Are there infinite irrigation trees?

Journal of Mathematical Fluid Mechanics

Volumn 8, Issue 3, 2006, Pages 311-332

  Bernot, M ^a   Caselles, V ^b   Morel, J M ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b UNIVERSITAT POMPEU FABRA   (Spain)

Author keywords

Kirchhoff law; Poiseuille law; Source to volume irrigation trees

Indexed keywords

FLOW PATTERNS; GEOMETRY; MATHEMATICAL MODELS; TREES (MATHEMATICS);

BIOLOGICAL MODELS; IRRIGATION TREES; KIRCHHOFF LAW; POISEUILLE LAW;

FLOW OF FLUIDS;

FLOW OF FLUIDS; FLOW PATTERNS; GEOMETRY; MATHEMATICAL MODELS; TREES (MATHEMATICS);

FLUID FLOW; GEOMETRY; IRRIGATION; MATHEMATICAL ANALYSIS; TREE;

EID: 33748556894     PISSN: 14226928     EISSN: 14226952     Source Type: Journal    
DOI: 10.1007/s00021-004-0146-2     Document Type: Article

References (27)

1. A. ALVINO, P. L. LIONS and G. TROMBETTI, A remark on comparison results via symmetrisation, Proceedings of the Royal Society of Edinburgh 102A (1986), 37-48.
2. L. AMBROSIO, Lecture notes on optimal transport problems, Preprint, 2000, available at http://cvgmt.sns.it.
3. A. BEJAN, Shape and Structure, from Engineering to Nature, Cambridge University Press, 2000.
4. A. BEJAN and M. R. ERRERA, Deterministic Tree Networks for Fluid Flow: Geometry for Minimal Flow Resistance between a Volume and one Point, Fractals 5(4) (1997), 685-695.
5. V. CASELLES and J. M. MOREL, Irrigation, in: Progress in Nonlinear Differential Equations and their Applications, VARMET, Trieste, June, 2001, vol. 51, F. TOMARELLI and G. DAL MASO (eds)., pp. 81-90, Birkhaüser, 2002.
6. P. S. DODDS and D. H. ROTHMAN, Unified view of scaling laws for river networks, Phys. Rev. E 59 (5) (1999), 4865-4877.
7. P. S. DODDS, D. H. ROTHMAN and J. S. WEITZ, Re-examination of the 3/4-law of metabolism, Journal of Theoretical Biology 209 (2001), 9-27.
8. R. E. HORTON, Erosional Development of Streams and their Drainage Basins; Hydrophysical Approach to Quantitative Morphology, Geol. Soc. Am. Bull. 56 (1945), 275.
9. E. H. LIEB and M. Loss, Analysis Graduate Studies in Mathematics Vol. 14, 1997.
10. F. MADDALENA, J. M. MOREL and S. SOLIMINI, A variational model of irrigation patterns, Interfaces and Free Boundaries 5 (4) (2003), 391-416.
11. F. MORGAN, Geometric measure theory. A beginner's guide, Academic Press, 1995.
12. th February, 2004, 633-636.
13. C. D. S. MURRAY, The physiological principle of minimum work. I, The vascular system and the cost of blood volume, Proc. Nat. Acad. Sci. USA 12 (1926), 207-214.
14. W. I. NEWMAN, D. L. TURCOTTE and A. M. GABRIELOV, Fractal Trees with Side Branching, Fractals 5 (4) (1997), 603-614.
15. I. RODRIGUEZ-ITURBE and A. RINALDO, Fractal river basins, chance and self-organization, Cambridge University Press, 2001.
16. B. SAPOVAL, Universalités et Fractales, Champs 466, Flammarion, Paris, 1997.
17. G. DEVILLANOVA and S. SOLIMINI, On the dimension of an irrigable measure, preprint.
18. A. N. STRAHLER, Quantitative Analysis of Watershed Geomorphology, Am. Geophys. Un. Trans. 38 (1957), 913.
19. G. TALENTI, Elliptic equations and rearrangements Ann. Scuola Norm. Sup. Pisa 3 (1976).
20. E. TOKUNAGA, Consideration on the Composition of Drainage Networks and their Evolution, Geographical Rep. Tokyo Metro. Univ. 13 (1978).
21. H. B. M. UYLINGS, Optimisation of diameters and bifurcation angles in lung and vascular tree structures, Bull. Math. Biol. 39, (1977), 509-520.
22. Q. XIA, Optimal paths related to transport problems, Commun. Contemp. Math. 5, (2003), 251-279.
23. Q. XIA, Interior regularity of optimal transport paths, Calculus of Variations and Partial Differential Equations 20 (3) (2004), 283-299.
24. Q. XIA, Boundary regularity of optimal transport paths, preprint.
25. G. B. WEST, The Origin of Universal Scaling Laws in Biology, Physica A 263 (1999), 104-113.
26. G. B. WEST, J. H. BROWN and B. J. ENQUIST, A General Model for the Origin of Allometric Scaling Laws in Biology, Science 276 (4) (1997), 122-126.
27. G. B. WEST, J. H. BROWN and B. J. ENQUIST, A general model for ontogenetic growth, Nature 413 (2001), 628-631.