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Author |
Couturier, E.; Dumais, J.; Cerda, E.; Katifori, E. |
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Title |
Folding of an opened spherical shell |
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Year |
2013 |
Publication |
Soft Matter |
Abbreviated Journal |
Soft Matter |
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Volume |
9 |
Issue |
34 |
Pages |
8359-8367 |
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Abstract |
Thin, doubly curved shells occur commonly in nature and their mechanical properties and modes of deformation are very important for engineering structures of all scales. Although there has been substantial work on the stability and modes of failure of thin shells, relatively little work has been done to understand the conditions that promote continuous large scale deformations. A major impediment to progress in this direction is the inherent difficulty in obtaining analytical expressions for the deformed shapes. In this work we propose a new integrable solution which describes the behavior under load of a thin spherical shell with an opening (aperture) of n-fold axial symmetry. We derive a two-parameter family of approximately isometric, constant positive Gaussian curvature shapes that is in excellent agreement with our experimental results of deformed shells (3D scans of compressed ping-pong balls) and simulations (tethered membrane simulations minimizing the stretching and bending energy). The integrable solutions that describe those shapes have n symmetrically arranged curvature singularities which correspond to cusps of the folded shape. We examine the properties of the folded shells and observe that in the analytic solutions isometric closure is more easily achieved when the singularities lie away from the center of the aperture. We find that when allowed by the geometry of the aperture and the nature of the load, physical shells expel the curvature singularities into the aperture. |
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[Couturier, E.; Cerda, E.] Univ Santiago Chile, Dept Fis, Santiago, Chile, Email: couturier_etienne@yahoo.fr |
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Royal Soc Chemistry |
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English |
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1744-683x |
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WOS:000322906900027 |
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UAI @ eduardo.moreno @ |
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305 |
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Author |
Abenza, J.F.; Couturier, E.; Dodgson, J.; Dickmann, J.; Chessel, A.; Dumais, J.; Salas, R.E.C. |
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Title |
Wall mechanics and exocytosis define the shape of growth domains in fission yeast |
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Year |
2015 |
Publication |
Nature Communications |
Abbreviated Journal |
Nat. Commun. |
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Volume |
6 |
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13 pp |
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Abstract |
The amazing structural variety of cells is matched only by their functional diversity, and reflects the complex interplay between biochemical and mechanical regulation. How both regulatory layers generate specifically shaped cellular domains is not fully understood. Here, we report how cell growth domains are shaped in fission yeast. Based on quantitative analysis of cell wall expansion and elasticity, we develop a model for how mechanics and cell wall assembly interact and use it to look for factors underpinning growth domain morphogenesis. Surprisingly, we find that neither the global cell shape regulators Cdc42-Scd1-Scd2 nor the major cell wall synthesis regulators Bgs1-Bgs4-Rgf1 are reliable predictors of growth domain geometry. Instead, their geometry can be defined by cell wall mechanics and the cortical localization pattern of the exocytic factors Sec6-Syb1-Exo70. Forceful re-directioning of exocytic vesicle fusion to broader cortical areas induces proportional shape changes to growth domains, demonstrating that both features are causally linked. |
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Address |
[Abenza, Juan F.; Dodgson, James; Dickmann, Johanna; Chessel, Anatole; Salas, Rafael E. Carazo] Univ Cambridge, Dept Genet, Cambridge CB2 3EH, England, Email: jfa27@cam.ac.uk; |
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Nature Publishing Group |
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English |
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2041-1723 |
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WOS:000364922900002 |
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UAI @ eduardo.moreno @ |
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553 |
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