Related papers: Fractal Heterogeneous Media
We propose an algorithm to estimate the Hurst exponent of high-dimensional fractals, based on a generalized high-dimensional variance around a moving average low-pass filter. As working examples, we consider rough surfaces generated by the…
Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling…
The science of fractography revolves around the correlation between topographic characteristics of the fracture surface and the mechanisms and external conditions leading to their creation. While being a topic of investigation for…
Fracture processes in heterogeneous materials comprise a large number of disordered spatial degrees of freedom, representing the dynamical state of a sample over the entire domain of interest. This complexity is usually modeled directly,…
The paper deals with fractal characteristics (Hurst exponent) and wavelet-scaleograms of the information distribution model, suggested by the authors. The authors have studied the effect of Hurst exponent change depending upon the model…
This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…
Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal…
This paper is devoted to the mechanics of fractal materials. A continuum framework accounting for the topological and metric properties of fractal domains in heterogeneous media is developed. The kinematics of deformations is elucidated and…
A quantitative evaluation of the influence of sampling on the numerical fractal analysis of experimental profiles is of critical importance. Although this aspect has been widely recognized, a systematic analysis of the sampling influence is…
In this article, we provide a simple and systematic way to represent general (inhomogeneous) fractals that may look different at different scales and places. By using set-valued compression maps, we express these general fractals as…
The propagation of waves in highly inhomogeneous media is a problem of interest in multiple fields including seismology, acoustics and electromagnetism. It is also relevant for technological applications such as the design of sound…
Homogeneity and isotropy of the universe at sufficiently large scales is a fundamental premise on which modern cosmology is based. Fractal dimensions of matter distribution is a parameter that can be used to test the hypothesis of…
Fractures are a critical process in how materials wear, weaken, and fail whose unpredictable behavior can have dire consequences. While the behavior of smooth cracks in ideal materials is well understood, it is assumed that for real,…
This article considers the computational (acoustic) wave propagation in strongly heterogeneous structures beyond the assumption of periodicity. A high contrast between the constituents of microstructured multiphase materials can lead to…
In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
Tracer diffusion and hydrodynamic dispersion in two-dimensional fractures with self-affine roughness is studied by analytic and numerical methods. Numerical simulations were performed via the lattice-Boltzmann approach, using a new boundary…
The distribution of fracture network is crucial to characterize the behaviors of flow field and solute transport, especially for enhanced geothermal systems, as fractures provide preferential flow paths. However, estimating the parameters…
An exact analytical analysis of anomalous diffusion on a fractal mesh is presented. The fractal mesh structure is a direct product of two fractal sets which belong to a main branch of backbones and side branch of fingers. The fractal sets…
Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the…