Phase-field models on graphs

Phase field models on graphs are a discrete analogue to phase field models, defined on a graph. They are used in image analysis, ...

Graph Ginzburg-Landau functional

For a graph with vertices V and edge weights $\omega _{i,j}$, the graph Ginzburg-Landau functional of a map $u:V\to \mathbb {R}$ is given by

$F_{\varepsilon }(u)={\frac {\varepsilon }{2}}\sum _{i,j\in V}\omega _{i,j\in V}(u_{i}-u_{j})^{2}+{\frac {1}{\varepsilon }}\sum _{i\in V}W(u_{i}),$

where W is bla bla bla. The graph Ginzburg-Landau functional was introduced by Bertozzi and Flenner