130 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
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
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
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
Interplay between geometry and flow distribution in an airway tree
Uniform fluid flow distribution in a symmetric volume can be realized through
a symmetric branched tree. It is shown here, however, that the flow
partitioning can be highly sensitive to deviations from exact symmetry if
inertial effects are present. This is found by direct numerical simulation of
the Navier-Stokes equations in a 3D tree geometry. The flow asymmetry is
quantified and found to depend on the Reynolds number. Moreover, for a given
Reynolds number, we show that the flow distribution depends on the aspect ratio
of the branching elements as well as their angular arrangement. Our results
indicate that physiological variability should be severely restricted in order
to ensure uniform fluid distribution in a tree. This study suggests that any
non-uniformity in the air flow distribution in human lungs should be influenced
by the respiratory conditions, rest or hard exercise
Exponential decay of Laplacian eigenfunctions in domains with branches
The behavior of Laplacian eigenfunctions in domains with branches is
investigated. If an eigenvalue is below a threshold which is determined by the
shape of the branch, the associated eigenfunction is proved to exponentially
decay inside the branch. The decay rate is twice the square root of the
difference between the threshold and the eigenvalue. The derived exponential
estimate is applicable for arbitrary domains in any spatial dimension.
Numerical simulations illustrate and further extend the theoretical estimate
In silico modelling to differentiate the contribution of sugar frequency versus total amount in driving biofilm dysbiosis in dental caries
Dental caries is the most prevalent infection globally and a substantial economic burden in developed countries. Dietary sugars are the main risk factor, and drive increased proportions of acid-producing and acid-tolerating (aciduric) bacterial species within dental bio lms. Recent longitudinal studies have suggested that caries is most strongly correlated with total sugar intake, contrasting with the prevailing view that intake frequency is the primary determinant. To explore this possibility, we employed a computational model for supragingival plaque to systematically sample combinations of sugar frequency and total amount, allowing their independent contributions on the ratio of aciduric (i.e. cariogenic) to non-aciduric bacteria to be unambiguously determined. Sugar frequency was found to be irrelevant for either very high or very low daily total amounts as the simulated bio lm was predicted to be always or never cariogenic, respectively. Frequency was a determining factor for intermediate total amounts of sugar, including the estimated average human consumption. An increased risk of caries (i.e. high prevalence of aciduric/non-aciduric species) was predicted for high intake frequencies. Thus, both total amount and frequency of sugar intake may combine to in uence plaque cariogenicity. These ndings could be employed to support public guidance for dietary change, leading to improved oral healthcare
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