Publication Date

Summer 7-28-2026

Abstract

This thesis develops a boundary integral method for a modified Mullins–Sekerka system arising as the sharp-interface limit of a nonreciprocal Cahn–Hilliard model. Nonreciprocal coupling changes the classical Cahn–Hilliard structure by introducing an additional conserved field, leading to coupled elliptic and parabolic dynamics at the interface. Using matched asymptotic expansions, we formally derive the modified Mullins–Sekerka model and then apply the boundary integral method to rewrite it on the moving interface. The elliptic component is represented using the periodic Green’s function for the Laplace equation, while the parabolic component is represented using the periodic heat kernel. This method reduces the bulk problem to an interface equation involving the normal velocity of the moving boundary and provides a foundation for future numerical and analytical studies of nonreciprocal interface motion.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Daniel Gomez

Second Committee Member

Stephen Lau

Third Committee Member

Owen Lewis

Language

English

Keywords

laplace, heat kernel, Periodic Green's function, Interface dynamics, Matched asymptotic expansions

Document Type

Thesis

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