Christian M. Schneider, 2, ∗ Tobias A. Kesselring, José S. Andrade Jr., and Hans J. Herrmann 3 Computational Physics, IfB, ETH Zurich, Schafmattstrasse 6, 8093 Zurich, Switzerland Department of Civil and Environmental Engineering, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA Departamento de F́ısica, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil (Dated: February 25, ...

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based” algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuz...

This study aims to evaluate the efficiency of the concentration-number (C-N) fractal model for discrimination of soil horizon regarding the depth distribution profile. In this regard, soil parameters such as pH, organic carbon content, calcareous mineral content, electrical conductivity and available phosphorus of Ziarat forestland in Golestan Province, north of Iran, has been investigated. The...

In this book, the author proposes a new approach to understand and possibly solve the Riemann Hypothesis. His reformulation builds upon earlier (joint) work on complex fractal dimensions and the vibrations of fractal strings, combined with string theory and noncommutative geometry. Accordingly, it relies on the new notion of a fractal membrane or quantized fractal string, along with the modular...

Diffusion towards a fractal adsorber is a well-researched problem with many applications. While the steady-state flux towards such adsorbers is known to be characterized by the fractal dimension (D{F}) of the surface, the more general problem of time-dependent adsorption kinetics of fractal surfaces remains poorly understood. In this Letter, we show that the time-dependent flux to fractal adsor...

We show that renormalization group (RG) theory applied to complex networks are useful to classify network topologies into universality classes in the space of configurations. The RG flow readily identifies a small-world/fractal transition by finding a trivial stable fixed point of a complete graph, and two unstable fixed points consisting of (i) a pure fractal topology and (ii) a fractal with s...

We show that renormalization group (RG) theory applied to complex networks is useful to classify network topologies into universality classes in the space of configurations. The RG flow readily identifies a small-world-fractal transition by finding (i) a trivial stable fixed point of a complete graph, (ii) a nontrivial point of a pure fractal topology that is stable or unstable according to the...

introduction: water and soil retention curve is one of the most important properties of porous media to obtain in a laboratory retention curve and time associated with errors. for this reason, researchers have proposed techniques that help them to more easily acquired characteristic curve. one of these methods is the use of fractal geometry. determining the relationship between particle size di...

Motivated by the need for new mathematical tools applicable to the study of fractal point-cloud distributions, expectations of complex-valued functions defined over general ‘deterministic’ fractal domains are considered, following the development of a measure-theoretic foundation for their analysis. In particular, we wish to understand and evaluate separation moments as given by integrals of th...