I worked on interesting problems while studying physics at Cal Poly; a few deserve to be put online. It’s a pity there isn’t anything nice looking to show from the reams of problem sets I spent many hours grinding through, but maybe some day I’ll scan a quantum mechanics midterm.
Pattern Recognition of Particle Trajectories in Hexagonal Geometry Drift Detectors
So many syllables. But that was the title of the talk I gave at the APS Sonoma conference, so I’m sticking with it.
I wrote a program in Python to group data generated by the NIFFTE atom fission experiment. Atoms are smashed inside a chamber with edges coated in hexagonal sensors. The fragments from the collision leave long trails, like fireworks. Assigning distinct trajectories from the sensor data is easy for a human but a thorny problem for a computer. Of course, automation of the process is necessary given the huge amounts of data generated. It also makes it possible to calculate the velocity and energy of each daughter particle created in the collision. For more detail, see the project on Github, particularly the iPython writeup and documentation.
Here are a few sample output plots of atoms breaking apart. The program’s goal was to identify and color code each of the tracks descending from the common origin.
First figure: An atom fragmenting into three separate particles.
Second figure: Two separate collisions, each generating a pair of daughter particles.
LED Spectrometer and Solar Tracker
When you apply a voltage across an LED, you get a colored light. It turns out LEDs work backwards too: shine the correct color of light on an LED and you get a (tiny) voltage back on the LED’s leads. My lab partner and I used this fact to make a spectrometer out of a handful of LEDs and an Arduino microcontroller. Each different color LED could detect the amount of that color of light present. Once the spectrometer was working, we added on servo motors, light/shadow sensors, and another microcontroller to enable it to track the sun as it moves across the sky.
The light sensors in the corners are shrouded by chunks of PVC pipe cut in half. Each shields the sun from one direction, so the motors can tilt the panel to minimize shadows. When there are no shadows on the sensors, the spectrometer must be pointed directly towards the sun. The five LEDs have their tops ground off to increase the amount of light collected.
Here’s the output. Each bar represents the relative intensity of the light recorded from one color of LED. The bar colors roughly match the LED colors except for dark red, which represents the infrared channel. As the sun nears the horizon, atmospheric scattering shifts the sun’s apparent light spectrum from blue and green to red and infrared. That’s why sunrises and sunsets have wonderful gold and pink colors.
A more complete (and more technical) description of the project is in the form of two youtube videos. Forgive the low production values, it was an electronics class with tight deadlines—no budget left for multimedia. Here are the links:
First Phase: LED Spectrometer
Second Phase: Tracking the Sun
Smectic Liquid Crystal Unwinding in Electric Fields
Theoretical research I did under Dr. Karl Saunders. Liquid crystals have a measurable order (hence crystals) but are easily influenced by small changes in temperature and, in some cases, electric fields. Smectic liquid crystals form stacked sheets of similarly aligned molecules. The scummy residue at the bottom of a soap dish is an interesting example of these. It’s slippery because the layers can freely slide against each other without much resistance. The layers can be stacked with the molecules oriented straight up and down (Smectic-A), stacked with the molecules angled (Smectic-C), or angled with a different angle for each layer (Smectic-C*). Of course, the arrangements may change as the temperature and electric fields are changed.
We studied the complex nonlinear behaviors and phase transitions that a smectic liquid crystal system undergoes when the temperature and electric field strength are changed. The full writeup is available here, but be warned that it is dense and math heavy. I gave a talk about our research [pdf] to a general audience at Cal Poly and had to spend much of it explaining the basic idea in lay terms.
Smectic liquid crystal phases and critical points. The system parameter responding to temperature change is r, and the electric field strength is given by E. The boundary between the Smectic-C and Smectic-C* state represents where the liquid crystals unwind: they have uniformly-tilted stacked layers instead of helically stacked layers.
Relaxation Solution to Laplacian Equations
If you assign voltage values to the edges of a region, the voltage inside it can be calculated numerically. Here’s another Python programming project with nice visuals and source code available on Github. The potential surface must obey mathematical rules: everything must adjust smoothly from the edges. Imagine a thin sheet of rubber being stretched tightly around the oddly-shaped edges. It wouldn’t have any tears, holes, or wrinkles in it. The code uses a relaxation method to progressively smooth out the surface until it meets the edge constraints. If any calculus textbook publishers want to use these for their cover art, drop me a line!
First figure: A voltage in the shape of a sine wave has been applied to the top edge.
Second figure: Adding small units of electric charge inside the region creates spikes: the potential mesh goes to infinity wherever they are. Here is an electric quadrupole in a region with gracefully curving boundaries. Don’t prick your finger.