Dynamics of unwinding of a simple entanglement

The dynamics of unwinding of a simple entanglement is studied in two ways, firstly using an optimal path approximation in the Rouse model and secondly by simulating the movement of a more realistic model using Brownian molecular dynamic

The distribution of Alexander polynomials of knots confined to a thin layer

Numerical hammagraphy is used to determine the statistical distribution of knots which are confined to a thin layer. The statistics used are based on more than 2*106 knots. Among various striking features is a marked regularity in the occurrence of the prime knots

Probability of knots in a polymer ring

We generate equilibrium configurations of a ring polymer in an infinite space, or confined to the interior of a sphere. Using a new algorithm, the a priori probability for the occurence of a knot is determined numerically. The results are compatible with power laws and scaling laws of striking simplicity

Variational perturbation theory compared with computer simulations

The variational perturbation theory has been applied to describe the compressibility of a 50% mixture of helium and nitrogen at room temperature and pressures up to 1 GPa. With parameters resulting from this perturbation theory, Monte Carlo simulations have been performed on model systems for these compounds as well as for the mixture. On comparison, clear restrictions are seen for the applicability of the perturbation theory combined with the one-fluid representation of mixtures

Gyration radius of a circular polymer under a topological constraint with excluded volume

It is nontrivial whether the average size of a ring polymer should become smaller or larger under a topological constraint. Making use of some knot invariants, we evaluate numerically the mean square radius of gyration for ring polymers having a fixed knot type, where the ring polymers are given by self-avoiding polygons consisting of freely-jointed hard cylinders. We obtain plots of the gyration radius versus the number of polygonal nodes for the trivial, trefoil and figure-eight knots. We discuss possible asymptotic behaviors of the gyration radius under the topological constraint. In the asymptotic limit, the size of a ring polymer with a given knot is larger than that of no topological constraint when the polymer is thin, and the effective expansion becomes weak when the polymer is thick enough.Comment: 12pages,3figure