This paper is devoted to fractal continuum hydrodynamics and its application model fluid flows in fractally permeable reservoirs. Hydrodynamics of flow developed on the basis a self-consistent employing vector local fractional differential operators allied with Hausdorff derivative. The generalized forms Green-Gauss Kelvin-Stokes theorems for calculus are proved. material derivative defined form Reynolds transport theorem obtained. fundamental conservation laws established. Stokes law analog...

A model of fractal continuum flow employing local fractional differential operators is suggested. The generalizations the Green-Gauss divergence and Reynolds transport theorems for a are fundamental conservation laws hydrodynamic equations an anisotropic derived. Some physical implications long-range correlations in briefly discussed. It noteworthy to point out that (quasi)metric defined this paper implies isotropic obeying Mandelbrot rule thumb intersection governed by conventional equations.

We argue that a non-Markovian random walk on fractal can be treated as Markovian process in fractional dimensional space with suitable metric. This allows us to define the allied $\ensuremath{\nu}$-dimensional ${F}^{\ensuremath{\nu}}$ equipped metric induced by topology. The relation between number of effective spatial degrees freedom walkers ($\ensuremath{\nu}$) and dimensionalities is deduced. intrinsic time inferred. Laplacian operator constructed. map physical problems fractals into...

The purpose of this survey is twofold. First, we the studies percolation on fractal networks. objective to assess current state art topic, emphasizing main findings, ideas and gaps in our understanding. Secondly, try offer guidelines for future research. In particular, focus effects attributes self-similar Some challenging questions are outlined.

The main goal of this work is to develop a robust framework for an exhaustive description essential properties fractal object. For purpose, the inherent features sets are scrutinized. topological, metrological, morphological, and topographical attributes systems delineated. criteria connectedness established. characteristics connectivity ramification ascertained. index loopiness introduced. quantifications heterogeneity, lacunarity, anisotropy briefly sketched out. A set key which enable...

The key issues in fractal geometry concern scale invariance (self-similarity or self-affinity) and the notion of a dimension D which exceeds topological d. In this regard, we point out that constitutive inequality D>d can have either geometric origin, both. main features fractals are their connectedness, connectivity, ramification, loopiness. We argue these be specified by six basic numbers generally independent from each other. However, for many kinds fractals, number dimensions may...

We studied the kinetic roughening dynamic of two coupled interfaces formed in paper wetting experiments at low evaporation rate. observed three different regimes impregnation which dynamics precursor and main fronts belong to universality classes; nevertheless both are pinned same configuration. Reported experimental observations provide a novel insight into nature phenomena occurring vast variety systems far from equilibrium.

We study the scaling properties of randomly folded aluminum sheets different thicknesses h and widths L . found that fractal dimension D=2.30+/-0.01 force exponent delta=0.21+/-0.02 are independent sheet thickness close to those obtained in numerical simulations with a coarse-grained model triangulated self-avoiding surfaces bending stretching rigidity. So our findings suggest finite rigidity self-avoidance play predominant roles behavior plastic sheets.

We study theoretically and experimentally the effect of long-range correlations in material microstructure on stress concentration vicinity notch tip. find that while a fractal continuum notch-tip displacements obey classic asymptotic for linear elastic continuum, power-law decay stresses is controlled by density correlations. The corresponding notch-size fracture strength good agreement with experimental tests performed notched sheets different kinds paper. In particular, we there no if...