Semiflexible Polymer Brushes

Non-crossing flexible polymer brush configurations with $N$ polymers correspond to $N$ vicious random walkers, i.e. the system stalls when any two random walkers meet. We study a system of $N$ vicious accelerating walkers with the velocity undergoing Gaussian fluctations, as opposed to the position, to model semiflexibility. We numerically compute the survival probability exponent, $\alpha$, for this system, which characterizes the probability for any two semiflexible polymers in the brush not to cross. The data suggest that $\alpha=\frac{1}{8}N(N-1)$ . We also numerically study $N$ vicious Levy flights and find, for example, for $N=3$ and a Levy index $\gamma=1$ that $\alpha=1.26\pm0.01$.