Interacting phase fields yielding phase separation on surfaces
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_ | 1866911964648701952 |
|---|---|
| author | Lledos, Benjamin Marziani, Roberta Olbermann, Heiner |
| author_facet | Lledos, Benjamin Marziani, Roberta Olbermann, Heiner |
| contents | In the present article we study diffuse interface models for two-phase biomembranes. We will do so by starting off with a diffuse interface model on $\mathbb{R}^n$ defined by two coupled phase fields $u,v$. The first phase field $u$ is the diffuse approximation of the interior of the membrane; the second phase field $v$ is the diffuse approximation of the two phases of the membrane. We prove a compactness result and a lower bound in the sense of $Γ$-convergence for pairs of phase functions $(u_\varepsilon,v_\varepsilon)$. As an application of this first result, we consider a diffuse approximation of a two-phase Willmore functional plus line tension energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15300 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interacting phase fields yielding phase separation on surfaces Lledos, Benjamin Marziani, Roberta Olbermann, Heiner Analysis of PDEs 49Q20, 49J45, 92C10 In the present article we study diffuse interface models for two-phase biomembranes. We will do so by starting off with a diffuse interface model on $\mathbb{R}^n$ defined by two coupled phase fields $u,v$. The first phase field $u$ is the diffuse approximation of the interior of the membrane; the second phase field $v$ is the diffuse approximation of the two phases of the membrane. We prove a compactness result and a lower bound in the sense of $Γ$-convergence for pairs of phase functions $(u_\varepsilon,v_\varepsilon)$. As an application of this first result, we consider a diffuse approximation of a two-phase Willmore functional plus line tension energy. |
| title | Interacting phase fields yielding phase separation on surfaces |
| topic | Analysis of PDEs 49Q20, 49J45, 92C10 |
| url | https://arxiv.org/abs/2406.15300 |