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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 extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for…
The structures formation of the Universe appears as if it were a classically self-similar random process at all astrophysical scales. An agreement is demonstrated for the present hypotheses of segregation with a size of astrophysical…
Granular crystallisation is an important phenomenon whereby ordered packing structures form in granular matter under vibration. However, compared with the well-developed principles of crystallisation at the atomic scale, crystallisation in…
We study the adsorption of flexible polymer macromolecules on a percolation cluster, formed by a regular two-dimensional disordered lattice at critical concentration p_c of attractive sites. The percolation cluster is characterized by a…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
The present paper describes a stochastic model of fracture, whose fragment size distribution can be calculated analytically as a power-law-like distribution. The model is basically cascade fracture, but incorporates the effect that each…
Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a new box-covering algorithm that is a modified version of the original…
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…
Fractal structures appear in a vast range of physical systems. A literature survey including all experimental papers on fractals which appeared in the six Physical Review journals (A-E and Letters) during the 1990's shows that experimental…
In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several…
We study pattern selection of cracks in directionally drying fractures by analyzing the experimental systems recently devised by C. Allain and L. Limat. [Phys. Rev. Lett. {\bf 74}, 2981 (1995).] Proposing a simple picture of crack…
The nature of randomness in disordered packings of frictional and frictionless spheres is investigated using theory and simulations of identical spherical grains. The entropy of the packings is defined through the force and volume ensemble…
The ordinal patterns of a fixed number of consecutive values in a time series is the spatial ordering of these values. Counting how often a specific ordinal pattern occurs in a time series provides important insights into the properties of…
Many natural or human-made systems encompassing local reactions and diffusion processes exhibit spatially distributed patterns of some relevant dynamical variable. These interactions, through self-organization and critical phenomena, give…
We study the packing fraction of clusters in free-falling streams of spherical and irregularly shaped particles using flash X-ray radiography. The estimated packing fraction of clusters is low enough to correspond to coordination numbers…
A class of random discrete distributions $P$ is introduced by means of a recursive splitting of unity. Assuming supercritical branching, we show that for partitions induced by sampling from such $P$ a power growth of the number of blocks is…
We study the time evolution of a chain of nonlinear oscillators. We focus on the fractal features of the spectral entropy and analyze its characteristic intermediate timescales as a function of the nonlinear coupling. A Brownian motion is…
Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a…
The nearest neighbor distribution (Chandrasekhar 1943) is generalized to fractal stellar systems.For such systems an asymptotic distribution of the magnitude of large random forces and a formula for the effective mean interparticle spacing…