Related papers: Cluster size in bond percolation on the Platonic s…
Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is…
In Poisson percolation each edge becomes open after an independent exponentially distributed time with rate that decreases in the distance from the origin. As a sequel to our work on the square lattice, we describe the limiting shape of the…
We consider the Voronoi tessellation based on a homogeneous Poisson point process in $\mathbf{R}^{d}$. For a geometric characteristic of the cells (e.g. the inradius, the circumradius, the volume), we investigate the point process of the…
We use molecular dynamics simulations to study a model of the gelation transition with a dynamic bond forming procedure. After establishing evidence for 3D percolation as the static universality class, we turn our attention to the dynamics…
Whether or not the initial star cluster mass function is established through a universal, galactocentric-distance-independent stochastic process, on the scales of individual galaxies, remains an unsolved problem. This debate has recently…
This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameter $p$ which controls the degree…
We investigate the formation of an infinite cluster of entangled threads in a (2+1)-dimensional system. We demonstrate that topological percolation belongs to the universality class of the standard 2D bond percolation. We compute the…
A simple three-dimensional model of a fluid whose constituent particles interact via a short range attractive and long range repulsive potential is used to model the aggregation into large spherical-like clusters made up of hundreds of…
The classical definitions of the Incipient Infinite Cluster (IIC) of percolation consist in conditioning the origin on being connected to radius $n$ and letting $n$ go to infinity. We provide a short proof of that convergence in the planar…
In this study, we investigate the stability and solid fraction of columns comprised of highly non-convex particles. These particles are constructed by extruding arms onto the faces of Platonic solids, a configuration we term \emph{Platonic…
Conductance-based graph clustering has been recognized as a fundamental operator in numerous graph analysis applications. Despite the significant success of conductance-based graph clustering, existing algorithms are either hard to obtain…
We study the optimal packing of short, hard spherocylinders confined to lie tangential to a spherical surface, using simulated annealing and molecular dynamics simulations. For clusters of up to twelve particles, we map out the changes in…
In this study we use simulations of 128$^3$ particles to study the ellipticity and orientation of clusters of galaxies in N-body simulations of differing power-law initial spectra (P(k) \propto k^n ,n = +1, 0, -1, -2$), and density…
We develop a method of constructing percolation clusters that allows us to build very large clusters using very little computer memory by limiting the maximum number of sites for which we maintain state information to a number of the order…
The problem of constrained $k$-center clustering has attracted significant attention in the past decades. In this paper, we study balanced $k$-center cluster where the size of each cluster is constrained by the given lower and upper bounds.…
The convex hull generated by the restriction to the unit ball of a stationary Poisson point process in the $d$-dimensional Euclidean space is considered. By establishing sharp bounds on cumulants, exponential estimates for large deviation…
We study percolation and the random cluster model on the triangular lattice with 3-body interactions. Starting with percolation, we generalize the star--triangle transformation: We introduce a new parameter (the 3-body term) and identify…
The problem of percolation along sites of square lattice is studied. The number of contours being external boundaries for finite clusters has been estimated using geometric considerations. This estimation makes it possible to determine more…
Using molecular dynamics simulation technique, we have studied the melting behaviours of free, icosahedral PtN clusters in the size range of N=12-14. Voter and Chen version of an embedded-atom model, derived by fitting to experimental data…
We have attempted to find the global minima of clusters containing between 20 and 80 atoms bound by the Morse potential as a function of the range of the interatomic force. The effect of decreasing the range is to destabilize strained…