Elliott, Charles M. ; Fritz, Hans ; Hobbs, Graham
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Mathematical Models and Methods in Applied Sciences |
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| Verlag: | WORLD SCIENTIFIC PUBL CO PTE LTD |
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| Ort der Veröffentlichung: | SINGAPORE |
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| Band: | 27 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 08 |
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| Seitenbereich: | S. 1547-1586 |
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| Datum: | 2017 |
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| Institutionen: | Mathematik |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.1142/S0218202517500269 | DOI |
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| Stichwörter / Keywords: | MEMBRANES; PROTRUSIONS; CURVATURE; DYNAMICS; VESICLES; WILLMORE; THEOREM; DRIVEN; FLOW; Surface deformations; Helfrich energy; point forces; PDEs on surfaces; existence and uniqueness of weak solutions; discretisation; surface finite element method |
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| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
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| Status: | Veröffentlicht |
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| Begutachtet: | Ja, diese Version wurde begutachtet |
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| An der Universität Regensburg entstanden: | Ja |
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| Dokumenten-ID: | 39417 |
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Zusammenfassung
In this paper, we introduce a mathematical model for small deformations induced by external forces of closed surfaces that are minimisers of Helfrich-type energies. Our model is suitable for the study of deformations of cell membranes induced by the cytoskeleton. We describe the deformation of the surface as a graph over the undeformed surface. A new Lagrangian and the associated Euler-Lagrange ...
Zusammenfassung
In this paper, we introduce a mathematical model for small deformations induced by external forces of closed surfaces that are minimisers of Helfrich-type energies. Our model is suitable for the study of deformations of cell membranes induced by the cytoskeleton. We describe the deformation of the surface as a graph over the undeformed surface. A new Lagrangian and the associated Euler-Lagrange equations for the height function of the graph are derived. This is the natural generalisation of the well-known linearisation in the Monge gauge for initially flat surfaces. We discuss energy perturbations of point constraints and point forces acting on the surface. We establish existence and uniqueness results for weak solutions on spheres and on tori. Algorithms for the computation of numerical solutions in the general setting are provided. We present numerical examples which highlight the behaviour of the surface deformations in different settings at the end of the paper.
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