Flat Self Assembly

Inputs: .mp4 top-down video of spherical beads at different

1. Number of particles, N
2. Amplitude of the vibration, A

Outputs: The estimated entropy of the system

Data Acquisition

1. Start the video record.
2. On an applied voltage (amplitude), put a set of 10 particles into the plate.
3. Wait for 30s for the system to equilibrate.
4. Repeat 2, 3 until 205 particles is in a plate.
5. Stop the video record.
6. Repeat the whole process with different amplitude.

This setup allow minimal perturbance to the data acquisition which help the system equilibrate with a smaller amount of time.

Data Workflow

1. Iterate through each frame in the video
2. Use circle detection to find the centroid position of each particles
3. Repeat for the next frame
4. Find optimal transport map between the two frames and correlated the particle in the first frame to the second frame.
5. Calculate the momentum from finite difference method
6. Bin the position and momentum into histogram
7. Calculate the shannon entropy and average energy using the probability estimation from histogram

Results

The phase transition is found near N ~ 100 from the discontinuity in free energy, indicating a second order phase transition.