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Particle models in connection with Kuramoto-Sivashinsky equation

Abstract : This work is concerned by systems of interacting particles, which are linked to partial derivative equations when the particle number becomes large enough. The Kuramoto-Sivashinsky equation is actually modeling as well the front flame propagation as the morphology of growing interfaces, in deposition, for example. Moreover, surface periodical macroscopic structuring is occurring. An interacting particle model through an harmonic velocity coupling, attractive with the first velocity-neighbor and repulsive for the second neighbors, associated with elestic collisions. This model thus provides us with velocity profiles close to those of front flame propagation. Creation and annihilation of particle clusters is also observed. Another model, where particle are merging during collisions, while retaining mass and momentum conservation and with only nearest neighbor attraction, allows to recover a viscous pressureless gas model. These models are studied using mathematical tools. Especially interaction scaling factors are determined for obtaining the suitable equations in the large particle number limit. The numerical simulations confirm the relevance of the models.
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  • HAL Id : tel-00789952, version 1

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Thanh Tam Phung. Particle models in connection with Kuramoto-Sivashinsky equation. General Mathematics [math.GM]. Université d'Orléans, 2012. English. ⟨NNT : 2012ORLE2031⟩. ⟨tel-00789952⟩

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