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A criterion of collective behavior of bacteria

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

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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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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

References

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• 2. Vladimir Mityushev, Cluster method in composites and its convergence, Applied Mathematics Letters, 2018, 77, 44, 10.1016/j.aml.2017.10.001
• 3. Wojciech Nawalaniec, Classifying and analysis of random composites using structural sums feature vector, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2019, 475, 2225, 20180698, 10.1098/rspa.2018.0698
• 4. Wojciech Nawalaniec, Basicsums: A Python package for computing structural sums and the effective conductivity of random composites, Journal of Open Source Software, 2019, 4, 39, 1327, 10.21105/joss.01327
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