Quantifying force networks in particulate systems

Kramar, Miroslav; Goullet, Arnaud; Kondic, Lou; Mischaikow, Konstantin

doi:10.1016/j.physd.2014.05.009

Cited by 68 publications

(80 citation statements)

References 26 publications

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“…However, TDA has been used to understand geometric structures in many applications, such as: force networks in particulate systems [25,23]; protein compressibility [16]; fullerene molecules [34]; amorphous solids [19]; the dynamics of flow patterns [26]; phase transitions [13]; sphere packing and colloids [30]; brain arteries [3]; craze formation in glassy polymers [20]; and pores in rocks [21].…”

Section: Introductionmentioning

confidence: 99%

Persistent homology detects curvature

et al. 2020

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In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals represent the "topological signal" and the short intervals represent "noise". We give evidence to dispute this thesis, showing that the short intervals encode geometric information. Specifically, we prove that persistent homology detects the curvature of disks from which points have been sampled. We describe a general computational framework for solving inverse problems using the average persistence landscape, a continuous mapping from metric spaces with a probability measure to a Hilbert space. In the present application, the average persistence landscapes of points sampled from disks of constant curvature results in a path in this Hilbert space which may be learned using standard tools from statistical and machine learning.

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Section: Introductionmentioning

confidence: 99%

Persistent homology detects curvature

et al. 2020

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“…To gain better insight to the lubricated-to-frictional rheology transition, we apply tools of topology, with a focus on the network theoretical methodology of persistent homology, which has previously been applied to the closely related question of jamming in dry granular systems [12][13][14]. Persistent homology provides precisely defined and quantitative measures of the global interaction network, which is built on top of the contact network, as discussed in Section II B.…”

Section: Introductionmentioning

confidence: 99%

Interaction network analysis in shear thickening suspensions

et al. 2020

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Dense, stabilized, frictional particulate suspensions in a viscous liquid undergo increasingly strong continuous shear thickening (CST) as the solid packing fraction, φ, increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for even higher packing fractions. Recent studies have related shear thickening to a transition from mostly lubricated to predominantly frictional contacts with the increase in stress. The rheology and networks of frictional forces from two and three dimensional simulations of shear-thickening suspensions are studied. These are analyzed using measures of the topology of the network, including tools of persistent homology. We observe that at low stress the frictional interaction networks are predominantly quasi-linear along the compression axis. With an increase in stress, the force networks become more isotropic, forming loops in addition to chain-like structures. The topological measures of Betti numbers and total persistence provide a compact means of describing the mean properties of the frictional force networks, and provide a key link between macroscopic rheology and the microscopic interactions. A total persistence measure describing the significance of loops in the force network structure, as a function of stress and packing fraction, shows behavior similar to that of relative viscosity, and displays a scaling law near the jamming fraction for both dimensionalities simulated. arXiv:1903.08493v1 [cond-mat.soft]

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“…Our future work will consider in detail other measures quantifying the force networks such as total persistence and related measures that we have considered in our previous works [14,17,34] to provide even better understanding of the properties of force networks and their connection to macroscopic response of particulate-based systems.…”

Section: Discussionmentioning

confidence: 99%

Characterizing granular networks using topological metrics

et al. 2018

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We carry out a direct comparison of experimental and numerical realizations of the exact same granular system as it undergoes shear jamming. We adjust the numerical methods used to optimally represent the experimental settings and outcomes up to microscopic contact force dynamics. Measures presented here range from microscopic through mesoscopic to systemwide characteristics of the system. Topological properties of the mesoscopic force networks provide a key link between microscales and macroscales. We report two main findings: (1) The number of particles in the packing that have at least two contacts is a good predictor for the mechanical state of the system, regardless of strain history and packing density. All measures explored in both experiments and numerics, including stress-tensor-derived measures and contact numbers depend in a universal manner on the fraction of nonrattler particles, f_{NR}. (2) The force network topology also tends to show this universality, yet the shape of the master curve depends much more on the details of the numerical simulations. In particular we show that adding force noise to the numerical data set can significantly alter the topological features in the data. We conclude that both f_{NR} and topological metrics are useful measures to consider when quantifying the state of a granular system.

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Quantifying force networks in particulate systems

Cited by 68 publications

References 26 publications

Persistent homology detects curvature

Persistent homology detects curvature

Interaction network analysis in shear thickening suspensions

Characterizing granular networks using topological metrics

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