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Geometry and Topology of Diatom Shape and Surface Morphogenesis for Use in Applications of Nanotechnology

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Diatoms have attracted the interest of those involved in nanotechnology and the development of this discipline for research and practical application. These microorganisms exhibit self-assembly of silica on the micrometer scale, with parts of diatoms measuring on the nanometer scale. They exhibit a wide variety of shapes and patterns. An interest in diatom development and the geometry and topology of diatom shapes and gross patterns formed the focus of this study. Diatoms may be theoretically created on the basis of conic sections and quadratic surfaces expressed in parametric two-dimensional (2D)and three-dimensional (3D)functions (as sheets). Recreated diatom shapes, surfaces, and gross patterns based on 3D parametric equations are presented. Changes from one form to another are discussed as changes in magnitude or functional element within a given set of 3D equations for sequences that are phylogenetically or taxonomically related. Topological evolution and combinations of diatom shapes and surfaces are explored. An example shows how diatom forms depicted as 2-manifolds can be subjected to topological gluing to create a form whose surface is topologically different from the original. Topological surgery and gluing of diatoms as geometric forms may be useful in hypotheses about creating nanosubstrates and nanopatterned nanomaterials or in other applications of nanotechnology.
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Keywords: 2-MANIFOLD; DIATOMS; NANOSTRUCTURED MATERIALS; PARAMETRIC EQUATIONS; QUADRATIC SURFACES; THEORETICAL MORPHOLOGY; TOPOLOGICAL SURGERY

Document Type: Research Article

Publication date: 2005-01-01

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  • Journal for Nanoscience and Nanotechnology (JNN) is an international and multidisciplinary peer-reviewed journal with a wide-ranging coverage, consolidating research activities in all areas of nanoscience and nanotechnology into a single and unique reference source. JNN is the first cross-disciplinary journal to publish original full research articles, rapid communications of important new scientific and technological findings, timely state-of-the-art reviews with author's photo and short biography, and current research news encompassing the fundamental and applied research in all disciplines of science, engineering and medicine.
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