Related papers: Fractality of eroded coastlines of correlated land…
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…
For self-similar fractals, the Minkowski content and fractal curvature have been introduced as a suitable limit of the geometric characteristics of its parallel sets, i.e., of uniformly thin coatings of the fractal. For some self-conformal…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
In impermeable media, a hydraulic fracture can continue to expand even without additional fluid injection if its volume exceeds the limiting volume of a hydrostatically loaded radial fracture. This limit depends on the mechanical properties…
We study the geometrical features of the order parameter's fluctuations near the critical point of mixed-order phase transitions in randomly interdependent spatial networks. In contrast to continuous transitions, where the structure of the…
The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a measure of scale dependence, which indicates the scale-free distribution of urban…
The statistics of sea state duration (persistence) have been found to be dependent upon the recording interval \Delta t. Such behavior can be explained as a consequence of the fact that the graph of a time series of an environmental…
Erosion shapes our landscape and occurs when a sufficient shear stress is exerted by a fluid on a sedimented layer. What controls erosion at a microscopic level remains debated, especially near the threshold forcing where it stops. Here we…
We assess if a characteristic length for a non-linear interfacial slip instability follows from theoretical descriptions of sliding friction. We examine friction laws and their coupling with the elasticity of bodies in contact and show that…
The strength and stability of frictional interfaces, ranging from tribological systems to earthquake faults, are intimately related to the underlying spatially-extended dynamics. Here we provide a comprehensive theoretical account, both…
The failure of frictional interfaces -- the process of frictional rupture -- is widely assumed to feature crack-like properties, with far-reaching implications for various disciplines, ranging from engineering tribology to earthquake…
This paper presents a framework for modeling failure in quasi-brittle geomaterials under different loading conditions. A micromechanics-based model is proposed in which the field variables are linked to physical mechanisms at the microcrack…
Fractal geometry proved to be an effective mathematical tool for exploring real geographical space based on digital maps and remote sensing images. Whether the fractal theory tool can be applied to abstract geographical space has not been…
Fracture networks are ubiquitous in nature, spanning scales from millimeter-sized cracks in botanical peels to hundred-kilometer-long lineae on planetary satellites. The propagation of a crack is a complex, nonlinear phenomenon governed by…
Using a two dimensional lattice model we investigate the crack growth under the influence of remote tensile forces as well as due to an internally applied pressure (hydraulic fracturing). For homogeneous elastic properties we present…
Classically, percolation critical exponents are linked to the power laws that characterize percolation cluster fractal properties. It is found here that the gradient percolation power laws are conserved even for extreme gradient values for…
A widespread framework for understanding frictional rupture, such as earthquakes along geological faults, invokes an analogy to ordinary cracks. A distinct feature of ordinary cracks is that their near edge fields are characterized by a…
The dynamic fragmentation of residually stressed solids involves a complex interplay between stored elastic energy, stress wave propagation, and crack instabilities. In this work, we investigate the fracture mechanics of chemically…
Patterns formed by the flow of an inhomogeneous fluid (suspension) over a smooth inclined surface were studied. It was observed that for inclination angle larger than a threshold, global fractal patterns are formed. The fractal dimensions…
Even though many objects and phenomena of importance in geophysics have been shown to have fractal character, there are still many of them which show self-similar character and yet to be studied. The objective of the present work is to…