Hardt, Robert M.2011-07-252011-07-252009Dunning, Ryan Patrick. "Asymptotics under self-intersection for minimizers of self-avoiding energies." (2009) Diss., Rice University. <a href="https://hdl.handle.net/1911/61838">https://hdl.handle.net/1911/61838</a>.https://hdl.handle.net/1911/61838A knot energy is a real-valued function on a space of curves which in some sense assigns higher energy values to more complicated curves. The key property of any knot energy is self-repulsiveness: for a sequence of curves approaching a self-intersection, the energy blows up to infinity. While the study of optimally embedded curves as minimizers of energy among a given knot class has been well-documented, this thesis investigates the existence of optimally immersed self-intersecting curves. Because any self-intersecting curve will have infinite knot energy, parameter-dependent renormalizations of the energy remove the singular behavior of the curve. This process allows for the careful selection of an optimally immersed curve.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.MathematicsThesisTHESIS MATH. 2009 DUNNING