Related papers: Stochastic Aggregation: Rate Equations Approach
We examine the classic problem of homogeneous nucleation and growth by deriving and analyzing a fully discrete stochastic master equation. Upon comparison with results obtained from the corresponding mean-field Becker-D\"{o}ring equations…
Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…
We study the evolution of random graphs where edges are added one by one between pairs of weighted vertices so that resulting graphs are scale-free with the degree exponent $\gamma$. We use the branching process approach to obtain scaling…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a model of coagulation with single-particle break up is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase…
This work observationally addresses the relative distribution of total and optically luminous matter in galaxy clusters by computing the radial profile of the stellar-to-total mass ratio. We adopt state-of-the-art accurate lensing masses…
Calculations for fission and cluster decay of $^{76}Sr$ are presented for this nucleus to be in its ground-state or formed as an excited compound system in heavy-ion reactions. The predicted mass distribution, for the dynamical collective…
We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution…
The dynamics of a general structured population is modelled using a general stochastic differential equation (SDE) with an infinite decomposability property. This property allows the population to be divided into an arbitrary number of…
We use an analogy with the statistical mechanics of gas to build the statistical mechanics of granular media. The case of an isotropic disordered packing of equal spheres submitted to an isotropic stress is considered. We use the assumption…
Brownian particles that are replicated and annihilated at equal rate have strongly correlated positions, forming a few compact clusters separated by large gaps. We characterize the distribution of the particles at a given time, using a…
Galaxies accrete their mass by means of both smooth accretion from the cosmic web, and the mergers of smaller entities. We wish to quantify the respective role of these two modes of accretion, which could determine the morphological types…
We give a quantitative analysis of clustering in a stochastic model of one-dimensional gas. At time zero, the gas consists of $n$ identical particles that are randomly distributed on the real line and have zero initial speeds. Particles…
The challenge of obtaining galaxy cluster masses is increasingly being addressed by multiwavelength measurements. As scatters in measured cluster masses are often sourced by properties of or around the clusters themselves, correlations…
We introduce a fast and explainable clustering method called CLASSIX. It consists of two phases, namely a greedy aggregation phase of the sorted data into groups of nearby data points, followed by the merging of groups into clusters. The…
We review recent work that investigates the formation of stellar clusters, ranging in scale from globular clusters through open clusters to the small scale aggregates of stars observed in T associations. In all cases, recent advances in…
In numerous papers, the behaviour of stochastic population models is investigated through the sign of a real quantity which is the growth rate of the population near the extinction set. In many cases, it is proven that when this growth rate…
A simple model of ballistic aggregation and fragmentation is proposed. The model is characterized by two energy thresholds, Eagg and Efrag, which demarcate different types of impacts: If the kinetic energy of the relative motion of a…
In this paper, we present a new approach of distributed clustering for spatial datasets, based on an innovative and efficient aggregation technique. This distributed approach consists of two phases: 1) local clustering phase, where each…
The mass evaporation rate of globular clusters evolving in a strong Galactic tidal field is derived through the analysis of large, multi-mass $N$-body simulations. For comparison, we also study the same evaporation rates using MOCCA Monte…