Periodic domain
= Periodic domain
A <periodic domain> identifies opposite faces of a fundamental cell, producing a <flat torus>. On an <interval> $[0,L]$, smooth <periodic boundary conditions> require $u(0,t)=u(L,t)$ and matching spatial <derivatives>. These endpoints are one location, rather than two independently controlled walls. Periodic <integration by parts> has no boundary term, and zero-mean <functions> have no zero <Fourier mode>.