140 research outputs found
Surface hardening and self-organized fractality through etching of random solids
No full textWhen a finite volume of etching solution is in contact with a disordered solid, complex dynamics of the solid-solution interface develop. If the etchant is consumed in the chemical reaction, the dynamics stop spontaneously on a self-similar fractal surface. As only the weakest sites are corroded, the solid surface gets progressively harder and harder. At the same time, it becomes rougher and rougher uncovering the critical spatial correlations typical of percolation. From this, the chemical process reveals the latent percolation criticality hidden in any random system. Recently, a simple minimal model was introduced by Sapoval et al. to describe this phenomenon. Through analytic and numerical study, we obtain a detailed description of the process. The time evolution of the solution corroding power and of the distribution of resistance of surface Sites is studied in detail. This study explains the progressive hardening of the solid surface. Finally, this dynamical model appears to belong to the universality class of gradient percolation
Chemical fracture statistics and universal distribution of extreme values
No full textWhen a corrosive solution reaches the limits of a solid sample, a chemical fracture occurs. An analytical theory for the probability of this chemical fracture is proposed and confirmed by extensive numerical experiments on a two-dimensional model. This theory follows from the general probability theory of extreme events given by Gumbel. The analytic law differs from the Weibull law commonly used to describe mechanical failures for brittle materials. However, a three-parameter fit with the Weibull law gives good results, confirming the empirical value of this kind of analysis
Self-stabilized fractality of seacoasts through damped erosion
No full textA minimal model for the self-stabilized fractality of seacoasts through damped erosion was analyzed. The model leads, through a complex dynamics of the earth-sea interface, to the appearance of a stationary fractal seacoast with a dimension close to 4/3. It was observed that the full complex dynamics, involving fast and slow processes, build a dynamic equilibrium that changes the shape of the coast but preserves its fractal properties. It was shown that the fractal geometry plays the role of a morphological attractor directly related to percolation geometry
Chemical etching of a disordered solid: From experiments to field theory
No full textWe present a two-dimensional theoretical model for the slow chemical corrosion of a thin film of a disordered solid by suitable etching solutions. This model explains different experimental results showing that the corrosion stops spontaneously in a situation in which the concentration of the etchant is still finite while the corrosion surface develops clear fractal features. We show that these properties are strictly related to the percolation theory, and in particular to its behavior around the critical point. This task is accomplished both by a direct analysis in terms of a self-organized version of the gradient percolation model and by field theoretical arguments. (c) 2005 Elsevier B.V. All rights reserved
A Simple Method to Compute the Response of Non-Homogeneous and Irregular Interfaces: Electrodes and Membranes
No full textWe present a detailed numerical test of the coarse-graining method proposed by Sapoval to compute the flux through an irregular interface in the case where the local response is inhomogeneously distributed. It is shown, through comparison with detailed finite elements simulations, that this method permits to deduce the flux across an irregular interface from its topography only, as for example in the case of non-uniform polarizability in electrochemistry. The interest of the method lies in its computational simplicity. It then constitutes an essential step towards the understanding of the flux across irregular interfaces in non-linear regimes
Can one hear the shape of an electrode? I. Numerical study of the active zone in Laplacian transfer
No full textThe concept of active zone in the Laplacian transport to and
across irregular interfaces is rigorously introduced. It applies to
arbitrary geometries and uses the coarse-graining method proposed by
Sapoval to compute the flux across an irregular interface from its
geometry without solving the general Laplace problem. Such transport
play a dominant role in electrochemistry, heterogeneous catalysis and
physiological diffusion processes. In the field of electrochemistry,
the method permits one to predict the impedance of an electrode of
arbitrary geometry for any value of the frequency. It shows that, for
systems with aspect ratios of the order of a few times unity or less,
impedance spectroscopy yields in principle a reliable approximate
measure of the length of the chord corresponding to a perimeter length
inversely proportional to the interface capacitance and frequency. For
these cases, impedance spectroscopy can determine the shape of an
electrode to the extent that the knowledge of the average chord length
as a function of the perimeter determines the shape. For systems of
arbitrary geometry, it is shown that impedance spectroscopy permits a
measure of the size of the active zone. These results can be
transposed to several problems related to Laplacian transfer, such as
etching of irregular solids and catalysis in the Eley-Rideal regime
Entropy Production Of Entirely Diffusional Laplacian Transfer And The Possible Role Of Fragmentation Of The Boundaries
No full textThe Entropy Production And The Variational Functional Of A Laplacian Diffusional Field Around The First Four Fractal Iterations Of A Linear Self-Similar Tree (Von Koch Curve) Is Studied Analytically And Detailed Predictions Are Stated. In A Next Stage, These Predictions Are Confronted With Results From Numerical Resolution Of The Laplace Equation By Means Of Finite Elements Computations. After A Brief Review Of The Existing Results, The Range Of Distances Near The Geometric Irregularity, The So-Called »Near Field», A Situation Never Studied In The Past, Is Treated Exhaustively. We Notice Here That In The Near Field, The Usual Notion Of The Active Zone Approximation Introduced By Sapoval Et Al. [M. Filoche And B. Sapoval, Transfer Across Random Versus Deterministic Fractal Interfaces, Phys. Rev. Lett. 84(25) (2000) 5776;1 B. Sapoval, M. Filoche, K. Karamanos And R. Brizzi, Can One Hear The Shape Of An Electrode? I. Numerical Study Of The Active Zone In Laplacian Transfer, Eur. Phys. J. B. Condens. Matter Complex Syst. 9(4) (1999) 739-753.]2 Is Strictly Inapplicable. The Basic New Result Is That The Validity Of The Active-Zone Approximation Based On Irreversible Thermodynamics Is Confirmed In This Limit, And This Implies A New Interpretation Of This Notion For Laplacian Diffusional Fields
Entropy production of entirely diffusional Laplacian transfer and the possible role of fragmentation of the boundaries
No full textThe entropy production and the variational functional of a Laplacian diffusional field around the first four fractal iterations of a linear self-similar tree (von Koch curve) is studied analytically and detailed predictions are stated. In a next stage, these predictions are confrontedwith results from numerical resolution of the Laplace equation by means of Finite Elements computations. After a brief review of the existing results, the range of distances near the geometric irregularity, the so-called “Near Field”, a situation never studied in the past, is treated exhaustively. We notice here that in the Near Field, the usual notion of the active zone approximation introduced by Sapoval et al. [M. Filoche and B. Sapoval, Transfer across random versus deterministic fractal interfaces, Phys. Rev. Lett. 84(25) (2000) 5776; B. Sapoval, M. Filoche, K. Karamanos and R. Brizzi, Can one hear the shape of an electrode? I. Numerical study of the active zone in Laplacian transfer, Eur. Phys. J. B. Condens. Matter Complex Syst. 9(4) (1999) 739-753.] is strictly inapplicable. The basic new result is that the validity of the active-zoneapproximation based on irreversible thermodynamics is confirmed in this limit, and this implies a new interpretation of this notion for Laplacian diffusional fields.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
Entropy production of entirely diffusional laplacian transfer and the possible role of fragmentation of the boundaries
No full textThe entropy production and the variational functional of a Laplacian diffusional field around the first four fractal iterations of a linear self-similar tree (von Koch curve) is studied analytically and detailed predictions are stated. In a next stage, these predictions are confronted with results from numerical resolution of the Laplace equation by means of Finite Elements computations. After a brief review of the existing results, the range of distances near the geometric irregularity, the so-called »Near Field», a situation never studied in the past, is treated exhaustively. We notice here that in the Near Field, the usual notion of the active zone approximation introduced by Sapoval et al. [M. Filoche and B. Sapoval, Transfer across random versus deterministic fractal interfaces, Phys. Rev. Lett. 84(25) (2000) 5776;1 B. Sapoval, M. Filoche, K. Karamanos and R. Brizzi, Can one hear the shape of an electrode? I. Numerical study of the active zone in Laplacian transfer, Eur. Phys. J. B. Condens. Matter Complex Syst. 9(4) (1999) 739-753.]2 is strictly inapplicable. The basic new result is that the validity of the active-zone approximation based on irreversible thermodynamics is confirmed in this limit, and this implies a new interpretation of this notion for Laplacian diffusional fields. © 2015 World Scientific Publishing Company
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