Persistence of force networks in compressed granular media

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

doi:10.1103/physreve.87.042207

Cited by 119 publications

(132 citation statements)

References 20 publications

Supporting

Mentioning

127

Contrasting

Order By: Relevance

“…Interestingly, traditional measurements based on particles' positions-like the pair correlation function, the bond order parameter and the Voronoi tessellation-were shown to be less sensitive to capture such differences among different states with the same packing fraction. In the same line is the recent work of Kramar et al [29] who have used persistent homology to study the evolution of the force network in compressed granular materials. Their approach is able to uncover the distinctive behavior displayed by different systems and, moreover, it is shown to be richer in information than the pair-correlation function, the bond orientational order parameter, and the distribution function of the forces.…”

Section: Introductionmentioning

confidence: 85%

Topological analysis of tapped granular media using persistent homology

et al. 2014

View full text Add to dashboard Cite

We use the first Betti number of a complex to analyze the morphological structure of granular samples in mechanical equilibrium. We investigate two-dimensional granular packings after a tapping process by means of both simulations and experiments. States with equal packing fraction obtained with different tapping intensities are distinguished after the introduction of a filtration parameter which determines the particles (nodes in the network) that are joined by an edge. This is accomplished by just using the position of the particles obtained experimentally and no other information about the possible contacts, or magnitude of forces.

show abstract

Section: Introductionmentioning

confidence: 85%

Topological analysis of tapped granular media using persistent homology

et al. 2014

View full text Add to dashboard Cite

show abstract

“…Other work has probed the dynamical nature of sheared systems by considering time-evolving networks of broken links [29,30], and grain property networks have been used to understand rearrangements in discrete element simulations of compressed systems [31]. Methods from algebraic topology and, in particular, persistent homology [32,33], have also been used to quantify the evolution of force networks, providing important insights into the nature of compressed [34][35][36] and tapped [37][38][39] granular materials.…”

Section: Published By the American Physical Society Under The Terms Omentioning

confidence: 99%

Evolution of network architecture in a granular material under compression

et al. 2016

View full text Add to dashboard Cite

As a granular material is compressed, the particles and forces within the system arrange to form complex and heterogeneous collective structures. Force chains are a prime example of such structures, and are thought to constrain bulk properties such as mechanical stability and acoustic transmission. However, capturing and characterizing the evolving nature of the intrinsic inhomogeneity and mesoscale architecture of granular systems can be challenging. A growing body of work has shown that graph theoretic approaches may provide a useful foundation for tackling these problems. Here, we extend the current approaches by utilizing multilayer networks as a framework for directly quantifying the progression of mesoscale architecture in a compressed granular system. We examine a quasi-two-dimensional aggregate of photoelastic disks, subject to biaxial compressions through a series of small, quasistatic steps. Treating particles as network nodes and interparticle forces as network edges, we construct a multilayer network for the system by linking together the series of static force networks that exist at each strain step. We then extract the inherent mesoscale structure from the system by using a generalization of community detection methods to multilayer networks, and we define quantitative measures to characterize the changes in this structure throughout the compression process. We separately consider the network of normal and tangential forces, and find that they display a different progression throughout compression. To test the sensitivity of the network model to particle properties, we examine whether the method can distinguish a subsystem of low-friction particles within a bath of higher-friction particles. We find that this can be achieved by considering the network of tangential forces, and that the community structure is better able to separate the subsystem than a purely local measure of interparticle forces alone. The results discussed throughout this study suggest that these network science techniques may provide a direct way to compare and classify data from systems under different external conditions or with different physical makeup.

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Persistence of force networks in compressed granular media

Cited by 119 publications

References 20 publications

Topological analysis of tapped granular media using persistent homology

Topological analysis of tapped granular media using persistent homology

Evolution of network architecture in a granular material under compression

Quantifying disorder in colloidal films spin-coated onto patterned substrates

Contact Info

Product

Resources

About