why set alpha=1/beat and sigma=alpha * psi?

[ZhouWeikun]

It's really a great job! iq(≧▽≦q)。
But i have a question about the parameter alpha. I saw you set alpha = 1/beta and sigma=alpha * psi in your code, that means sigma/density will >1 when beta < 1. Why not set sigma = psi, that will keep sigma <= 1?