相关论文: Persistence in Cluster--Cluster Aggregation
We show that the persistence probability $P(t,L)$, in a coarsening system of linear size $L$ at a time $t$, has the finite size scaling form $P(t,L)\sim L^{-z\theta}f(\frac{t}{L^{z}})$ where $\theta$ is the persistence exponent and $z$ is…
The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows to find the critical threshold and the size of the giant component. Numerical simulations…
The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This…
We have performed large-scale Lennard-Jones molecular dynamics simulations of homogeneous vapor-to-liquid nucleation, with $10^9$ atoms. This large number allows us to resolve extremely low nucleation rates, and also provides excellent…
We numerically investigate the heterogeneity in cluster sizes in the two-dimensional Ising model and verify its scaling form recently proposed in the context of percolation problems [Phys. Rev. E 84, 010101(R) (2011)]. The scaling exponents…
The ubiquitous occurrence of cluster patterns in nature still lacks a comprehensive understanding. It is known that the dynamics of many such natural systems is captured by ensembles of Stuart-Landau oscillators. Here, we investigate…
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between…
In clustering, strong dominance in the size of a particular cluster is often undesirable, motivating a measure of cluster size uniformity that can be used to filter such partitions. A basic requirement of such a measure is stability:…
It appears that the dynamical status of clusters and groups of galaxies is related to the large-scale structure of the Universe. A few interesting trends have been established: (1) The Cluster Substructure - Alignment Connection, by which…
We simulate the dynamics of fractal star clusters, in order to investigate the evolution of substructure in recently formed clusters. The velocity dispersion is found to be the key parameter determining the survival of substructure. In…
We analyze the cluster formation in a non-ergodic stochastic system as a result of counter-flow, with the aid of an exactly solvable model. To illustrate the clustering, a two species asymmetric simple exclusion process with impurities on a…
Star clusters are found in all sorts of environments and their formation and evolution is inextricably linked to the star formation process. Their eventual destruction can result from a number of factors at different times, but the process…
Velocity dispersions have been employed as a method to measure masses of clusters. To complement this conventional method, we explore the possibility of constraining cluster masses from the stacked phase space distribution of galaxies at…
Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the…
A commonly used characteristic of statistical dependence of adjacency relations in real networks, the clustering coefficient, evaluates chances that two neighbours of a given vertex are adjacent. An extension is obtained by considering…
In the presence of attraction, the jamming transition of packings of frictionless particles corresponds to the rigidity percolation. When the range of attraction is long, the distribution of the size of rigid clusters, $P(s)$, is continuous…
We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a $k$-component mixture distribution $D = \sum_{i =1}^k w_i P_i$, where each $w_i…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
We develop a unified approach to the problem of clustering in the three different fields of applications, as indicated in the title the paper. The approach is based on Khintchine's probabilistic method that grew out of the Darwin-Fawler…
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction…