I can not answer for the box wing, but I can tell you that the ring (annular) wing is nowhere near as efficient as you might believe.

I don't know of any scientific research that might have been done, so I can not quote you any lengthy and worthy links on the topic.

But, having built one (Lee Richards III) I can tell you it is a real B*T*H to get to fly. When it does, it is not very good at it either.

Personally, I think that the aerodynamics at the "tip" of an annular wing would be almost impossible to "model" (as in mathematical model). Perhaps the nearest example in recent times would be the "Flying Pancake" series of prototypes.