Gaussian Approximation Potential: an interatomic potential derived from first principles Quantum Mechanics

Simulation of materials at the atomistic level is an important tool in studying microscopic structure and processes. The atomic interactions necessary for the simulation are correctly described by Quantum Mechanics. However, the computational resources required to solve the quantum mechanical equations limits the use of Quantum Mechanics at most to a few hundreds of atoms and only to a small fraction of the available configurational space. This thesis presents the results of my research on the development of a new interatomic potential generation scheme, which we refer to as Gaussian Approximation Potentials. In our framework, the quantum mechanical potential energy surface is interpolated between a set of predetermined values at different points in atomic configurational space by a non-linear, non-parametric regression method, the Gaussian Process. To perform the fitting, we represent the atomic environments by the bispectrum, which is invariant to permutations of the atoms in the neighbourhood and to global rotations. The result is a general scheme, that allows one to generate interatomic potentials based on arbitrary quantum mechanical data. We built a series of Gaussian Approximation Potentials using data obtained from Density Functional Theory and tested the capabilities of the method. We showed that our models reproduce the quantum mechanical potential energy surface remarkably well for the group IV semiconductors, iron and gallium nitride. Our potentials, while maintaining quantum mechanical accuracy, are several orders of magnitude faster than Quantum Mechanical methods.

Flow field measurements of a series of turbulent premixed and stratified methane/air flames

This paper presents flow field measurements for the turbulent stratified burner introduced in two previous publications in which high resolution scalar measurements were made by Sweeney et al. [1,2] for model validation. The flow fields of the series of premixed and stratified methane/air flames are investigated under turbulent, globally lean conditions (φg=0.75). Velocity data acquired with laser Doppler anemometry (LDA) and particle image velocimetry (PIV) are presented and discussed. Pairwise 2-component LDA measurements provide profiles of axial velocity, radial velocity, tangential velocity and corresponding fluctuating velocities. The LDA measurements of axial and tangential velocities enable the swirl number to be evaluated and the degree of swirl characterized. Power spectral density and autocorrelation functions derived from the LDA data acquired at 10kHz are optimized to calculate the integral time scales. Flow patterns are obtained using a 2-component PIV system operated at 7Hz. Velocity profiles and spatial correlations derived from the PIV and LDA measurements are shown to be in very good agreement, thus offering 3D mapping of the velocities. A strong correlation was observed between the shape of the recirculation zones above the central bluff body and the effects of heat release, stoichiometry and swirl. Detailed analyses of the LDA data further demonstrate that the flow behavior changes significantly with the levels of swirl and stratification, which combines the contributions of dilatation, recirculation and swirl. Key turbulence parameters are derived from the total velocity components, combining axial, radial and tangential velocities. © 2013 The Combustion Institute.

Reversible jump sampler for autoregressive time series

We use reversible jump Markov chain Monte Carlo (MCMC) methods to address the problem of model order uncertainty in autoregressive (AR) time series within a Bayesian framework. Efficient model jumping is achieved by proposing model space moves from the full conditional density for the AR parameters, which is obtained analytically. This is compared with an alternative method, for which the moves are cheaper to compute, in which proposals are made only for new parameters in each move. Results are presented for both synthetic and audio time series.

Modal scattering at an impedance transition in a lined flow duct

An explicit Wiener-Hopf solution is derived to describe the scattering of duct modes at a hard-soft wall impedance transition in a circular duct with uniform mean flow. Specifically, we have a circular duct r = 1, - ∞ < x < ∞ with mean flow Mach number M > 0 and a hard wall along x < 0 and a wall of impedance Z along x > 0. A minimum edge condition at x = 0 requires a continuous wall streamline r = 1 + h(x, t), no more singular than h = Ο(x1/2) for x ↓ 0. A mode, incident from x < 0, scatters at x = 0 into a series of reflected modes and a series of transmitted modes. Of particular interest is the role of a possible instability along the lined wall in combination with the edge singularity. If one of the "upstream" running modes is to be interpreted as a downstream-running instability, we have an extra degree of freedom in the Wiener-Hopf analysis that can be resolved by application of some form of Kutta condition at x = 0, for example a more stringent edge condition where h = Ο(x3/2) at the downstream side. The question of the instability requires an investigation of the modes in the complex frequency plane and therefore depends on the chosen impedance model, since Z = Z (ω) is essentially frequency dependent. The usual causality condition by Briggs and Bers appears to be not applicable here because it requires a temporal growth rate bounded for all real axial wave numbers. The alternative Crighton-Leppington criterion, however, is applicable and confirms that the suspected mode is usually unstable. In general, the effect of this Kutta condition is significant, but it is particularly large for the plane wave at low frequencies and should therefore be easily measurable. For ω → 0, the modulus fends to |R001| → (1 + M)/(1 -M) without and to 1 with Kutta condition, while the end correction tends to ∞ without and to a finite value with Kutta condition. This is exactly the same behaviour as found for reflection at a pipe exit with flow, irrespective if this is uniform or jet flow.

Bayesian model selection for time series using Markov chain Monte Carlo

We present a stochastic simulation technique for subset selection in time series models, based on the use of indicator variables with the Gibbs sampler within a hierarchical Bayesian framework. As an example, the method is applied to the selection of subset linear AR models, in which only significant lags are included. Joint sampling of the indicators and parameters is found to speed convergence. We discuss the possibility of model mixing where the model is not well determined by the data, and the extension of the approach to include non-linear model terms.

Microstructural modelling in friction stir welding of 2000 series aluminium alloys

Simple process models are applied to predict microstructural changes due to the thermal cycle imposed in friction stir welding. A softening model developed for heat-treatable aluminium alloys of the 6000 series is applied to the aerospace alloy 2014 in the peak-aged (T6) condition. It is found that the model is not readily applicable to alloy 2024 in the naturally aged (T3) temper, but the softening behaviour can still be described semi-empirically. Both analytical and numerical (finite element) thermal models are used to predict the thermal histories in trial welds. These are coupled to the microstructural model to investigate: (a) the hardness profile across the welded plate; (b) alloy softening ahead of the approaching welding tool. By incorporating the softening model applied to 6082-T6 alloy, the hardness profile of friction stir welds in dissimilar alloys is also predicted. © AFM, EDP Sciences 2005.