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Recent advances on the Smoluchowski coagulation equation under non-equilibrium conditions
Multi angle
Authors : Nota, Alessia (Author of the conference)
CIRM (Publisher )
82C05 - Classical dynamic and nonequilibrium statistical mechanics (general)
82C40 - Kinetic theory of gases
35Q82 - PDEs in connection with statistical mechanics
CIRM (Publisher )
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Abstract :
The Smoluchowski's coagulation equation is an integro-differential equation of kinetic type which provides a mean-field description for mass aggregation phenomena. In this talk I will present some recent results on the problem of existence or non-existence of stationary solutions, both for single and multi-component systems, under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. The most striking feature of these stationary solutions is that, whenever they exist, the solutions to multi-component systems exhibit an unusual “spontaneous localization” phenomenon: they localize along a line in the composition space as the total size of the particles increase. This localization is a universal property of multicomponent systems and it has also been recently proved to occur in time dependent solutions to mass conserving coagulation equations.
Keywords : Smoluchowski's equation; multicomponent Smoluchowski's equation; non-equilibrium dynamics; source term; stationary injection solutions; constant flux solutions; mass flux; mass localization
MSC Codes : Keywords : Smoluchowski's equation; multicomponent Smoluchowski's equation; non-equilibrium dynamics; source term; stationary injection solutions; constant flux solutions; mass flux; mass localization
82C05 - Classical dynamic and nonequilibrium statistical mechanics (general)
82C40 - Kinetic theory of gases
35Q82 - PDEs in connection with statistical mechanics
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 04/04/2025 Conference Date : 25/03/2025 Subseries : Research talks arXiv category : Mathematical Physics ; Analysis of PDEs Mathematical Area(s) : Mathematical Physics ; PDE Format : MP4 (.mp4) - HD Video Time : 00:48:52 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-03-25_Nota.mp4 
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Information on the Event
Event Title : SMF RC. Kinetic theory and fluid mechanics: couplings, scalings and asymptotics. / ER SMF. Théorie cinétique et mécanique des fluides : couplages, échelles et asymptotiques.Event Organizers : Han-Kwan, Daniel ; Lods, Bertrand ; Moussa, Ayman ; Tristani, Isabelle Dates : 24/03/2025 - 28/03/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3205.html
Citation Data
DOI : 10.24350/CIRM.V.20331903Cite this video as: Nota, Alessia (2025). Recent advances on the Smoluchowski coagulation equation under non-equilibrium conditions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20331903 URI : http://dx.doi.org/10.24350/CIRM.V.20331903 |
See Also
- [Multi angle] Homogenization of Stokes-Brinkman type models and mean field limit - lecture 1 / Author of the conference Mecherbet, Amina.
- [Multi angle] Homogenization of Stokes-Brinkman type models and mean field limit - lecture 2 / Author of the conference Mecherbet, Amina.
- [Multi angle] Homogenization of Stokes-Brinkman type models and mean field limit - lecture 3 / Author of the conference Mecherbet, Amina.
- [Multi angle] Diffusion asymptotic of a kinetic model for gas-particle mixture with energy exchanges / Author of the conference Charles, Frédérique.
Bibliography
- FERREIRA, Marina A., LUKKARINEN, Jani, NOTA, Alessia, et al. Stationary non-equilibrium solutions for coagulation systems. Archive for Rational Mechanics and Analysis, 2021, vol. 240, p. 809-875. - https://doi.org/10.1007/s00205-021-01623-w
- FERREIRA, Marina A., LUKKARINEN, Jani, NOTA, Alessia, et al. Localization in stationary non-equilibrium solutions for multicomponent coagulation systems. Communications in Mathematical Physics, 2021, vol. 388, p. 479-506. - https://doi.org/10.1007/s00220-021-04201-z
- FERREIRA, Marina A., LUKKARINEN, Jani, NOTA, Alessia, et al. Non-equilibrium stationary solutions for multicomponent coagulation systems with injection. Journal of Statistical Physics, 2023, vol. 190, no 5, p. 98. - https://doi.org/10.1007/s10955-023-03107-5
- FERREIRA, Marina A., LUKKARINEN, Jani, NOTA, Alessia, et al. Asymptotic localization in multicomponent mass conserving coagulation equations. Pure and Applied Analysis, 2024, vol. 6, no 3, p. 731-764. - https://doi.org/10.2140/paa.2024.6.731
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