Upscaled equations for the Fokker-Planck diffusion through arrays of permeable and of impermeable inclusions
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913371692990464 |
|---|---|
| author | Amar, M. Andreucci, D. Cirillo, E. N. M. |
| author_facet | Amar, M. Andreucci, D. Cirillo, E. N. M. |
| contents | We study the Fokker-Planck diffusion equation with diffusion coefficient depending periodically on the space variable. Inside a periodic array of inclusions the diffusion coefficient is reduced by a factor called the diffusion magnitude. We find the upscaled equations obtained by taking both the degeneration and the homogenization limits in which the diffusion magnitude and the scale of the periodicity tends, respectively, to zero. Different behaviors, classified as pure diffusion, diffusion with mass deposition, and absence of diffusion, are found depending on the order in which the two limits are taken and on the ratio between the size of the inclusions and the scale of the periodicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20741 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Upscaled equations for the Fokker-Planck diffusion through arrays of permeable and of impermeable inclusions Amar, M. Andreucci, D. Cirillo, E. N. M. Analysis of PDEs Statistical Mechanics Mathematical Physics We study the Fokker-Planck diffusion equation with diffusion coefficient depending periodically on the space variable. Inside a periodic array of inclusions the diffusion coefficient is reduced by a factor called the diffusion magnitude. We find the upscaled equations obtained by taking both the degeneration and the homogenization limits in which the diffusion magnitude and the scale of the periodicity tends, respectively, to zero. Different behaviors, classified as pure diffusion, diffusion with mass deposition, and absence of diffusion, are found depending on the order in which the two limits are taken and on the ratio between the size of the inclusions and the scale of the periodicity. |
| title | Upscaled equations for the Fokker-Planck diffusion through arrays of permeable and of impermeable inclusions |
| topic | Analysis of PDEs Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2405.20741 |