Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Knots in Macromolecules in Constraint Space   We find a power law for the number of knot-monomers with an exponent $0.39
\pm0.13$ in agreement with previous simulations. For the average size of a knot
we also obtain a power law $N_m=2.56\cdot N^{0.20\pm0.04}$. We further present
data on the average number of knots given a certain chain length and confirm a
power law behaviour for the number of knot-monomers. Furthermore we study the
average crossing number for random and self-avoiding walks as well as for a
model polymer with and without geometric constraints. The data confirms the
$aN\log N + bN$ law in the case of without excluded volume and determines the
constants $a$ and $b$ for various cases. For chains with excluded volume the
data for chains up to N=1500 is consistent with $aN\log N + bN$ rather than the
proposed $N^{4/3}$ law. Nevertheless our fits show that the $N^{4/3}$ law is a
suitable approximation.

13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci