### The Calibrated Leak and AVS Awards

The leak detector is up and running!  After draining,flushing, and filling the roughing vacuum pump and cleaning the liquid nitrogen trap, we put the system back online.

Once all that was done, I found out something else that's very cool!  You can make your system leak in a calibrated manner to test the leak detector!  The gadget for doing this is called a calibrated leak!  I'd read about these in the documentation, but never expected to actually see one in the field!  Here's a picture

The calibrated leak is the silver cylinder with the white label in the center of the picture.  A few weeks ago when the I first started playing with the leak detector[1], I mentioned that it detects leaks by looking for helium using a built-in atomic mass spectrometer.  The calibrated leak has a small container of helium that is released at a calibrated rate into the vacuum system once the black valve at the bottom is opened.  After that, the leak detector gauge reads the rate at which helium is being introduced into the system and makes a noise very similar to what you might you might expect to hear from a Geiger counter.  When the valve is first opened, the leak rate meter rails and the clicks from the audible detector ramp way up as the excess helium behind the valve is released.  After a second or so, the clicks even out to a nice constant rate and the meter settles back down reading the rate of the constant leak attached to the system.

Speaking of vacuum systems, graduate students working with vacuums should check out the student awards offered by the American Vacuum Society[2]!

References
1.  http://copaseticflow.blogspot.com/2014/03/leak-detector-at-last.html

2.  https://www.avs.org/Awards-Recognition

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

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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 differe…

### Division: Distributing the Work

Our unschooling math comes in bits and pieces.  The oldest kid here, seven year-old No. 1 loves math problems, so math moves along pretty fast for her.  Here’s how she arrived at the distributive property recently.  Tldr; it came about only because she needed it.
“Give me a math problem!” No. 1 asked Mom-person.

“OK, what’s 18 divided by 2?  But, you’re going to have to do it as you walk.  You and Dad need to head out.”

And so, No. 1 and I found ourselves headed out on our mini-adventure with a new math problem to discuss.

One looked at the ceiling of the library lost in thought as we walked.  She glanced down at her fingers for a moment.  “Is it six?”

“I don’t know, let’s see,” I hedged.  “What’s two times six?  Is it eighteen?”

One looked at me hopefully heading back into her mental math.

I needed to visit the restroom before we left, so I hurried her calculation along.  “What’s two times five?”

I got a grin, and another look indicating she was thinking about that one.

I flashed eac…