I am looking for a device which works with US home electricity: 110
VAC, 60 Hz, 15 Amps. The device should when plugged into the wall, at
the flick of a switch, slowly ramp up the voltage and current over
about 5 seconds and deliver the electricity to anything plugged into
the device. A rheostat is insufficient. The device should produce
minimal heating and have no moving parts.

I want one of the following, in order:

1) To know where to order such a device as a commercial product
available for sale in the US for under $10 US.
2) A patent report of such a device, in English.
3) A circuit design of such a device that I can use to build it with
off the shelf components.

My guess is what you are looking for is an inductor

Check this out

http://www.vonwentzel.net/ABS/InternalSupply.html
explanation

http://www.inductech.com/
products


I am not much knowledable in this area hopefully did not mess up

There are commerical switch products with a "soft on" or fade out
feature, but they seem rather expensive.  It should be easy to build
your own circuit with a variant of a standard triac type dimmer
circuit.
A triac is normally off but can be activated very quickly by a control
signal to its gate contact. The timing of the control signal relative
to the 60 Hz power waveform controls the duty cycle that your load
receives through the triac.  Turn the triac on early in the wave cycle
and almost full power goes through.  Turn the triac on late and very
little power goes through.
For your application, you need a circuit that, over a 5 second period,
advances the application time of the control signal from very late in
the cycle to the beginning of the cycle. This could probably be done
with a couple 555's, some resistors, and a couple capacitors.

See this link about triacs:

<a HREF=http://www.play-hookey.com/semiconductors/diac_triac.html>Triacs</a>