Related papers: Fractal Plate Tectonics
The `plate tectonics' is an observed fact and most models of earthquake incorporate that through the frictional dynamics (stick-slip) of two surfaces where one surface moves over the other. These models are more or less successful to…
Minimal fragmentation models intend to unveil the statistical properties of large ensembles of identical objects, each one segmented in {\it two} parts only. Contrary to what happens in the multifragmentation of a single body, minimally…
A simple fragmentation model is introduced and analysed. We show that, under very general conditions, an effective power law for the mass distribution arises with realistic exponent. This exponent has a universal limit, but in practice the…
We use a model whose rules were inspired by population genetics, the random capability growth model, to describe the statistical details observed in experiments of fragmentation of brittle platelike objects, and in particular the existence…
The Earth's surface is subdivided into eight large tectonic plates and many smaller ones. We reconstruct the plate tessellation history and demonstrate that both large and small plates display two distinct hierarchical patterns, described…
The most important characteristics of the fragmentation of heterogeneous solids is that the mass (size) distribution of pieces is described by a power law functional form. The exponent of the distribution displays a high degree of…
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…
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 introduce here the two-fractal model of earthquake dynamics. As the fractured surfaces have self-affine properties, we consider the solid-solid interface of the earth's crust and the tectonic plate below as fractal surfaces. The overlap…
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…
Following the observations of the self-similarity in various length scales in the roughness of the fractured solid surfaces, we propose here a new model for the earthquake. We demonstrate rigorously that the contact area distribution…
We investigated two-dimensional brittle fragmentation with a flat impact experimentally, focusing on the low impact energy region near the fragmentation-critical point. We found that the universality class of fragmentation transition…
Sea ice is a complex system, and observations have shown that ice segments (i.e., floes) have a wide range of sizes, with a floe size distribution that follows a power law. However, a theory for the power law and its exponent have remained…
A lattice model with a spatial dispersion corresponding to a power-law type is suggested. This model serves as a microscopic model for elastic continuum with power-law non-locality. We prove that the continuous limit maps of the equations…
The size of large cliff failures may be described in several ways, for instance considering the horizontal eroded area at the cliff top and the maximum local retreat of the coastline. Field studies suggest that, for large failures, the…
The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such…
The Universe that we know is populated by structures made up of aggregated matter that organizes into a variety of objects; these range from stars to larger objects, such as galaxies or star clusters, composed by stars, gas and dust in…
We offer a fractonic perspective on a familiar observation -- a flat sheet of paper can be folded only along a straight line if one wants to avoid the creation of additional creases or tears. Our core underlying technical result is the…
In this letter we address the fragmentation of thin, brittle layers due to the impact of high-velocity projectiles. Our approach is a geometric statistical one, with lines and circles playing the role of cracks, randomly distributed over…
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…