A criterion of collective behavior of bacteria
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 ba...
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| Language: | English |
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AIMS Press
2016-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017018 |
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| author | Roman Czapla Vladimir V. Mityushev |
| author_facet | Roman Czapla Vladimir V. Mityushev |
| author_sort | Roman Czapla |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-7624a34a45b94588b73860f20cd6b900 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-7624a34a45b94588b73860f20cd6b9002025-01-24T02:39:32ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-12-0114127728710.3934/mbe.2017018A criterion of collective behavior of bacteriaRoman Czapla0Vladimir V. Mityushev1Institute of Computer Science, Pedagogical University, ul. Podchorazych 2, Krakow 30-084, PolandInstitute of Computer Science, Pedagogical University, ul. Podchorazych 2, Krakow 30-084, PolandIt 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.https://www.aimspress.com/article/doi/10.3934/mbe.2017018collective behavior of bacteriadisordered random setsgeneralized eisenstein-rayleigh sumsrvenon-overlapping segments on plane |
| spellingShingle | Roman Czapla Vladimir V. Mityushev A criterion of collective behavior of bacteria Mathematical Biosciences and Engineering collective behavior of bacteria disordered random sets generalized eisenstein-rayleigh sums rve non-overlapping segments on plane |
| title | A criterion of collective behavior of bacteria |
| title_full | A criterion of collective behavior of bacteria |
| title_fullStr | A criterion of collective behavior of bacteria |
| title_full_unstemmed | A criterion of collective behavior of bacteria |
| title_short | A criterion of collective behavior of bacteria |
| title_sort | criterion of collective behavior of bacteria |
| topic | collective behavior of bacteria disordered random sets generalized eisenstein-rayleigh sums rve non-overlapping segments on plane |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017018 |
| work_keys_str_mv | AT romanczapla acriterionofcollectivebehaviorofbacteria AT vladimirvmityushev acriterionofcollectivebehaviorofbacteria AT romanczapla criterionofcollectivebehaviorofbacteria AT vladimirvmityushev criterionofcollectivebehaviorofbacteria |