Plenary Talk
Alexander Grosberg,
Department of Physics,
New York University
Self-avoiding knots
The root-mean-squared gyration radius of a non-phantom loop of zero thickness and fixed knot topology is believed to scale as $N^{\nu}$, where $N$ is the number of segments and $\nu$ is the critical exponent which describes the self-avoiding random walk. What happens if self avoidance and topological constraints are presented simultaneously? The zero thickness model has no unitless parameters apart from $N$, while the self-avoiding model has parameter $d/a$, where $d$ and $a$ are the segment thickness and length, respectively. There are several numerical studies of the concurrent effect of self-avoidance (chain thickness or ionic strength in case of DNA). In this work, and attempt of a simple minded scaling estimate is presented.