### Abstract

A simple reaction-diffusion-advection equation is proposed in a dichotomous tree network to discuss an optimal network. An optimal size ratio r is evaluated by the principle of maximization of total reaction rate. In the case of reaction-limited conditions, the optimal ratio can be larger than (1/2)1/3 for a fixed value of branching number n, which is consistent with observations in mammalian lungs. We find furthermore that there is an optimal branching number nc when the Péclet number is large. Under the doubly optimal conditions with respect to the size ratio and branching number, the optimal value of r is close to (1/2)1/3.

Original language | English |
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Article number | 040801 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 90 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 10 2014 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

**Reaction-diffusion-advection equation in binary tree networks and optimal size ratio.** / Sakaguchi, Hidetsugu.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Reaction-diffusion-advection equation in binary tree networks and optimal size ratio

AU - Sakaguchi, Hidetsugu

PY - 2014/10/10

Y1 - 2014/10/10

N2 - A simple reaction-diffusion-advection equation is proposed in a dichotomous tree network to discuss an optimal network. An optimal size ratio r is evaluated by the principle of maximization of total reaction rate. In the case of reaction-limited conditions, the optimal ratio can be larger than (1/2)1/3 for a fixed value of branching number n, which is consistent with observations in mammalian lungs. We find furthermore that there is an optimal branching number nc when the Péclet number is large. Under the doubly optimal conditions with respect to the size ratio and branching number, the optimal value of r is close to (1/2)1/3.

AB - A simple reaction-diffusion-advection equation is proposed in a dichotomous tree network to discuss an optimal network. An optimal size ratio r is evaluated by the principle of maximization of total reaction rate. In the case of reaction-limited conditions, the optimal ratio can be larger than (1/2)1/3 for a fixed value of branching number n, which is consistent with observations in mammalian lungs. We find furthermore that there is an optimal branching number nc when the Péclet number is large. Under the doubly optimal conditions with respect to the size ratio and branching number, the optimal value of r is close to (1/2)1/3.

UR - http://www.scopus.com/inward/record.url?scp=84907842311&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907842311&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.90.040801

DO - 10.1103/PhysRevE.90.040801

M3 - Article

C2 - 25375425

AN - SCOPUS:84907842311

VL - 90

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 4

M1 - 040801

ER -