Related papers: Multifractality and multiscaling in two dimensiona…
Stochastic growth processes give rise to diverse intricate structures everywhere and across all scales in nature. Despite the seemingly unrelated complex phenomena at their origin, the Laplacian growth theory has succeeded in unifying their…
Shape is one of the most important visual attributes to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape…
The method of iterated conformal maps is developed for quasi-static fracture of brittle materials, for all modes of fracture. Previous theory, that was relevant for mode III only, is extended here to mode I and II. The latter require…
A new type of elasticity of random (multifractal) structures is suggested. A closed system of constitutive equations is obtained on the basis of two proposed phenomenological laws of reversible deformations of multifractal structures. The…
Using large scale numerical simulations we analyze the statistical properties of fracture in the two dimensional random spring model and compare it with its scalar counterpart: the random fuse model. We first consider the process of crack…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
An abstract mathematical concept of fractal organization of certain complex objects received significant attention in astrophysics during last decades. The concept evolved into a broad field including multi-fractality and intermittency,…
We study domain formation in the two-dimensional O(3) model near criticality. The fractal dimension of these domains is determined with good statistical accuracy.
Fractal/non-fractal morphological transitions allow for the systematic study of the physics behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and…
Mode-I fracture exhibits microbranching in the high velocity regime where the simple straight crack is unstable. For velocities below the instability, classic modeling using linear elasticity is valid. However, showing the existence of the…
This article illustrates the application of multiple scales analysis to two archetypal quasilinear systems; i.e. to systems involving fast dynamical modes, called fluctuations, that are not directly influenced by fluctuation--fluctuation…
We establish links between three different models for multifragmentation: the percolation model, the lattice gas model and the statistical multifragmentation model. There are remarkable similarities between the lattice gas model and the…
In this article, we extend the idea of stochastic dyadic Cantor set to weighted planar stochastic lattice that leads to a stochastic porous lattice. The process starts with an initiator which we choose to be a square of unit area for…
Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments…
Galaxies and clusters distributions show two major properties: (i) the positions of galaxies and clusters are characterized by a power law distribution indicating properties with respect to their positions. (ii) The distribution of masses…
In variational phase-field modeling of brittle fracture, the functional to be minimized is not convex, so that the necessary stationarity conditions of the functional may admit multiple solutions. The solution obtained in an actual…
We propose and investigate a simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication. An exact solution and the scaling theory are presented alongside numerical simulation which fully…
Fracton topological phases host fractionalized excitations that are either completely immobile or only mobile along certain lines or planes. We demonstrate how such phases can be understood in terms of two fundamentally different types of…
Topography is the expression of both internal and external processes of a planetary body. Thus hypsometry (the study of topography) is a way to decipher the dynamic of a planet. For that purpose, the statistics of height and slopes may be…
We study how the loading rate, specimen geometry and microstructural texture select the dynamics of a crack moving through an heterogeneous elastic material in the quasi-static approximation. We find a transition, fully controlled by two…