title: A criterion of collective behavior of bacteria.
abstract: It was established in the previous works that hydrodynamic interactions between the swimmers can lead to collective motion. Its implicit evidences were confirmed by reduction in the effective viscosity. We propose a new quantitative criterion to detect such a collective behavior. Our criterion is based on a new computationally effective RVE (representative volume element) theory based on the basic statistic moments (e-sums or generalized Eisenstein-Rayleigh sums). The criterion can be applied to various two-phase dispersed media (biological systems, composites etc). The locations of bacteria are modeled by short segments having a small width randomly embedded in medium without overlapping. We compute the e-sums of the simulated disordered sets and of the observed experimental locations of Bacillus subtilis. The obtained results show a difference between these two sets that demonstrates the collective motion of bacteria.
authors.affiliation: Institute of Computer Science, Pedagogical University, ul. Podchorazych 2, Krakow 30-084, Poland. email: czapla@up.krakow.pl.
authors.forename: Roman
authors.initials: R
authors.lastname: Czapla
authors.forename: Vladimir V
authors.initials: VV
authors.lastname: Mityushev
mesh_terms: D001412:Bacillus subtilis / Q000502:physiology; D018407:Bacterial Physiological Phenomena; D057446:Hydrodynamics; D008954:Models, Biological; D009038:Motion; D014783:Viscosity