Planet-disk interactions, where an embedded massive body interacts gravitationally with the protoplanetary disk it was formed in, can play an important role in reshaping both the disk and the orbit of the planet. Spiral density waves are launched into the disk by the planet, which, if they are strong enough, can lead to the formation of a gap. Both effects are observable with current instruments. The back-reaction of perturbations induced in the disk, both wave-like and non-wavelike, is a change in orbital elements of the planet. The efficiency of orbital migration is a long-standing problem in planet formation theory. We discuss recent progress in planet-disk interactions for different planet masses and disk parameters, in particular the level of turbulence, and progress in modeling observational signatures of embedded planets @en

Relaxation oscillators consist of periodic variations of a physical quantity triggered by a static excitation. They are a typical consequence of nonlinear dynamics and can be observed in a variety of systems. VO₂ is a correlated oxide with a solid-state phase transition above room temperature, where both electrical resistance and lattice parameters undergo a drastic change in a narrow temperature range. This strong nonlinear response allows to realize spontaneous electrical oscillations in the megahertz range under a DC voltage bias. These electrical oscillations are employed to set into mechanical resonance a microstructure without the need of any active electronics, with small power consumption and with the possibility to selectively excite specific flexural modes by tuning the value of the DC electrical bias in a range of few hundreds of millivolts. This actuation method is robust and flexible and can be implemented in a variety of autonomous DC-powered devices.

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