We have pursued in the literature a fractal-like structure for the fractional quantum Halll effect-FQHE which consider the Hausdorff dimension associated with the quantum mechanics paths and the spin of the particles or quasiparticles termed fractons. These objects carry rational or irrational values of spin and satisfy a fractal distribution function associated with a fractal von Neumann entro...

Herein we present mathematical ideas for assessing the fractal character of distributions of brain synapses. Remarkably, laboratory data are now available in the form of actual 3-dimensional coordinates for millions of mouse-brain synapses (courtesy of Smithlab at Stanford Medical School). We analyze synapse datasets in regard to statistical moments and fractal measures. It is found that moment...

Collapsing gullies are among the most severe soil erosion problems in the tropical and subtropical areas of southern China. However, few studies have examined the relationship of soil particle size distribution (PSD) changes with land-use patterns in the alluvial fans of collapsing gullies. Recently, the fractal method has been applied to estimate soil structure and has proven to be an effectiv...

Molecular dynamics simulation is applied to study the electroosmotic flow in rough nanochannels, with particular attention given to the fluid–solid interactions. In the simulation, the surface roughness is characterized by a fractal Cantor. The roles of roughness height and fractal dimension on nanoscale electroosmotic flow are examined and analyzed. The concentration distributions, zeta potent...

Tissue image classification is a challenging problem due to the fact that the images contain highly irregular shapes in complex spatial arrangement. The multi-fractal formalism has been found useful in characterizing the intensity distribution present in such images, as it can effectively resolve local densities and also represent various structures present in the image. This paper presents a d...