Biological transportation networks: Modeling and simulation

Handle URI:
http://hdl.handle.net/10754/622521
Title:
Biological transportation networks: Modeling and simulation
Authors:
Albi, Giacomo; Artina, Marco; Foransier, Massimo; Markowich, Peter A. ( 0000-0002-3704-1821 )
Abstract:
We present a model for biological network formation originally introduced by Cai and Hu [Adaptation and optimization of biological transport networks, Phys. Rev. Lett. 111 (2013) 138701]. The modeling of fluid transportation (e.g., leaf venation and angiogenesis) and ion transportation networks (e.g., neural networks) is explained in detail and basic analytical features like the gradient flow structure of the fluid transportation network model and the impact of the model parameters on the geometry and topology of network formation are analyzed. We also present a numerical finite-element based discretization scheme and discuss sample cases of network formation simulations.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Albi G, Artina M, Foransier M, Markowich PA (2016) Biological transportation networks: Modeling and simulation. Analysis and Applications 14: 185–206. Available: http://dx.doi.org/10.1142/S0219530515400059.
Publisher:
World Scientific Pub Co Pte Lt
Journal:
Analysis and Applications
Issue Date:
15-Sep-2015
DOI:
10.1142/S0219530515400059
Type:
Article
ISSN:
0219-5305; 1793-6861
Sponsors:
G. Albi and M. Foransier acknowledge the support of the ERC-starting Grant Project High-dimensional Sparse Optimal Control. This research was also supported by TUM through the Von Neumann Professorship of PAM.
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorAlbi, Giacomoen
dc.contributor.authorArtina, Marcoen
dc.contributor.authorForansier, Massimoen
dc.contributor.authorMarkowich, Peter A.en
dc.date.accessioned2017-01-02T09:55:28Z-
dc.date.available2017-01-02T09:55:28Z-
dc.date.issued2015-09-15en
dc.identifier.citationAlbi G, Artina M, Foransier M, Markowich PA (2016) Biological transportation networks: Modeling and simulation. Analysis and Applications 14: 185–206. Available: http://dx.doi.org/10.1142/S0219530515400059.en
dc.identifier.issn0219-5305en
dc.identifier.issn1793-6861en
dc.identifier.doi10.1142/S0219530515400059en
dc.identifier.urihttp://hdl.handle.net/10754/622521-
dc.description.abstractWe present a model for biological network formation originally introduced by Cai and Hu [Adaptation and optimization of biological transport networks, Phys. Rev. Lett. 111 (2013) 138701]. The modeling of fluid transportation (e.g., leaf venation and angiogenesis) and ion transportation networks (e.g., neural networks) is explained in detail and basic analytical features like the gradient flow structure of the fluid transportation network model and the impact of the model parameters on the geometry and topology of network formation are analyzed. We also present a numerical finite-element based discretization scheme and discuss sample cases of network formation simulations.en
dc.description.sponsorshipG. Albi and M. Foransier acknowledge the support of the ERC-starting Grant Project High-dimensional Sparse Optimal Control. This research was also supported by TUM through the Von Neumann Professorship of PAM.en
dc.publisherWorld Scientific Pub Co Pte Lten
dc.subjectenergy dissipationen
dc.subjectnumerical modelingen
dc.subjectPattern formationen
dc.subjectsingular limiten
dc.subjectweak solutionsen
dc.titleBiological transportation networks: Modeling and simulationen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalAnalysis and Applicationsen
dc.contributor.institutionM15-Fakultät Mathematik, Technische Universität München, Boltzmann straße 3, Garching bei Mnchen, D-85748, Germanyen
kaust.authorMarkowich, Peter A.en
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