Related papers: Dense random packing with a power-law size distrib…
We analyse with simple real-space statistics the Virgo consortium's cosmological N-body simulations. Significant clustering rapidly develops well below the initial mean interparticle separation \Lambda_i, where the gravitational force on a…
A theoretical study based on dimensional analysis and fractal geometry of crack profiles is proposed to establish the relation between their fractal dimension D (1<D<2) and the parameters defining the fatigue crack propagation rate. The…
We consider a fractal with a variable fractal dimension, which is a generalization of the well known triadic Cantor set. In contrast with the usual Cantor set, the fractal dimension is controlled using a scaling factor, and can vary from…
A statistical model of fragmentation of aggregates is proposed, based on the stochastic propagation of cracks through the body. The propagation rules are formulated on a lattice and mimic two important features of the process -- a crack…
We report two-dimensional phase-field simulations of locally-conserved coarsening dynamics of random fractal clusters with fractal dimension D=1.7 and 1.5. The correlation function, cluster perimeter and solute mass are measured as…
We study mode-I fracture in lattices with noisy bonds. In contrast to previous attempts, by using a small parameter that perturbs the force-law between the atoms in perfect lattices and using a 3-body force law, simulations reproduce the…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
Dependence of structural self-organization of granular materials on preparation and grain parameters is key to predictive modelling. We study 60 different mechanically equilibrated polydisperse disc packs, generated numerically by two…
Mechanical responses of soft particle packings to quasi-static deformations are determined by the microscopic restructuring of force-chain networks, where complex non-affine displacements of constituent particles cause the irreversible…
Sequentially-built random sphere-packings have been numerically studied in the packing fraction interval $0.329 < \gamma < 0.586$. For that purpose fast running geometrical algorithms have been designed in order to build about 300…
This paper investigates fractal dimension of linear combination of fractal continuous functions with the same or different fractal dimensions. It has been proved that: (1) $BV_{I}$ all fractal continuous functions with bounded variation is…
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically…
We perform direct numerical simulation (DNS) to study the clustering of small, heavy, monodisperse particles subject to collision-coagulation in turbulent flow (i.e., colliding particles always coagulate (coalesce) into large ones). We find…
A recent letter titled "Explicit Analytical Solution for Random Close Packing in d=2 and d=3" published in Physical Review Letters proposes a first-principle computation of the random close packing (RCP) density in spatial dimensions d=2…
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows,…
We are interested in investigating the statistical properties of extreme values for strongly correlated variables. The starting motivation is to understand how the strong-correlation properties of power-law distributed processes affect the…
The fractal dimension of excitations in glassy systems gives information on the critical dimension at which the droplet picture of spin glasses changes to a description based on replica symmetry breaking where the interfaces are space…
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight…