Long-range correlations in pinned athermal networks

Das, Debankur; Acharya, Pappu; Ramola, Kabir

doi:10.1103/physreve.104.014503

Cited by 8 publications

(11 citation statements)

References 43 publications

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“…We use the theory developed recently in Refs. [26,27,29], which allows an exact determination of the perturbed configuration as a response to the disorder. This provides a one to one map between a given realization of the quenched disorder {ζ i } and the position of the system in the configuration space of particle positions.…”

Section: Linearized Trajectories In Configuration Spacementioning

confidence: 99%

“…We next detail a procedure to obtain the exact displacement fields generated in response to the introduction of small disorder in particle sizes, as developed in Refs. [26,27,29]. As the starting and ending configurations both satisfy the conditions of mechanical equilibrium, we have j f x ij = 0, and j f y ij = 0, for each particle at site i ≡ r. Here f x ij , f y ij are the components of the inter-particle contact force between particles i and j.…”

Section: A Linearized Displacement Fieldsmentioning

confidence: 99%

“…( 1) is non-linear in the displacement fields {δx, δy}. This non-linearity can be circumvented with a systematic perturbation expansion about the crystalline ordered state, to linear order as well as higher orders [26,27,29]. With the introduction of disorder in the particle sizes, the positions of the particles deviate from their crystalline values { r…”

Section: A Linearized Displacement Fieldsmentioning

confidence: 99%

“…(Inset) Comparison of the numerical results obtained from Monte-Carlo simulations of the individual contact breaking conditions and the theoretical predictions in Eqs. ( 27), ( 28) and (29). The results displayed are for a system size N = 16.…”

Section: A Local Contact Breaking Distributionsmentioning

confidence: 99%

“…In this work, we provide a step in this direction, making predictions for the distribution of first plastic drops in response to external strain for a near-crystalline athermal system. We consider an interesting example of a jammed near-crystalline system where several exact predictions of correlations and response can be made [26][27][28][29]. This system has allowed for the exact computation of many quantities of interest such as displacement fields in response to defects, interaction energies between defects [30], as well as correlation functions [28], starting from microscopic interactions.…”

Section: Introductionmentioning

confidence: 99%

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First contact breaking distributions in strained disordered crystals

Maharana¹,

Nampoothiri²,

Ramola³

2022

Preprint

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We derive exact probability distributions for the strain ( ) at which the first plastic drop event occurs in uniformly strained disordered crystals, with quenched disorder introduced through polydispersity in particle sizes. We identify the first plastic drop in the system with the first contact breaking event and characterize these events numerically as well as theoretically. Our theoretical results are corroborated with numerical simulations of quasistatic volumetric strain applied to disordered near-crystalline configurations of athermal soft particles. We develop a general technique to determine the distribution of strains at which the first contact breaking events occur, through an exact mapping between the cumulative distribution of such events and the volume of a convex polytope whose dimension is determined by the number of defects N d in the system. An exact numerical computation of this polytope volume for systems with small numbers of defects displays a remarkable match with the distribution of strains generated through direct numerical simulations. Finally, we derive the distribution of strains at which the first plastic failure occurs, assuming that individual contact breaking events are uncorrelated, which accurately reproduces distributions obtained from direct numerical simulations.

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Section: Linearized Trajectories In Configuration Spacementioning

confidence: 99%

Section: A Linearized Displacement Fieldsmentioning

confidence: 99%

Section: A Linearized Displacement Fieldsmentioning

confidence: 99%

Section: A Local Contact Breaking Distributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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First contact breaking distributions in strained disordered crystals

Maharana¹,

Nampoothiri²,

Ramola³

2022

Preprint

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Displacement Correlations in Disordered Athermal Networks

2022

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Athermal fluctuations in three dimensional disordered crystals

Maharana¹

2022

J. Stat. Mech.

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We study jammed near-crystalline materials composed of frictionless spheres in three dimensions. We analyse the fluctuations in positions and forces produced by small polydispersity in particle sizes. We generalize a recently developed perturbation expansion about the crystalline ordered state to three dimensional systems. This allows us to exactly predict changes in positions and forces as a response to the changes in particle radii. We show that fluctuations in forces orthogonal to the lattice directions are highly constrained as compared to the fluctuations along lattice directions. Additionally, we analyse the correlations in the displacement fields produced by the microscopic disorder, which we show displays long ranged behaviour.

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Long-range correlations in pinned athermal networks

Cited by 8 publications

References 43 publications

First contact breaking distributions in strained disordered crystals

First contact breaking distributions in strained disordered crystals

Displacement Correlations in Disordered Athermal Networks

Athermal fluctuations in three dimensional disordered crystals

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