164 research outputs found
Explicit Construction of the Brownian Self-Transport Operator
Applying the technique of characteristic functions developped for
one-dimensional regular surfaces (curves) with compact support, we obtain the
distribution of hitting probabilities for a wide class of finite membranes on
square lattice. Then we generalize it to multi-dimensional finite membranes on
hypercubic lattice. Basing on these distributions, we explicitly construct the
Brownian self-transport operator which governs the Laplacian transfer. In order
to verify the accuracy of the distribution of hitting probabilities, numerical
analysis is carried out for some particular membranes.Comment: 30 pages, 9 figures, 1 tabl
Diffusion-Reorganized Aggregates: Attractors in Diffusion Processes?
A process based on particle evaporation, diffusion and redeposition is
applied iteratively to a two-dimensional object of arbitrary shape. The
evolution spontaneously transforms the object morphology, converging to
branched structures. Independently of initial geometry, the structures found
after long time present fractal geometry with a fractal dimension around 1.75.
The final morphology, which constantly evolves in time, can be considered as
the dynamic attractor of this evaporation-diffusion-redeposition operator. The
ensemble of these fractal shapes can be considered to be the {\em dynamical
equilibrium} geometry of a diffusion controlled self-transformation process.Comment: 4 pages, 5 figure
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
Optimal villi density for maximal oxygen uptake in the human placenta
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 an optimal villi density
providing a maximal oxygen uptake as a trade-off between the incoming oxygen
flow and the absorbing villus surface. The predicted optimal villi density
is compatible to previous experimental measurements. Several
other ways to experimentally validate the model are also proposed. The proposed
stream-tube model can serve as a basis for analyzing the efficiency of human
placentas, detecting possible pathologies and diagnosing placental health risks
for newborns by using routine histology sections collected after birth
Screening effects in flow through rough channels
A surprising similarity is found between the distribution of hydrodynamic
stress on the wall of an irregular channel and the distribution of flux from a
purely Laplacian field on the same geometry. This finding is a direct outcome
from numerical simulations of the Navier-Stokes equations for flow at low
Reynolds numbers in two-dimensional channels with rough walls presenting either
deterministic or random self-similar geometries. For high Reynolds numbers,
when inertial effects become relevant, the distribution of wall stresses on
deterministic and random fractal rough channels becomes substantially dependent
on the microscopic details of the walls geometry. In addition, we find that,
while the permeability of the random channel follows the usual decrease with
Reynolds, our results indicate an unexpected permeability increase for the
deterministic case, i.e., ``the rougher the better''. We show that this complex
behavior is closely related with the presence and relative intensity of
recirculation zones in the reentrant regions of the rough channel.Comment: 4 pages, 5 figure
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
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