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Showing posts from June, 2014

Cuneiform to Computers and the MAA Lattice Points Problem

Imagine living thousands of years ago in ancient Sumeria as a mathematician.  Your medium for storing infomration is cuneiform on clay tablets.  As you work, you stamp each equation into wet clay by making wedge shaped marks using the blunt end of a reed to make a finished document that looks like this (picture 1)[1] When your instructor tells you to investigate the properties of a table of let's say, a hundred numbers or so, you might sigh in resignation, and plan on having results by sometime next week. With the advent of paper and pencil, things become much easier.  There's still lots of work to be done, but the recording of the information so that it can be viewed and worked with is, comparatively speaking, a piece of cake. Finally, though, the computer comes along and getting a table of 100 numbers is more like playing.  With  +The SageMathCloud   the 100 number task suggested in the +Mathematical Association of America  video below can be done easily by anyone w

Speaking of tubes: Introducing the Grid Dip Meter

+Jonah Miller  is currently working on a multi-part series of articles on how computers work.  In one of the installmetns he mentioned the good old triode vacuum tube with a cathode, plate, and grid.  That brings up the subject of today's post, the grid dip meter, (GDM).  If you wandered over here from the ham radio practice tests [1], and you want the shortest answer possible, then click here, or scroll down the page.  If you want more information, read on: The grid Dip meter schematic is shown in picture 1. The main purpose of the circuit, at least for amateur radio operators, is to determine the resonant frequency of some other circuit or device, (like an antenna).  Let's say you've built you're latest radio and you'd like to get all the power you can from the driving finals, into the antenna.  To do that, you'd like to make sure that the antenna resonates at the same frequency you'd like to send and receive at.  If the antenna resonates at a litt

Superconductors and Friction

I spent most of yesterday travelling between Austin and College Station, but I did manage to get a little bit of research in.  I'm looking for other experiments related to Hirsch's theories we can do in conjunction to the search for H-rays.  One of the measurable predictions of Hirsch's theory is a change in the coefficient of sliding friction when a material enters it's superconducting state. All about friction [6] New to the lab book?  Scroll to the bottom for background and a summary of the experiment. Hirsch mentions [1] that a finding of reduced friction in superconductors might be evidence in support of his hole theory of superconductivity. Furthermore, the electronic layer outside the surface is likely to affect the friction properties of the superconductor, by providing a ‘lubricating layer’ on top of which another material would slide. As a matter of fact, an abrupt drop in sliding friction between a lead surface and solid nitrogen has be

The Alcubierre Drive's Tophat Shift Function In Motion

The Alcubierre drive works, (theoretically), by warping space 'downwards' in front of a spaceship and 'upwards' behind it, (picture 1). The net effect is that the spaceship always feels like it's free-falling through space.  We have to be careful not to let the spaceship approach either the upward or downward walls of the curved space shown above.  In these regions, gravity due to the curvature of space is changing rapidly, and will cause uneven forces, known as tidal forces, on different portions of the spaceship that can cause it to break apart.  That's where Alcubierre's tophat function comes in.  The tophat is the input to the operation that describes how space is warped by the drive.  It's nice, flat top becomes the flat area in the middle of the warp shown above where the spaceship can safely rest. In case you weren't there, here's the description of the tophhat function I provided in the last post on the Alcubierre drive [1], (s

Meanwhile, in the lab... Dewar Moves and Leaky Vacuum Pumps

Lab Book 2014_06_20     Hamilton Carter New to the lab book?  Scroll to the bottom for background and a summary of the experiment. Pulling the Dewar from the Table The spray Styrofoam was shaved off the Dewar this morning revealing that the Dewar had originally been installed on a piece of regular Styrofoam and the spray coating was added later The plan is to peel away as much of the spray foam as is practicable, and then do a two person lift of the Dewar out of the table.  The Dewar will be immediately placed in a padded box. The Dewar was successfully removed!  Next, I’ll remove the shelf and put the magnet in place.  There’s one cooling tube that was knocked off the magnet as it turns out, so that will have to be fixed. Vacuum Pump Down! The leak detector vacuum pump appears to be broken.  The reading on it is a much worse vacuum than from the auxiliary one on the lower shelf of the cart Leak Detector Pump Auxil

Embedding Sage Cells in HTML Pages

Update:   I finally found what looks like very complete documentation on the Sage cell server . I'm taking a little break from the Alcubierre work [1] and jotting down a few notes on how to embed  +Sage Mathematical Software System  cells into html pages.  I couldn't find any documentation or howto pages for this, so here are my instructions for the next time I get ready to do this. Insert Sage Javascript at the Bottom of the Page For whatever reason, my blogspot entries will erease code placed at the top of a post.  They will however allow scripts that are included at the end of the page, go figure.  So, at the bottom of the page place the following html code: <script> $(function() { sagecell.makeSagecell({ inputLocation: '#graphdemo', evalButtonText: 'Analyze the Alcubierre tophat function'}); }); </script> In the position on the page where you want your actualy sage cell to be displayed insert a div wrapping your sage code like

The Alcubierre Warp Drive Tophat Function and Open Science with Sage

I transferred yesterday's Mathematica file with the Alcubierre warp drive[2] line element and space curvature calculations to the  +Sage Mathematical Software System  today, (the files been  added to the public repository [3]).  If you haven't used Sage before, it's a Python based software package that's similar in functionality to Mathematica.  Oh, and it' free.  I also worked a little more on understanding the theory, but frankly, I made far more progress with the software than the theory.  What follows will be a little more of the Alcubierre theory, plus, a cool Sage interactive demo of one of the Alcubierre functions[1], as well as a bit about my first experience with using Sage. Theory The theory is fun, but it's moving slowly.  Here's the chalk board from this morning's discussion Alcubierre setup the derivation using something called the 3+1 formalism which means we consider space to be flat, (in this case), slices that are labelled with th

Alcubierre Derivations in Open Access

I was able to play with the Alcubierre warp drive derivations for a bit today!  I'm still trying to absorb all the niceties, but here's what I understand so far.  I'm just getting started on all of this and everything is very shaky.  So, please, anyone who happens to be familiar with oh, I don't know, the 3+1 formalism of GR say, please feel free to jump in.  Actually the more involvement the merrier, whether it be with suggestions, corrections, or questions. Which brings up the Alcubierre github repository [1].  I went ahead and made an open access github project that for the moment holds only a mathematica file with the derivation details I've been able to compile so far, a wiki, and one open issue, (the space curvature graph looks a little too jaggy).  Here's the graph by the way, king of the 'Hello World' moment for Alcubierre work I suppose, (picture 1): I'd hoped to have more to say about this tonight, but hopefully I can check in again

Unintended Benefits of Unit Testing: Documentation for Nothing and Testing for Free

I'm working on the geochrono[1]  project a little bit at the time.  I unexpectedly came across a benefit of unit testing I'd forgotten about, documentation by testcase.  One of the first requirements for geochrono is: The user will be allowed to add events or person chrono-locations by adding markers to a map at the appropriate location. First implementation  The user will be required to enter the year, month, and day of the month in three distinct textboxes before clicking on OK. The date will be checked as valid using code available at stackexchange [2]. Testcase: Send bad and good dates to date checker code. Something like this: The requirements and testcsases seemed simple enough.  Form a bad date and pass it into the date checking function.  Something like this should have done the trick: assert.equal(isValidDate(new Date(1980, 100, 150)), false); You get the idea, pass in a month that doesn't exist, (100), and a day of the month that doesn't

I Stand Corrected Regarding the Alcubierre Drive

I jotted down a quick post on the Alcubierre Drive and faster than light travel.  I had assumed that like many FTL misconceptions, the media had been confused by speed measured as proper velocity, (space in the Earth's rest frame divided by time in the spaceships frame), as opposed to lab velocity.  +Jonah Miller quickly pointed out, however, that the claims for the drive were that it could go faster than the speed of light with regard to the laboratory frame, and hence with laboratory velocity.  I found the original paper by Alcubierre on arxiv[1], and... Jonah's absolutely right! The paper is amazingly well written and anyone that's had a grad level general relativity class should be able to easily traipse through it.  Alcubierre even shows that causality won't be violated.  I haven't had time to digest the material enough to say why causality isn't violated except with the very unsatisfying statement, "Well, the math works out."  Alcubierre w

Selling Science with Glossy Pictures and FTL Travel Baby!!!

The Washington Post published pictures of NASA's concept of what a Alcubierre drive spaceship might look like.  A few pundits immediately pointed out that perhaps hyping what amounts to a set of mathematical equations with a spacecraft design might not have been the classiest move on NASA's part.  NASA collaborator  Mark Rademaker [1] maintains it was done with the intent of convincing people that STEM is cool, you know, 'for the kids'.  Here's Mark's big, glossy, futuristic design It's cool and soooo pretty! Discussion of how STEM should be sold aside, there are now conversations circulating the internet regarding whether or not the ship would violate causality by flying faster than the speed of light.  The answer is, that this might be an issue if the ship actually violated the speed of light by traveling 4.3 light years in 14 days.  As it is though, it doesn't.  Read on: Travelling Faster than the Speed of Light Without Really Trying, (but n

Mapping Historical Events in Chronological Order: geochrono

In my history of physics research, I've come up with a data visualization application I need that I can't find.  It would be nice to be able to author a list of events and people tied to places and dates and then display them on a map in chronological order.  Using this visualization of information, I'm hoping to find individuals in my research who may have known or worked with each other, or who might have been instrumental in, or related to events in the history of physics.  I did my due diligence and tried to find a free application that already existed, but was unsuccessful.  Here's the open source GitHub for the new application  .  The details follow. Failing that, I wrote down a very brief description of what I'd like the app to do: I'm trying to find relationships between individuals that may not be obvious based on their chronological locations. I find myself in need of a tool that will let me map the locatio

Joseph Weber, Gravity Waves, and Robert L. Forward

I got to spend a little time today pursuing one of my hobbies, the history of physics.  I had noticed earlier this week that there were three Trimbles all involved in disparately similar activities, Virginia Trimble, astrophysicist, Charles Trimble, GPS inventor and executive, and George Trimble, NASA deputy director of manned spacecraft during the Apollo missions.  For one of the projects I'm working on I was attempting to find out of the three of them were in any way related, either familially, or by career or professional avenues.  I did find out that Virginia and Charles Trimble attended the California Insittute of Technology during the same time period, but that's about it so far.  Today I got sidetracked by the fact that Virginia Trimble,(picture 1) in addition to being featured in Life Magazine [1], and Twilight Zone promotions [2], was married to Joseph Weber [4]. Joseph Weber is shown in picture 2 Although you can read all about him on Wikipedia, I thought I

Electric Fields from Magnetic Using Special Relativistic Hyperbolic Rotations

I'm trying out  +MathJax  today.  It's not the most inclusive test in the world, but I figured a good easy runthrough was to publish one of my physics  +Stack Exchange  answers over here.  A few weeks ago, a user asked why the force on a moving particle due to a magnetic field is perpenicular to both the field and the direciton of motion.  I attempted to answer it using special relativity and Karapetoff's hyperbolic rotation approach to show that to the particle, the magnetic field looks like an electric field at a right angle to its motion.  By the way, everything appears to have worked like a champ, matrices, and all!  Here goes. One way to think about the answer is using special relativity.  In short, the particle itself sees the magnetic field in, (say the z direction), in our stationary frame transformed into an electric field in the -y direction in its moving frame.  This electric field has the correct magnitude to create a force on the charge equal to the Lorent

Getting Back to Basics, Generating the Quenching Magnetic Field

A question from +Yannick Selles  inspired today's post which is a rerun of the answer I posted yesterday on G+ with a few more pictures and an additional book reference.  I blame the evil stomach spirits that attacked for the lack of originality :)  Yannick asked how the magnetic fields required to drive the superconducting samples into their normal states, (quenching), for the H-ray experiment, were generated.  Here are the basics When an electric current travels through a wire, it creates a magnetic field surrounding the wire. By wrapping a wire into a coil, (a solenoid), the magnetic fields from each turn of wire align to produce a stronger magnetic field.  The black cylinders you see in the picture of the magnet below are solenoids of copper wire.  The black casing carries water to cool off the wire since it also heats up as current is passed through it. If you want to make an even larger magnetic field, this is where a material like iron comes in.  Iron is made u

Lab Book 2014_06_09 Fixing the Superconducting Quench Yoke Magnet

Scroll to the bottom for background on the experiment. Checked that the pole faces of the yoke magnet retract fully leaving enough room for the glass Dewar.  The poles do retract far enough, but there is a trick to it.  The rotator that advances and retracts the pole piece should have two metal collars associated with it.  On the side I initially tried to adjust, one of the collars was missing and the pole would not move.  When I moved the second collar to that side of the magnet, the pole piece moved after applying a little bit of force Here's how it works  The collar the handle protudes from is threaded on the inside.  It turns on the threads that are visible and are attached to the pole piece.  If the second collar is in place, then the torque created by the handle is applied to the threads of the pole piece and it slides back and forth through the treads of the handled piece along a small rail at the bottom of the threaded pole.  A screwing motion on the handled col

Kinetic Energy Lowering, Covalent bonds,and the Theory of Hole Superconductivity

My review of the material I mentioned yesterday [1] paid off pretty quickly.  Dr. Hirsch is quick to point out that one of the key differences between his 'hole theory of superconductivity'[4] and the more typical explanation of Cooper pair formation is that his theory predicts kinetic energy lowering after two holes in an energy band pair as opposed to the usual potential energy lowering after two electrons pair . While reading Hirsch's articles, I didn't remember ever coming across kinetic energy lowering pairing before.  It turned out that I had read about it in Dr. Likharev's notes , (see section 2.6, 'Coupled Quantum Wells'), but without an immediate application for the information, I promptly forgot it. Here are the basics 1.  Crystalline materials, (like superconductors, or semiconductors), in which electrons reside can be very roughly modeled as repeated delta function wells, (picture 1)[2] where the delta functions represent the potentia