## Kinetic theory with newton's interaction

**De** 2002-10-01
**à** 2004-09-30

## Détails concernant le projet

### Coût total:

EUR 118 400
### Contribution de l'UE:

EUR 118 400
### Coordonné à/au(x)/en:

France

### Sujet(s):

### Régime de financement:

RGI - Research grants (individual fellowships)
## Objectif

We aim to address some conceptual questions arising in kinetic theory with particular emphasis on the case where the interactions between particles are of the Newtonian type. This problem has applications in several astrophysical contexts, such as in the study of globular clusters, as well as being of intrinsic interest from a statistical mechanics point of view. It is known that the partition function describing an ensemble of point masses with a gravitational interaction is divergent owing to the strength of the interaction at short distances. This divergence prevents the system from reaching equilibrium in the classical sense. As a result, the time evolution of the density, as described by the appropriate Boltzmann equation, must be studied. We have reason to believe that this equation may possess a finite time singularity that would lead to the accumulation of particles in low velocity regions of the phase space. If true, this singularity would endow the system with an intrinsic dynamical mechanism for aggregation that we believe would be a sound basis for further study of structure formation. In order to more fully understand the physics under lying the dynamics we aim to extend the conventional mean field approach, which has been used to study this problem in the past, to include collision effects. This will enable us to understand how irreversibility, absent at the mean field level, enters problem. From the point of view of the applicant this project provides an opportunity to develop skills from the physicist's point of view which will differ in many ways from the training obtained in the past few years spent in a mathematics department. Although there are many connections with previous problems I have studied, training in many new concepts and methodologies will be necessary. Specific training will include, but will not be limited to, kinetic theory, numerical simulation methods for N-body problems and conceptual foundations of statistical physics. In addition, possible astrophysical applications of this work will provide a window into a completely new field. It is hoped that by spending some time as active researcher at an institution playing such a central role in European science as the ENS, that my academic horizons will be also broadened in more general terms, providing a strong foundation for a future career in research.

## Coordinateur

ECOLE NORMALE SUPERIEURE

France

Rue Lhomond 24

75231 PARIS

France

See on map**Contact administratif: **Gabriel RUGET