David wrote:
How does a vertical monopole antenna with elevated quarterwave radials work
when receiving?

Exactly as it does when transmitting, in reverse.

The radials are in free space.

No, not really. If high enough, they behave like they are, but they're
not that high in typical HF applications.

Do the radials reflect or
emit a wave that cancels out?

No. The radials radiate very little. They certainly interact with the
vertical portion of the antenna, but not in a way that could be
described as "reflection" in any sense.

Is it possible to model this antenna in
receive mode with a NEC program?

Yes. Look up the explanation and examples of plane wave excitation in
the NEC manual. If done correctly, you should get identical but
reciprocal results as when modeled as a transmitting antenna. (EZNEC
doesn't implement plane wave excitation, but you can create an
essentially plane wave by adding a small "transmitting" antenna with
source a few wavelengths away.)

I am trying to work out whether the
electromagnetic principles that apply in transmit mode also apply in receive
mode.

Others have wondered the same thing, but somewhere around a hundred
years ago the problem was solved. They do. A google search on antenna
reciprocity should get you started in the learning process.

Roy Lewallen, W7EL