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Gravitational collapse of a Brownian gas

100%

Sire C., Chavanis P.-H.

Banach Center Publications

2004

tom 66

nr 1

287-304

We investigate a model describing the dynamics of a gas of self-gravitating Brownian particles. This model can also have applications for the chemotaxis of bacterial populations. We focus here on the collapse phase obtained at sufficiently low temperature/energy and on the post-collapse regime following the singular time where the central density diverges. Several analytical results are illustrated by numerical simulations.

On the analogy between self-gravitating Brownian particles and bacterial populations

81%

Chavanis P.-H., Ribot M., Rosier C., Sire C.

Banach Center Publications

2004

tom 66

nr 1

103-126

We develop the analogy between self-gravitating Brownian particles and bacterial populations. In the high friction limit, the self-gravitating Brownian gas is described by the Smoluchowski-Poisson system. These equations can develop a self-similar collapse leading to a finite time singularity. Coincidentally, the Smoluchowski-Poisson system corresponds to a simplified version of the Keller-Segel model of bacterial populations. In this biological context, it describes the chemotactic aggregation of the bacterial colonies. We extend these classical models by introducing a small-scale regularization. In the gravitational context, we consider a gas of self-gravitating Brownian fermions and in the biological context we consider finite size effects. In that case, the collapse stops when the system feels the influence of the small-scale regularization. A phenomenon of "explosion", reverse to the collapse, is also possible.

Ograniczanie wyników

2 Banach Center Publications

2 Chavanis P.-H.

2 Sire C.

1 Ribot M.

1 Rosier C.

2 2004

Wyniki wyszukiwania

Gravitational collapse of a Brownian gas

On the analogy between self-gravitating Brownian particles and bacterial populations