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. Author manuscript; available in PMC: 2007 Dec 10.
Published in final edited form as: Phys Rev E Stat Nonlin Soft Matter Phys. 2005 May 5;71(5 Pt 1):051902. doi: 10.1103/PhysRevE.71.051902

TABLE I.

Algorithm for the motion of a single chain.


1 Randomly select a monomer, mi.
2 If mi is not bonded to its own chain:
2.1 List all the empty neighboring sites that fulfill the stiffness constrains with at least one of the sites occupied by the two neighboring monomers in the chain mi-1 and mi+1.
2.2 Randomly select a new site from the list for the selected monomer to move to.
2.3 Select the direction of the chain that will reptate:
  2.3.1 If the new position of the selected monomer is a neighbor of only the site occupied by the left (right) neighboring monomer in the chain, the monomers toward the right (left) end of the chain reptate.
  2.3.2 If the selected site is a neighbor of the sites occupied by both mi-1 andmi+1, then:
     2.3.2.1 If the new configuration satisfies stiffness constraints:
        2.3.2.1.1 With probability p, only the selected monomer moves to the selected site. No other monomers reptate.
        2.3.2.1.2 With probability 1-p, select randomly one of the ends (right or left), and allow the monomers along the chain toward the selected end to reptate.
     2.3.2.2 If the new configuration does not satisfy stiffness constraints with the left (right) neighboring monomer in the chain, allow the monomers along the chain toward the left (right) end of the chain to reptate.
2.4 Move the selected monomer to the selected site and iterate the following steps for the monomers between the selected monomer and the selected end.
  2.4.1 For the following monomer, build a list of empty neighboring sites that satisfy stiffness conditions with the previous monomers in the chain.
  2.4.2 Select randomly a new site from the list for this monomer to move to.
  2.4.3 If the selected site is a neighbor of the sites occupied by the two neighboring monomers in the chain and the new configuration satisfies stiffness conditions, stop the reptation with probability p.
3 If mi is bonded to its own chain, propose a change of orientation. Accept or reject the change using the METROPOLIS algorithm.
3.1 If the change is accepted, follow the procedure described in step 2.
3.2 If the change is rejected, the pair of bonded monomers move simultaneously in the same direction while the remaining monomers remain in the previous position.
  3.2.1 List the pair of neighboring sites of the pair of bonded monomers that are neighbors of the consecutive monomers in the chain and satisfy stiffness conditions.
  3.2.2 Select randomly a pair of sites among the list and perform the movement.
4 Verify that none of the pin orientations overlaps with the backbone.
4.1 If a pin orientation overlaps with the backbone, select randomly a new orientation for that pin.
5 Compute the energy of the new configuration.
6 Accept or reject the change in configuration using the METROPOLIS algorithm.
7 For a number of times equal to the number of monomers in the chain, repeat the following steps:
7.1 Randomly select a monomer mj.
7.2 Randomly select a new orientation for the pin of mj that does not overlap with the backbone of the polymer.
7.3 Compute the new energy.
7.4 Accept or reject the change in orientation using the METROPOLIS algorithm.