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Cell$-$cell and Cell$-$noise Interactions of Bacterial Cells in a Shallow Circular Pool and Transitions of Collective Motions

We have experimentally investigated the transitions of collective motions of bacterial cells in a shallow circular pool using the bacterial species $Bacillus$ $subtilis$. In our previous paper, we reported that the collective motions were classified into six phases on a phase diagram with two parameters, namely, the reduced cell length $λ$ and the cell density $ρ$. In this study, we focused on the sharp transitions at $λ\cong0.1$ ($\equiv λ_{\rm C1}$) with low values of $ρ$ between the $random$ $motion$ phase and the $one$-$way$ $rotational$ $motion$ phase. By introducing the order parameter $Q$ which measures the aligned cell motion along the circumferential direction of a pool, the transitions at $λ=λ_{\rm C1}$ were clearly characterized. On the basis of the detailed observations of single-cell trajectories in a pool, we verified that the effect of cell$-$noise interactions was widely distributed. We conclude that, even in such random environment, the sharp transitions of collective motions were caused by the cell$-$cell interactions at $λ=λ_{\rm C1}$.