Wireless multi-hop ad hoc communication networks represent an infrastructure-less and self-organized generalization of todays wireless cellular networks. Connectivity within such a network is an important issue. Continuum percolation and technologydriven mutations thereof allow to address this issue in the static limit and to construct a simple distributed protocol, guaranteeing strong connectivity almost surely and independently of various typical uncorrelated and correlated random spatial patterns of participating ad hoc nodes.

We present the results of numerical calculations of the channelling and undulator radiation generated by an ultra-relativistic positron channelling along a crystal plane, which is periodically bent. The bending might be due either to the propagation of a transverse acoustic wave through the crystal, or due to the static strain as it occurs in superlattices. The periodically bent crystal serves as an undulator. We investigate the dependence of the intensities of both the ordinary channelling and the undulator radiations on the parameters of the periodically bent channel with simultaneous account for the dechannelling effect of the positrons. We demonstrate that there is a range of parameters in which the undulator radiation dominates over the channelling one and the characteristic frequencies of both types of radiation are well separated. This result is important, because the undulator radiation can be used to create a tunable source of X-ray and γ-radiation.In this Letter we present for the first time the results of calculations of the total spectrum of emitted photons accompanying the channelling process of ultra-relativistic

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