## Archive for December 2009

### Alpha helix to carbon nanotube

31 December 2009

Alpha helices in proteins and carbon nanotubes look alike.  I wonder if it is possible to grow nanotubes from alpha-helices.   I see there is one article out there – Carbon nanotubes self -assembled by amphiphilic alpha peptide helices – have to check it out.  Generating graphene from a beta sheet seems less likely, because of the natural twist present in a beta sheet – I don’t find any articles at this time on that.

### World of Warcraft

25 December 2009

Taking a short vacation, I gave the now mature online game of World of Warcraft a try.  A fun, Blizzard did a good job creating a game with an immersive environment.  I can see why it is so popular.  Also found the add-ons and customizability using Lua very interesting, skimmed a couple books on writing add-ons, and wrote one for myself.  The  webisodes of the Guild, which play off of Wow, are entertaining.

### Snowflake formation

13 December 2009

Stellar dendrite snow crystal

The forecasts predicting snow for this weekend were wrong, but it reminded me of a question I had – why would snowflakes form symmetrically?   How does one individual branch “know” how the other 5 are growing?   It turns out that the local conditions (temperature, altitude, etc) govern the crystal growth, and that snowflakes are different because of their trajectories through the atmosphere. Any one snowflake sees the same conditions and will grow in a symmetric fashion (though the majority of snowflakes are actually irregular)

Kenneth Libbrecht is a physicist studying snowflake formation, and has a great website discussing this, with great micrographs of snowflakes.   He also has a paper The physics of snow crystals.

### SAGE history and ODE solvers

12 December 2009

William Stein recently wrote up an interesting history of his trajectory in mathematics and creation of SAGE (which I’m a big fan of).   This document lead me to discover (Pyrex and) Cython, which looks very useful for my work.

Also, after reviewing and debugging my RKF method, I’m ready to use the scipy solution, scipy.integrate.odeint, which provides and interface to LSODA in the ODEPACK.   Getting to know ODEPACK intimately will be the key for implementing my ode.

### Kinematic closure applied to protein folding

10 December 2009

Introduced to the work of Dr. Evangelos Coutsias at UNM, an read through a couple of his papers

### Reviewing ODE solvers

5 December 2009

Coded up primitive ODE solvers for Euler, RK2, RK4, RKF in Python on the plane and graphed comparative results.  Here they are for $y' = 1 + y^2$

The green points are Euler, red are Runge-Kutta second order, light-blue RK4, and small purple are Runge-Kutta-Fehlberg (lying on the blue line for the mathematical solution $y= \tan(t + c)$