Irrigation and draining systems, plants and trees together with their root systems, lungs and cardiovascular systems have a common morphology which seems to derive from topological constraints together with energy saving requirements. All of these systems look like spatial trees and succeed in spreading out a fluid from a source onto a volume. The associated morphology is a tree of bifurcating vessels. Their intuitive explanation is that transport energy is saved by using broad vessels as long as possible rather than thin spread out vessels. In this paper, we define a general formalism dealing with irrigation patterns. Related to martingale theory, this formalism permits to define irrigation trees and their vessels, to give a generic form to their energy, and to show compactness for the irrigation patterns with bounded energy as well as a lower semi-continuity result for the cost functional. As a consequence, we show that a variety of source to volume irrigation problems are well posed.
1
Politecnico di Bari, Italy
2
CMLA - ENS, Cachan, France
Francesco Maddalena; Sergio Solimini; Jean-Michel Morel. A variational model of irrigation patterns. Interfaces and free boundaries, Tome 5 (2003) no. 4, pp. 391-416. doi: 10.4171/ifb/85
@article{10_4171_ifb_85,
author = {Francesco Maddalena and Sergio Solimini and Jean-Michel Morel},
title = {A variational model of irrigation patterns},
journal = {Interfaces and free boundaries},
pages = {391--416},
year = {2003},
volume = {5},
number = {4},
doi = {10.4171/ifb/85},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/85/}
}
TY - JOUR
AU - Francesco Maddalena
AU - Sergio Solimini
AU - Jean-Michel Morel
TI - A variational model of irrigation patterns
JO - Interfaces and free boundaries
PY - 2003
SP - 391
EP - 416
VL - 5
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/85/
DO - 10.4171/ifb/85
ID - 10_4171_ifb_85
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