Solid-State Boundary and Invariant Scans

Lattice Fixed-Length Three-Row Scan

Cell count and spacing trade off while total length stays fixed. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Coarse cells keep the same total length

The cell count and spacing trade off while total length stays 12 m. The reciprocal row is 1/6 per m.

L=2⋅6=12 m,b=1/6 per m,sites=3L=2\cdot 6=12\ \mathrm{m},\quad b=1/6\ \mathrm{per\ m},\quad sites=3
Fixed-length lattice row coarseThe reciprocal spacing cites the same lattice source.a=6 mb=1/6 1/ma*b=1

Middle cells keep the same total length

The cell count and spacing trade off while total length stays 12 m. The reciprocal row is 1/4 per m.

L=3⋅4=12 m,b=1/4 per m,sites=4L=3\cdot 4=12\ \mathrm{m},\quad b=1/4\ \mathrm{per\ m},\quad sites=4
Fixed-length lattice row middleThe reciprocal spacing cites the same lattice source.a=4 mb=1/4 1/ma*b=1

Fine cells keep the same total length

The cell count and spacing trade off while total length stays 12 m. The reciprocal row is 1/2 per m.

L=6⋅2=12 m,b=1/2 per m,sites=7L=6\cdot 2=12\ \mathrm{m},\quad b=1/2\ \mathrm{per\ m},\quad sites=7
Fixed-length lattice row fineThe reciprocal spacing cites the same lattice source.a=2 mb=1/2 1/ma*b=1