Related papers: Dense random packing with a power-law size distrib…
City size distributions are known to be well approximated by power laws across a wide range of countries. But such distributions are also meaningful at other spatial scales, such as within certain regions of a country. Using data from…
We studied the geometrical and topological rules underlying the dispositions and the size distribution of non-overlapping, polydisperse circle-packings. We found that the size distribution of circles that densely cover a plane follows the…
The static pair correlation (distribution) function and the structure factor of particle distributions in three-dimensional homogeneous isotropic systems are explicitly restored from two-dimensional data observed in a thin slab sliced out…
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…
We study the spectral width as a function of the external momentum for the dynamical structure factor of a disordered harmonic solid, considered as a toy model for supercooled liquids and glasses. Both in the context of single-link coherent…
We focus on mesoscopic dislocation patterning via a continuum dislocation dynamics theory (CDD) in three dimensions (3D). We study three distinct physically motivated dynamics which consistently lead to fractal formation in 3D with rather…
The close packing density of log-normal and bimodal distributed, surface-adsorbed particles or discs in 2D is studied by numerical simulation. For small spread in particle size, the system orders in a polycrystalline structure of hexagonal…
Collisions resulting in fragmentation are important in shaping the mass spectrum of minor bodies in the asteroid belt, the Kuiper belt, and debris disks. Models of fragmentation cascades typically find that in steady-state, the solution for…
We study the space of all compact structures on a two-dimensional square lattice of size $N=6\times6$. Each structure is mapped onto a vector in $N$-dimensions according to a hydrophobic model. Previous work has shown that the…
Fracture functions are parton distributions of an initial hadron in the presence of an almost collinear particle observed in the final state. They are important ingredients in QCD factorization for processes where a particle is produced…
Large scale molecular dynamics (MD) simulations are performed to study and to model the ejecta production from the dynamic fragmentation of shock-loaded metals under melt conditions. A generic 3D crystal in contact with vacuum containing…
The shapes of individual self-gravitating structures of an ensemble of identical, collisionless particles have remained elusive for decades. In particular, a reason why mass density profiles like the Navarro-Frenk-White or the Einasto…
Optical scattering strength of fractal optical disordered media with varying fractal dimension is reported. The diffusion limited aggregation (DLA) technique is used to generate fractal samples in 2D and 3D, and fractal dimensions are…
We study the fragment size distributions after crushing of single and many particles under uniaxial compression inside a cylindrical container by means of numerical simulations. Under the assumption that breaking goes through the bulk of…
Circles of a single size can pack together densely in a hexagonal lattice, but adding in size variety disrupts the order of those packings. We conduct simulations which generate dense random packings of circles with specified size…
We investigate a recent suggestion that the spatial distribution of earthquake hypocenters makes a fractal set with a structure and fractal dimensionality close to those of the backbone of critical percolation clusters, by analyzing four…
Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction…
There is a general agreement that galaxy structures exhibit fractal properties, at least up to some small scale. However the presence of an eventual crossover towards homogenization, as well as the exact value of the fractal dimension, are…
We derive the probability distribution of product of two independent random variables, each distributed according the one-dimensional stable law. We represent the density by its power series and its asymptotic expansions. As Fox's…
We study the fractal structure of Diffusion-Limited Aggregation (DLA) clusters on the square lattice by extensive numerical simulations (with clusters having up to $10^8$ particles). We observe that DLA clusters undergo strongly anisotropic…