2021
DOI: 10.48550/arxiv.2112.08752
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Mean area of the convex hull of a run and tumble particle in two dimensions

Prashant Singh,
Anupam Kundu,
Satya N. Majumdar
et al.

Abstract: We investigate the statistics of the convex hull for a single run-and-tumble particle in two dimensions. Run-and-tumble particle (RTP), also known as persistent random walker, has gained significant interest in the recent years due to its biological application in modelling the motion of bacteria. We consider two different statistical ensembles depending on whether (i) the total number of tumbles n or (ii) the total observation time t is kept fixed. Benchmarking the results on perimeter, we study the statistic… Show more

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Cited by 1 publication
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“…We establish the possibilities created by recoil and persistence by solving exactly for the stationary interparticle distribution function for a pair of persistent random walkers in a periodic one-dimensional system, from which an effective attraction or repulsion between them can be identified. Despite persistence being a core property of active particles, exact results for interacting particles at the microscopic scale are very sparse [10,11,[17][18][19][20] compared to the noninteracting case (e.g., [21][22][23][24][25][26][27][28][29]). Enlarging the set of exact results for interacting systems constitutes a key step towards a physical theory for many-body systems of active matter that is fully grounded in microscopic principles and eludes us at present [30].…”
mentioning
confidence: 99%
“…We establish the possibilities created by recoil and persistence by solving exactly for the stationary interparticle distribution function for a pair of persistent random walkers in a periodic one-dimensional system, from which an effective attraction or repulsion between them can be identified. Despite persistence being a core property of active particles, exact results for interacting particles at the microscopic scale are very sparse [10,11,[17][18][19][20] compared to the noninteracting case (e.g., [21][22][23][24][25][26][27][28][29]). Enlarging the set of exact results for interacting systems constitutes a key step towards a physical theory for many-body systems of active matter that is fully grounded in microscopic principles and eludes us at present [30].…”
mentioning
confidence: 99%