Run-and-tumble bacteria slowly approaching the diffusive regime
Author
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Villa Torrealba, Andrea
Author
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Chávez Raby, Cristóbal
Author
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Castro, Pablo de
Author
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Soto, Rodrigo
Admission date
dc.date.accessioned
2020-08-13T23:49:39Z
Available date
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2020-08-13T23:49:39Z
Publication date
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2020
Cita de ítem
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Physical Review E Volumen: 101 Número: 6 Número de artículo: 062607 Jun 2020
es_ES
Identifier
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10.1103/PhysRevE.101.062607
Identifier
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https://repositorio.uchile.cl/handle/2250/176429
Abstract
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The run-and-tumble (RT) dynamics followed by bacterial swimmers gives rise first to a ballistic motion due to their persistence and later, through consecutive tumbles, to a diffusive process. Here we investigate how long it takes for a dilute swimmer suspension to reach the diffusive regime as well as what is the amplitude of the deviations from the diffusive dynamics. A linear time dependence of the mean-squared displacement (MSD) is insufficient to characterize diffusion and thus we also focus on the excess kurtosis of the displacement distribution. Four swimming strategies are considered: (i) the conventional RT model with complete reorientation after tumbling; (ii) the case of partial reorientation, characterized by a distribution of tumbling angles; (iii) a run-and-reverse model with rotational diffusion; and (iv) a RT particle where the tumbling rate depends on the stochastic concentration of an internal protein. By analyzing the associated kinetic equations for the probability density function and simulating the models, we find that for models (ii), (iii), and (iv) the relaxation to diffusion can take much longer than the mean time between tumble events, evidencing the existence of large tails in the particle displacements. Moreover, the excess kurtosis can assume large positive values. In model (ii) it is possible for some distributions of tumbling angles that the MSD reaches a linear time dependence but, still, the dynamics remains non-Gaussian for long times. This is also the case in model (iii) for small rotational diffusivity. For all models, the long-time diffusion coefficients are also obtained. The theoretical approach, which relies on eigenvalue and angular Fourier expansions of the van Hove function, is in excellent agreement with the simulations.
es_ES
Patrocinador
dc.description.sponsorship
Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT)
CONICYT FONDECYT
1180791
Millennium Nucleus Physics of Active Mater of ANID (Chile)