“…A pinning force F p is a short-range force that holds the core of a vortex in place at, inter alia, a point defect (Giapintzakis et al, 1992;Hylton and Beasley, 1990), columnar defect (Nelson and Vinokur, 1992;Prost et al, 1993), screw dislocation (Ivlev and Jin et al, 1991), oxygen vacancy (Chudnovsky, 1990;, inclusion (Murakami et al, 1991;Sagdahl et al, 1991;Shi et al, 1989Shi et al, , 1990a, grain boundary (Muller et al, 1991b), twin boundary (Kwok et al, 1990a;Lairson et al, 1990a,b;Liu et al, 1991b;Svensmark and Falicov, 1990), intragranular or intergranular nonsuperconducting region Jung et al, 1990), or praseodymium (Pr) doping (Paulius et al, 1993;Radousky, 1992). The density of pinning centers can be high, with average separations of 100 Å or less (Martin et al, 1992;Tessler et al, 1991).…”