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An analysis of extensive simulations of interacting self-avoiding polygons on cubic lattice shows that the frequencies of different knots realized in a random, collapsed polymer ring decrease as a negative power of the ranking order, and suggests that the total number of different knots realized grows exponentially with the chain length. Relative frequencies of specific knots converge to definite values because the free energy per monomer, and its leading finite size corrections, do not depend on the ring topology, while a subleading correction only depends on the crossing number of the knots.
We introduce and implement a Monte Carlo scheme to study the equilibrium statistics of polymers in the globular phase. It is based on a model of interacting elastic lattice polymers and allows a sufficiently good sampling of long and compact configur
A compressed knotted ring polymer in a confining cavity is modelled by a knotted lattice polygon confined in a cube in ${mathbb Z}^3$. The GAS algorithm [17] is used to sample lattice polygons of fixed knot type in a confining cube and to estimate th
We study the translocation dynamics of a polymer chain threaded through a nanopore by an external force. By means of diverse methods (scaling arguments, fractional calculus and Monte Carlo simulation) we show that the relevant dynamic variable, the t
We show that the collapsed globular phase of a polymer accommodates a scale-free incompatibility graph of its contacts. The degree distribution of this network is found to decay with the exponent $gamma = 1/(2-c)$ up to a cut-off degree $d_c propto L
We develop a theory for polymer translocation driven by a time-dependent force through an oscillating nanopore. To this end, we extend the iso-flux tension propagation theory (IFTP) [Sarabadani textit{et al., J. Chem. Phys.}, 2014, textbf{141}, 21490