Related papers: Jamming and Tiling in Aggregation of Rectangles

We investigate the kinetics of constant-kernel aggregation which is augmented by either: (a) evaporation of monomers from finite-mass clusters, or (b) continuous cluster growth -- \ie, condensation. The rate equations for these two…

In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts increasing the coverage are accepted. A finite system eventually gets congested, and we study the statistics of congested…

We consider an infinite spatial inhomogeneous random graph model with an integrable connection kernel that interpolates nicely between existing spatial random graph models. Key examples are versions of the weight-dependent random connection…

We study the sedimentation of finite-size inertial particles in a Rayleigh-Taylor-like setup using state-of-the-art direct numerical simulations. The falling particles are observed to produce two distinct regions: a leading mixing layer…

A diffusion-limited aggregation process, in which clusters coalesce by means of 3-particle reaction, A+A+A->A, is investigated. In one dimension we give a heuristic argument that predicts logarithmic corrections to the mean-field asymptotic…

The assembly of molecular networks into structures such as random tilings and glasses has recently been demonstrated for a number of two-dimensional systems. These structures are dynamically-arrested on experimental timescales so the…

Clustering is one of the mayor collective phenomena observed in active matter. We study the overdamped motion of interacting active Brownian particles in two dimensions. An instability in the pair correlation function causes the onset of…

In random sequential adsorption (RSA), objects are deposited on a substrate randomly, irreversibly, and sequentially. Attempts of deposition that lead to an overlap with previously deposited objects are discarded. The process continues…

We have found that the ability of long thin rods to jam into a solid-like state in response to a local perturbation depends upon both the particle aspect ratio and the container size. The dynamic phase diagram in this parameter space…

Natural flocks (aligned) and swarms (non-aligned) both exhibit features of near-criticality, challenging their treatment as two ends of the same phase transition. We present a model for the aggregation of active individuals, in which their…

We count tilings of a rectangle of integer sides m-1 and n-1 by a special set of tiles. The result is obtained fron the study of the kernel of the adjacency matrix of an n x n rectangular graph of Z x Z.

Due to significant computational expense, discrete element method simulations of jammed packings of size-dispersed spheres with size ratios greater than 1:10 have remained elusive, limiting the correspondence between simulations and…

Collective and directed motility or swarming is an emergent phenomenon displayed by many self-organized assemblies of active biological matter such as clusters of embryonic cells during tissue development, cancerous cells during tumor…

We investigate irreversible aggregation processes driven by a source of small mass clusters. In the spatially homogeneous situation, a well-mixed system is consists of clusters of various masses whose concentrations evolve according to an…

The paper concerns lattice triangulations, that is, triangulations of the integer points in a polygon in $\mathbb{R}^2$ whose vertices are also integer points. Lattice triangulations have been studied extensively both as geometric objects…

A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…

We perform numerical studies including Monte Carlo simulations of high rotational symmetry random tilings. For computational convenience, our tilings obey fixed boundary conditions in regular polygons. Such tilings are put in correspondence…

We study the emerging collective states in a simple mechanical model of a dense group of self-propelled polar disks with off-centered rotation, confined within a circular arena. Each disk presents self-alignment towards the sum of contact…

Inertial particles advected in chaotic flows often accumulate in strange attractors. While moving in these fractal sets they usually approach each other and collide. Here we consider inertial particles aggregating upon collision. The new…

We investigate the entanglement within a system undergoing a random, local process. We find that there is initially a phase of very fast generation and spread of entanglement. At the end of this phase the entanglement is typically maximal.…