This was my dissertation for the MSc. Mathematical Modelling program at UCL. Abstract:

This dissertation analyses the asymptotic behaviour of the solution of problems on periodic quantum graphs as the period tends to zero. We consider variants of periodic quantum graphs with periodicity in one and two directions. Variants analysed include contrasts and stretching, and the question of existence of spectral gaps is addressed for the case of a contrasting graph with periodicity in one direction.

The whole text is available for download at the following url in pdf format: https://ext.kazeno.net/HomogenisationOfPeriodicQuantumGraphs-Kazeno2017.pdf