In this paper we construct a model to describe some
aspects of the
deformation of the central region of the human lung
considered as a
continuous
elastically deformable medium. To achieve this purpose, we study
the interaction
between the pipes composing the tree and the fluid that goes
through it. We use a stationary model to determine the deformed radius of each branch. Then, we solve a constrained minimization problem, so as to minimize the viscous (dissipated) energy in the tree. The key...
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 with dissipation. The key feature of our approach is the nature of this dissipation phenomena, which is related here to the flow of a viscous fluid through a dyadic tree of pipes (the branches), each exit of which being connected to an air pocket (alvelola) delimited by two successive masses.
The...
We consider variational problems of P. D. E. depending on a small parameter when the limit process implies vanishing of the higher order terms. The perturbation problem is said to be sensitive when the energy space of the limit problem is out of the distribution space, so that the limit problem is out of classical theory of P. D. E. We present here a review of the subject, including abstract convergence theorems and two very different model problems (the second one is presented for the first...
This article is devoted to the construction of a mathematical model describing the early
formation of atherosclerotic lesions. The early stage of atherosclerosis is an
inflammatory process that starts with the penetration of low density lipoproteins in the
intima and with their oxidation. This phenomenon is closely linked to the local blood flow
dynamics. Extending a previous work [5] that was mainly restricted to a
one-dimensional setting, we couple...
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