### A Horse Trough a Quonset Hut and Data Acquisition

It gets hot in Las Cruces, and sometimes there's nothing to do for it but take a dip.  That's how I found myself sitting in our horse trough with Junior this weekend cogitating about the new data acquisition system.  I had a glass of McAllen, and Junior had her boat, (at 17 months, she's much too young for McAllen), and a good time was had by all.  The horse trough is left over from when we lived in a Quonset hut.  The building didn't come with a bathtub, but a short trip to the local feed store a few blocks away and we were set.  It was kind of cush, the trough sat near the back door about five paces from the train tracks, so you could sit there and watch the trains go by, (see the video below).

That was before our landlord decided the space would make a better art gallery.

I digress though!  Back to the data acquisition system and its requirements.  I've come across two articles about the effect of alternating current magnetic fields on superconductors that seem to have contradictory findings.

http://copaseticflow.blogspot.com/2012/07/superconductor-trapped-field-and-its-ac.html

Both agree that AC magnetic fields will gradually 'erase' any pinned magnetic flux in a YBCO superconductor.  Where they disagree is how the frequency of the AC field influences things.  Ueda et. al. see a decrease in the attenuation of the pinned field with increasing frequency.  They took there measurements between .1 and 1 Hz and extrapolated up to 50 Hz.  Ogawa et. al. see a pronounced increase in the attenuation of pinned field with increase in frequency.  They took their data between 7 and 61 Hz.  Ogawa et. al. attribute this attenuation to AC heating in the superconductor.  If Ogawa is correct, then I should see the levitation force on my superconductor decrease with time.

So, there are two things that I need to measure this week: what the strength of the AC field is that first accomplishes levitation at a variety of frequency, and how long levitation can be maintained.  I'll be using the little Arduino board for data acquisition again.  I've rigged a contact breaker on the superconductor sample holder.  When the superconductor levitates, an electrical contact will be broken and the Arduino print a message to my laptop screen and start a timer.  When the superconductor falls again, the Arduino will output the amount of time the superconductor was levitated.  I'll post in more detail on all this as the week progresses.  Hopefully, there will also be a video post on whether or not liquid nitrogen conducts.

### 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…

### The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1.  While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero.  This is typically explained in the following way.  While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare.  That doesn't stop us from looking for them though!

Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2].  Cabrera was utilizing a loop type of magnetic monopole detector.  Its operation is in concept very simpl…

### Unschooling Math Jams: Squaring Numbers in their own Base

Some of the most fun I have working on math with seven year-old No. 1 is discovering new things about math myself.  Last week, we discovered that square of any number in its own base is 100!  Pretty cool!  As usual we figured it out by talking rather than by writing things down, and as usual it was sheer happenstance that we figured it out at all.  Here’s how it went.

I've really been looking forward to working through multiplication ala binary numbers with seven year-old No. 1.  She kind of beat me to the punch though: in the last few weeks she's been learning her multiplication tables in base 10 on her own.  This became apparent when five year-old No. 2 decided he wanted to do some 'schoolwork' a few days back.

"I can sing that song... about the letters? all by myself now!"  2 meant the alphabet song.  His attitude towards academics is the ultimate in not retaining unnecessary facts, not even the name of the song :)

After 2 had worked his way through the so…