Related papers: Universal cluster size distribution in a system of…
The distribution of masses of clusters smaller than the infinite cluster is evaluated at the percolation threshold. The clusters are ranked according to their masses and the distribution $P(M/L^D,r)$ of the scaled masses M for any rank r…
The equilibrium size distribution function of clusters (nanoparticles) in the system of finite number of molecules (atoms) in finite closed volume with constant total energy (isolated system) is found using methods of statistical…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
How to distribute a set of points uniformly on a spherical surface is a very old problem that still lacks a definite answer. In this work, we introduce a physical measure of uniformity based on the distribution of distances between points,…
In the framework of the Gibbs statistical theory, the question of the size of the particles forming the statistical system is investigated. This task is relevant for a wide variety of applications. The distribution for particle sizes and…
We introduce and analyse a class of fragmentation-coalescence processes defined on finite systems of particles organised into clusters. Coalescent events merge multiple clusters simultaneously to form a single larger cluster, while…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
In this note we will consider the question when from the appropriate behavior of a sequence of points on caps we can conclude that the sequence is uniformly distributed on the sphere.
We develop a general theory for estimating the probability that a galaxy cluster of a given shape exists. The theory is based on the observed result that the distribution of galaxies is very close to quasi-equilibrium, in both its linear…
Topology and geometry of a sphere create constraints for particles that lie on its surface which they otherwise do not experience in Euclidean space. Notably, the number of particles and the size of the system can be varied separately,…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset…
A most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics. A necessary step in this line of endeavour is to find regularities in data referring to large scale…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
Galaxies and clusters distributions show two major properties: (i) the positions of galaxies and clusters are characterized by a power law distribution indicating properties with respect to their positions. (ii) The distribution of masses…
Understanding how particles are arranged on the sphere is not only central to numerous physical, biological, and materials systems but also finds applications in mathematics and in analysis of geophysical and meteorological measurements. In…
We present a systematic investigation of the distribution of normal forces at the boundaries of static packings of spheres. A new method for the efficient construction of large hexagonal-close-packed crystals is introduced and used to study…
As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…
In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…
Components of large-scale structure (LSS) of Universe includes galaxy clusters, walls, filaments, groups and field galaxies. The question of spatial organization of all these components remains open despite of a number of recently developed…
The aim of this review article is to give a comprehensive description of the scaling properties detected for the distribution of cosmic structures. Due to the great variety of statistical methods to describe the large-scale structure of the…