Related Experiment Video
Updated: Jan 23, 2026
05:47
Author Spotlight: Advanced Techniques for Visualizing Endogenous Axonal Transport Dynamics
Published on: February 16, 2024
1.2K
Optimal geometry of transportation networks
David Aldous1, Marc Barthelemy2,3
1Department of Statistics, 367 Evans Hall No. 3860, University of California Berkeley, Berkeley, California 94720, USA.
Physical Review. E
|June 20, 2019
Summary
This study explores optimal transportation network shapes, like subways, by minimizing travel time between points. As network length increases, radial branches are favored, with loops appearing at a critical length.
Area of Science:
- Operations Research
- Network Science
- Applied Mathematics
Background:
- Transportation networks, such as subway systems, are complex structures.
- Optimizing these networks is crucial for efficient travel and resource allocation.
- Understanding how network shape evolves with length is key to urban planning.
Purpose of the Study:
- To determine the optimal shape of a transportation network of a given length L.
- To investigate how network topology changes as length increases.
- To minimize average travel time between points in a planar distribution.
Main Methods:
- Mathematical modeling of transportation networks.
- Optimization techniques to find network configurations.
- Analytical and numerical simulations to study network properties.
- Analysis of travel time considering different speeds on network routes versus free space.
Main Results:
- The simplest case minimizes average distance to the network.
- For a central destination, star and ring networks are analyzed.
- In the general model, average travel time between all pairs of points is minimized.
- A scaling form for average time is proposed and numerically verified.
- Radial branches are prioritized in medium-length networks, with loops forming at a critical length (Lc).
Conclusions:
- Network shape is highly dependent on total length L.
- A transition occurs where loops become advantageous.
- The findings offer insights into the design of efficient transportation systems.
Related Concept Videos
02:57Coordination Number and Geometry
19.0K
For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.
19.0K
02:27Predicting Molecular Geometry
45.5K
VSEPR Theory for Determination of Electron Pair Geometries
45.5K
02:36Molecular Geometry and Dipole Moments
18.6K
The VSEPR theory can be used to determine the electron pair geometries and molecular structures as follows:
18.6K
01:07Radicals: Electronic Structure and Geometry
5.0K
This lesson delves into the geometry of a radical, which is influenced by the electronic structure of the molecule. The principle is similar to that of a lone pair, where the unpaired electron influences the geometry at the radical center.
Accordingly, the structure of a trivalent radical lies between the geometries of carbocations and carbanions. An sp2-hybridized carbocation is trigonal planar, while an sp3-hybridized carbanion is trigonal pyramidal. Here, the difference in geometry is...
Accordingly, the structure of a trivalent radical lies between the geometries of carbocations and carbanions. An sp2-hybridized carbocation is trigonal planar, while an sp3-hybridized carbanion is trigonal pyramidal. Here, the difference in geometry is...
5.0K
02:26Protein Networks
4.5K
An organism can have thousands of different proteins, and these proteins must cooperate to ensure the health of an organism. Proteins bind to other proteins and form complexes to carry out their functions. Many proteins interact with multiple other proteins creating a complex network of protein interactions.
These interactions can be represented through maps depicting protein-protein interaction networks, represented as nodes and edges. Nodes are circles that are representative of a protein,...
These interactions can be represented through maps depicting protein-protein interaction networks, represented as nodes and edges. Nodes are circles that are representative of a protein,...
4.5K
01:19Facilitated Transport
146.7K
The chemical and physical properties of plasma membranes cause them to be selectively permeable. Since plasma membranes have both hydrophobic and hydrophilic regions, substances need to be able to transverse both regions. The hydrophobic area of membranes repels substances such as charged ions. Therefore, such substances need special membrane proteins to cross a membrane successfully. In facilitated transport, also known as facilitated diffusion, molecules and ions travel across a...
146.7K