The phantom limb

Thesis (M.D.)—Boston Universit

Evaporative Deposition in Receding Drops

We present a framework for calculating the surface density profile of a stain deposited by a drop with a receding contact line. Unlike a pinned drop, a receding drop pushes fluid towards its interior, continuously deposits mass across its substrate as it evaporates, and does not produce the usual "coffee ring." For a thin, circular drop with a constant evaporation rate, we find the surface density of the stain goes as $\eta(r) \propto \left(\left(r/a_0\right)^{-1/2}-r/a_0\right)$, where $r$ is the radius from the drop center and $a_0$ is the initial outer radius. Under these conditions, the deposited stain has a mountain-like morphology. Our framework can easily be extended to investigate new stain morphologies left by drying drops.Comment: 6 pages, 4 figure

Anomalies and Invertible Field Theories

We give a modern geometric viewpoint on anomalies in quantum field theory and illustrate it in a 1-dimensional theory: supersymmetric quantum mechanics. This is background for the resolution of worldsheet anomalies in orientifold superstring theory.Comment: 21 pages, based talk at String-Math 2013; small corrections in v

Supersolutions

We develop classical globally supersymmetric theories. As much as possible, we treat various dimensions and various amounts of supersymmetry in a uniform manner. We discuss theories both in components and in superspace. Throughout we emphasize geometric aspects. The beginning chapters give a general discussion about supersymmetric field theories; then we move on to detailed computations of lagrangians, etc. in specific theories. An appendix details our sign conventions. This text will appear in a two-volume work "Quantum Fields and Strings: A Course for Mathematicians" to be published soon by the American Mathematical Society. Some of the cross-references may be found at http://www.math.ias.edu/~drm/QFT/Comment: 130 pages, AMSTe