nferring 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.

Inferring the size of a collective of self-propelled Vicsek particles from the random motion of a single unit

Pietro De Lellis
Primo
;
Maurizio Porfiri
2022

Abstract

nferring 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.
File in questo prodotto:
File Dimensione Formato  
s42005-022-00864-9.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 588.58 kB
Formato Adobe PDF
588.58 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/902023
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? ND
social impact