Readers ask: By what mechanism is a reactor shut down (to replace spent fuel, for instance)? Did that mechanism fail after the quake? If not, why are the cores experiencing meltdowns?
Science answers: A reactor is shut down by inserting control rods between the fuel rods. The control rods are made of a neutron-absorbing material, so that they slow the rate of fission reactions. In a boiling water reactor like the ones at Fukushima, the fuel rods remain hot even after the reactor is shut down because of spontaneous fissions from the nuclear fuel and fission products. Hence the reactor needs to have a supply of cooling water even when shut down.
Following the earthquake, automatic systems shut down those reactors that were still operating, inserting control upward from below the core in a boiling water reactor. But the loss of electricity from the power grid meant that the water pumps stopped working. When the backup generators, powered by diesel fuel, where knocked out by the tsunami, there was no system left to replenish the cooling water. The heat from fuel rods continued to boil away the cooling water until eventually the core was exposed to the air.
As the temperature rose around the core, the zircaloy cladding on the fuel rods began to react with the steam, oxidizing and releasing hydrogen. Nuclear plant workers, concerned about the buildup of pressure in the containment vessels, vented some of the gas inside. It was the hydrogen in this escaping gas that exploded, destroying the buildings around reactors 1, 3, and 4.