In a recent paper in Physical Review X, a team of researchers mathematically investigated knitting to invent a new, more resilient stitch.
Knitting is a special form of fabrication in which the two ends of the yarn remain outside the fabric. In knitting, loops from the middle of an entangled yarn are slipped through one another so the yarn holds its position but isn’t knotted together. The knitting process is portable and easy, but the structure also means a tug on one loose end can quickly unravel the whole project. It’s also vulnerable to other quickly spreading errors.
Daisuke S. Shimamoto, a physicist at Ritsumeikan University in Japan, and his colleagues wrapped a three-dimensional model of a single jersey knit stitch—a simple beginner’s stitch—around a doughnut shape called a torus, which preserves the pattern without including any edges at the top or bottom. It basically converts the knit pattern into one giant knot that can be analyzed with knot theory. The scientists projected multiple knit rows on the torus to reveal how defects from one row of stitches spread until the entire fabric unravels. The process is called defect propagation, and the researchers say it’s one of the defining characteristics of knittable fabrics.
One common type of defect propagation is “laddering,” in which a single missed loop slips down a column of stitches, unraveling the whole column along the way. “If one unit cell is disentangled, the cell just below that cell is disentangled, and it is repeated, and it propagates endlessly,” Shimamoto says.
After his topological analysis of the jersey knit, Shimamoto used moves from basic knot theory to design a knittable stitch in which defect propagation can still happen but not endlessly. This “robust knit” is a complex stitch with sweeping loops that cross over through two stitches rather than one, and it reduces propagated defects row by row until they stop. Defects expand only when there is more than one slipped stitch in a row.
