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)
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 results of computer simulation of random Voronoi tessellations of the plane are presented. Statistics tallied include frequencies, area, and perimeter of n-sided cells, and the frequencies of n-and m-sided cells abutting.
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)
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)
This paper presents a physics-based modeling approach for the creation of high quality surfaces for application in CAGD. Physics-based modeling is commonly used in animation and scientific modeling, and simulates realistic dynamic motion for computer graphics. We propose a physics-based modeling of liquid surface motion as a means to generate complex… (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)
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)