English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We provide an exact analytical solution of the collapse dynamics ofself-gravitating Brownian particles and bacterial populations at zerotemperature. These systems are described by the Smoluchowski-Poisson system orKeller-Segel model in which the diffusion term is neglected. As a result, thedynamics is purely deterministic. A cold system undergoes a gravitationalcollapse leading to a finite time singularity: the central density increasesand becomes infinite in a finite time t_coll. The evolution continues in thepost collapse regime. A Dirac peak emerges, grows and finally captures all themass in a finite time t_end, while the central density excluding the Dirac peakprogressively decreases. Close to the collapse time, the pre and post collapseevolution is self-similar. Interestingly, if one starts from a parabolicdensity profile, one obtains an exact analytical solution that describes thewhole collapse dynamics, from the initial time to the end, and accounts for nonself-similar corrections that were neglected in previous works. Our resultshave possible application in different areas including astrophysics,chemotaxis, colloids and nanoscience.

Exact analytical solution of the collapse of self-gravitating Brownian particles and bacterial populations at zero temperature