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Additional info for Allgemeine Theorie der kettenbruchaehnlichen Algorithmen
Just as for CBMC, RG introduces a bias in the generation of a chain which can be removed exactly by a modification of the acceptance/rejection rule. In ref. , the RG algorithm was tested for self-avoiding walks on a lattice and its efficiency was compared £ This chapter is based on ref. . Appendix C is unpublished. 26 Recoil growth algorithm for chain molecules with continuous interactions with CBMC. g. ¿¼% occupancy of the lattice), CBMC performs better than RG for both short and long polymer chains.
2 (right) and it corresponds to Ð 36 Recoil growth algorithm for chain molecules with continuous interactions 6 8 l=2; alt. method l=2 CBMC (f=10,k=15) 5 l=5; alt. 3: Efficiency (arbitrary units) as a function of the number of trial directions ( ) for a given recoil length (Ð) for the two different algorithms to compute the Rosenbluth weight ¼ . 2 and the alternative method of appendix A). Æ Å ¾¼ and . Note that for CBMC, the number of trial directions is constant ( ½¼, ½ ). Right: Ð the probability that segment is open.
114]). Of course, in the acceptance step, conformations with a very low weight will most likely be rejected. In contrast, in the RG scheme, unlikely configurations are weeded out at an early stage because, most likely, they will be “closed”. e. if Ô ´Ù µ is always equal to one). However, if we do that, all generated configurations are equally likely to be selected, irrespective of their Boltzmann weight. e. random insertion). Otherwise, RG is only equivalent to CBMC in the case that Ð ½ provided that all configurations that have a non-zero Boltzmann weight, do in fact have the same Boltzmann weight.
Allgemeine Theorie der kettenbruchaehnlichen Algorithmen by Jacobi.