Analytical and numerical solutions for shapes of quiescent two-dimensional vesicles

Veerapaneni, Shravan; Raj, Ritwik; Biros, George; Purohit, Prashant K.

doi:10.1016/j.ijnonlinmec.2008.10.004

Cited by 26 publications

(25 citation statements)

References 22 publications

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“…One of the first studies on these was done by Radon [23], When dealing with closed elasticae several different constraints can be considered. In the planar case, for instance, together with fixed length an additional area constraint has been considered among others by [1,3,28,29,30]. Another possibility is to restrict the set of curves to those which lie inside a given domain, see for instance [4].…”

Section: Introductionmentioning

confidence: 99%

The elastica problem under area constraint

2015

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Section: Introductionmentioning

confidence: 99%

The elastica problem under area constraint

2015

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“…A wide variety of models were developed to describe the deformation of RBCs, for example, . Because of the incompressibility, the main mode of the deformation of vesicles is bending, and the bending energy describes the cell shapes.…”

Section: Introductionmentioning

confidence: 99%

“…These cells exhibit a wide and rich set of shapes in various physical environments. Effective mathematical models, seconded by the use of accurate numerical methodologies, are needed to study, in particular, the equilibrium shapes of RBCs.A wide variety of models were developed to describe the deformation of RBCs, for example, [4,5,[11][12][13][14][15][16][17][18]. Because of the incompressibility, the main mode of the deformation of vesicles is bending, and the bending energy describes the cell shapes.…”

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confidence: 99%

An adaptive finite element method for the modeling of the equilibrium of red blood cells

Laadhari

Saramito

Misbah

2015

Numerical Methods in Fluids

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International audienceThis contribution is concerned with a the numerical modeling of an isolated red blood cell (RBC), and more generally of phospholipid membranes. We propose an adaptive Eulerian finite element approximation, based on the level set method, of a shape optimization problem arising in the study of RBC's equilibrium. We simulate the equilibrium shapes that minimize the elastic bending energy under prescribed constraints of fixed volume and surface area. An anisotropic mesh adaptation technique is used in the vicinity of the cell's membrane to enhance the robustness of the method. Efficient time and spatial discretizations are considered and implemented. We address in detail the main features of the proposed method and finally we report several numerical experiments in the two-dimensional and the three-dimensional axisymmetric cases. The effectiveness of the numerical method is further demonstrated through numerical comparisons with semi-analytical solutions provided by a reduced order model

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“…Indeed, this problem is related to the modelling of vesicles which attracts much attention recently. For a study of critical points of the functional and some numerical results, we refer to [16].…”

Section: Introductionmentioning

confidence: 99%

Elastic energy of a convex body

Bianchini

Henrot

Takahashi

2015

Mathematische Nachrichten

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In this paper a Blaschke-Santaló diagram involving the area, the perimeter and the elastic energy of planar convex bodies is considered. More precisely we give a description of setwhere A is the area, P is the perimeter and E is the elastic energy, that is a Willmore type energy in the plane. In order to do this, we investigate the following shape optimization problem:where C is the class of convex bodies with fixed perimeter and µ 0 is a parameter. Existence, regularity and geometric properties of solutions to this minimum problem are shown.

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Analytical and numerical solutions for shapes of quiescent two-dimensional vesicles

Cited by 26 publications

References 22 publications

The elastica problem under area constraint

The elastica problem under area constraint

An adaptive finite element method for the modeling of the equilibrium of red blood cells

Elastic energy of a convex body

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