January 19, 2000
A numerical study of the transfer across random fractal surfaces shows that their responses are very close to the response of deterministic model geometries with the same fractal dimension. The simulations of several interfaces with prefractal geometries show that, within very good approximation, the flux depends only on a few characteristic features of the interface geometry: the lower and higher cut-offs and the fractal dimension. Although the active zones are different for different geometries, the electrode reponses are very nearly the same. In that sense, the fractal dimension is the essential "universal" exponent which determines the net transfer.
Similar papers 1
May 19, 2007
In this letter, a theoretical method for the analysis of diffusive flux/current to limited scale self-affine random fractals is presented and compared with experimentally measured electrochemical current for such roughness. The theory explains the several experimental findings of the temporal scale invariance as well as deviation from this of current transients in terms of three dominant fractal parameters for the limited-length scales of roughness. This theoretical method is...
October 2, 1995
It is shown that conductance fluctuations due to phase coherent ballistic transport through a chaotic cavity generically are fractals. The graph of conductance vs. externally changed parameter, e.g. magnetic field, is a fractal with dimension D=2-b/2 between 1 and 2. It is governed by the exponent b (<2) of the power law distribution P(t) ~ t^{-b} for a classically chaotic trajectory to stay in the cavity up to time t, which is typical for chaotic systems with a mixed (chaoti...
July 15, 2011
We numerically investigate the electric potential distribution over a two-dimensional continuum percolation model between the electrodes. The model consists of overlapped conductive particles on the background with an infinitesimal conductivity. Using the finite difference method, we solve the generalized Laplace equation and show that in the potential distribution, there appear the {\it{quasi-equipotential clusters}} which approximately and locally have the same values like ...
August 4, 2020
Self-affine morphology of random interfaces governs their functionalities across tribological, geological, (opto-)electrical and biological applications. However, the knowledge of how energy carriers or generally classical/quantum waves interact with structural irregularity is still incomplete. In this work, we study vibrational energy transport through random interfaces exhibiting different correlation functions on the two-dimensional hexagonal lattice. We show that random i...
November 26, 2015
The present work is aimed to find suitable exchange conditions for saturated fluid flow in a porous medium, when a fractal microstructure is embedded in the porous matrix. Two different deterministic models are introduced and rigorously analyzed. Also, numerical experiments for each of them are presented to verify the theoretically predicted behavior of the phenomenon and some probabilistic versions are explored numerically, to gain further insight on the phenomenon.
April 18, 2016
The free volume comprised between rough surfaces in contact governs the fluid/gas transport properties across networks of cracks and the leakage/percolation phenomena in seals. In this study, a fundamental insight into the evolution of the free volume depending on the mean plane separation, on the real contact area and on the applied pressure is gained in reference to fractal surfaces whose contact response is solved using the boundary element method. Particular attention is ...
April 27, 2000
We investigate the influence of fractal structure on material properties. We calculate the statistical correlation functions of fractal media defined by level-cut Gaussian random fields. This allows the modeling of both surface fractal and mass fractal materials. Variational bounds on the conductivity, diffusivity and elastic moduli of the materials are evaluated. We find that a fractally rough interface has a relatively strong influence on the properties of composites. In co...
June 14, 2007
In this paper we investigate the behavior of particles crossing a neat interface between two media. A Monte Carlo and analytical model, based on fractional derivatives, are presented and discussed in detail, together with a comparison. Anomalous and normal diffusion are consdered.
August 19, 2015
We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physica...
July 8, 2011
We derive equation describing distribution of energy losses of the particle propagating in fractal medium with quenched and dynamic heterogeneities. We show that in the case of the medium with fractal dimension $2<D<3$ the losses $\Delta$ are characterized by the sublinear anomalous dependence $\Delta\sim x^{\alpha}$ with power-law dependence on the distance $x$ from the surface and exponent $\alpha=D-2$.