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On anomalous diffusion - lecture 1
Multi angle
Authors : Armstrong, Scott (Author of the conference)
CIRM (Publisher )
35B27 - Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50]
35K15 - Initial value problems for second-order parabolic equations
CIRM (Publisher )
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Abstract :
Anomalous diffusion is the fundamental ansatz of phenomenological theories of passive scalar turbulence. In this talk we construct a class of incompressible vector fields that have many of the properties observed in a fully turbulent velocity field, and for which the associated scalar advection-diffusion equation generically displays anomalous diffusion. We also propose an analytical framework to study anomalous diffusion, via a backward cascade of renormalized eddy viscosities. Our proof is by “fractal” homogenization, that is, we perform a cascade of homogenizations across arbitrarily many length scales.
MSC Codes : 35B27 - Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50]
35K15 - Initial value problems for second-order parabolic equations
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 20/06/2025 Conference Date : 29/05/2025 Subseries : Research School arXiv category : Analysis of PDEs ; Fluid Dynamics ; Mathematical Physics Mathematical Area(s) : PDE ; Mathematical Physics Format : MP4 (.mp4) - HD Video Time : 01:18:44 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-05-29_Armstrong_Part1.mp4 
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Information on the Event
Event Title : Physics and Mathematics of hydrodynamic and wave turbulence / Physique et Mathématiques de la turbulence hydrodynamique et de la turbulence d'ondesEvent Organizers : Chevillard, Laurent ; Cortet, Pierre-Philippe ; Mordant, Nicolas ; Saint-Raymond, Laure ; Shatah, Jalal Dates : 26/05/2025 - 30/05/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3173.html
Citation Data
DOI : 10.24350/CIRM.V.20355903Cite this video as: Armstrong, Scott (2025). On anomalous diffusion - lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20355903 URI : http://dx.doi.org/10.24350/CIRM.V.20355903 |
See Also
- [Multi angle] On anomalous diffusion Lecture 2 / Author of the conference Vicol, Vlad.
- [Multi angle] On anomalous diffusion Lecture 1 / Author of the conference Vicol, Vlad.
- [Multi angle] Wave-wave interactions in rotating stratified flows - lecture 1 / Author of the conference Krstulovic, Giorgio.
- [Multi angle] Inertia-gravity waves interacting with background flows- lecture 2 - Strong-dispersion regime / Author of the conference Gallet, Basile.
- [Multi angle] Whither spontaneous stochasticity ? - lecture 3 / Author of the conference Eyink, Gregory.
- [Multi angle] Eulerian spontaneous stochasticity - lecture 2 / Author of the conference Eyink, Gregory.
- [Multi angle] Instabilities and singularities within fluid boundary layers - lecture 3 / Author of the conference Dalibard, Anne-Laure.
- [Multi angle] Instabilities and singularities within fluid boundary layers - lecture 2 / Author of the conference Dalibard, Anne-Laure.
- [Multi angle] Wave-wave interactions in rotating stratified flows - lecture 2 / Author of the conference Krstulovic, Giorgio.
- [Multi angle] Inertia-gravity waves interacting with background flows - lecture 1 / Author of the conference Gallet, Basile.
- [Multi angle] Lagrangian spontaneous stochasticity - lecture 1 / Author of the conference Eyink, Gregory.
- [Multi angle] Instabilities and singularities within fluid boundary layers - lecture 1 / Author of the conference Dalibard, Anne-Laure.
Bibliography
- ARMSTRONG, Scott et VICOL, Vlad. Anomalous diffusion via iterative quantitative homogenization: an overview of the main ideas. arXiv preprint arXiv:2503.11744, 2025. - https://doi.org/10.48550/arXiv.2503.11744
- ARMSTRONG, Scott et VICOL, Vlad. Anomalous diffusion by fractal homogenization. Annals of PDE, 2025, vol. 11, no 1, p. 2. - https://doi.org/10.48550/arXiv.2305.05048
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