-to-bulk modulus ratio and the emergence of an excess of low-frequency vibrational modes. We establish a relation between the pressure-to-bulk modulus ratio and the distance to unjamming in each of our model systems. This allows us to predict the dependence of other key observables on the distance to unjamming. Our results provide the means for a quantitative estimation of the proximity of generic glass-forming models to the unjamming transition in the absence of a clear-cut definition of the coordination number and highlight the general irrelevance of nonaffine contributions to the bulk modulus.

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“…Such "temperature" is actually thought of as a quantification of the mechanical noise induced by the flow itself [19][20][21] and triggers activated hopping through the energy landscape of the system. Moreover, it has been clearly demonstrated both experimentally [23][24][25] and numerically [26] that soft glasses exhibit a nontrivial size dependence. This may give rise to "nonlocal" rheological effects [7,8] parameterized by a cooperativity length [6][7][8]27] estimating the typical size of the region involved in plastic rearrangements of the constituents following local elastic deformations.…”

Section: Introductionmentioning

confidence: 93%

“…1). A very similar setting has been used in previous experimental [26] and numerical [52,53] works. The choice of a fully periodic setup is initially taken in order to avoid possible wall effects and dependence on boundary conditions, which may alter the rheological response (4)] at each droplet; the region where a plastic rearrangement occurs (i.e., an edge-flip in the triangulation [59]) is highlighted with thicker lines.…”

Section: Modelmentioning

confidence: 99%

Metastability at the Yield-Stress Transition in Soft Glasses

2018

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We study the solid-to-liquid transition in a two-dimensional fully periodic soft-glassy model with an imposed spatially heterogeneous stress. The model we consider consists of droplets of a dispersed phase jammed together in a continuous phase. When the peak value of the stress gets close to the yield stress of the material, we find that the whole system intermittently tunnels to a metastable "fluidized" state which relaxes back to a metastable "solid" state by means of an elastic-wave dissipation. This macroscopic scenario is studied through the microscopic displacement field of the droplets, whose time-statistics displays a remarkable bimodality. Metastability is rooted in the existence, in a given stress range, of two distinct stable rheological branches as well as long-range correlations (e.g., large dynamic heterogeneity) developed in the system. Finally, we show that a similar behavior holds for a pressure-driven flow, thus suggesting possible experimental tests.

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Nonlocal Elasticity near Jamming in Frictionless Soft Spheres

Cited by 25 publications

References 53 publications

Phonon transport and vibrational excitations in amorphous solids

Phonon transport and vibrational excitations in amorphous solids

Unjamming in models with analytic pairwise potentials

Metastability at the Yield-Stress Transition in Soft Glasses

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