TY - JOUR
T1 - A variational model of irrigation patterns
AU - Maddalena, F.
AU - Solimini, S.
AU - Morel, J. M.
N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].
PY - 2003
Y1 - 2003
N2 - 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 one 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 semicontinuity result for the cost functional. As a consequence, we show that a variety of source to volume irrigation problems are well posed. © European Mathematical Society 2003.
AB - 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 one 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 semicontinuity result for the cost functional. As a consequence, we show that a variety of source to volume irrigation problems are well posed. © European Mathematical Society 2003.
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U2 - 10.4171/ifb/85
DO - 10.4171/ifb/85
M3 - RGC 21 - Publication in refereed journal
SN - 1463-9963
VL - 5
SP - 391
EP - 415
JO - Interfaces and Free Boundaries
JF - Interfaces and Free Boundaries
IS - 4
ER -