On the issue of ultracold neutron generation at pulsed neutron sources: Transport of very slow neutrons in the fast heated cold moderators and in granular moderators

A simple method is proposed and the calculation of the transport of very slow neutrons in a cold moderator with a fast changing temperature is performed. Neutron transport in granulated medium was calculated. The calculation is suitable for the optimization of moderators for ultracold and very cold moderators at pulsed sources.