Kenneth A. Brakke

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The Surface Evolver is a computer program that minimizes the energy of a surface subject to constraints. The surface is represented as a simplicial complex. The energy can include surface tension, gravity, and other forms. Constraints can be geometrical constraints on vertex positions or constraints on integrated quantities such as body volumes. The(More)
A “dry” conical soap film on a cubical frame is not stable. Recent experimental evidence seems to indicate that adding liquid to form Plateau borders stabilizes the conical film, perhaps to arbitrarily low liquid fractions. This paper presents numerical simulation evidence that the the wet cone is unstable for low enough liquid fraction, with the critical(More)
Epithelial cells acquire functionally important shapes (e.g., squamous, cuboidal, columnar) during development. Here, we combine theory, quantitative imaging, and perturbations to analyze how tissue geometry, cell divisions, and mechanics interact to shape the presumptive enveloping layer (pre-EVL) on the zebrafish embryonic surface. We find that, under(More)
We consider an eversion of a sphere driven by a gradient flow for elastic bending energy. We start with a halfway model which is an unstable Willmore sphere with 4-fold orientation-reversing rotational symmetry. The regular homotopy is automatically generated by flowing down the gradient of the energy from the halfway model to a round sphere, using the(More)
The microbial secondary metabolome encompasses great synthetic diversity, empowering microbes to tune their chemical responses to changing microenvironments. Traditional metabolomics methods are ill-equipped to probe a wide variety of environments or environmental dynamics. Here we introduce a class of microscale culture platforms to analyse chemical(More)
Weaire was supported in part by the EC Science Programme, contract SC*-CT92-0777 and HCM Network Contract ERBCHRX940542. Phelan was supported in part by Shell Research (Amsterdam) and an Irish-American Partnership studentship. The Surface Evolver has been used to minimise the surface area of various ordered structures for monodisperse foam. Additional(More)
We study theoretically the influence of an external magnetic field on the orientation of an ellipsoidal magnetic particle adsorbed at a liquid interface. Using the finite element program Surface Evolver, we calculate the equilibrium meniscus shape around the ellipsoidal particle and its equilibrium tilt angle with respect to the undeformed interface θt when(More)
The formation of complex inorganic superstructures in nature relies on the interaction between organic and inorganic species to direct the inorganic form away from its “usual” morphology. During synthesis the superstructures are soft and dynamic which makes a study of the nature of the ephemeral interface difficult. However, the inorganic skeletons formed(More)
Inverse bicontinuous cubic lyotropic phases are a complex solution to the dilemma faced by all self-assembled water-amphiphile systems: how to satisfy the incompatible requirements for uniform interfacial curvature and uniform molecular packing. The solution reached in this case is for the water-amphiphile interfaces to deform hyperbolically onto triply(More)