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Streets tree networks and urban growth: Optimal geometry for quickest access between a finite-size volume and one point

Publication ,  Journal Article
Bejan, A; Ledezma, GA
Published in: Physica A: Statistical Mechanics and its Applications
June 15, 1998

The geometric form of the tree network is deduced from a single mechanism. The discovery that the shape of a heat-generating volume can be optimized to minimize the thermal resistance between the volume and a point heat sink, is used to solve the kinematics problem of minimizing the time of travel between a volume (or area) and one point. The optimal path is constructed by covering the volume with a sequence of volume sizes (building blocks), which starts with the smallest size and continues with stepwise larger sizes (assemblies). Optimized in each building block is the overall shape and the angle between constituents. The speed of travel may vary from one assembly size to the next, however, the lowest speed is used to reach the infinity of points located in the smallest volume elements. The volume-to-point path that results is a tree network. A single design principle - the geometric optimization of volume-to-point access - determines all the features of the tree network. © 1998 Elsevier Science B.V. All rights reserved.

Duke Scholars

Published In

Physica A: Statistical Mechanics and its Applications

DOI

ISSN

0378-4371

Publication Date

June 15, 1998

Volume

255

Issue

1-2

Start / End Page

211 / 217

Related Subject Headings

  • Fluids & Plasmas
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0206 Quantum Physics
  • 0105 Mathematical Physics
  • 0102 Applied Mathematics
 

Citation

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Bejan, A., & Ledezma, G. A. (1998). Streets tree networks and urban growth: Optimal geometry for quickest access between a finite-size volume and one point. Physica A: Statistical Mechanics and Its Applications, 255(1–2), 211–217. https://doi.org/10.1016/S0378-4371(98)00085-5
Bejan, A., and G. A. Ledezma. “Streets tree networks and urban growth: Optimal geometry for quickest access between a finite-size volume and one point.” Physica A: Statistical Mechanics and Its Applications 255, no. 1–2 (June 15, 1998): 211–17. https://doi.org/10.1016/S0378-4371(98)00085-5.
Bejan A, Ledezma GA. Streets tree networks and urban growth: Optimal geometry for quickest access between a finite-size volume and one point. Physica A: Statistical Mechanics and its Applications. 1998 Jun 15;255(1–2):211–7.
Bejan, A., and G. A. Ledezma. “Streets tree networks and urban growth: Optimal geometry for quickest access between a finite-size volume and one point.” Physica A: Statistical Mechanics and Its Applications, vol. 255, no. 1–2, June 1998, pp. 211–17. Scopus, doi:10.1016/S0378-4371(98)00085-5.
Bejan A, Ledezma GA. Streets tree networks and urban growth: Optimal geometry for quickest access between a finite-size volume and one point. Physica A: Statistical Mechanics and its Applications. 1998 Jun 15;255(1–2):211–217.
Journal cover image

Published In

Physica A: Statistical Mechanics and its Applications

DOI

ISSN

0378-4371

Publication Date

June 15, 1998

Volume

255

Issue

1-2

Start / End Page

211 / 217

Related Subject Headings

  • Fluids & Plasmas
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0206 Quantum Physics
  • 0105 Mathematical Physics
  • 0102 Applied Mathematics