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A criterion of collective behavior of bacteria

. Institute of Computer Science, Pedagogical University, ul. Podchorazych 2, Krakow 30-084, Poland

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.

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Keywords Collective behavior of bacteria; disordered random sets; generalized Eisenstein-Rayleigh sums; RVE; non-overlapping segments on plane

Citation: Roman Czapla, Vladimir V. Mityushev. A criterion of collective behavior of bacteria. Mathematical Biosciences and Engineering, 2017, 14(1): 277-287. doi: 10.3934/mbe.2017018

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Copyright Info: 2017, Vladimir V. Mityushev, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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