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Stuart McKaige , Computational Algorithms for Packing Circles in a Square Box

CAREER: Mapping the Packing Geometry of Twisted Bundles Gregory M. Grason, University of Massachusetts Amherst, DMR 0955760.

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Stuart McKaige , Computational Algorithms for Packing Circles in a Square Box

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  1. CAREER: Mapping the Packing Geometry of Twisted BundlesGregory M. Grason, University of Massachusetts Amherst, DMR 0955760 Densely packed and twisted assemblies of filaments and strands are crucial structural motifs in macroscopic materials (ropes, textiles) as well as synthetic and biological nanomaterials (fibrous proteins). We have developed a new theory of the packing limits of optimal assemblies of molecular filaments into ropes, or bundles. The theory derives from a hidden connection between the geometry of bundles and the packing of discs on curved surfaces.  The results provide novel insight into the complex and heterogeneous structure of twisted filament assemblies found in natural materials and suggest new design principles for human-made fibrous nanomaterials. I. R. Bruss and G. M. Grason, “Non-Euclidean Geometry of Twisted Filament Bundle Packing,” Proc. Nat. Acad. Sci. USA 109, 10781 (2012). Three views of a twisted bundle packing. In (a), the horizontal cross section of a twisted bundle, in (b), a vertical slice through the bundle and in (c), the dual representation of the twisted bundle packing as a disc packing covering a bundle-equivalent dome.

  2. Soft Matter Research in Theory REU (SMaRT)Gregory M. Grason, University of Massachusetts Amherst, DMR 0955760 The SMaRT program coordinates the research activities of a group of undergraduates involved in a 10-week summer REU program at UMass Amherst. To introduce students to the scope, methods and opportunities of soft matter theory, faculty mentors give a series of “short-courses” targeted to each SMART participants’ research project. Taking advantage of the peer-learning opportunity, participants meet weekly to discuss ongoing progress and challenges. During the 2012 program, four undergraduates from programs around the country participated in research projects on a diverse range of topics in soft matter and statistical physics. 2012 SMaRT Research Projects: Kyle Vanderwerf, Modeling the Shape of Surfaces Buckled by Halftone Gel Lithography Stuart McKaige, Computational Algorithms for Packing Circles in a Square Box Christian Dane Gentry, Dislocations in Twisted Bundles Morgan Opie, Wrinkles in Radial Geometries

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