TY - JOUR
T1 - Inferring the size of a collective of self-propelled Vicsek particles from the random motion of a single unit
AU - De Lellis, Pietro
AU - Porfiri, Maurizio
N1 - Funding Information:
The authors wish to thank Agnieszka Truszkowska for setting up and performing numerical simulations for large collectives. P.D.L. was supported by the program “STAR 2018” of the University of Naples Federico II and Compagnia di San Paolo, Istituto Banco di Napoli - Fondazione, project ACROSS. M.P. was supported by the National Science Foundation under grant numbers CMMI 1561134 and CMMI 1932187.
Funding Information:
The authors wish to thank Agnieszka Truszkowska for setting up and performing numerical simulations for large collectives. P.D.L. was supported by the program “STAR 2018” of the University of Naples Federico II and Compagnia di San Paolo, Istituto Banco di Napoli - Fondazione, project ACROSS. M.P. was supported by the National Science Foundation under grant numbers CMMI 1561134 and CMMI 1932187.
Publisher Copyright:
© 2022, The Author(s).
PY - 2022/12
Y1 - 2022/12
N2 - Inferring the size of a collective from the motion of a few accessible units is a fundamental problem in network science and interdisciplinary physics. Here, we recognize stochasticity as the commodity traded in the units’ interactions. Drawing inspiration from the work of Einstein-Perrin-Smoluchowski on the discontinuous structure of matter, we use the random motion of one unit to identify the footprint of every other unit. Just as the Avogadro’s number can be determined from the Brownian motion of a suspended particle in a liquid, the size of the collective can be inferred from the random motion of any unit. For self-propelled Vicsek particles, we demonstrate an inverse proportionality between the diffusion coefficient of the heading of any particle and the size of the collective. We provide a rigorous method to infer the size of a collective from measurements of a few units, strengthening the link between physics and collective behavior.
AB - Inferring the size of a collective from the motion of a few accessible units is a fundamental problem in network science and interdisciplinary physics. Here, we recognize stochasticity as the commodity traded in the units’ interactions. Drawing inspiration from the work of Einstein-Perrin-Smoluchowski on the discontinuous structure of matter, we use the random motion of one unit to identify the footprint of every other unit. Just as the Avogadro’s number can be determined from the Brownian motion of a suspended particle in a liquid, the size of the collective can be inferred from the random motion of any unit. For self-propelled Vicsek particles, we demonstrate an inverse proportionality between the diffusion coefficient of the heading of any particle and the size of the collective. We provide a rigorous method to infer the size of a collective from measurements of a few units, strengthening the link between physics and collective behavior.
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U2 - 10.1038/s42005-022-00864-9
DO - 10.1038/s42005-022-00864-9
M3 - Article
AN - SCOPUS:85128179006
SN - 2399-3650
VL - 5
JO - Communications Physics
JF - Communications Physics
IS - 1
M1 - 86
ER -