The key issues in fractal geometry concern scale invariance (self-similarity or self-affinity)
and the notion of a fractal dimension D which exceeds the topological dimension d. In this …

The main aim of this paper is to reveal effects of fractal features on the formation factors
associated with different transport processes in scale invariant pore-fracture networks …

The main goal of this work is to develop a robust framework for an exhaustive description of
essential properties of a fractal object. For this purpose, the inherent features of fractal sets …

This paper is devoted to the development of the fractional space approach to physical
problems on fractals and in confined quasi-low-dimensional systems. The aim of this …

This Letter is focused on the impact of fractal topology on the transport processes governed
by different kinds of random walks on Cantor tartans. We establish that the spectral …

With a view toward fractal spaces, by using a Korevaar–Schoen space approach, we
introduce the class of bounded variation (BV) functions in the general framework of strongly …

In this Letter, the analytical expression of topological Hausdorff dimension D t H is derived
for some kinds of infinitely ramified Sierpiński carpets. Furthermore, we deduce that the …

In this Letter, we emphasize that methods of fractal homogenization should take into account
a loop structure of the fractal, as well as its connectivity and geodesic metric. The fractal …

A new analytic model of fractal imbibition in porous media is derived. The topological
Hausdorff dimension is used as a fractal parameter in the proposed model. The fractal …

This work is devoted to the fractal features of Bernoulli percolation in different space
dimensions. The focus is made on the fractal attributes associated with the connectivity …