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This version is close but not identical to the published version in Experimental Mathematics, 1 (1992) 141– 165. Some figures have been regenerated, and the bibliography updated. Pagination is different, and the text may not be exactly identical. Abstract The Surface Evolver is a computer program that minimizes the energy of a surface subject to(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)
A systematic feature extraction procedure is proposed. It is based on successive extractions of features. At each stage a dimensionality reduction is made and a new feature is extracted. A specific example is given using the Gaussian minus-log-likelihood ratio as a basis for the extracted features. This form has the advantage that if both classes are(More)
The Surface Evolver has been used to minimise the surface area of various ordered structures for monodisperse foam. Additional features have enabled its application to foams of arbitrary liquid fraction. Early results for the case of dry foam (negligible liquid fraction) produced a structure having lower surface area, or energy, than Kelvin's 1887 minimal(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)
Although the field of microfluidics has made significant progress in bringing new tools to address biological questions, the accessibility and adoption of microfluidics within the life sciences are still limited. Open microfluidic systems have the potential to lower the barriers to adoption, but the absence of robust design rules has hindered their use.(More)
Physics-based modeling techniques have been shown to be advanced methods for creating high quality surfaces for application in CAGD. In this paper we propose a physics-based Temporal Computational Object (TCO) as a modeling process that simulates a liquid membrane to generate organic free-form models. This process compliments existing solid and elastic(More)