TY - JOUR
T1 - Biological transportation networks: Modeling and simulation
AU - Albi, Giacomo
AU - Artina, Marco
AU - Foransier, Massimo
AU - Markowich, Peter A.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.
PY - 2015/9/15
Y1 - 2015/9/15
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/622521
UR - https://www.worldscientific.com/doi/abs/10.1142/S0219530515400059
UR - http://www.scopus.com/inward/record.url?scp=84952980156&partnerID=8YFLogxK
U2 - 10.1142/S0219530515400059
DO - 10.1142/S0219530515400059
M3 - Article
SN - 0219-5305
VL - 14
SP - 185
EP - 206
JO - Analysis and Applications
JF - Analysis and Applications
IS - 01
ER -