Self-optimized construction of transition rate matrices from accelerated atomistic simulations with Bayesian uncertainty quantification

A massively parallel method to build large transition rate matrices from temperature accelerated molecular dynamics trajectories is presented. Bayesian Markov model analysis is used to estimate the expected residence time in the known state space, providing crucial uncertainty quantification for higher scale simulation schemes such as kinetic Monte Carlo or cluster dynamics. The estimators are additionally used to optimize where exploration is performed and the degree of temperature ac- celeration on the fly, giving an autonomous, optimal procedure to explore the state space of complex systems. The method is tested against exactly solvable models and used to explore the dynamics of C15 interstitial defects in iron. Our uncertainty quantification scheme allows for accurate modeling of the evolution of these defects over timescales of several seconds.Comment: 14 pages, 7 figure

Measuring material wastage on construction sites: a case study of local authority highway projects

The construction industry in the UK is vast. It is one of the largest sectors of the economy with an output of over £100 billion, representing approximately 8% of the country’s GDP. The enormous amount of resources the industry consumes and produces coupled with the large number of construction companies in the market place has resulted in a growing awareness of the environmental impact of the construction industry. Construction produces more than 100 million tonnes of waste a year, representing more than 50% of the total waste production of the country. Of this waste, more than 60 million tonnes goes straight to landfill, three times more than all the domestic waste produced by the UK’s twenty one million homes. Increasing pressure on landfill sites coupled with the growing awareness of the environmental impact of the industry has made the minimisation of construction waste absolutely essential. The research project outlined in this paper attempts to measure material wastage occurring on selected Local Authority highway construction sites. To achieve this, a review will be undertaken to determine the main areas of interest in sustainable construction, construction waste production, and waste minimisation. Primary data will be collected in the form of measurements taken of theoretical and actual quantities of construction materials used during the course of selected highway projects. The results will be used to compare actual on-site material quantities against theoretical material quantities. The difference in these quantities will then be calculated, giving the amount of wastage occurring on site. The findings from this paper are drawn from both the secondary and the primary data analysis and statistical testing. The research concludes by suggesting a waste minimisation strategy for use on highway construction sites to try and reduce, re-use, and recycle the amount of construction waste local authority highway projects generate

Computing energy barriers for rare events from hybrid quantum/classical simulations through the virtual work principle

Hybrid quantum/classical techniques can flexibly couple ab initio simulations to an empirical or elastic medium to model materials systems that cannot be contained in small periodic supercells. However, due to electronic non-locality a total energy cannot be defined, meaning energy barriers cannot be calculated. We provide a general solution using the principle of virtual work in a modified nudged elastic band algorithm. Our method enables the first ab initio calculations of the kink formation energy for edge dislocations in molybdenum and lattice trapping barriers to brittle fracture in silicon

The phonon drag force acting on a mobile crystal defect: full treatment of discreteness and non-linearity

Phonon scattering calculations predict the drag force acting on defects and dislocations rises linearly with temperature, in direct contradiction with molecular dynamics simulations that often finds the drag force to be independent of temperature. Using the Mori-Zwanzig projection technique, with no recourse to elasticity or scattering theories, we derive a general Langevin equation for a crystal defect, with full treatment of discreteness and non-linearity in the defect core. We obtain an analytical expression for the drag force that is evaluated in molecular statics and molecular dynamics, extracting the force on a defect directly from the inter-atomic forces. Our results show that a temperature independent drag force arises because vibrations in a discrete crystal are never independent of the defect motion, an implicit assumption in any phonon-based approach. This effect remains even when the Peierls barrier is effectively zero, invalidating qualitative explanations involving the radiation of phonons. We apply our methods to an interstitial defect in tungsten and solitons in the Frenkel-Kontorova model, finding very good agreement with trajectory-based estimations of the thermal drag force.Comment: 20 pages, 8 figure

Collective transport in the discrete Frenkel-Kontorova model

Through multiscale analysis of the adjoint Fokker-Planck equation, strict bounds are derived for the center of mass diffusivity of an overdamped harmonic chain in a periodic potential, often known as the discrete Frenkel-Kontorova model. Significantly, it is shown that the free energy barrier is a lower bound to the true finite temperature migration barrier for this general and popular system. Numerical simulation confirms the analysis, whilst effective migration potentials implied by the bounds are employed to give a surprisingly accurate prediction of the non-linear response.Comment: 7 pages, 3 figures, submitte

Hybrid quantum/classical study of hydrogen-decorated screw dislocations in tungsten : ultrafast pipe diffusion, core reconstruction, and effects on glide mechanism

The interaction of hydrogen (H) with dislocations in tungsten (W) must be understood in order to model the mechanical response of future plasma-facing materials for fusion applications. Here, hybrid quantum mechanics/molecular mechanics (QM/MM) simulations are employed to study the ⟨111⟩ screw dislocation glide in W in the presence of H, using the virtual work principle to obtain energy barriers for dislocation glide, H segregation, and pipe diffusion. We provide a convincing validation of the QM/MM approach against full DFT energy-based methods. This is possible because the compact core and relatively weak elastic fields of ⟨111⟩ screw dislocations allow them to be contained in periodic DFT supercells. We also show that H segregation stabilizes the split-core structure while leaving the Peierls barrier almost unchanged. Furthermore, we find an energy barrier of less than 0.05 eV for pipe diffusion of H along dislocation cores. Our quantum-accurate calculations provide important reference data for the construction of larger-scale material models