Mathematical analysis of a mesoscale model for multiphase membranes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914724454596608 |
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| author | Fuchs, Jakob Röger, Matthias |
| author_facet | Fuchs, Jakob Röger, Matthias |
| contents | In this paper we introduce a mesoscale continuum model for membranes made of two different types of amphiphilic lipids. The model extends work by Peletier and the second author [Arch. Ration. Mech. Anal. 193, 2009] for the one-phase case. We present a mathematical analysis of the asymptotic reduction to the macroscale when a key length parameter becomes arbitrarily small. We identify two main contributions in the energy: one that can be connected to bending of the overall structure and a second that describes the cost of the internal phase separations. We prove the $Γ$-convergence towards a perimeter functional for the phase separation energy and construct, in two dimensions, recovery sequences for the convergence of the full energy towards a 2D reduction of the Jülicher-Lipowsky bending energy with a line tension contribution for phase separated hypersurfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05069 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mathematical analysis of a mesoscale model for multiphase membranes Fuchs, Jakob Röger, Matthias Analysis of PDEs 74K15, 49J45, 49Q20, 74L15, 74Q05 In this paper we introduce a mesoscale continuum model for membranes made of two different types of amphiphilic lipids. The model extends work by Peletier and the second author [Arch. Ration. Mech. Anal. 193, 2009] for the one-phase case. We present a mathematical analysis of the asymptotic reduction to the macroscale when a key length parameter becomes arbitrarily small. We identify two main contributions in the energy: one that can be connected to bending of the overall structure and a second that describes the cost of the internal phase separations. We prove the $Γ$-convergence towards a perimeter functional for the phase separation energy and construct, in two dimensions, recovery sequences for the convergence of the full energy towards a 2D reduction of the Jülicher-Lipowsky bending energy with a line tension contribution for phase separated hypersurfaces. |
| title | Mathematical analysis of a mesoscale model for multiphase membranes |
| topic | Analysis of PDEs 74K15, 49J45, 49Q20, 74L15, 74Q05 |
| url | https://arxiv.org/abs/2402.05069 |