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We have studied numerically the dynamics of sliding charge-density waves (CDWs) in the presence of impurities in d=1,2. The model considered exhibits a first order dynamical transition at a critical driving force F_c between "rough" (disorder dominated) (FF_c) sliding phases where disorder is washed out by the external drive. The effective model for the sliding CDWs in the presence of impurities can be mapped onto that of a magnetic flux line pinned by columnar defects and tilted by an applieddoi:10.1103/physrevb.54.12798 pmid:9985136 fatcat:t7bnwmilkzbivklzzsbztnwegq