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It is demonstrated that the renormalization group (RG) flows of depinning transitions do not depend on whether the driving force or the system velocity is kept constant. This allows for a comparison between RG results and corresponding self-organized critical models. However, close to the critical point, scaling functions cross over to forms that can have singular behavior not seen in equilibrium thermal phase transitions. These can be different for the constant force and constant velocitydoi:10.1103/physreve.62.r7563 pmid:11138101 fatcat:6bano3whg5hnhakcqnbzpmyate