Hypoelliptic multiscale Langevin diffusions: Large deviations, invariant measures and small mass asymptotics

We consider a general class of non-gradient hypoelliptic Langevin diffusions and study two related questions. The first one is large deviations for hypoelliptic multiscale diffusions. The second one is small mass asymptotics of the invariant measure corresponding to hypoelliptic Langevin operators and of related hypoelliptic Poisson equations. The invariant measure corresponding to the hypoelliptic problem and appropriate hypoelliptic Poisson equations enter the large deviations rate function due to the multiscale effects. Based on the small mass asymptotics we derive that the large deviations behavior of the multiscale hypoelliptic diffusion is consistent with the large deviations behavior of its overdamped counterpart. Additionally, we rigorously obtain an asymptotic expansion of the solution to the related density of the invariant measure and to hypoelliptic Poisson equations with respect to the mass parameter, characterizing the order of convergence. The proof of convergence of invariant measures is of independent interest, as it involves an improvement of the hypocoercivity result for the kinetic Fokker-Planck equation. We do not restrict attention to gradient drifts and our proof provides explicit information on the dependence of the bounds of interest in terms of the mass parameter

Modelling zinc oxide thin-film growth

Photovoltaics have a significant role in the solution of energy supply and energy security. Research on photovoltaic devices and their production processes has been carried out for decades. The transparent conducting oxide layer, in the photovoltaic solar cell, composed of aluminium doped zinc oxide, is produced through deposition techniques. By modelling these depositions using classical molecular dynamics, a better understanding on the short term kinetics occurring on the growing surface has been achieved. Compared to the molecular dynamics, the employment of the adaptive kinetic Monte Carlo method enabled such surface growth dynamics simulation to reach much longer time scale. Parallelised transition searching was carried out in an on-the-fly manner without lattice approximation or predefined events table. The simulation techniques allowed deposition conditions to be easily changed, such as deposition energy, deposition rate, substrate temperature, plasma pressure, etc. Therefore, in this project three main deposition techniques were modelled including evaporation (thermal and assisted electron beam), reactive magnetron sputtering and pulsed laser depositions. ZnO as a covalent compound with many uses in semiconductors was investigated in its most energy favourable wurtzite configuration. The O-terminated surface was used as the substrate for the growth simulation. Evaporation deposition at room temperature (300 K) with a stoichiometric distribution of deposition species produced incomplete new layers. Holes were observed existing for long times in each layer. Also, stacking faults were formed during the low-energy (1 eV) growth through evaporation. The reactive sputtering depositions were more capable of getting rid of these holes structures and diminished these stacking faults through high energy bombardments but could also break these desirable crystalline structure during the growth. However, single deposition results with high energies showed that the ZnO lattice presented good capacity of self-healing after energetic impacts. Additionally, such self-healing effects were seen for substrate surface during thin film growth by the sputtering depositions. These facts shed some light on that the sputtering technique is the method of choice for ZnO thin film depositions during industrial production. Simulation results of pulsed laser deposition with separated Zn and O species showed the thin films were grown in porous structures as the O-terminated surface could be severely damaged by Zn atoms during the very short pulse window (10 microseconds). An important growth mechanism with ZnO dimer deposited on the O-terminated polar surface was the coupling of these single ZnO dimers, forming highly mobile strings along the surface and thus quenching its dipole moments, whilst the isolated single ZnO dimers were hardly of this mobility. Such strings were the building blocks for the fabrication occurring on the surface resulting in new layers. Last but not least, a reactive force field for modelling Al doped ZnO was fitted. DFT calculations showed that the Al atoms on the surface were likely to replace Zn atoms in their lattice sites for more energy favourable structures. Al on the ZnO surfaces, structures with Al in the bulk as well as configurations with Al interstitials were used to train the force field to reproduce favourable surface binding sites, cohesive energies and lattice dimensions. The combination scheme of MD and the AKMC allowed simulation work to reach over experimentally realistic time scale. Therefore, crucial mechanisms occurring during the growth could be precisely understood and investigated on an atomistic level. It has been shown from the simulation results that certain types of deposition play significant roles in the quality of resultant thin films and surface morphology, thus providing insight to the optimal deposition conditions for growing complete crystalline ZnO layers

Variational deep learning of equilibrium transition path ensembles

We present a time dependent variational method to learn the mechanisms of equilibrium reactive processes and efficiently evaluate their rates within a transition path ensemble. This approach builds off variational path sampling methodology by approximating the time dependent commitment probability within a neural network ansatz. The reaction mechanisms inferred through this approach are elucidated by a novel decomposition of the rate in terms of the components of a stochastic path action conditioned on a transition. This decomposition affords an ability to resolve the typical contribution of each reactive mode and their couplings to the rare event. The associated rate evaluation is variational and systematically improvable through the development of a cumulant expansion. We demonstrate this method in both over- and under-damped stochastic equations of motion, in low-dimensional model systems and the isomerization of solvated alanine dipeptide. In all examples, we find that we can obtain quantitatively accurate estimates of the rates of the reactive events with minimal trajectory statistics, and gain unique insight into the transitions through the analysis of their commitment probability