A phase separation problem and geodesic disks on Cassinian oval surfaces

Barg, Michael; Mangum, Amanda

doi:10.1016/j.amc.2019.02.037

Cited by 2 publications

(1 citation statement)

References 11 publications

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“…The direction of movement for the spi cules is from the highly curved rim towards the regions with lower curvature. Small patches of lipids that separate would be expected to localise on the surface region with the highest Gauss curvature: this result has been found for ellipsoids [15,16], as well as for shapes more closely resembling discocytes, with regions of positive, zero and nega tive Gauss curvature [17]. For the RBCs, the region of highest Gauss curvature is on the rim, where the spicules are formed initially.…”

Section: Cytoskeleton Contributions To Spicule Behaviourmentioning

confidence: 81%

Spicule movement on RBCs during echinocyte formation and possible segregation in the RBC membrane

Melzak¹,

Moreno‐Flores²

2020

Biochimica et Biophysica Acta (BBA) - Biomembranes

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Section: Cytoskeleton Contributions To Spicule Behaviourmentioning

confidence: 81%

Spicule movement on RBCs during echinocyte formation and possible segregation in the RBC membrane

Melzak¹,

Moreno‐Flores²

2020

Biochimica et Biophysica Acta (BBA) - Biomembranes

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Statistical analysis of numerical solutions to constrained phase separation problems

Barg

Mangum

2023

era

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<abstract><p>We compute numerical solutions to a linearly constrained phase separation problem and a nonlinearly constrained phase separation problem on compact surfaces. Results are presented for oblate and prolate ellipsoids and Cassinian ovals. We implement a finite element, phase field method to determine solutions in the form of patches that are approximately geodesic disks for some values of the parameters. Our patches are numerical solutions to diffuse interface problems, and they exhibit qualitative features of solutions to corresponding sharp interface problems that are often studied in a $ \Gamma $-convergence setting. Our use of a nonlinear conservation constraint is motivated by a desire to sharpen the interface between two distinct regions: the patch and the rest of the surface. To this end, we explore features of the patches arising in both problems. A "geodesic protocol" is implemented to generate various statistics concerning the patch that are useful for measuring patch deviation from a geodesic disk shape. We then perform the Student's $ t $-test on paired differences of these statistics to determine whether or not there is a significant statistical difference between the linear constraint and nonlinear constraint approaches. The novel use of statistical analysis to compare these two methods reveals noteworthy differences. We show that the two approaches yield significantly different results for some of the statistics. The statistical results are found to depend on both the type of geometry and the patch size in some situations. Small patches are difficult to compute numerically, but we find that the use of a nonlinear constraint aids in their computation.</p></abstract>

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A phase separation problem and geodesic disks on Cassinian oval surfaces

Cited by 2 publications

References 11 publications

Spicule movement on RBCs during echinocyte formation and possible segregation in the RBC membrane

Spicule movement on RBCs during echinocyte formation and possible segregation in the RBC membrane

Statistical analysis of numerical solutions to constrained phase separation problems

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