Research
Friction at the atomic scale
Thesis work on stick-slip AFM friction; post-thesis reanalysis of molecular dynamics simulation data.
Thesis — Stick-slip friction in the Prandtl–Tomlinson model
My thesis studied atomic-scale friction using the Prandtl–Tomlinson (PT) model — a driven particle in a periodic potential with a spring coupling to a moving stage. Depending on the ratio of tip stiffness to potential corrugation and the damping coefficient, the system exhibits qualitatively different regimes: smooth sliding, periodic stick-slip, and chaotic multiple-slip sequences.
The numerical core is a Langevin SDE integrator: deterministic PT dynamics plus a thermal noise term scaled to satisfy the fluctuation-dissipation theorem. I implemented this in Python with Numba JIT compilation, which brought single-trajectory integration from ~40s to ~80ms — fast enough to sweep parameter space and build regime diagrams. The integrator supports overdamped, underdamped, and critically damped regimes and handles multiple-slip events through a detection pass on the tip-velocity trace.
Post-thesis — MD simulation reanalysis
After the thesis, I collaborated with a group running molecular dynamics simulations of tip-surface sliding contacts. Their data produced lateral force traces with characteristic sawtooth patterns — individual slip events visible as sharp force drops. The analysis problem was extracting reliable slip statistics (event frequency, slip amplitude, pre-slip stiffness) from noisy traces with variable baseline drift.
I wrote a slip-detection pipeline in Python: a damped-oscillator fit to the pre-slip loading curve (giving effective contact stiffness), a threshold-based event segmenter tuned to the signal-to-noise characteristics of their simulation output, and bootstrap resampling for uncertainty estimation on derived quantities. The extracted parameters were compared against PT model predictions across a range of drive velocities — the agreement was good in the overdamped regime, with systematic deviations at low velocity consistent with thermal activation effects the deterministic PT model doesn't capture.
Methods
- Langevin SDE integration — stochastic RK4 drift + Euler–Maruyama noise term
- Numba JIT compilation for parameter-sweep performance
- Damped-oscillator curve fitting (scipy.optimize) for contact stiffness extraction
- Bootstrap resampling for uncertainty quantification on slip statistics
- Python · NumPy · SciPy · Numba · Matplotlib