  We study the effect of long-range elastic interactions in the dynamical
behavior of an elastic chain driven quasi-statically in a quenched random
pinning potential and in the strong pinning limit. This is a generic situation
occuring in solid friction, crack propagation, wetting front motion, ... Tuning
the exponent of the algebraic decay of the elastic interaction with the
distance is shown to give rise to three regimes: a Mean-Field (MF) regime, a
Laplacian (L) regime and an intermediate regime where the critical exponents
interpolate continuously between the MF and L limit cases. The effect of the
driving mode on the avalanche statistics is also analyzed.
