We observe dark and bright intrinsic localized modes (ILMs) or discrete breathers (DB) experimentally and numerically in a diatomic-like electrical lattice. The generation of dark ILMs by driving a dissipative lattice with spatially-homogenous amplitude is, to our knowledge, unprecedented. In addition, the experimental manifestation of bright breathers within the bandgap is also novel in this system. In experimental measurements the dark modes appear just below the bottom of the top branch in frequency. As the frequency is then lowered further into the band-gap, the dark DBs persist, until the nonlinear localization pattern reverses and bright DBs appear on top of the finite background. Deep into the bandgap, only a single bright structure survives in a lattice of 32 nodes. The vicinity of the bottom band also features bright and dark self-localized excitations. These results pave the way for a more systematic study of dark breathers and their bifurcations in diatomic-like chains.

We demonstrate experimentally and corroborate numerically that an electrical lattice with nearest-neighbor and second-neighbor coupling can simultaneously support long-lived coherent structures in the form of both standard intrinsic localized modes (ILMs), as well as resonant ILMs. In the latter case, the wings of the ILM exhibit oscillations due to resonance with a degenerate plane-wave mode. This kind of localized mode has also been termed nanopteron. Here we show experimentally and using realistic simulations of the system that the nanopteron can be stabilized via both direct and subharmonic driving. In the case of excitations at the zone center (i.e., at wavenumber k = 0), we observed stable ILMs, as well as a periodic localization pattern in certain driving regimes. In the zone boundary case (of wavenumber k = π/a, where a is the lattice spacing), the ILMs are always resonant with a plane-wave mode, but can nevertheless be stabilized by direct (staggered) and subharmonic driving.

In a paper (Zanchini E 2012 Phys. Scr. 86 015004), the two experiments on the transverse Doppler shift in the rotating accelerating systems performed by Hay et al and Kündig are reinterpreted. Contrary to the widely accepted view, the author concluded that this transverse Doppler effect is not purely a relativistic effect. We argue that his interpretation is based on a fundamental misunderstanding of the valid scope for the expressions of the relativistic Doppler effect. Here, we also clarify that the expressions of the relativistic Doppler effect are strictly valid only when dealing with a plane light wave propagating along an arbitrary direction, or with a spherical light wave produced by a point light source in motion along the direction of the line connecting the source and the observer.

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