Topological analysis of tapped granular media using persistent homology

Ardanza-Trevijano, Sergio; Zuriguel, Iker; Arévalo, Roberto; Maza, Diego

doi:10.1103/physreve.89.052212

Cited by 49 publications

(39 citation statements)

References 45 publications

(55 reference statements)

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“…We simulated a quasi-2D cell containing a number N of spherical particles of diameter d and mass m in a gravity field of acceleration g. We choose a quasi-2D cell (1.1d in thickness) to obtain a realistic representation of usual experimental devices, where direct imaging can be used [7,18]. We use a model for soft dissipative spheres as described in Refs.…”

Section: Numerical Modelmentioning

confidence: 99%

Relevance of system size to the steady-state properties of tapped granular systems

2015

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We investigate the steady-state packing fraction φ and force moment tensor of quasi-two-dimensional granular columns subjected to tapping. Systems of different height h and width L are considered. We find that φ and , which describe the macroscopic state of the system, are insensitive to L for L > 50d (with d the grain diameter). However, results for granular columns of different heights cannot be conciliated. This suggests that comparison between results of different laboratories on this type of experiments can be done only for systems of same height. We show that a parameter ε = 1 + (Aω) 2 /(2gh), with A and ω the amplitude and frequency of the tap and g the acceleration of gravity, can be defined to characterize the tap intensity. This parameter is based on the effective flight of the granular bed, which takes into account the h dependency. When φ is plotted as a function of ε, the data collapses for systems of different h. However, this parameter alone is unable to determine the steady state to be reached since different can be observed for a given ε if different column heights are considered.

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Section: Numerical Modelmentioning

confidence: 99%

Relevance of system size to the steady-state properties of tapped granular systems

2015

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“…Real-space methods such as those discussed here can also be used in tandem with new developments in coherent x-ray diffractive imaging [34]. In this work, we show that information about orientational order in spin-coated colloidal deposits, obtained by using orientationalorder based Minkowski structure metric [31,35,36], can be complemented by an examination of structural heterogeneity via persistent homology using the first Betti number [37].…”

Section: Introductionmentioning

confidence: 92%

“…It has been notably successful in the analysis of particulate systems [37,[43][44][45][46][47][48]. To describe what persistent homology measures, we first introduce the Vietoris-Rips complex.…”

Section: B Persistent Homologymentioning

confidence: 99%

Quantifying disorder in colloidal films spin-coated onto patterned substrates

et al. 2017

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Polycrystals of thin colloidal deposits, with thickness controlled by spin-coating speed, exhibit axial symmetry with local 4-fold and 6-fold symmetric structures, termed orientationally correlated polycrystals (OCPs). While spin-coating is a very facile technique for producing large-area colloidal deposits, the axial symmetry prevents us from achieving true long-range order. To obtain true long-range order, we break this axial symmetry by introducing a patterned surface topography and thus eliminate the OCP character. We then examine symmetryindependent methods to quantify order in these disordered colloidal deposits. We find that all the information in the bond-orientational order parameters is well captured by persistent homology analysis methods that only use the centers of the particles as input data. It is expected that these methods will prove useful in characterizing other disordered structures.

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“…Although there exists a number of tools to extract network information, see [5,6] for reviews, recent work [7][8][9][10][11][12][13][14] demonstrates that topological methods are well suited to characterize force networks in granular packings. In this work, we use the Betti numbers β 0 and β 1 to quantify the topology of a network, where β 0 indicates the number of clusters or connected components of the network, and β 1 characterizes the number of loops.…”

Section: Topological Metricsmentioning

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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Topological analysis of tapped granular media using persistent homology

Cited by 49 publications

References 45 publications

Relevance of system size to the steady-state properties of tapped granular systems

Relevance of system size to the steady-state properties of tapped granular systems

Quantifying disorder in colloidal films spin-coated onto patterned substrates

Characterizing granular networks using topological metrics

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