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Twisted assemblies of filaments in ropes, cables, and bundles are essential structural elements in both macroscopic materials and living organisms. We have recently exploited the non-linear elastic theory of filament bundles to reveal a surprising formal equivalence between the elastic stresses induced by bundle twist and those induced by the positive curvature in thin, elastic sheets. These geometrically induced stresses are screened by fivefold disclination defects in the lattice packing, and we predict a discrete spectrum of elastic-energy ground states associated with integer numbers of disclinations in cylindrical bundles. Hence, twisted filament bundles, a common motif of biological filament assemblies, belong to the unusual class of materials in which defects are necessary components of the thermodynamically preferred groundstate.
Topological Defects and Twist in Filament BundlesGregory M. Grason, University of MassachusetsAmherse, DMR 0955760
G. M. Grason, Physical Review Letters 105,
The SMART program coordinates the research activities of undergraduates involved in a 10-week summer REU program at UMass Amherst. To quickly introduce students to the scope, methods and opportunities of theoretical research in the field of soft materials, faculty mentors give a series of “short-courses” targeted to the unique challenges of the SMART participants’ research. SMART participants meet weekly to discuss the progress and challenges of their ongoing work. During the 2010 program, participating UMass faculty contributed to these “group meetings” a series of topical discussions–on pattern formation, lattices & defects and geometry of soap films—with SMART participants to further stimulate their minds about the horizons of theoretic research in soft condensed matter.
Soft MAtter Research in Theory (SMART)Gregory M. Grason, University of MassachusetsAmherse, DMR 0955760
Above: Brian Hildebrandt and Dan Jardinget “hands on” experience with double-stranded DNA packaging with a scaled-up model of the Lambda phage virus
“Theory of Interactions Between Helical Filaments”
“dsDNA Viral Dynamics”
“Shape Transitions Along Thin Elastic Sheets”
Above: Michael Himmelsbach and graduate student, Stephanie Trittschuh, working out the kinks with a rope model of twisted filament assemblies