Related papers: Dense random packing with a power-law size distrib…
The correlation properties of a random system of densely packed disks, obeying a power-law size distribution, are analyzed in reciprocal space in the thermodynamic limit. This limit assumes that the total number of disks increases…
We study fractal properties of systems of densely and randomly packed disks, obeying a power-law distribution of radii, which is generated by using various protocols: Delaunay triangulation (DT) and constant pressure (CP) protocols, and the…
Static structure factors are computed for large-scale, mechanically stable, jammed packings of frictionless spheres (three dimensions) and disks (two dimensions) with broad, power-law size dispersity characterized by the exponent $-\beta$.…
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…
Due to significant computational expense, discrete element method simulations of jammed packings of size-dispersed spheres with size ratios greater than 1:10 have remained elusive, limiting the correspondence between simulations and…
The size distribution of dust particles in nuclear fusion devices is close to the power function. A function of this kind can be the result of brittle destruction. From the similarity assumption it follows that the size distribution obeys…
Several materials, such as rocks, powders and molecules, are multi-component systems. However, compared to single-component systems, it is difficult to understand the physical component. In this study, as a coarse-grained model for powders…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
We examine the proposal that a model of the large-scale matter distribution consisting of randomly placed haloes with power-law profile, as opposed to a fractal model, can account for the observed power-law galaxy-galaxy correlations. We…
We consider scattering exponents arising in small-angle scattering from power-law polydisperse surface and mass fractals. It is shown that a set of fractals, whose sizes are distributed according to a power-law, can change its fractal…
We study the (newtonian) gravitational force distribution arising from a fractal set of sources. We show that, in the case of real structures in finite samples, an important role is played by morphological properties and finite size…
A better understanding of the optical properties of random photonic structures is beneficial for many applications, such as random lasing, optical imaging and photovoltaics. Here we investigated the light transmission properties of…
We analyze the local structure of two dimensional packings of frictional disks numerically. We focus on the fractions x_i of particles that are in contact with i neighbors, and systematically vary the confining pressure p and friction…
Random tilings or packings in the plane are characterized by a size distribution of individual elements (domains) and by the statistics of neighbor relations between the domains. Most systems occurring in nature or technology have a…
The different between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law…
In analogy to recent results on non-universal roughening in surface growth [Lam and Sander, Phys. Rev. Lett. {\bf 69}, 3338 (1992)], we propose a variant of diffusion-limited aggregation ($DLA$) in which the radii of the particles are…
We study a one-dimensional particles system, in the overdamped limit, where nearest particles attract with a force inversely proportional to a power of their distance and coalesce upon encounter. The detailed shape of the distribution…
This paper proposes a new method to analyze the spatial structure of urban systems using ideas from fractals. Regarding a system of cities as a set of "particles" distributed randomly on a triangular lattice, we construct a spatial…
The notion of fractality, in the context of positive-valued probability distributions, is conventionally associated with the class of Paretian probability laws. In this research we show that the Paretian class is merely one out of six…
Parton distribution function (PDF) at small $x$ in a fast-moving proton is investigated within an upgraded parton model that includes parton splitting with branching cascades and parton fusion. In the region of moderately small $x$, we…