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  1. Journal of Mathematical Fluid Mechanics
  2. Journal of Mathematical Fluid Mechanics : Volume 8
  3. Journal of Mathematical Fluid Mechanics : Volume 8, Issue 3, August 2006
  4. Are There Infinite Irrigation Trees?
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Journal of Mathematical Fluid Mechanics : Volume 19
Journal of Mathematical Fluid Mechanics : Volume 18
Journal of Mathematical Fluid Mechanics : Volume 17
Journal of Mathematical Fluid Mechanics : Volume 16
Journal of Mathematical Fluid Mechanics : Volume 15
Journal of Mathematical Fluid Mechanics : Volume 14
Journal of Mathematical Fluid Mechanics : Volume 13
Journal of Mathematical Fluid Mechanics : Volume 12
Journal of Mathematical Fluid Mechanics : Volume 11
Journal of Mathematical Fluid Mechanics : Volume 10
Journal of Mathematical Fluid Mechanics : Volume 9
Journal of Mathematical Fluid Mechanics : Volume 8
Journal of Mathematical Fluid Mechanics : Volume 8, Issue 4, December 2006
Journal of Mathematical Fluid Mechanics : Volume 8, Issue 3, August 2006
Are There Infinite Irrigation Trees?
Density-Dependent Incompressible Fluids in Bounded Domains
Interface Vanishing for Solutions to Maxwell and Stokes Systems
Vorticities in a LES Model for 3D Periodic Turbulent Flows
A New Class of Weak Solutions of the Navier–Stokes Equations with Nonhomogeneous Data
Singularities in the Density Gradient
Journal of Mathematical Fluid Mechanics : Volume 8, Issue 2, April 2006
Journal of Mathematical Fluid Mechanics : Volume 8, Issue 1, February 2006
Journal of Mathematical Fluid Mechanics : Volume 7
Journal of Mathematical Fluid Mechanics : Volume 6
Journal of Mathematical Fluid Mechanics : Volume 5
Journal of Mathematical Fluid Mechanics : Volume 4
Journal of Mathematical Fluid Mechanics : Volume 3
Journal of Mathematical Fluid Mechanics : Volume 2
Journal of Mathematical Fluid Mechanics : Volume 1

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Are There Infinite Irrigation Trees?

Content Provider SpringerLink
Author Morel, J. M. Bert, M. Caselles, V.
Copyright Year 2006
Abstract In many natural or artificial flow systems, a fluid flow network succeeds in irrigating every point of a volume from a source. Examples are the blood vessels, the bronchial tree and many irrigation and draining systems. Such systems have raised recently a lot of interest and some attempts have been made to formalize their description, as a finite tree of tubes, and their scaling laws [25], [26]. In contrast, several mathematical models [5], [22], [10], propose an idealization of these irrigation trees, where a countable set of tubes irrigates any point of a volume with positive Lebesgue measure. There is no geometric obstruction to this infinitesimal model and general existence and structure theorems have been proved. As we show, there may instead be an energetic obstruction. Under Poiseuille law R(s)  =  s−2 for the resistance of tubes with section s, the dissipated power of a volume irrigating tree cannot be finite. In other terms, infinite irrigation trees seem to be impossible from the fluid mechanics viewpoint. This also implies that the usual principle analysis performed for the biological models needs not to impose a minimal size for the tubes of an irrigating tree; the existence of the minimal size can be proven from the only two obvious conditions for such irrigation trees, namely the Kirchhoff and Poiseuille laws.
Ending Page 332
Page Count 22
Starting Page 311
File Format PDF
ISSN 14226928
e-ISSN 14226952
Journal Journal of Mathematical Fluid Mechanics
Issue Number 3
Volume Number 8
Language English
Publisher Birkhäuser-Verlag
Publisher Date 2005-06-14
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Mechanics, Fluids, Thermodynamics Mathematical Methods in Physics Fluids Kirchhoff law Poiseuille law Source to volume irrigation trees
Content Type Text
Resource Type Article
Subject Applied Mathematics Mathematical Physics Condensed Matter Physics Computational Mathematics
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