Crystallography on Curved Surfaces:
Virus Buckling and Grain Boundary Scars

David R. Nelson
Lyman Laboratory of Physics
Harvard University

Ordered states on spheres require a minimum number of topological defects.
The difficulty of constructing ordered states was recognized by J. J.
Thomson, who discovered the electron and then attempted regular tilings of
the sphere in an ill-fated attempt to explain the periodic table. One set
of solutions to this "Thomson problem" requires that regular triangular
lattices be interrupted by an array of at least 12 five-fold disclination
defects, typically sitting at the vertices of an icosahedron. For R>>a,
where R is the sphere radius and a is the particle spacing, the energy
associated with these defects is very large. This energy can be lowered,
however, either by buckling, as appears to be the case for large viruses,
or by introducing unusual finite length grain boundary scars. The latter
have been observed recently for colloidal particles adsorbed onto water
droplets in oil. Related problems involving crystalline and liquid
crystal patterns on other curved surfaces will be discussed as well.

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Non-Hermitian Luttinger Liquids and Vortex Physics

David R. Nelson
Lyman Laboratory of Physics
Harvard University

As a model of two thermally excited flux liquids connected by a weak link,
we describe the effect of a single line defect on vortex filaments
oriented parallel to the surface of a thin planar superconductor. When
the applied field is tilted relative to the line defect, the physics is
described by a nonhermitian Luttinger liquid of interacting quantum bosons
in one spatial dimension with a point defect. We find a delicate
interplay between enhancement of pinning due to Luttinger liquid effects
and depinning due to the tilted magnetic field. Interactions dramatically
improve the ability of a single columnar pin to suppress vortex tilt when
the Luttinger liquid parameter g is less than or equal to one. Exact
results are also possible via a free fermion mapping for flux lines
interacting with many columnar pins for the special case g = 1. Results
inspired by magnetic force microscope experiments which tear away a flux
line from various pinning structures will also be presented.

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Neutral Mutations and Gene Surfing in Microorganisms

David R. Nelson
Lyman Laboratory of Physics
Harvard University

It is widely appreciated that population waves have played a crucial role
in the evolutionary history of many species. Genetic footprints of many
pioneer species are still recognizable today, and neutral genetic markers
can be used to infer information about growth, ancestral population size,
colonization pathways, etc. Neutral mutations optimally positioned on a
the front of a growing population wave can increase their abundance via a
"surfing" phenomenon. Experimental and theoretical studies of this effect
will be presented, using bacteria and yeast as model systems.