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The geometry and dimensions of branched structures such as blood vessels or airways are important factors in determining the efficiency of physiological processes. It has been shown that fractal trees can be space filling and can ensure minimal dissipation. The bronchial tree of most mammalian lungs is a good example of an efficient distribution system with(More)
It has recently been shown that the acinus can have a reduced efficiency due to a "screening effect" governed by the ratio of oxygen diffusivity to membrane permeability, the gas flow velocity, as well as the size and configuration of the acinus. We present here a top to bottom calculation of the functioning of a machine acinus at exercise that takes this(More)
Peripheral airways combine branched tubes for ventilation with the gas exchanging alveoli in the pulmonary acini, defined as the complex of airways supplied by one first order respiratory or transitional bronchiole. In this part, the replenishment of oxygen at the alveolar surface occurs by a combination of convective air flow with diffusion of oxygen in(More)
Gas exchange at the acinar level involves several physico-chemical phenomena within a complex geometry. A gas transport model, which takes into account both the diffusion into the acinus and the diffusion across the alveolar membrane, is used to understand gas mixing in realistic systems. It is first shown that the behaviour of the system, computed on model(More)
We discover a strong localization of flexural (bi-Laplacian) waves in rigid thin plates. We show that clamping just one point inside such a plate not only perturbs its spectral properties, but essentially divides the plate into two independently vibrating regions. This effect progressively appears when increasing the plate eccentricity. Such a localization(More)
The present study is concerned with the properties of 2D shallow cavities having an irregular boundary. The eigenmodes are calculated numerically on various examples, and it is shown first that, whatever the shape and characteristic sizes of the boundary, irregularity always induces an increase of localized eigenmodes and a global decrease of the existence(More)
Localization of stationary waves occurs in a large variety of vibrating systems, whether mechanical, acoustical, optical, or quantum. It is induced by the presence of an inhomogeneous medium, a complex geometry, or a quenched disorder. One of its most striking and famous manifestations is Anderson localization, responsible for instance for the(More)
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(More)
We present a stream-tube model of oxygen exchange inside a human placenta functional unit (a placentone). The effect of villi density on oxygen transfer efficiency is assessed by numerically solving the diffusion-convection equation in a 2D+1D geometry for a wide range of villi densities. For each set of physiological parameters, we observe the existence of(More)
We propose an analytical approach to solving the diffusion-convection equations governing oxygen transport in the human placenta. We show that only two geometrical characteristics of a placental cross-section, villi density and the effective villi radius, are needed to predict fetal oxygen uptake. We also identify two combinations of physiological(More)