Related papers: Multifractality, percolation threshold and critica…
Macroscopic systems often display phase transitions where certain physical quantities are singular or self-similar at different (spatial) scales. Such properties of systems are currently characterized by some order parameters and a few…
The nuclear reaction network is usually studied via precise calculation of differential equation sets, and much research interest has been focused on the characteristics of nuclides, such as half-life and size limit. In this paper, however,…
The fractal nature of graphs has traditionally been investigated by using the nodes of networks as the basic units. Here, instead, we propose to concentrate on the graph edges, and introduce a practical and computationally not demanding…
We give a characterization of the percolation threshold for a multirange model on oriented trees, as the first positive root of a polynomial, with the use of a multi-type Galton-Watson process. This gives in particular the exact value of…
We show that the coalescence model for fragment formation leads to an approximate site percolation model. Features characteristic of a percolation model also appear in microscopic models of disassembly.
Atomic nuclei exhibit multiple energy scales ranging from hundreds of MeV in binding energies to fractions of an MeV for low-lying collective excitations. As the limits of nuclear binding is approached near the neutron- and proton…
We study a simple model of conducting polymers in which a single electron propagates through a randomly tangled chain. The model has the geometry of a small-world network, with a small density $p$ of crossings of the chain acting as…
In this article, we have employed fractal formalism to calculate the Fracture Functions of the Leading neutron produced in \textit{ep} collisions. The fractal concept describes the self-similar behavior of the proton structure at Leading…
For the first time we apply the methodologies of nonlinear analysis to investigate atomic matter. We use these methods in the analysis of Atomic Weights and of Mass Number of atomic nuclei. Using the AutoCorrelation Function and Mutual…
We propose a model that provides a unified description of nuclear equation of state and fragmentations. The equation of state is evaluated in Bragg-Williams as well as in Bethe-Peierls approximations and compared with that in the mean field…
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…
Multifractality in time series analysis characterizes the presence of multiple scaling exponents, indicating heterogeneous temporal structures and complex dynamical behaviors beyond simple monofractal models. In the context of digital…
In a recent Letter, Friedman and Landsberg discussed the underlying mechanism of explosive phase transitions on complex networks [Phys. Rev. Lett. 103, 255701 (2009)]. This Brief Report presents a modest, though more insightful extension of…
While cracking is a complex dynamics that involves material intrinsic properties like grain shape and size distribution, elastic properties of grain and cementing materials, and extrinsic properties of loading, in this work, the focus has…
Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of the system but depends strongly on the dimension in which the…
We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
An abstract mathematical concept of fractal organization of certain complex objects received significant attention in astrophysics during last decades. The concept evolved into a broad field including multi-fractality and intermittency,…
Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component…
We examine bootstrap percolation in d-dimensional, directed metric graphs in the context of recent measurements of firing dynamics in 2D neuronal cultures. There are two regimes, depending on the graph size N. Large metric graphs are…