Figure 3.

Simplified model of thread being drawn from a skein. The thread has length $L(t)$ with initial length $L(0)=L_0$. Here s is the arclength material (Lagrangian) coordinate along the unravelled thread, with $0\le s\le L(t)$. The fixed laboratory (Eulerian) coordinate of the thread is $\mathit{x}(s,t)$, with the thread peeling from the skein at $\mathit{x}(L(t),t)=\mathit{X}(t)$. (Online version in colour.)