Related papers: Apollonian packings as physical fractals
The random packing fraction of binary particles in D-dimensional Euclidean space R^D is studied using a geometric approach. First, the binary packing fraction of assemblies with small size difference are studied, using the excluded volume…
The mechanism responsible for the emission of clusters from heavy ion irradiated solids is proposed to be thermal spikes. Collision cascade-based theories describe atomic sputtering but cannot explain the consistently observed experimental…
We investigate fractal aspects of elliptical polynomial spirals; that is, planar spirals with differing polynomial rates of decay in the two axis directions. We give a full dimensional analysis of these spirals, computing explicitly their…
We present a new use of Answer Set Programming (ASP) to discover the molecular structure of chemical samples based on the relative abundance of elements and structural fragments, as measured in mass spectrometry. To constrain the…
This study proposes a method for producing an infinite number of fractals using aperiodic substitution tilings, exemplified by the Ammann Chair tiling. Higher-order substitutions of aperiodic tilings are utilized in relation to the…
We present a new framework to explain the link between cooling and fragmentation in gravitationally unstable protostellar discs. This framework consists of a simple model for the formation of spiral arms, as well as a criterion, based on…
Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not…
Given a set of squares and a strip of bounded width and infinite height, we consider a square strip packaging problem, which we call the square independent packing problem (SIPP), to minimize the strip height so that all the squares are…
We generalize the fractional packing framework of Garg and Koenemann to the case of linear fractional packing problems over polyhedral cones. More precisely, we provide approximation algorithms for problems of the form $\max\{c^T x : Ax…
We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which are governed the relation between the…
Inspired by the boolean discrepancy problem, we study the following optimization problem which we term \textsc{Spherical Discrepancy}: given $m$ unit vectors $v_1, \dots, v_m$, find another unit vector $x$ that minimizes $\max_i \langle x,…
At low volume fraction, disordered arrangements of frictionless spheres are found in un--jammed states unable to support applied stresses, while at high volume fraction they are found in jammed states with mechanical strength. Here we show,…
We study fractal measures on Euclidean space through the dynamics of "zooming in" on typical points. The resulting family of measures (the "scenery"), can be interpreted as an orbit in an appropriate dynamical system which often…
A sphere packing bound (SPB) with a prefactor that is polynomial in the block length $n$ is established for codes on a length $n$ product channel $W_{[1,n]}$ assuming that the maximum order $1/2$ Renyi capacity among the component channels,…
We forge connections between the theory of fractal sets obtained as attractors of iterated function systems and process calculi. To this end, we reinterpret Milner's expressions for processes as contraction operators on a complete metric…
We derive production yields for massive pseudo-scalar and scalar axion-like-particles (ALPs), through non-linear Compton scattering of an electron in the background of low- and high-intensity electromagnetic fields. In particular, we focus…
A simple scaling theory for the sintering of fractal aerogels is presented. The densification at small scales is described by an increase of the lower cut-off length $a$ accompanied by a decrease of the upper cut-off length $\xi$, in order…
We discuss the definition and measurability questions of random fractals and find under certain conditions a formula for upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.
Combining experimental procedures and theoretical modeling, we studied patterns, shapes, and growth of a special type of SuperAbsorbent Polymers (SAP). At the initial stage, embed in water, we have a polygonal pattern over a spherical form,…
We study the physical properties derived from interstellar cloud complexes having a fractal structure. We first generate fractal clouds with a given fractal dimension and associate each clump with a maximum in the resulting density field.…