Related papers: Granular convergence as an iterated local map
We consider the time dependent probability distribution of a coarse grained observable Y whose evolution is governed by a discrete time map. If the map is mixing, the time dependent one-step transition probabilities converge in the long…
After rainfall, pine needles often float on the surface of small puddles. As the water evaporates, they self-assemble into distinct clusters. Motivated by this natural phenomenon, we experimentally investigate the dynamic evolution of…
This work explores the manner in which classical phase space distribution functions converge to the microcanonical distribution. We first prove a theorem about the lack of convergence, then define a generalization of the coarse-graining…
Several mechanisms cause a granular material to strengthen over time at low applied stress. The strength is determined from the maximum frictional force F_max experienced by a shearing plate in contact with wet or dry granular material…
Multiscale molecular modeling is widely applied in scientific research of molecular properties over large time and length scales. Two specific challenges are commonly present in multiscale modeling, provided that information between the…
Classical clustering methods usually return either a finite partition of the observed data or a finite dendrogram over it. This finite-sample view is inadequate when the hierarchy of interest is a recursive geometric object with fine-scale…
Compaction is considered and embedded into broader granular behavior. Reversible compaction is related to the pressure exerted by agitated grains, a quantity relevant to dense flow. Irreversible compaction is derived from the loss of…
We examine the role of small-scale granulation in helping to drive supergranulation and even larger scales of convection. The granulation is modeled as localized cooling events introduced at the upper boundary of a 3-D simulation of…
Granular materials such as sand, powders, foams etc. are ubiquitous in our daily life, as well as in industrial and geotechnical applications. Although these disordered systems form stable structures if unperturbed, in practice they do…
Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
Granular materials -- aggregates of many discrete, disconnected solid particles -- are ubiquitous in natural and industrial settings. Predictive models for their behavior have wide ranging applications, e.g. in defense, mining,…
This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper…
Rigid particles pack into structures, such as sand dunes on the beach, whose overall stability is determined by the average number of contacts between particles. However, when packing spatially extended objects with flexible shapes,…
Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic "puzzle graph" by using connectivity properties of a random "people graph" on the same set of vertices. We presume the Erdos--Renyi…
The origin of the transition from asymptotically reversible to asymptotically irreversible response in amorphous solids subject to oscillatory shear is still unknown. It is known that the plastic events that result from shearing always…
We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
Steady state dynamics of clustering, long range order, and inelastic collapse are experimentally observed in vertically shaken granular monolayers. At large vibration amplitudes, particle correlations show only short range order like…
Jamming is a common feature of out of equilibrium systems showing slow relaxation dynamics. Here we review our efforts in understanding jamming in granular materials using experiments and computer simulations. We first obtain an estimation…