Reptons dynamics

Thus, the axioms of repton dynamics are equivalent to very simple local rules 3 in the bond representation oj, with ai-O or 1. 

The dynamics of a single chain in a tube is mapped onto the dynamics of the cluster of reptons along the one-dimensional lattice. To properly describe chain motion along the tube, the motion of reptons must obey a specific set of rules. The reptons can never vacate a site in the middle of the... 

An alternative to the continuous Rouse motion inside the tube is the repton model,which represents the chain dynamics by free diffusion of stored length in discrete space. Namely, at each moment of time, the chain is represented by a set of integer variables S, (one for each tube segment i = 1... Z), which records the number of chain beads in the i-th tube segment. At each time step, the segment is chosen at random. If it contains more than one monomer S,>1, one of the monomers can move either to the left or to the right ... 

The subject of this paper is limited to the dynamics of a single entangled polymer chain, just as in the original de Gennes paper on reptation. In a melt or concentrated solution, the dynamics of any chain would be affected by the motion of surrounding polymers (by constraint release), and this effect has to be self-consistently taken into account. In order to do that, one has to start from a reliable model of the single-chain dynamics, such the reptation model, Doi s fluctuation theory,or the repton modeldescribed in the present paper. 

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