- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:02
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
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5
2003
4
A variational model of irrigation patterns
Francesco
Maddalena
Università degli Studi di Bari, BARI, ITALY
Giovanni
Taglialatela
Università degli Studi di Bari, BARI, ITALY
Jean-Michel
Morel
, CACHAN CEDEX, FRANCE
irrigation patterns; variational calculus
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.
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
391
416
10.4171/IFB/85
http://www.ems-ph.org/doi/10.4171/IFB/85