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 …

" 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 …

For various polymers with different structures in chemical connectivity expressed by graphs,
we numerically evaluate the mean-square radius of gyration and the hydrodynamic radius …

The study of knots and links from a probabilistic viewpoint provides insight into the behavior
of “typical” knots, and opens avenues for new constructions of knots and other topological …

Frames provide redundant, stable representations of data which have important applications
in signal processing. We introduce a connection between symplectic geometry and frame …

The collection of d× N complex matrices with prescribed column norms and singular values
forms an algebraic variety, which we refer to as a frame space. Elements of frame spaces …

Sampling equilateral closed polygons is of interest in the statistical study of ring polymers.
Over the past 30 years, previous authors have proposed a variety of simple Markov chain …

For X a finite subset of the circle and for 0< r≤ 1 fixed, consider the function fr: X→ X which
maps each point to the clockwise furthest element of X within angular distance less than 2 π …

We present the first algorithm for sampling random configurations of closed-gons with any
fixed edgelengths in any dimension which is proved to sample correctly from standard …