相关论文: Randomness and Apparent Fractality
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…
Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of study area. This phenomenon has been puzzling many researchers. This…
We present a generalized stochastic Cantor set by means of a simple {\it cut and delete process} and discuss the self-similar properties of the arising geometric structure. To increase the flexibility of the model, two free parameters, $m$…
We discuss the definition and measurability questions of random fractals and find under certain conditions a formula for upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.
This paper proposes a new method to analyze the spatial structure of urban systems using ideas from fractals. Regarding a system of cities as a set of "particles" distributed randomly on a triangular lattice, we construct a spatial…
We introduce a model for the dynamics of mud cracking in the limit of of extremely thin layers. In this model the growth of fracture proceeds by selecting the part of the material with the smallest (quenched) breaking threshold. In…
The soft condensed matter of biological organisms exhibits atomic motions whose properties depend strongly on temperature and hydration conditions. Due to the superposition of rapidly fluctuating alternative motions at both very low…
The variation of fine structure constant with the variation of velocity of light has been studied considering contribution to the permeability and permittivity of the vacuum and incorporating contribution of fractal potential originated…
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…
Power law distributed fluctuations are known to accompany \emph{terminal} failure in disordered brittle solids. The associated intermittent scale-free behavior is of interest from the fundamental point of view as it emerges universally from…
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…
Scale invariance of intrinsic patterns is an important concept in geology that can be observed in numerous geological objects and phenomena. These geological objects and phenomena are described as containing statistically selfsimilar…
We propose a new model to account for the main structural characteristics of rock fracture networks (RFNs). The model is based on a generalization of the random neighborhood graphs to consider fractures embedded into rectangular spaces. We…
This paper develops a technical and practical reinterpretation of the real interval [a,b] under the paradigm of fractal countability. Instead of assuming the continuum as a completed uncountable totality, we model [a,b] as a layered…
The distribution of visible matter in the universe, such as galaxies and galaxy clusters, has its origin in the week fluctuations of density that existed at the epoch of recombination. The hierarchical distribution of the universe, with its…
In this work, we present a mathematical model to describe the adsorption-diffusion process on fractal porous materials. This model is based on the fractal continuum approach and considers the scale-invariant properties of the surface and…
The fractal and self-similarity properties are revealed in many real complex networks. However, the classical information dimension of complex networks is not practical for real complex networks. In this paper, a new information dimension…
Active fluids, composed of individual self-propelled agents, can generate complex large-scale coherent flows. A particularly important laboratory realization of such an active fluid is a system composed of microtubules, aligned in a…