Related papers: Packing-limited growth of irregular objects
Random growth models are fundamental objects in modern probability theory, have given rise to new mathematics, and have numerous applications, including tumor growth and fluid flow in porous media. In this article, we introduce some of the…
We consider random rectangles in $\mathbb{R}^2$ that are distributed according to a Poisson random measure, i.e., independently and uniformly scattered in the plane. The distributions of the length and the width of the rectangles are…
We investigate the problem of growing clusters, which is modeled by two dimensional disks and three dimensional droplets. In this model we place a number of seeds on random locations on a lattice with an initial occupation probability, $p$.…
This note presents a simulation method for investigating the relationship between porosity and particle size distribution in porous media characterization. The method simulates particle packing based on particle size distributions,…
The densest amorphous packing of rigid particles is known as random close packing. It has long been appreciated that higher densities are achieved by using collections of particles with a variety of sizes. The variety of sizes is often…
We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…
Obstructions influence the growth and expansion of bodies in a wide range of settings -- but isolating and understanding their impact can be difficult in complex environments. Here, we study obstructed growth/expansion in a model system…
Assemblies of anisotropic particles commonly appear in studies of active many-body systems. However, in two dimensions, the geometric ramifications of the finite density of such objects are not entirely understood. To fully characterize…
The random packing fraction of binary particles in D-dimensional Euclidean space R^D is studied using a geometric approach. First, the binary packing fraction of assemblies with small size difference are studied, using the excluded volume…
The mechanical, optical, and chemical properties of a wide variety of soft materials are enabled and constrained by their bulk structure. How this structure emerges at small system sizes during self-assembly has been the subject of decades…
Collective dynamics in proliferating anisotropic particle systems arise from an interplay between growth, division, and mechanical interactions, often mediated by particle shape. In classical models of prolate, rod-like growth, flow-induced…
Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…
We study the influence of structural obstacles in a disordered environment on the size and shape characteristics of long flexible polymer macromolecules. We use the model of self-avoiding random walks on diluted regular lattices at the…
We introduce a nonlinear and nonlocal model that describes the range expansion of a population resulting from growth and competition for space. This type of phenomenon underlies the expansion of colonies of immotile cells which motivated…
A linear bubble model of grain growth is introduced to study the conditions under which an isolated grain can grow to a size much larger than the surrounding matrix average (abnormal growth). We first consider the case of bubbles of two…
Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct…
Controlling growth via cell division is crucial in the development of higher organisms, and yet the mechanisms through which this is achieved, e.g., in epithelial tissue, is not yet fully understood. We show that by coupling the cell cycle…
We present an experimental and theoretical study of the shape of fragments generated by explosive and impact loading of closed shells. Based on high speed imaging, we have determined the fragmentation mechanism of shells. Experiments have…
We discover unexpected connections between packing configurations and rare fluctuations in dense systems of active particles subject to pulsation of size. Using large deviation theory, we examine biased ensembles which select atypical…
We studied phase separation in a particle interacting system under a large drive along x. We here identify the basic growth mechanisms, and demonstrate time self-similarity, finite-size scaling, as well as other interesting features of both…