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arXiv · 1812.06395

Lifetime distributions for adjacency relationships in a Vicsek model

Takuma Narizuka·Yoshihiro Yamazaki
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Abstract

We investigate the statistical properties of adjacency relationships in a two-dimensional Vicsek model. We define adjacent edges for all particles at every time step by (a) Delaunay triangulation and (b) Euclidean distance, and obtain cumulative distributions $ P(\tau) $ of lifetime $ \tau $ of the edges. We find that the shape of $ P(\tau) $ changes from an exponential to a power law depending on the interaction radius, which is a parameter of the Vicsek model. We discuss the emergence of the power-law distribution from the viewpoint of first passage time problem for a fractional Brownian motion.

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Takuma Narizuka, Yoshihiro Yamazaki. 2018-12-16. Lifetime distributions for adjacency relationships in a Vicsek model. https://doi.org/10.1103/physreve.100.032603

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