Granular and Particulate Networks

In recent years, different measures from network analysis have been applied to granular networks (i.e., network representations of granular materials) to gain more insights into their transport and failure propagation mechanisms. So far, only a small number of network diagnostics has been applied to a few selected granular networks. A systematic study of different network measures and granular networks is still missing. As a consequence, it is not clear to what extent certain network measures are able to generally characterize granular networks. To close this gap, we consider a variety of common network measures and systematically study their ability to characterize different simulated and empirical granular networks in two and three dimensions. In particular, we identify network measures which are able to distinguish between physical granular networks and examples of unphysical counterparts which consist of randomly embedded and connected particles.

A new microscopic derivation of the elastic constants of amorphous solids is presented within the framework of nonaffine lattice dynamics, which makes use of a perturbative form of the low-frequency eigenvectors of the dynamical matrix introduced in [V. Mazzacurati, G. Ruocco, M. Sampoli EPL 34, 681 (1996)]. The theory correctly recovers the shear modulus at jamming, $\mu \sim (z-2d)$, including prefactors in quantitative agreement with simulations. Furthermore, this framework allows us, for the first time, to include the effect of internal stresses. The theory shows that the Maxwell rigidity criterion $z=2d$ is violated with internal stress. In particular, $\mu \sim (z-2df)$ where $f<1$ if the bonds are, on average, stretched, and the solid is thus rigid below the Maxwell isostatic limit, while $f>1$ if the bonds are, on average, compressed. The coefficient $f$ is derived in analytical form and depends only on $d$ and on the average particle displacement from the interaction energy minimum.

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.

I will talk about evolution of network connectivity during intermittent stick-slip dynamics of a sheared granular media and its implications for forecasting approach of failure.

Dense particulate assemblies arise in a remarkable number of applications, from pharmaceuticals to soils, mined materials, and metal powders. It is reasonably well-understood that the bulk behavior of granular materials is an emergent manifestation of collective interactions at the particle scale. Traditionally, structure at the particle scale is characterized by tensorial metrics that quantify the magnitude and directionality of contacts and forces between particles. These measures have been shown to be inextricably linked to the engineering-scale behavior of jammed granular matter (i.e., the so-called “stress-force-fabric” relationship). However, there is increasing interest in the quantification of granular assemblies using other microscale descriptors, e.g., betweenness centrality (connectivity), keramicity (state), and entropy (information content and disorder). We present results of such analyses on a series of discrete element method simulations of collections of polydisperse spheres. We analyze the statistics and evolution of these metrics and quantify their relationship to collective macroscale response.

Foams and emulsions are composed of tightly packed bubbles or droplets, which can be treated as soft highly deformable objects spheres : one is made of air-in-water droplets and the other of oil/water emulsions. Despite their different composition, many physical considerations can be deduced for both systems interchangeably. This concerns in particular the interaction forces between bubbles/drops, which are entirely driven by the interfacial tension of the air/liquid or liquid/liquid interfaces. Near the jamming transition, deformations induced by contact forces will expand the bubbles/drops orthogonally to the applied force. In a tightly packed foam/emulsions, however, this lateral expansion, though, is hindered by other neighbouring bubbles/drops. Consequentially, deformation cannot be deduced without considering all contact forces simultaneously, thus making bubble-bubble or drop-drop interactions near jamming intrinsically “non-pairwise”. Using a simple model-system of bubble trains in square capillaries, we propose a first experimental verification of the theoretical relation developped by Morse and Witten [insert citation] and reexamined by Höhler et al. [insert citation], along with numerical simulations (using Surface Evolver [insert citation]). The corroboration of the approaches results strongly advocate for this non-pairwise interaction model quantitatively with no free parameter in the range of small deformations (near jamming). Application ranges in foams and emulsion will be explained, as well as future developments.

Authors: Jakob Kreismann, Jaewon Kim, Marti Bosch, and Martina Hentschel (TU Ilmenau) Microcavity lasers made of single deformed dielectric disk resonators such as the so-called Limaçon-shaped cavity have attracted a lot of interest due to directional light emission from high-quality resonance modes [1]. Here we investigate networks of optical microcavities. We study various array configurations of Limaçon-shaped microresonators, especially linear configurations and perturbations thereof. We find that the directional emission is enhanced drastically (super-directional light emission) and emission into side peaks is reduced. Under certain specific conditions, we observe the full reversal of the main emission directionality. We show that the far-field properties of the resonator network depend strongly on the coupling between the resonators in the array that is mostly determined by the inter-cavity distance as well as geometric imperfections [2]. [1] J. Wiersig and M. Hentschel, “Combining unidirectional light output and ultralow loss in deformed microdisks”, Phys. Rev. Lett. 100, 033901(1-4) (2008). [2] J. Kreismann and M. Hentschel, “Super-directional light emission and emission reversal from microcavity arrays”, submitted, preprint (2019).

We introduce a Phase Field Crystal (PFC) model to simulate a two-dimensional monolayer of periodically structured atoms in three dimensions. The work focuses on developing an appropriate form of two-point correlation function in the free energy functional and tuning corresponding parameters to obtain a structure with periodicity along two Cartesian directions but confined in the direction perpendicular to these directions. The model can simulate the phenomenon of buckling of a compressed atomic layer. In addition, we will show how this model can be adapted to study the two-dimensional defects such as dislocations formed at grain boundaries. Finally, we will report our progress in optimizing the algorithm to compute the convolution involved in the simulation.

Kinetically Constrained Models, where the dynamics is controlled by the number of neighbors of a site that are in a favorable state, have long been used to study the glass transition. Perhaps the concept is even more naturally applied to the jamming transition that depends on a backbone of particles being (over) constrained. In fact, the concept of rigidity percolation has also been introduced in this context. We have recently shown that under certain conditions, the slow dynamics of certain kinetically constrained models can be described exactly in terms of analytically computed critical exponents. I will discuss the derivation of this results and comment on its application to toy models of rigidity percolation.

We set up and carried out experiments to study impact processes in a photoelastic granular medium. The birefringent properties of the material allow for the extraction of information about the form and propagation of the force network. Starting from the contact network of the granular system we are looking for network metrics that are predictive of this observed force network.

Reconstitution techniques in the laboratory such as pluviation in a water column, pluviation in air are often used for replicating the fabric of naturally occurring sands, i.e. to replicate alluvial deposits, sand dunes etc. This fabric is quantified using a fabric tensor, which is an indicator of the inherent anisotropy of the sand. We obtain the initial deposition fabric of a model granular material reconstituted using water pluviation, air pluviation through x-ray computed tomography, and subsequent image segmentation analysis. Additionally, we replicate these deposition processes using DEM simulations. We compare the signatures of the experimentally obtained fabric to those obtained through DEM simulations. While the fabric tensor provides an interesting quantitative way for an macro level description of the ensemble, we investigate some microscopic (i.e. interparticle arrangement both from our DEM simulations and our tomography experiments) signatures We propose techniques for recreating different fabrics through our DEM simulations that are compatible to the fabric obtained at the ensemble level as well as at the microlevel.

Dense suspensions of particles in a fluid are used in formulations of products such as paints, ceramic pastes, and cements among others. Understanding the rheology of such suspensions is essential for their manufacture, transport or use. Dense suspensions of stabilised particles often exhibit shear thickening, where there is a large increase in viscosity with increase in applied stress. Here, we seek to understand suspension rheology by taking advantage of their relation with the physics of jammed granular materials. Dense suspensions of non-Brownian spheres in a Newtonian fluid are studied using discrete element method (DEM) simulations. The contact force network properties of suspensions of particles with different friction coefficients and volume fractions are examined. We find that suspensions exhibit several similarities with jammed granular materials. As suspensions approach the jamming point, the relation between extrapolated values of jamming volume fraction and average contact number of particles in flowing suspensions are quantitatively close to those obtained from the simulations of isotropically compressed and sheared grains. Similarly, the distributions of contact force in suspensions is close to that of granular packings. These findings suggest potential refinements to the mean field models used to understand the rheology of shear thickening suspensions.

Soft particulate media include a wide range of systems involving athermal dissipative particles both in non-living and biological materials. Characterization of flows of particulate media is of great practical and theoretical importance. A fascinating feature of these systems is the existence of a critical rigidity transition in the dense regime dominated by highly intermittent fluctuations that severely affects the flow properties. Here, we unveil the underlying mechanisms of rare fluctuations in soft particulate flows. We find that rare fluctuations have different origins above and below the critical jamming density and become suppressed near the jamming transition. We then conjecture a time-independent local fluctuation relation, which we verify numerically, and that gives rise to an effective temperature. We discuss similarities and differences between our proposed effective temperature with the conventional kinetic temperature in the system by means of a universal scaling collapse.

Thousands of black soldier larvae hatch simultaneously from eggs laid within rotting vegetation or animal carcasses. Over the next few weeks, they grow while compressed by both their surroundings and each other. Just like people in a subway readjust to new passengers, larvae rearrange to avoid being crushed. How quickly can larvae rearrange, and what final state do they choose? In this experimental study, we use a universal testing machine to squeeze larvae and measure their reaction force. Live larvae rearrange ten times faster than dead larvae, and at rates that scale with stretched exponentials, similar to balls of crumpled aluminum foil. The steady-state pressures generated by live larvae are comparable to those of dead larvae, suggesting that such pressures are dictated by physical properties rather than by choice. Live larvae perform fluctuations to maintain this equilibrium pressure, suggesting they act according to a control system that responds to the difference between the current and desired pressure. The ability to survive large pressures allows them to burrow into substrate to escape predators and adverse conditions outside their substrate.

Granular and amorphous materials deform plastically via localized structural rearrangements, although it remains unclear how microscopic structure and material preparation control such events. To address this question, many tools have been developed that use features of the linear response or dynamical matrix to predict the locations of localized rearrangements using structural information alone. However, these methods become less predictive across an avalanche, where stress fluctuations generated by one localized rearrangement can trigger other rearrangements resulting in a large-scale structural change that is not captured by the linear response at the beginning of the avalanche. Therefore, we develop a method to study the linear response of a system during an avalanche. Specifically, we use dimensionality reduction to project the Hessian and forces into the space orthogonal to the minimization direction, and other unstable directions. We extend existing tools for identifying structural defects using this reduced Hessian and study how the population of structural defects evolves during an avalanche with a goal of developing a statistical description of structural evolution during large-scale mechanical instabilities.

While the large majority of theoretical and numerical studies of the jamming transition consider athermal packings of purely repulsive spheres, real complex fluids and soft solids generically display attraction between particles. By studying the statistics of rigid clusters in simulations of soft particles with an attractive shell, we present evidence for two distinct jamming scenarios. Strongly attractive systems undergo a continuous transition in which rigid clusters grow and ultimately diverge in size at a critical packing fraction. Purely repulsive and weakly attractive systems jam via a first-order transition, with no growing cluster size. We further show that the weakly attractive scenario is a finite size effect, so that for any nonzero attraction strength, a sufficiently large system will fall in the strongly attractive universality class. We therefore expect attractive jamming to be generic in the laboratory and in nature.