I don't think you guys are right about the F1 diffs AT ALL. They are NOTHING like a regular road car.
AFAIK, they are hydraulically operated clutch-patch units that allow for various locking behavior on corner entry, mid-corner (neutral), and corner exit. Some drivers change the diff setting from corner to corner to increase or decrease braking stability.
From an older article:
The FIA allows the use of these devices provided that their Characteristics are fixed once the car is out on the track.
A Moog electrohydraulyc valve (from RaceCar-Engineering, Charles Armstrong Wilson, 2008) will constantly adjust the friction between the two shafts around the track to maximize the performance of the car dependent on what characteristics have been entered into the on-board computer.
The Moog valve opens and closes depending on what the software is telling it to do, but the valve must work to the same set of conditions that are pre-programmed whilst the car is in the pits. This means that the driver cannot actually alter the characteristics of the differential due to a change in tracks conditions for instance, which was allowed in the days of the many driver aids around 1993.