Wyniki wyszukiwania

1

Generalized kinetic equations and effective thermodynamics

100%

Chavanis P.-H.

Banach Center Publications

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2004

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tom 66

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nr 1

79-101

EN

We introduce a new class of nonlocal kinetic equations and nonlocal Fokker-Planck equations associated with an effective generalized thermodynamical formalism. These equations have a rich physical and mathematical structure that can describe phase transitions and blow-up phenomena. On general grounds, our formalism can have applications in different domains of physics, astrophysics, hydrodynamics and biology. We find an aesthetic connexion between topics (stars, vortices, bacteries,...) which were previously disconnected. The common point between these systems is the (attractive) long-range nature of the interactions.

2

Gravitational collapse of a Brownian gas

63%

Sire C., Chavanis P.-H.

Banach Center Publications

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2004

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tom 66

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nr 1

287-304

EN

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.

3

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

51%

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

Banach Center Publications

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2004

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tom 66

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nr 1

103-126

EN

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

3 Banach Center Publications

3 Chavanis P.-H.

2 Sire C.

1 Ribot M.

1 Rosier C.

3 2004

Generalized kinetic equations and effective thermodynamics

Gravitational collapse of a Brownian gas

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