Copasetic Flow

Just a quick note today on a fun article [1] and a new word, (hodograph), I found in the American Mathematical Monthly journal from the +Mathematical Association of America  .  The article uses Mamikon's theorem to prove Kepler's second law.  Mamikon's theorem states that the area swept out by the velocity, (tangent), vector to a parameterized position position curve is the same as the area swept out by the same set of velocity vectors if you laid them out with a their tails all placed at a common center.  The curve swept out by all the velocity vectors with their tails placed at the same point is called the hodograph and was defined by W. R. Hamilton.  The hodograph in this scenario defines the acceleration curve for the particle!  Haimlton's article defining the hodograph can be found freely available at  http://www.jstor.org/stable/20489607 . [2] References: (2013). Visual Angular Momentum: Mamikon Meets Kepler, The American Mathematical Mo...

I've been following a literature search for the last few days that's led to a very interesting point.  Superconducting tin has different quench points, (via magnetic field), depending on the orientation of the direction of current flow in the sample and the direction of the applied external magnetic field[ 1 ].  My next job will be to determine if Pb has the same qualities, and if so what that means for the experiment. Pb was chosen as the sample for our experiment because of the relatively low magnetic field strengths at which it can be quenched.  It was mentioned by Hirsch in one of his articles predicting Bremsstrahlung radiation from quenched superconductors that the super conductor should be quenched 'quickly'.  It's unclear at the moment what effect this squirmy quality of supercurrents vs. magnetic field orientation will have. Flow of the Literature Search: And now, just a few notes on how I arrived at the Shubnikov article.  Hirsch who originat...

You may have noticed that I left you hanging with the arctangent series a few weeks ago.  I told you how to get the series for arctan for x > 1, but not for x < 1.  By now, I bet my EM grader has noticed as well, and I've lost a few points.  So, a little after the fact, here's how to get a series for arctangent for x < 1. The useful bit you need that I didn't have is that the arctan of x can also be expressed as (picture 1): The following picture, (picture 2), has the geometric interpretation that helped me see things more easily as well as the required series.  If you think of the tangent of an angle being equal to the opposite side divided by adjacent side, and then take a look at the lower left corner of the picture below, I think you'll see why the expression above is true.  It took forever for me to see it after my  professor derived it analytically.  I think I could have seen it much more quickly derived geometrica...

The linked document below contains an integration 'trick' that's very interesting to me, but it arguably shouldn't be.  First, the interesting bit.  The problem shown is from a derivation of the Fourier transform of the ground state of the hydrogen atom from position space into momentum space  The trick here shows how to easily integrate theta dependency using simple 'u substitution'.  There' a second possibly much more interesting bit that I have to check out later, we wind up with sin(kr)/kr which is a prototype for a delta function, which is related to the whole Fourier transform process, but I digress. While I'm very proud of my u substitution, I arguably shouldn't be.  I'll out myself.  I'm in grad school and I'm not an expert at integrals!  The shame!  After all, I learned the technique of u substitution in freshman calculus. Here's a little bit of history followed by a suggestion I'd appreciate your thoughts on.  When I...

The experiment[1] I'll be working on this summer involves using a sodium iodide scintillator to detect gamma rays with an energy of around  318 keV emitted from the interior of a liquid helium cryostat.  In the event that a null result is achieved, (no gamma rays detected), I want to make sure that it's related to the phenomena we're researching and not due to our equipment.  To that end, one of my first experiments will be to place a gamma ray source in the cryostat.  Measurements will be taken using the scintillator to make sure that gammas of the expected energy can in fact penetrate the cryostat. I found an excellent web site for deciding on a gamma ray source.  You can search gamma sources based on energy, half life, intensity and number of (spectral?) lines.  It turned up cesium 137 which looks like a good fit.  It emits a 283 keV gamma ray and it's used in academia and the oilfield, (see the cool truck below).  Being right in the midd...

First, the really great news!  My research proposal won first place at the Texas Academy of Sciences meeting on Friday!  That means I've got the money to purchase liquid helium and play with a superconductor this summer.  The proposal can be viewed below on the blog, or you can grab it from [1] if you're reading this somewhere else. Now, the question.  I've been reading lots of posts from G+ers like  +Mark Hahnel ,  +Laura Wheeler , and  +Emily Coren  on the value of open access and communicating science to the public.  I'm thinking of doing something cool like Google+er  +Katrina Badiola  has done with her lab notebooks.  I'm curious how this works out and what experience people have had with it.  If you can answer any of the following questions, that would be awesome!  If you'd like to answer anonymously, leave and anonymous comment on the blog post. What do you think the benefits of an entirely...