### Radio Direction Finding and Sense Antennas... Oh and the Equivalence Principle

For what's going on with research, scroll down.  But first, another study topic for the amateur radio extra class exam.  One of the questions asks what the purpose of a sense antenna is.  The correct answer is that "It modifies the the pattern of a DF antenna array to provide a null in one direction."  Whatever that means.  The DF referred to in the answer is direction finding.  Small loop antennas, like the one shown in the picture to the left (picture 1), can be used to find the direction that radio signals are transmitted from.  By rotating the loop until the received signal becomes the weakest, you can locate the direction.  There's only one problem, you can't tell whether the signal is coming from in front of, or behind the loop.  This is where the small vertical antenna in the picture comes in.  That's the 'sense antenna' or 'sense aerial'.  Its signal is added to the signal of the loop antenna and the net result is that it provides a uni-directional antenna pattern, (see the second picture).  I hope to be back soon with lots of cool information on exactly how it does it.

A little History
The first radio direction finder was invented by John Stone Stone an American electrical engineer and physicist.

Research Blog
I'm reading through several papers on the equivalence principal, which I used to think said that you can't tell the difference between a gravitational field and say a centrifugal force[2].  It looks like, at least at relativistic speeds, I may have been wrong.  There's been quite a bit written on this[4][5], and it's taking me a while, but I'll keep you up to date.

References
1.  Awesome listing of direction finding radios
http://www.angelfire.com/space/proto57/rdf.html

2.  Equivalence principle
http://copaseticflow.blogspot.com/2013/01/benchtop-tests-of-general-relativity.html

http://copaseticflows.appspot.com/hamtest

4.
http://dx.doi.org/10.1119%2F1.3272719
Muñoz G. & Jones P. (2010). The equivalence principle, uniformly accelerated reference frames, and the uniform gravitational field, American Journal of Physics, 78 (4) 377. DOI:
open access version:  http://arxiv.org/abs/1003.3022

5.
http://dx.doi.org/10.1016%2F0003-4916%2863%2990051-4
Rohrlich F. (1963). The principle of equivalence, Annals of Physics, 22 (2) 169-191. DOI:

### Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

### Lost Phone

We were incredibly lucky to have both been in university settings when our kids were born.  When No. 1 arrived, we were both still grad students.  Not long after No. 2 arrived, (about 10 days to be exact), mom-person defended her dissertation and gained the appellation prependage Dr.

While there are lots of perks attendant to grad school, not the least of them phenomenal health insurance, that’s not the one that’s come to mind for me just now.  The one I’m most grateful for at the moment with respect to our kids was the opportunities for sheer independence.  Most days, we’d meet for lunch on the quad of whatever university we were hanging out at at the time, (physics research requires a bit of travel), to eat lunch.  During those lunches, the kids could crawl, toddle, or jog off into the distance.  There were no roads, and therefore no cars.  And, I realize now with a certain wistful bliss I had no knowledge of at the time, there were also very few people at hand that new what a baby…

### Lab Book 2014_07_10 More NaI Characterization

Summary: Much more plunking around with the NaI detector and sources today.  A Pb shield was built to eliminate cosmic ray muons as well as potassium 40 radiation from the concreted building.  The spectra are much cleaner, but still don't have the count rates or distinctive peaks that are expected.
New to the experiment?  Scroll to the bottom to see background and get caught up.
Lab Book Threshold for the QVT is currently set at -1.49 volts.  Remember to divide this by 100 to get the actual threshold voltage. A new spectrum recording the lines of all three sources, Cs 137, Co 60, and Sr 90, was started at approximately 10:55. Took data for about an hour.
Started the Cs 137 only spectrum at about 11:55 AM

Here’s the no-source background from yesterday
In comparison, here’s the 3 source spectrum from this morning.

The three source spectrum shows peak structure not exhibited by the background alone. I forgot to take scope pictures of the Cs137 run. I do however, have the printout, and…