Plastic deformations in tubular crystals
When a 2D crystal is rolled up into the topology of a cylinder, the resulting tubular crystal is characterized by a pair of integers called parastichy numbers. Dislocation defects moving through the crystal cause plastic deformations by changing the parastichy numbers. Using continuum analytic calculations and numerical modeling of discretized surfaces, my work with David Nelson maps out pathways of deformation under external stresses in the space of tubular configurations. The crystal's bending rigidity plays an important role in resisting extensile stresses, and it can even cause narrow tubes to spontaneously widen themselves plastically.
Dislocation glide in a tubular crystal
Defects in liquid crystals
As singularities where liquid crystalline order breaks down, defects are the keys to an immense variety of complex material behaviors beyond those in the ubiquitous liquid crystal display technologies. Despite their local energetic cost, defects can be robust features when boundary conditions frustrate the material order. My work on this subject involves diverse approaches to studying defects in three liquid crystal phases: nematic, cholesteric, and smectic-A.
Smectic focal conic domains
Biological range expansions
When a species expands into new territory, population genetics at the front differs markedly from the situation in well-mixed populations, including diminished genetic diversity. The backwards-time view of coalescing genetic lineages (signifying common ancestry) provides a useful way to connect genetic measurements at the front with evolutionary events in the past. I am studying the effects of front roughness, superdiffusive genetic lineages, curved topographies, and other environmental heterogeneities on the statistics of these coalescences, and the resulting effects on the genetics of the expanding population.
Stepping-stone simulation of range expansion with rough front, with many neutral alleles (rainbow colors) and ancestral lineages of survivors shown in black.