Energy around a ring: the corrugation is the resistance
A ring of H atoms with one extra electron in the corona just outside it. The excess is slid around
by angle and the energy recorded.
Flat means nothing opposes the flow;
rippled means
the ripple amplitude is what a carrier must overcome, which is resistance in its most elementary
form — the periodic lattice corrugating the path.
Why a ring, and why this is answerable statically. Time evolution is needed to compute a
rate, not to establish whether flow is possible. If the path is flat, nothing opposes it and
the current is set by however fast charge is fed in and tapped off — the rate is bookkeeping.
Whether the path is flat is a static question. A ring realises feed-and-tap exactly: no ends, no
edge artefacts, and every site equivalent by construction.
Built-in check. By symmetry the energy must repeat every 360°/n. If the computed
curve does not, the calculation is wrong — which is the validity test every earlier attempt in
this line lacked.
URL: ?n=6 ring atoms, &a=2.2 arc spacing,
&dr=1.4 how far outside the ring the excess sits,
&th=0 its angle in units of the site spacing (0 = over an atom,
0.5 = between two), &bs=0.25 boundary speed, &reset clears.
relaxing…