Related papers: Granular convergence as an iterated local map
In both nature and engineering, loosely packed granular materials are often compacted inside confined geometries. Here, we explore such behaviour in a quasi-two dimensional geometry, where parallel rigid walls provide the confinement. We…
A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles…
Discrete conformal mappings based on circle packing, vertex scaling, and related structures has had significant activity since Thurston proposed circle packing as a way to approximate conformal maps in the 1980s. The first convergence…
This paper is an adaptation of a method used in \cite{K} to the model of random quadrangulations. We prove local weak convergence of uniform measures on quadrangulations and show that the local growth of quadrangulation is governed by…
Mixing of two fractions of a granular material in a slowly rotating two-dimensional drum is considered. The rotation is around the axis of the upright drum. The drum is filled partially, and mixing occurs only at a free surface of the…
We propose a mechanism to explain what occurs when a mixture of grains of different sizes and different shapes (i.e. different repose angles) is poured into a quasi-two-dimensional cell. Specifically, we develop a model that displays…
Random intersection graphs model networks with communities, assuming an underlying bipartite structure of groups and individuals, where these groups may overlap. Group memberships are generated through the bipartite configuration model.…
Tightly packed granular particles under shear often exhibit intriguing intermittencies, specifically, sudden stress drops that we refer to as quaking. To probe the nature of this phenomenon, we prototype a circular shear cell that is…
We investigate the segregation of a dense binary mixture of granular particles that only differ in their restitution coefficient. The mixture is vertically vibrated in the presence of gravity. We find a partial segregation of the species,…
GROUSE (Grassmannian Rank-One Update Subspace Estimation) is an iterative algorithm for identifying a linear subspace of R^n from data consisting of partial observations of random vectors from that subspace. This paper examines local…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…
We investigate the mechanical properties of a static dense granular assembly in response to a local forcing. To this end, a small cyclic displacement is applied on a grain in the bulk of a 2D disordered packing under gravity and the…
A model for the dynamical evolution of a granular binary mixture is analyzed. This system is submitted to a tapping procedure, similarly to what is done in real experiments. In the weak vibration limit, an effective dynamics for the tapping…
Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…
A granular instability driven by gravity is studied experimentally and numerically. The instability arises as grains fall in a closed Hele-Shaw cell where a layer of dense granular material is positioned above a layer of air. The initially…
We study the convergence of stochastic fixed point iterations in the consistent case (in the sense of Butnariu and Fl{\aa}m (1995)) in several different settings, under decreasingly restrictive regularity assumptions of the fixed point…
Granular flows through pipes show interesting phenomena, e.g. clogging and density waves, 1/f-noise. These things are fairly good studied by computer-experiments, but there is a lack in theoretical and analytical consideration. We introduce…
Soft-granular media, such as dense emulsions, foams or tissues, exhibit either fluid- or solid-like properties depending on the applied external stresses. Whereas bulk rheology of such materials has been thoroughly investigated, the…
We study the discrete dynamical system obtained by repeatedly applying the Pearson correlation operator to a real matrix. Each step centers every row, normalizes each centered row to unit Euclidean norm, and forms the Gram matrix of the…