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Aggregation of chemotactic bacteria under a unimodal distribution of chemicalcues was investigated by Monte Carlo (MC) simulation based on a kinetictransport equation, which considers an internal adaptation dynamics as well asa finite tumbling duration. It was found that there exist two different regimesof the adaptation time, between which the effect of the adaptation time on theaggregation behavior is reversed; that is, when the adaptation time is as smallas the running duration, the aggregation becomes increasingly steeper as theadaptation time increases, while, when the adaptation time is as large as thediffusion time of the population density, the aggregation becomes morediffusive as the adaptation time increases. Moreover, the aggregation profilebecomes bimodal (volcano) at the large adaptation-time regime when the tumblingduration is sufficiently large while it is always unimodal at the smalladaptation-time regime. A remarkable result of this study is the identificationof the parameter regime and scaling for the volcano effect. That is, bycomparing the results of MC simulations to the continuum-limit models obtainedat each of the small and large adaptation-time scalings, it is clarified thatthe volcano effect arises due to the coupling of diffusion, adaptation, andfinite tumbling duration, which occurs at the large adaptation-time scaling.

Numerical study of the volcano e ect in chemotactic aggregation based on a kinetic transport equation with non-instantaneous tumbling