Charged Elastic Rod (DNA Supercoiling) – BFGS Programming Assignment

This repo is a starter kit for a Numerical Methods programming assignment on quasi-Newton optimization (BFGS).

Students will minimize the energy of a closed, charged elastic filament in 3D, discretized as N points. The energy combines:

• Bending (curvature penalty),
• Stretching (near-inextensibility),
• Screened Coulomb repulsion (Debye–Hückel).

The core energy + gradient kernel is implemented in C++ for speed and exposed to Python via ctypes. You will implement BFGS (and a line search) in Python and use it to find low-energy configurations.

Quickstart

1) Create environment

python -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt
pip install -e .

2) Build the C++ shared library

Linux/macOS (clang/gcc):

bash csrc/build.sh

This produces csrc/librod.so (Linux) or csrc/librod.dylib (macOS).

3) Run a gradient check

pytest -q

4) Run the optimizer (after you implement BFGS)

python scripts/run_opt.py --N 120 --steps 200

What you need to implement

• src/elastic_rod/bfgs.py: BFGS update + line search (Wolfe or backtracking).
• csrc/rod_energy.cpp: The code described in the TODO: comment.
• (Optional) better initialization and plotting in scripts/run_opt.py.

Repo layout

• csrc/: C++ energy + gradient, builds a shared library
• src/elastic_rod/: Python wrapper + optimization code
• docs/background.tex: short LaTeX background note (assignment handout)
• tests/: finite-difference gradient checks

Parameters (default)

• kb: bending stiffness
• ks: stretching stiffness
• l0: rest segment length
• q: charge magnitude per node
• kappa: screening parameter (0 gives unscreened Coulomb)

See src/elastic_rod/model.py.

License

MIT (for the starter code). Add your course policy as needed.

Gradescope

Staff: see gradescope/README_GRADESCOPE.md for an autograder skeleton. Students: see docs/AUTOGRADING.md and run python scripts/autograde_local.py --mode accuracy.