Pierre-Henri Chavanis, Clement Sire
Published 2004-02-08Version 1
We determine an asymptotic expression of the blow-up time t_coll for self-gravitating Brownian particles or bacterial populations (chemotaxis) close to the critical point. We show that t_coll=t_{*}(eta-eta_c)^{-1/2} with t_{*}=0.91767702..., where eta represents the inverse temperature (for Brownian particles) or the mass (for bacterial colonies), and eta_c is the critical value of eta above which the system blows up. This result is in perfect agreement with the numerical solution of the Smoluchowski-Poisson system. We also determine the asymptotic expression of the relaxation time close but above the critical temperature and derive a large time asymptotic expansion for the density profile exactly at the critical point.
Journal: Phys. Rev. E, 70, 026115 (2004)
On the analogy between self-gravitating Brownian particles and bacterial populations
Integrability of the critical point of the Kagomé three-state Potts mode
Critical exponents and scaling invariance in the absence of a critical point
