  The competition between reptation and Rouse Dynamics is incorporated in the
Rubinstein-Duke model for polymer motion by extending it with sideways motions,
which cross barriers and create or annihilate hernias. Using the Density-Matrix
Renormalization-Group Method as solver of the Master Equation, the renewal time
and the diffusion coefficient are calculated as function of the length of the
chain and the strength of the sideways motion. These new types of moves have a
strong and delicate influence on the asymptotic behavior of long polymers. The
effects are analyzed as function of the chain length in terms of effective
exponents and crossover scaling functions.
