Related papers: Cluster size in bond percolation on the Platonic s…
The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…
Macroscopic properties of heterogeneous media are frequently modelled by regular lattice models, which are based on a relatively small basic cluster of lattice sites. Here, we extend one of such models to any cluster's size kxk. We also…
With numerical simulations of the mW model of water, we investigate the energetic stability of crystalline clusters for both Ice I (cubic and hexagonal ice) and for the metastable Ice 0 phase as a function of the cluster size. Under a large…
Linkage methods are among the most popular algorithms for hierarchical clustering. Despite their relevance the current knowledge regarding the quality of the clustering produced by these methods is limited. Here, we improve the currently…
Two dimensional (2D) classical system of dipole particles confined by a quadratic potential is studied. For clusters of N < 81 particles ground state configurations and appropriate eigenfrequencies and eigenvectors for the normal modes are…
The incipient infinite cluster (IIC) measure is the percolation measure at criticality conditioned on the cluster of the origin to be infinite. Using the lace expansion, we construct the IIC measure for high-dimensional percolation models…
Nucleation plays a critical role in the birth of crystals and is associated with a vast array of phenomena such as protein crystallization and ice formation in clouds. Despite numerous experimental and theoretical studies, many aspects of…
It is shown that the rotational band structure of the cluster states in 12C and 16O can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral…
We consider a system of spherical particles interacting by means of a pair potential equal to a finite constant for interparticle distances smaller than the sphere diameter and zero outside. The model may be a prototype for the interaction…
We establish basic properties of cluster algebras associated with oriented bordered surfaces with marked points. In particular, we show that the underlying cluster complex of such a cluster algebra does not depend on the choice of…
Icosahedron and dodecahedron can be dissected into tetrahedral tiles projected from 3D-facets of the Delone polytopes representing the deep and shallow holes of the root lattice D_6. The six fundamental tiles of tetrahedra of edge lengths 1…
We perform direct numerical simulations of sub-Kolmogorov, inertial spheroids settling under gravity in homogeneous, isotropic turbulence and find that small-scale clustering, measured via the correlation dimension, depends sensitively on…
We consider the density of two-dimensional critical percolation clusters, constrained to touch one or both boundaries, in infinite strips, half-infinite strips, and squares, as well as several related quantities for the infinite strip. Our…
We explore structural and dynamical behavior of concentrated colloidal suspensions made up by C-shape particles using Brownian dynamics computer simulations and theory. In particular, we focus on the entanglement process between nearby…
A simple pair potential, which equilibrium pair separation can be varied under a fixed interaction range, has been proposed. The new potential can make both face-centered-cubic(fcc) and body-centered-cubic(bcc) structure stable by simply…
The strip projection method is the most important way to generate quasiperiodic patterns with predefined local structure. We have obtained a very efficient algorithm for this method which allows one to use it in superspaces of very high…
We study bond percolation on the simple cubic (SC) lattice with various combinations of first, second, third, and fourth nearest-neighbors by Monte Carlo simulation. Using a single-cluster growth algorithm, we find precise values of the…
In this article we review some problems in physics, chemistry and mathematics that lead naturally to a class of polyhedra which include the Platonic solids. Examples include the study of electrons on a sphere, cages of carbon atoms, central…
We study frozen percolation on the (planar) triangular lattice, where connected components stop growing ("freeze") as soon as their "size" becomes at least $N$, for some parameter $N \geq 1$. The size of a connected component can be…
We derive an exact, simple relation between the average number of clusters and the wrapping probabilities for two-dimensional percolation. The relation holds for periodic lattices of any size. It generalizes a classical result of Sykes and…