# A 2-adic approach of the human respiratory tree

@article{Bernicot2010A2A, title={A 2-adic approach of the human respiratory tree}, author={Fr{\'e}d{\'e}ric Bernicot and Bertrand Maury and Delphine Salort}, journal={Networks Heterog. Media}, year={2010}, volume={5}, pages={405-422} }

We propose here a general framework to address the question of trace operators on a dyadic tree. This work is motivated by the modeling of the human bronchial tree which, thanks to its regularity, can be extrapolated in a natural way to an infinite resistive tree. The space of pressure fields at bifurcation nodes of this infinite tree can be endowed with a Sobolev space structure, with a semi-norm which measures the instantaneous rate of dissipated energy. We aim at describing the behaviour of…

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## References

SHOWING 1-10 OF 12 REFERENCES

### Trace theorems for trees and application to the human lungs

- MathematicsNetworks Heterog. Media
- 2009

A model for the ventilation process that takes the form of a boundary problem, where the role of the boundary is played by a full domain in the physical space, and the elliptic operator is defined over an infinite dyadic tree is proposed.

### A viscoelastic model with non-local damping application to the human lungs

- Mathematics
- 2006

In this paper we elaborate a model to describe some aspects of the human lung considered as a continuous, deformable, medium. To that purpose, we study the asymptotic behavior of a spring-mass system…

### Harmonic Analysis in the p-Adic Lizorkin Spaces: Fractional Operators, Pseudo-Differential Equations, p-Adic Wavelets, Tauberian Theorems

- Mathematics
- 2006

In this article the p-adic Lizorkin spaces of test functions and distributions are introduced. Multi-dimensional Vladimirov’s and Taibleson’s fractional operators, and a class of p-adic…

### OUTLET DISSIPATIVE CONDITIONS FOR AIR FLOW IN THE BRONCHIAL TREE

- Mathematics
- 2005

We propose inflow and outflow boundary conditions to handle the airflow through the upper part of bronchial tree-like domains. This approach is based on a condensation of the part of the domain which…

### Homogenization of Elastic Media with Gaseous Inclusions

- MathematicsMultiscale Model. Simul.
- 2008

This work studies the asymptotic behavior of a system modeling a composite material made of an elastic periodically perforated support, with period $\varepsilon > 0$, and identifies the corresponding homogenized and periodic cell equations which allow us to find the first corrector term.

### Analytic potential theory over the $p$-adics

- Mathematics
- 1993

© Annales de l’institut Fourier, 1993, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions…

### The Lung: Scientific Foundations

- Medicine, Education
- 1997

No wonder you activities are, reading will be always needed, it will encourage your mind and thoughts and greatly develop your experiences about everything.

### Potential Theory on Infinite Networks

- Mathematics
- 1994

Kirchhoff's laws.- Finite networks.- Currents and potentials withfinite energy.- Uniqueness and related topics.- Some examples and computations.- Royden's compactification.- Rough isometries.