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Discrete models for reptation are discussed. It is shown that in the weak field limit a formula for the drift velocity exists, which is applicable to a wide class of dynamical models. In the long polymer limit the behavior is dominated by the existence of a permanent head and tail of the polymer which influences the statistics and the expressions for drift and mobility in a fundamental way.
An outline is given of the position space renormalization group approach to phase transition and critical phenomena. The method is illustrated by simple examples of renormalization transformations for the two-dimensional Ising model.
Voltage-driven polymer translocation is studied by means of a stochastic lattice model. The model incorporates voltage drop over the membrane as a bias in the hopping rate through the pore and exhibits the two main ingredients of the translocation process: driven motion through the pore and diffusive supply of chain length towards the pore on the cis-side and the drift away from the pore on the trans-side...
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