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A hybrid model of molecular dynamics and continuum mechanics is introduced to study a system of vertically shaken granular layers. Despite the simplicity the model shows pattern formation in the granular layers due to the formation of…
A microscopic model of adsorption in cluster forming systems with competing interaction is considered. The adsorption process is described by the master equation and modelled by a kinetic Monte Carlo method. The evolution of the particle…
Self-propelled particles undergoing persistent motion can accumulate either through excluded-volume interactions or through quorum sensing, where self-propulsion decreases at high local density. Using kinetic balance theory and simulations,…
Three fundamental segregation and pattern formation processes are known in granular mixtures in a rotating cylindrical drum: radial segregation, axial banding, and coarsening of the band pattern. While the mechanism for the first effect is…
In the context of clustering, we assume a generative model where each cluster is the result of sampling points in the neighborhood of an embedded smooth surface; the sample may be contaminated with outliers, which are modeled as points…
An extremely broad and important class of phenomena in nature involves the settling and aggregation of matter under gravitation in fluid systems. Some examples include: sedimenting marine snow particles in lakes and oceans (central to…
Deep generative models are able to suggest new organic molecules by generating strings, trees, and graphs representing their structure. While such models allow one to generate molecules with desirable properties, they give no guarantees…
Receptor-ligand binding is a critical first step in signal transduction and the duration of the interaction can impact signal generation. In mammalian cells, clustering of receptors may be facilitated by heterogeneous zones of lipids, known…
The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…
Observations suggest that filaments in molecular clouds can grow by mass accretion while forming cores via fragmentation. Here we present one of the first large sample studies of filament accretion using velocity gradient measurements of…
Based on the competition between members of a hierarchy of length scales in complex multi-scale systems, it is shown how clustering of active quantities into concentrated sets, like bubbles in a Swiss cheese, is a generic property that…
Classical clustering algorithms typically either lack an underlying probability framework to make them predictive or focus on parameter estimation rather than defining and minimizing a notion of error. Recent work addresses these issues by…
Model-based clustering of moderate or large dimensional data is notoriously difficult. We propose a model for simultaneous dimensionality reduction and clustering by assuming a mixture model for a set of latent scores, which are then linked…
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, $p$.…
Equilibrium gels of colloidal particles can be realized through the introduction of a second species, a linker that mediates the bonds between the colloids. A gel forming binary mixture whose linkers can self-assemble into linear chains…
Particle beams are important tools for probing atomic and molecular interactions. Here we demonstrate that particle beams also offer a unique opportunity to investigate interactions in macroscopic systems, such as granular media. Motivated…
Identification of the clusters from an unlabeled data set is one of the most important problems in Unsupervised Machine Learning. The state of the art clustering algorithms are based on either the statistical properties or the geometric…
Recent advancements in the ability to construct three-dimensional (3D) tissues and organoids from stem cells and biomaterials have not only opened abundant new research avenues in disease modeling and regenerative medicine but also have…
Dirichlet process mixtures are flexible non-parametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size…
During the past century, biologists and mathematicians investigated two mechanisms underlying bacteria motion: the run phase during which bacteria move in straight lines and the tumble phase in which they change their orientation. When…