Band Warping

DFT of Geometric Matrices

Here we plot special matrices (where any element can only be 0,i,-1,-i, and 1) and the DFT of those matrices.  Click on a cell of the matrix to cycle through element values.  To change the color, select from the drop down box.  To select a larger size, find select the size then press "Reset".  The numerical value of the DFT gets annoying, so hide it by unchecking the checkbox.

Two-band Tight-Binding Band Plot z=0

Two-band tight-binding model with 3rd NN interactions

Graphite Q Point

Here is a demonstration of the energy dispersion near the Q point of Graphite.

Another Attempt. This one is useful.

I think the last post was too short and did not explain enough.  I am attempting (as are many others) to put Wolfram's CDF documents online.  It seems like it is possible to view in major browsers (unless viewing on a Linux machine).  If you are using Mac or Windows and you do not see anything for this post and the last, just click on the icon in the middle and download the plugin.  This is like the Adobe Flash plugin or any other kind of plugin.  You need it to view the content.

If this works (and I work out all of the bugs, like re-sizing of the last entry), I hope to put a lot more on here.  It is just easier than making movies and trying to explain everything.

Here is an attempt at plotting the absorption coefficient for the indirect phonon-assisted transitions in a crystal:

CDF Example of Rolling Disk

I recently did this for my class.  This will be a test of Wolfram's CDF plugin.  Here is a disk slipping on a surface:

 

Musical Spiral

This is fantastic!  I found this in a link off of mathpuzzle.com. 

There is so many different directions you can go with this!  I love that if you close your eyes, the music has some structure, but it mostly sounds too complicated to understand.  However, if we found a way to graph it, to represent it in another way, we could understand the complexity.  That is why representation of data and ideas is so important.  The right notation can make all the difference in the world. 

What other geometric music could be attempted?  Something that would be very simple geometrically, but complicated musically. 

Is there a three dimensional analogue?  What is the best scale to use?

My favorite is probably this one or this one.

Have fun!