Some solutions of the 3D Laplace equation in a layer with oscillating boundary describing an array of nanotubes with applications to cold field emission. II. Irregular arrays

As in the first part (J. Brüning, S.Yu. Dobrokhotov, D.S. Minenkov, 2011), we construct a family of special solutions of the Dirichlet problem for the Laplace equation in a domain with fast changing boundary. Using these solutions, we construct an analytic model of cold field electron emission from surfaces simulating arrays of vertically aligned nanotubes. Explicit analytic formulas lead to fast computations and also allow us to study the case of random arrays of tubes with stochastic distribution of parameters. We present these results and compare them with numerical approximations given in 1].