AeroAstro-CSE PhD Thesis Defense: Julien Luzzatto

Abstract:

Direct atomistic integration cannot reach experimental timescales for activated processes: the rare events that carry the dynamics lie orders of magnitude beyond the vibrational timestep it must resolve, and because integration is intrinsically sequential, more computational resources buy larger systems, not longer simulated times. Kinetic Monte Carlo (KMC), the foundational engine of this thesis, exploits the separation between fast vibrations and rare barrier crossings. This thesis identifies three further bottlenecks that limit KMC itself and develops one method for each.

First, we replace per-event saddle searches with a machine-learned surrogate that predicts activation barriers and minimum-energy paths from the endpoints alone, at four orders of magnitude lower cost; a rate-space error theory bounds the bias introduced. Second, we extract escape rates from short, confined trajectories via spectral analysis, enabling efficient, unbiased parallel simulation of rare events. Third, we use adaptive domain decomposition to confine KMC to a thin reactive front while delegating the inert bulk to a continuum solver, so that step cost no longer grows with the system size.

These three methods combine into a nested simulator, validated on hafnium oxidation — a system that suffers from all three bottlenecks. Monolithic KMC stalls far short of any measured thickness; with no fitted parameters, the composed simulator reproduces oxide thicknesses to order of magnitude across the experimental temperature range, including the slowing of growth as temperature falls. The methods developed and validated here generalize beyond oxidation: each applies to any activated process exhibiting its enabling structure — barrier locality, a spectral gap, or a localized front — and the composition to any process exhibiting all three. Together they extend first-principles atomistic simulation to macroscopically relevant timescales.

Thesis Committee Members:

• Prof. Nicolas Hadjiconstantinou, Quentin Berg (1937) Professor of Mechanical Engineering, MIT (Chair)
• Prof. Youssef Marzouk, Breene M. Kerr (1951) Professor, Department of Aeronautics and Astronautics, MIT
• Dr. Danny Perez, Staff Scientist, Theoretical Division, Los Alamos National Laboratory
• Dr. Ngoc Cuong Nguyen, Principal Research Scientist, Department of Aeronautics and Astronautics, MIT (Reader)
• Dr. Tim Germann, Staff Member, Applied Physics & Theoretical Divisions, Los Alamos National Laboratory (Reader)