Related papers: Universal cluster size distribution in a system of…
Motivated by the fundamental problem of modeling the frequency of frequencies (FoF) distribution, this paper introduces the concept of a cluster structure to define a probability function that governs the joint distribution of a random…
The number of clusters per site $n(p)$ in percolation at the critical point $p = p_c$ is not itself a universal quantity---it depends upon the lattice and percolation type (site or bond). However, many of its properties, including…
Self-similarity induced by critical gravitational collapse is used as a paradigm to probe the mass distribution of subsolar objects. At large mass (solar mass and above) there is widespread agreement as to both the form and parameter values…
A general formulation of translationally invariant, parametrically correlated random matrix ensembles, is used to classify universality in correlation functions. Surprisingly, the range of possible physical systems is bounded, and can be…
Grouping similar objects is a fundamental tool of scientific analysis, ubiquitous in disciplines from biology and chemistry to astronomy and pattern recognition. Inspired by the torque balance that exists in gravitational interactions when…
We realized one dimensional disordered photonic structures by grouping high refractive index layers in clusters, randomly distributed in such structure. We have control on the maximum size of the cluster and on the ratio high-low refractive…
As observers of the universe we are physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions is replicated at other locations in…
Probability density functions (PDF) of statistical distributions of cluster sizes N, where N is the number of particles in the cluster, often seem to have less freedom than expected from considering the number of degrees of freedom at the…
The partition function of the finite $1+\epsilon$ state Potts model is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are…
Star clusters are ideal tracers of star formation activity in systems outside the volume that can be studied using individual, resolved stars. These unresolved clusters span orders of magnitude in brightness and mass, and their formation is…
Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number…
These lecture notes concentrate on a few specific topics concerning the distribution of galaxies on scales from 0.1 to nearly 1000/h Mpc. The main aim is to provide the students with the information and tools to familiarize with a few basic…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
We conduct numerical experiments to investigate the spatial clustering of particles and bubbles in simulations of homogeneous and isotropic turbulence. Varying the Stokes parameter and the densities, striking differences in the clustering…
Motivated by the fundamental problem of measuring species diversity, this paper introduces the concept of a cluster structure to define an exchangeable cluster probability function that governs the joint distribution of a random count and…
In ballistic annihilation, infinitely many particles with randomly assigned velocities move across the real line and mutually annihilate upon contact. We introduce a variant with superimposed clusters of multiple stationary particles. Our…
We study discrete random fields $\{X_t: t\in \mathbb{Z}^d\}$ parameterized on the $d$-dimensional integer lattice $\mathbb{Z}^d$. For a fixed threshold $u$, the excursion set $\{t \in \mathbb{Z}^d : X_t > u\}$ decomposes into connected…
The distribution of the number of clusters as a function of mass M and age T suggests that clusters get eroded or dispersed in a regular way over time, such that the cluster number decreases inversely as an approximate power law with T…
Universality, encompassing critical exponents, scaling functions, and dimensionless quantities, is fundamental to phase transition theory. In finite systems, universal behaviors are also expected to emerge at the pseudocritical point.…
Force networks form the skeleton of static granular matter. They are the key ingredient to mechanical properties, such as stability, elasticity and sound transmission, which are of utmost importance for civil engineering and industrial…