A diagrammatic derivation of (convective) pattern equations

The resulting pattern equation is nonlocal but it reduces without approximation to the 1-D Swift-Hohenberg equation in the case of 2-D convection. Like the S-H equation, the nonlocal version admits a Lyapunov functional and we briefly indicate its utility in pattern selection both for the Swift-Hohenberg equation and its nonlocal extension. We conclude by describing the kinds of problems for which we intend the combined method but reserve the exhibition of the required calculations for a future festschrift.