Dynamical process3D self-locking of self-avoiding walks

The self-locking of self-avoiding walks (SAWs) on a three-dimensional cubic lattice was numerically and analytically studied. It was shown that self-locking in three-dimensional space is a local effect and is not related to the entanglement of a walk in a ball. The lenght distribution P(l) of the SAWʹs trajectory before self-locking was numerically obtained. P(l) can be approximated by the formula P(l) = const.lγexp(−l/a). The estimation of a was obtained analytically considering the self-locking as a local effect, and it is of the same order of magnitude as the value obtained numerically.