Hybrid expansions for local structural relaxations

A model is constructed in which pair potentials are combined with the cluster expansion method in order to better describe the energetics of structurally relaxed substitutional alloys. The effect of structural relaxations away from the ideal crystal positions, and the effect of ordering is described by interatomic-distance dependent pair potentials, while more subtle configurational aspects associated with correlations of three- and more sites are described purely within the cluster expansion formalism. Implementation of such a hybrid expansion in the context of the cluster variation method or Monte Carlo method gives improved ability to model phase stability in alloys from first-principles.Comment: 8 pages, 1 figur

Valorization of sweet corn (Zea mays) cob by extraction of valuable compounds

The main objective of this study was to investigate the proximate, mineral and phytochemical compositions of sweet corn cob (SCC), often neglected and regarded as agricultural waste. Compositional analysis showed that more than 60% of SCC was composed of insoluble dietary fibre, with cellulose being the major constituent. Results also showed that SCC can be a good source of non-essential protein and minerals (phosphorus,potassium and manganese). SCC had a total phenolic content of 6.74 g GAE kg-1 dry weight DW), of which bound phenolics were predominant. The bound phenolics fraction showed the highest antioxidant capacity in all three antioxidant capacity assays (TEAC, FRAP and DPPH) and contained the highest amount of ferulic and p-coumaric acid. The main carotenoids present in SCC were β-carotene, zeaxanthin and lutein. This investigation shows that SCC can be a potential source of natural colorant (carotenoids), antioxidants (phenolics)and nutritional supplements (proteins and phytochemicals)

First-principles equation of state and phase stability for the Ni-Al system under high pressures

The equation of state (EOS) of alloys at high pressures is generalized with the cluster expansion method. It is shown that this provides a more accurate description. The low temperature EOSs of Ni-Al alloys on FCC and BCC lattices are obtained with density functional calculations, and the results are in good agreement with experiments. The merits of the generalized EOS model are confirmed by comparison with the mixing model. In addition, the FCC phase diagram of the Ni-Al system is calculated by cluster variation method (CVM) with both spin-polarized and non-spin-polarized effective cluster interactions (ECI). The influence of magnetic energy on the phase stability is analyzed. A long-standing discrepancy between ab initio formation enthalpies and experimental data is addressed by defining a better reference state. This aids both evaluation of an ab initio phase diagram and understanding the thermodynamic behaviors of alloys and compounds. For the first time the high-pressure behavior of order-disorder transition is investigated by ab initio calculations. It is found that order-disorder temperatures follow the Simon melting equation. This may be instructive for experimental and theoretical research on the effect of an order-disorder transition on shock Hugoniots.Comment: 27 pages, 12 figure

iPINNs: Incremental learning for Physics-informed neural networks

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and non-unique due to the complexity of the loss landscape that needs to be traversed. Although a variety of multi-task learning and transfer learning approaches have been proposed to overcome these issues, there is no incremental training procedure for PINNs that can effectively mitigate such training challenges. We propose incremental PINNs (iPINNs) that can learn multiple tasks (equations) sequentially without additional parameters for new tasks and improve performance for every equation in the sequence. Our approach learns multiple PDEs starting from the simplest one by creating its own subnetwork for each PDE and allowing each subnetwork to overlap with previously learned subnetworks. We demonstrate that previous subnetworks are a good initialization for a new equation if PDEs share similarities. We also show that iPINNs achieve lower prediction error than regular PINNs for two different scenarios: (1) learning a family of equations (e.g., 1-D convection PDE); and (2) learning PDEs resulting from a combination of processes (e.g., 1-D reaction-diffusion PDE). The ability to learn all problems with a single network together with learning more complex PDEs with better generalization than regular PINNs will open new avenues in this field

Using bond-length dependent transferable force constants to predict vibrational entropies in Au-Cu, Au-Pd, and Cu-Pd alloys

A model is tested to rapidly evaluate the vibrational properties of alloys with site disorder. It is shown that length-dependent transferable force constants exist, and can be used to accurately predict the vibrational entropy of substitutionally ordered and disordered structures in Au-Cu, Au-Pd, and Cu-Pd. For each relevant force constant, a length- dependent function is determined and fitted to force constants obtained from first-principles pseudopotential calculations. We show that these transferable force constants can accurately predict vibrational entropies of L1$_{2}$-ordered and disordered phases in Cu$_{3}$Au, Au$_{3}$Pd, Pd$_{3}$Au, Cu$_{3}$Pd, and Pd$_{3}$Au. In addition, we calculate the vibrational entropy difference between L1$_{2}$-ordered and disordered phases of Au$_{3}$Cu and Cu$_{3}$Pt.Comment: 9 pages, 6 figures, 3 table