Stretching of Polymers and turbulence: Fokker Planck equation, special stochastic scaling limit and stationary law
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910706676269056 |
|---|---|
| author | Flandoli, Franco Tahraoui, Yassine |
| author_facet | Flandoli, Franco Tahraoui, Yassine |
| contents | The aim of this work is understanding the stretching mechanism of stochastic models of turbulence acting on a simple model of dilute polymers. We consider a turbulent model that is white noise in time and activates frequencies in a shell $N\leq |k|\leq 2N$ and investigate the scaling limit as $N\rightarrow \infty$, under suitable intensity assumption, such that the stretching term has a finite limit covariance. The polymer density equation, initially an SPDE, converges weakly to a limit deterministic equation with a new term. Stationary solutions can be computed and show power law decay in the polymer length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00520 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stretching of Polymers and turbulence: Fokker Planck equation, special stochastic scaling limit and stationary law Flandoli, Franco Tahraoui, Yassine Probability Mathematical Physics Analysis of PDEs 35Q84, 60H15, 60H30, 76F25 The aim of this work is understanding the stretching mechanism of stochastic models of turbulence acting on a simple model of dilute polymers. We consider a turbulent model that is white noise in time and activates frequencies in a shell $N\leq |k|\leq 2N$ and investigate the scaling limit as $N\rightarrow \infty$, under suitable intensity assumption, such that the stretching term has a finite limit covariance. The polymer density equation, initially an SPDE, converges weakly to a limit deterministic equation with a new term. Stationary solutions can be computed and show power law decay in the polymer length. |
| title | Stretching of Polymers and turbulence: Fokker Planck equation, special stochastic scaling limit and stationary law |
| topic | Probability Mathematical Physics Analysis of PDEs 35Q84, 60H15, 60H30, 76F25 |
| url | https://arxiv.org/abs/2410.00520 |