Alexander S. Balankin

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The aim of this Reply is to elucidate the difference between the fractal continuum models used in the preceding Comment and the models of fractal continuum flow which were put forward in our previous articles [Phys. Rev. E 85, 025302(R) (2012); 85, 056314 (2012)]. In this way, some drawbacks of the former models are highlighted. Specifically,(More)
A model of fractal continuum flow employing local fractional differential operators is suggested. The generalizations of the Green-Gauss divergence and Reynolds transport theorems for a fractal continuum are suggested. The fundamental conservation laws and hydrodynamic equations for an anisotropic fractal continuum flow are derived. Some physical(More)
We study the effect of weak vibrations on the imbibition of water in granular media. In our experiments, we have observed that as soon as the vibration is applied, an initially pinned wetting front advances in the direction of imbibition. We found that the front motion is governed by the avalanches of localized intermittent advances directed at 45° to the(More)
We study the scaling properties of randomly folded aluminum sheets of different thicknesses h and widths L . We found that the fractal dimension D=2.30+/-0.01 and the force scaling exponent delta=0.21+/-0.02 are independent of the sheet thickness and close to those obtained in numerical simulations with a coarse-grained model of triangulated self-avoiding(More)
A general technique is developed to retrieve the fractal dimension of self-similar soils through microwave (radar) scattering. The technique is based on a mathematical model relating the fractal dimensions of the georadargram to that of the scattering structure. Clear and different fractal signatures have been observed over four geosystems (soils and(More)
We propose insight into the analysis of the record-breaking fluctuations in random time series, which permits to distinguish between the self-organized criticality and the record dynamics (RD) scenarios of system evolution, using a finite time series realization. Performed analysis of the time series associated with the historical prices of different(More)
We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν-dimensional space F(ν) equipped with the metric induced by the fractal topology. The relation between the number of(More)
Stress and strain relaxation in randomly folded paper sheets under axial compression is studied both experimentally and theoretically. Equations providing the best fit to the experimental data are found. Our findings suggest that, in an axially compressed ball folded from an elastic or elasto-plastic material, the relaxation dynamics is ruled by activated(More)
We studied the kinetic roughening dynamic of two coupled interfaces formed in paper wetting experiments at low evaporation rate. We observed three different regimes of impregnation in which kinetic roughening dynamics of coupled precursor and main fronts belong to different universality classes; nevertheless both interfaces are pinned in the same(More)
Using a combination of laboratory experiments and computer simulation we show that microwaves reflected from and transmitted through soil have a fractal dimension correlated to that of the soil's hierarchic permittivity network. The mathematical model relating the ground-penetrating radar record to the mass fractal dimension of soil structure is also(More)