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Biological transportation networks: modeling and simulation. (English) Zbl 1329.35313

Summary: We present a model for biological network formation originally introduced by D. Cai and D. Hu [“Adaptation and optimization of biological transport networks”, Phys. Rev. Lett. 111, Article ID 138701 (2013; doi:10.1103/PhysRevLett.111.138701)]. 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.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
35K55 Nonlinear parabolic equations
35B36 Pattern formations in context of PDEs
92C42 Systems biology, networks
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