Self-avoiding walks (SAWs) and random-flight walks (RFWs) of various lengths embedded on a simple cubic lattice have been computer generated inside cubes of varying side. If B is the side of the confining cube, we define the reduced cube side size B, as B, = (B -1)/(r2)'l2, where (r2)'12 is the root-mean-square end-to-end distance of the nonconfined chains. Dimensionless diagrams are then given of the Monte Carlo estimates for the dimensions, the entropy, and the compressibility parameter Pv/(kT) of the confined chains as a function of B, . The comparative behaviour of the confined SAWs and RFWs is established, scaling properties are examined, and the Monte Carlo estimates compared with theory when such theory is available.
The entropy of confined walks in reflecting statistics has been
estimated through Monte Carlo simulations
and compared with the corresponding entropy in usual absorbing
statistics. This comparison is primarily
viewed as one involving two distinct problems in combinatorial
analysis. However, the authors believe
reflecting statistics may also find applications in physics, physical
chemistry, or other fields. Arguments,
e.g., are given in the Discussion, tending to show that for severely
confined polymer chains usual absorbing
statistics cannot apply, and therefore that reflecting statistics might
be followed instead.
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