Related papers: Zipf's law in Nuclear Multifragmentation and Perco…

We analyse correspondence of a text to a simple probabilistic model. The model assumes that the words are selected independently from an infinite dictionary. The probability distribution correspond to the Zipf---Mandelbrot law. We count…

Fractal percolation has been introduced by Mandelbrot in 1974. We study the two-dimensional case, with integer subdivision index M and survival probability p. It is well known that there exists a non-trivial critical value p_c(M) such that…

We prove rigorously several results about the site-percolation on random recursive trees, observed in the previous work by Kalay and Ben-Naim [J. Phys. A48(2015), no.4, 0405001, 15 pp.]. For a random recursive tree of size $n$, let every…

We study the size properties of a general model of fractal sets that are based on a tree-indexed family of random compacts and a tree-indexed Markov chain. These fractals may be regarded as a generalization of those resulting from the…

We examine the relationship between two different types of ranked data, frequencies and magnitudes. We consider data that can be sorted out either way, through numbers of occurrences or size of the measures, as it is the case, say, of moon…

The frequency distributions of DNA k-mers are shaped by fundamental biological processes and offer a window into genome structure and evolution. Inspired by analogies to natural language, prior studies have attempted to model genomic k-mer…

Zipf's law is shown to arise as the variational solution of a problem formulated in Fisher's terms. An appropriate minimization process involving Fisher information and scale-invariance yields this universal rank distribution. As an example…

We introduce a method based on the finite size scaling assumption which allows to determine numerically the critical point and critical exponents related to observables in an infinite system starting from the knowledge of the observables in…

Why does Zipf's law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous random group division: the elements can be…

We present a brief overview of nuclear multifragmentation reaction. Basic formalism of canonical thermodynamical model based on equilibrium statistical mechanics is described. This model is used to calculate basic observables of nuclear…

We consider a system composed of a fixed number of particles with total energy smaller or equal to some prescribed value. The particles are non-interacting, indistinguishable and distributed over fixed number of energy levels. The energy…

We study the problem of the existence of a giant component in a random multipartite graph. We consider a random multipartite graph with $p$ parts generated according to a given degree sequence $n_i^{\mathbf{d}}(n)$ which denotes the number…

The multifragmentation of excited spherical nuclear sources with various N/Z ratios and fixed mass number is studied within dynamical and statistical models. The dynamical model treats the multifragmentation process as a final stage of the…

Rank-ordering statistics provides a perspective on the rare, largest elements of a population, whereas the statistics of cumulative distributions are dominated by the more numerous small events. The exponent of a power law distribution can…

A percolation model of nuclear fragmentation is used to interpret 10.2 GeV/c p+197Au multi-fragmentation data. Emphasis is put on finding signatures of a continuous nuclear matter phase transition in finite nuclear systems. Based on model…

Two models of binary fragmentation are introduced in which a time dependent transition size produces two regions of fragment sizes above and below the transition size. In the models we consider a fixed rate of fragmentation for the largest…

The trajectories of neutrons in the reactor, the points of their fission of uranium nuclei, the points of neutron absorption, fission chains and chain reactions are considered from the standpoint of fractal geometry and percolation theory.…

Zipf's law can be used to describe the rank-size distribution of cities in a region. It was seldom employed to research urban internal structure. In this paper, we demonstrate that the space-filling process within a city follows Zipf's law…

The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is…

Modern nuclear theory provides qualitative insights into the fundamental mechanisms of nuclear fission and is increasingly capable of making reliable quantitative predictions. Most quantities of interest pertain to the primary fission…