Mean field theory of jamming of nonspherical particles

Ikeda, Hisako; Urbani, Pierfrancesco; Zamponi, Francesco

doi:10.1088/1751-8121/ab3079

Cited by 16 publications

(22 citation statements)

References 64 publications

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“…For small n, z J increases upon increasing μ; see the data for n ¼ 10. Since μ=n represents the deviation from disks, this behavior is qualitatively similar to that observed in convex-shaped particles [5,[32][33][34][35][36][37][38]. Contrarily, for large n, z J decreases with μ [41].…”

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confidence: 53%

“…In this work, we construct a new model to take into account the effect of surface roughness by means of a perturbative expansion around the reference case of spherical disks. By performing numerical simulations, we show that, for a smooth surface, z J of the model increases upon increasing asphericity, suggesting that a small deviation from perfect disks plays a similar role to the asphericity of convexshaped particles [5,[32][33][34][35][36][37][38]. Contrarily, for a rough surface, z J decreases upon increasing asphericity, as for frictional particles.…”

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confidence: 82%

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Jamming with Tunable Roughness

et al. 2020

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We introduce a new model to study the effect of surface roughness on the jamming transition. By performing numerical simulations, we show that for a smooth surface, the jamming transition density and the contact number at the transition point both increase upon increasing asphericity, as for ellipsoids and spherocylinders. Conversely, for a rough surface, both quantities decrease, in quantitative agreement with the behavior of frictional particles. Furthermore, in the limit corresponding to the Coulomb friction law, the model satisfies a generalized isostaticity criterion proposed in previous studies. We introduce a counting argument that justifies this criterion and interprets it geometrically. Finally, we propose a simple theory to predict the contact number at finite friction from the knowledge of the force distribution in the infinite friction limit.

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confidence: 53%

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confidence: 82%

Jamming with Tunable Roughness

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“…Note that the same equation of eq. (42) holds exactly in the case of mean-field model of nonspherical particles [5,9] and the spherical particles slightly above the jamming transition point, where δz ∼ p 1/2 [23]. For the force distribution P (f ), one can apply a similar argument, and it has been shown that…”

Section: General Scaling Form Of the Distribution Functions Near Isosmentioning

confidence: 85%

“…Using the previous theoretical analysis [5,9], one can interpret the above results as follows: (i) The lowest band corresponds to the zero modes stabilized by the positive part of the pre-stress. As the pre-stress scales as k R ∼ p∆, eq.…”

Section: Characteristic Frequenciesmentioning

confidence: 88%

Infinitesimal asphericity changes the universality of the jamming transition

2020

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The jamming transition of nonspherical particles is fundamentally different from the spherical case. Systems of nonspherical particles are hypostatic at the jamming point, while isostaticity is ensured in the case of the jamming of spherical particles. This structural difference implies that critical exponents related to the contact number and the vibrational density of states are affected in the presence of an asphericity. Moreover, while the force and gap distributions of isostatic jamming present a power-law behavior, even an infinitesimal asphericity is enough to smooth out these singularities. In a recent work [PNAS 115(46), 11736], we have used a combination of marginal stability arguments and the replica method to explain these observations. We argued that systems with internal degrees of freedom, like the rotations in the ellipsoids or spherocylinders or the variation of the radii in the case of the breathing particles fall in the same universality class. In this paper we review comprehensively the results about the jamming of nonspherical particles, use theoretical arguments to derive the critical exponents of the contact number, shear modulus, and the characteristic frequencies of the density of states which can be applied for any model having an extra degree of freedom in addition to translational degrees of freedom. Moreover, we present additional numerical data supporting the theoretical results which were not shown in the previous work.

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“…Then one wants to minimize the volume of the phase space of the vector x, for example by minimizing |x| 2 , such that there is a configuration that satisfies all constraints. This problem is related to the packing problem and has been analyzed in [2][3][4][5][6][7][8][9], see also [10] for a review with the corresponding connection to deep learning.…”

Section: Introductionmentioning

confidence: 99%

High dimensional optimization under non-convex excluded volume constraints

Sclocchi,

Urbani

2021

Preprint

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We consider high dimensional random optimization problems where the dynamical variables are subjected to non-convex excluded volume constraints. We focus on the case in which the cost function is a simple quadratic cost and the excluded volume constraints are modeled by a perceptron constraint satisfaction problem. We show that depending on the density of constraints, one can have different situations. If the number of constraints is small, one typically has a phase where the ground state of the cost function is unique and sits on the boundary of the island of configurations allowed by the constraints. In this case there is an hypostatic number of constraints that are marginally satisfied. If the number of constraints is increased one enters in a glassy phase where the cost function has many local minima sitting again on the boundary of the regions of allowed configurations. At the phase transition point the total number of constraints that are marginally satisfied becomes equal to the number of degrees of freedom in the problem and therefore we say that these minima are isostatic. We conjecture that increasing further the constraints the system stays isostatic up to the point where the volume of available phase space shrinks to zero. We derive our results using the replica method and we also analyze a dynamical algorithm, the Karush-Kuhn-Tucker algorithm, through dynamical mean field theory and we show how to recover the results of the replica approach in the replica symmetric phase.

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Mean field theory of jamming of nonspherical particles

Cited by 16 publications

References 64 publications

Jamming with Tunable Roughness

Jamming with Tunable Roughness

Infinitesimal asphericity changes the universality of the jamming transition

High dimensional optimization under non-convex excluded volume constraints

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