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...

We present analysis of WFPC2 imaging of two spiral galaxies partially backlit by E/S0 systems in the pairs AM1316-241 and AM0500-620, as well as the (probably spiral) foreground system in NGC 1275. Images in B and I are used to determine the reddening curve of dust in these systems. The foreground spiral component of AM1316-241 shows dust strongly concentrated in discrete arms, with a reddening...

The capillary pressure model proposed empirically by Brooks and Corey has been used widely for several decades. However it is not clear why the Brooks-Corey capillary pressure model works so well. In this study, it has been found that the empirical Brooks-Corey capillary pressure model can be derived theoretically from fractal modeling of porous media. Also found was the correlation between the...

Catchment travel time distributions reflect how precipitation from different storms is stored and mixed as it is transported to the stream. Catchment travel time distributions can be described by the mean travel time and the shape of the distribution around the mean. Whereas mean travel times have been quantified in a range of catchment studies, only rarely has the shape of the distribution bee...

The ubiquity of fractal vascular trees throughout the plant and animal kingdoms is postulated to be due to evolutionary advantages conferred through efficient distribution of nutrients to multicellular organisms. The implicit, and untested, assertion in this theory is that the geometry of vascular trees is heritable. Because vascular trees are constructed through the iterative use of signaling ...

We present analysis of WFPC2 imaging of two spiral galaxies partially backlit by E/S0 systems in the pairs AM1316-241 and AM0500-620, as well as the (probably spiral) foreground system in NGC 1275. Images in B and I are used to determine the reddening curve of dust in these systems. The foreground spiral component of AM1316-241 shows dust strongly concentrated in discrete arms, with a reddening...

This short communication advances the hypothesis that the observed fractal structure of large-scale distribution of galaxies is due to a geometrical effect, which arises when observational quantities relevant for the characterization of a cosmological fractal structure are calculated along the past light cone. If this hypothesis proves, even partially, correct, most, if not all, objections rais...

Recent studies by mathematicians and physicists have identified a close association between the distribution of prime numbers and quantum mechanical laws governing the subatomic dynamics of quantum systems such as the electron or the photon. It is now recognised that Cantorian fractal space-time fluctuations characterise dynamical systems of all space-time scales ranging from the microscopic su...

Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during...