The writhe of a self-avoiding walk

The writhe of a self-avoiding walk in a three-dimensional space is the average over all projections onto a plane of the sum of the signed crossings. We compute this number using a Monte Carlo simulation. Our results suggest that the average of the absolute value of the writhe of self-avoiding walks increases as n alpha , where n is the length of the walks and alpha approximately=0.5. The mean crossing number of walks is also computed and found to have a power-law dependence on the length of the walks. In addition, we consider the effects of solvent quality on the writhe and mean crossing number of walks.