Transfer across Random versus Deterministic Fractal Interfaces

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.Comment: 4 pages, 6 figure

Chemical fracture and distribution of extreme values

When 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 parameters fit with the Weibull law gives good results, confirming the empirical value of this kind of analysis.Comment: 7 pages, 5 figures, to appear in Europhysics Letter

Etching of random solids: hardening dynamics and self-organized fractality

When a finite volume of an etching solution comes in contact with a disordered solid, a complex dynamics of the solid-solution interface develops. Since only the weak parts are corroded, the solid surface hardens progressively. If the etchant is consumed in the chemical reaction, the corrosion dynamics slows down and stops spontaneously leaving a fractal solid surface, which reveals the latent percolation criticality hidden in any random system. Here we introduce and study, both analytically and numerically, a simple model for this phenomenon. In this way we obtain a detailed description of the process in terms of percolation theory. In particular we explain the mechanism of hardening of the surface and connect it to Gradient Percolation.Comment: Latex, aipproc, 6 pages, 3 figures, Proceedings of 6th Granada Seminar on Computational Physic

Percolation-dependent Reaction Rates in the Etching of Disordered Solids

A prototype statistical model for the etching of a random solid is investigated in order to assess the influence of disorder and temperature on the dissolution kinetics. At low temperature, the kinetics is dominated by percolation phenomena, and the percolation threshold determines the global reaction time. At high temperature, the fluctuations of the reaction rate are Gaussian, whereas at low temperature they exhibit a power law tail due to chemical avalanches. This is an example where microscopic disorder directly induces non-classical chemical kinetics.Comment: Revtex, 4 pages, 5 figure

Self-stabilised fractality of sea-coasts through damped erosion

Erosion of rocky coasts spontaneously creates irregular seashores. But the geometrical irregularity, in turn, damps the sea-waves, decreasing the average wave amplitude. There may then exist a mutual self-stabilisation of the waves amplitude together with the irregular morphology of the coast. A simple model of such stabilisation is studied. It leads, through a complex dynamics of the earth-sea interface, to the appearance of a stationary fractal seacoast with dimension close to 4/3. Fractal geometry plays here the role of a morphological attractor directly related to percolation geometry.Comment: 4 pages, 5 figure

Following red blood cells in a pulmonary capillary

The red blood cells or erythrocytes are biconcave shaped cells and consist mostly in a membrane delimiting a cytosol with a high concentration in hemoglobin. This membrane is highly deformable and allows the cells to go through narrow passages like the capillaries which diameters can be much smaller than red blood cells one. They carry oxygen thanks to hemoglobin, a complex molecule that have very high affinity for oxygen. The capacity of erythrocytes to load and unload oxygen is thus a determinant factor in their efficacy. In this paper, we will focus on the pulmonary capillary where red blood cells capture oxygen. We propose a camera method in order to numerically study the behavior of the red blood cell along a whole capillary. Our goal is to understand how erythrocytes geometrical changes along the capillary can affect its capacity to capture oxygen. The first part of this document presents the model chosen for the red blood cells along with the numerical method used to determine and follow their shapes along the capillary. The membrane of the red blood cell is complex and has been modelled by an hyper-elastic approach coming from Mills et al (2004). This camera method is then validated and confronted with a standard ALE method. Some geometrical properties of the red blood cells observed in our simulations are then studied and discussed. The second part of this paper deals with the modeling of oxygen and hemoglobin chemistry in the geometries obtained in the first part. We have implemented a full complex hemoglobin behavior with allosteric states inspired from Czerlinski et al (1999).Comment: 17 page

Optimal branching asymmetry of hydrodynamic pulsatile trees

Most of the studies on optimal transport are done for steady state regime conditions. Yet, there exists numerous examples in living systems where supply tree networks have to deliver products in a limited time due to the pulsatile character of the flow. This is the case for mammals respiration for which air has to reach the gas exchange units before the start of expiration. We report here that introducing a systematic branching asymmetry allows to reduce the average delivery time of the products. It simultaneously increases its robustness against the unevitable variability of sizes related to morphogenesis. We then apply this approach to the human tracheobronchial tree. We show that in this case all extremities are supplied with fresh air, provided that the asymmetry is smaller than a critical threshold which happens to fit with the asymmetry measured in the human lung. This could indicate that the structure is adjusted at the maximum asymmetry level that allows to feed all terminal units with fresh air.Comment: 4 pages, 4 figure