Excitable London: Street map analysis with Oregonator model (1803.01632v2)

Abstract: We explore geometry of London's streets using computational mode of an excitable chemical system, Belousov-Zhabotinsky (BZ) medium. We virtually fill in the streets with a BZ medium and study propagation of excitation waves for a range of excitability parameters, gradual transition from excitable to sub-excitable to non-excitable. We demonstrate a pruning strategy adopted by the medium with decreasing excitability when wider and ballistically appropriate streets are selected. We explain mechanics of streets selection and pruning. The results of the paper will be used in future studies of studying dynamics of cities with living excitable substrates.

• The paper demonstrates that in highly excitable conditions, wave fronts fully propagate across London’s street network.
• The simulation reveals that as excitability decreases, waves exhibit ballistic behavior by favoring wider streets and paths at acute junction angles.
• The study highlights the method’s potential to inform urban planning and enhance emergency evacuation strategies through dynamic network analysis.

An Analysis of Urban Street Networks via the Oregonator Model in Excitable Chemical Systems

In the paper "Excitable London: Street Map Analysis with the Oregonator Model," the authors leverage the Belousov-Zhabotinsky (BZ) medium's properties to explore the dynamics of street networks through computational modeling. The BZ medium, characterized by excitable dynamics, serves as an analog to biological processes that similarly exhibit wave-like excitation patterns. In this research, the authors utilize this medium to examine London's street map, simulating how excitation waves propagate through the network under varying degrees of medium excitability.

Methodology

The authors employ the Oregonator model, a well-recognized mathematical framework for simulating reactions in the BZ system, to paper the propagation of excitation waves across London's street network. The streets are modeled as nodes in a discrete grid, whereby each node can be in an excitable or non-excitable state under the influence of inhibitor and activator concentrations. Adjustments to the excitability parameter $\phi$ allow transformation of the medium's behavior from excitable, through sub-excitable, to non-excitable states. The medium's response to perturbation is studied, simulating scenarios ranging from unrestricted wave propagation to selective path pruning as excitability decreases.

Dynamics and Results

The paper reveals that in an excitable medium, wave fronts propagate extensively, covering all accessible streets. However, as the medium transitions to a sub-excitable state, the behavior changes significantly. Here, waves begin to demonstrate ballistic propagation, selecting pathways and avoiding others based on the geometry of the network and the position of junctions. The simulation results demonstrate how decreasing the medium's excitability results in a strategic pruning decision: waves favor wider streets and bypass narrower, less energetically favorable routes.

Coverage of the network by excitation waves, which was complete in highly excitable states, becomes partial in lower excitability states. For instance, at $\phi$ values greater than 0.076, coverage is markedly reduced, with excitation appearing only along major routes. Moreover, the paper finds that coverage correlates with the angle of junctions—wave fronts have a higher probability of entering branch streets at acute angles than at obtuse angles.

Implications and Future Directions

From a theoretical perspective, this research enhances our understanding of how chemical wave dynamics apply to complex urban systems. The utilization of the BZ medium model to simulate urban exploration offers a fresh viewpoint for interpreting traffic flow, architectural planning, and even crowd dynamics during emergency evacuations.

Practically, this modeling approach could inform urban planning by identifying critical paths within city layouts that maintain connectivity and flow efficiency. Moreover, the Oregonator model can simulate scenarios reflecting real-world stress conditions, such as emergency evacuations, further enhancing urban safety protocols.

In terms of future research, this paper opens the avenue to exploring different urban layouts or other excitable media. Extensions of this model could integrate variable densities of obstacles or further examine non-linearities, such as traffic controls or pedestrian flows, to provide more robust insights into urban dynamics.

Conclusion

This exploration of London's street network via the Oregonator model and the BZ medium illustrates a novel intersection of chemical dynamics and urban paper. It underscores the potential of leveraging biological analogs to inform our understanding of urban environments, offering pathways for practical urban planning and theoretical exploration of dynamic systems.