P. Ziswiler et al., DEFORMATIONS AND DYNAMICS OF AN ELASTIC STRING IN A PERIODIC POTENTIAL, Physical review. B, Condensed matter, 56(1), 1997, pp. 416-424
We study the dissipative dynamics of a driven elastic string subject t
o a periodic potential. The deformations of the elastic string are det
ermined in the static and dynamic situations for various geometries. W
e find the average velocity of the string, particularly the dependence
of the velocity on the mean angle theta between the string and the po
tential. Our theoretical analysis produces both a sharp drop in the av
erage velocity at small angles due to the trapping of the elastic stri
ng in the potential and a crossover from free motion to a pinning-inhi
bited motion at the critical driving ford.