i'm wondering about the main design principle of the reactor cores - by default they are "hot", ie. producing heat/energy, so one needs to make effort to keep them "cold", ie. non-producing heat/energy. This hot-by-default principle was the main reason of Chernobyl catastrophe and here as well. Why not reverse the principle and design the cold-by-default core? For example, instead of inserting graphite rods into the…
Fukushima, however, has a negative void coefficient. Moreover, the fission reaction was stopped immediately after the earthquake successfully by the automatic insertion of control rods. The heat that is being generated is from short-lived fission products (ie, nuclear waste) undergoing spontaneous decay events, thus producing heat (but only a small fraction of the heat of an active reactor).
It is physically impossible to design a reactor in which such spontaneous decay can be stopped. You can only remove the energy actively until these short-lived products decay to the point where air cooling is sufficient to keep them at a safe temperature. You can, however, design a reactor in which the passive containment structures can withstand the temperatures of fresh waste material with no active cooling; however such technology was not available at the time the Fukushima plants were built.