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Collisions of the supercritical Keller-Segel particle system| title | Collisions of the supercritical Keller-Segel particle system |
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| start_date | 2024/12/04 |
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| schedule | 14h15 |
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| online | no |
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| location_info | salle Sophie Germain 1013 |
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| summary | We study a particle system naturally associated to the 2-dimensional Keller-Segel equation. It consists of N Brownian particles in the plane, interacting through a binary attraction in θ/(Nr), where r stands for the distance between two particles. When the intensity θ of this attraction is greater than 2, this particle system explodes in finite time. We assume that N>3θ and study in details what happens near explosion. There are two slightly different scenarios, depending on the values of N and θ, here is one: at explosion, a cluster consisting of precisely k0 particles emerges, for some deterministic k0≥7 depending on N and θ. Just before explosion, there are infinitely many (k0−1)-ary collisions. There are also infinitely many (k0−2)-ary collisions before each (k0−1)-ary collision. And there are infinitely many binary collisions before each (k0−2)-ary collision. Finally, collisions of subsets of 3,…,k0−3 particles never occur. The other scenario is similar except that there are no (k0−2)-ary collisions. |
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| responsibles | Vernier, Merle |
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Workflow history| from state (1) | to state | comment | date |
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| submitted | published | | 2024/11/28 16:01 UTC |
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