Scale-invariant string evolution with friction

We study the effects of friction on the scaling evolution of string networks in condensed matter and cosmological contexts. We derive a generalized ``one-scale'' model with the string correlation length L and velocity v as dynamical variables. In nonrelativistic systems, we obtain a well-known L~t^1/2 law, showing that loop production is important. For electroweak cosmic strings, we show transient damped epoch scaling with L~t^5/4 (or, in the matter era, L~t^3/2). A low initial density implies an earlier period with L~t^1/2. For GUT strings, the approach to linear scaling L~t is faster than previously estimated.