We review recent theoretical studies on the statistical and dynamical properties of polymers
with nontrivial structures in chemical connectivity and those of polymers with a nontrivial …

The thermal properties of coarse-grained knotted copolymer rings fluctuating in a highly
screening solution are investigated on a simple cubic lattice using the Wang-Landau Monte …

In Escherichia coli DNA replication yields interlinked chromosomes. Controlling topological
changes associated with replication and returning the newly replicated chromosomes to an …

" Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics.
This enyclopedia is filled with valuable information on a rich and fascinating subject."–Ed …

We present an algorithmic approach to discover, study, and design multistable elastic knots.
Elastic knots are physical realizations of closed curves embedded in 3-space. When …

The knot nomenclature in common use, summarized in Rolfsen's knot table [Rolfsen (1990)
Knots and Links, American Mathematical Society], was not originally designed to distinguish …

The ropelength of a knot is the minimum contour length of a tube of unit radius that traces out
the knot in three dimensional space without self-overlap, colloquially the minimum amount of …

We report calculations on three classes of knotted ring polymers:(1) simple-cubic lattice self-
avoiding rings (SARs),(2)“true” theta-state rings, ie, SARs generated on the simple-cubic …

We here address two problems concerning the writhe of random polygons. First, we study
the behavior of the mean writhe as a function length. Second, we study the variance of the …

Let pn denote the number of self-avoiding polygons of length n on a regular three-
dimensional lattice, and let pn (K) be the number which have knot type K. The probability …