On the adaptive finite element analysis of the Kohn–Sham equations: methods,algorithms, and implementation

In this paper, details of an implementation of a numerical code for computing the Kohn–Sham equations are presented and discussed. A fully self‐consistent method of solving the quantum many‐body problem within the context of density functional theory using a real‐space method based on finite element discretisation of realspace is considered. Various numerical issues are explored such as (i) initial mesh motion aimed at co‐aligning ions and vertices; (ii) a priori and a posteriori optimization of the mesh based on Kelly's error estimate; (iii) the influence of the quadrature rule and variation of the polynomial degree of interpolation in the finite element discretisation on the resulting total energy. Additionally, (iv) explicit, implicit and Gaussian approaches to treat the ionic potential are compared. A quadrupole expansion is employed to provide boundary conditions for the Poisson problem. To exemplify the soundness of our method, accurate computations are performed for hydrogen, helium, lithium, carbon, oxygen, neon, the hydrogen molecule ion and the carbon‐monoxide molecule. Our methods, algorithms and implementation are shown to be stable with respect to convergence of the total energy in a parallel computational environment. Copyright © 2015 John Wiley & Sons, Ltd.     

Hysteresis‐Free 1D Network Mixed Halide‐Perovskite Semitransparent Solar Cells

The morphology of hybrid organic–inorganic perovskite films is known to strongly affect the performance of perovskite‐based solar cells. CH₃NH₃PbI_3‐xCl_x (MAPbI_3‐xCl_x) films have been previously fabricated with 100% surface coverage in glove boxes. In ambient air, fabrication generally relies on solvent engineering to obtain compact films. In contrast, this work explores the potential of altering the perovskites microstructure for solar cell engineering. This work starts with CH₃NH₃PbI_3‐xCl_x, films with grain morphology carefully controlled by varying the deposition speed during the spin‐coating process to fabricate efficient and partially transparent solar cells. Devices produced with a CH₃NH₃PbI_3‐xCl_x film and a compact thick top gold electrode reach a maximum efficiency of 10.2% but display a large photocurrent hysteresis. As it is demonstrated, the introduction of different concentrations of bromide in the precursor solution addresses the hysteresis issues and turns the film morphology into a partially transparent interconnected network of 1D microstructures. This approach leads to semitransparent solar cells with negligible hysteresis and efficiencies up to 7.2%, while allowing average transmission of 17% across the visible spectrum. This work demonstrates that the optimization of the perovskites composition can mitigate the hysteresis effects commonly attributed to the charge trapping within the perovskite film.     

A new methodology for Bayesian history matching using parallel interacting Markov chain Monte Carlo

This paper presents an innovative application of a new class of parallel interacting Markov chains Monte Carlo to solve the Bayesian history matching (BHM) problem. BHM consists of sampling a posterior distribution given by the Bayesian theorem. Markov chain Monte Carlo (MCMC) is well suited for sampling, in principle, any type of distribution; however the number of iteration required by the traditional single-chain MCMC can be prohibitive in BHM applications. Furthermore, history matching is typically a highly nonlinear inverse problem, which leads in very complex posterior distributions, characterized by many separated modes. Therefore, single chain can be trapped into a local mode. Parallel interacting chains is an interesting way to overcome this problem, as shown in this paper. In addition, we presented new approaches to define starting points for the parallel chains. For validation purposes, the proposed methodology is firstly applied in a simple but challenging cross section reservoir model with many modes in the posterior distribution. Afterwards, the application to a realistic case integrated to geostatistical modelling is also presented. The results showed that the combination of parallel interacting chain with the capabilities of distributed computing commonly available nowadays is very promising to solve the BHM problem.     

Transverse Spin Diffusion in a Dilute Spin-Polarized Degenerate Fermi Gas

We re-examine the calculation of the transverse spin-diffusion coefficient in a dilute degenerate spin-polarized Fermi gas, for the case of s-wave scattering. The special feature of this limit is that the dependence of the spin diffusion coefficient on temperature and field can be calculated explicitly with no further approximations. This exact solution uncovers a novel intermediate behaviour between the high field spin-rotation dominated regime in which D H^–2 , D T^–2 , and the low-field isotropic, collision dominated regime with D = D T^–2 . In this intermediate regime, D_, T^–2 but D D. We emphasize that the low-field crossover cannot be described within the relaxation time approximation. We also present an analytical calculation of the self-energy in the s-wave approximation for a dilute spin-polarized Fermi gas, at zero temperature. This emphasizes the failure of the conventional Fermi-liquid phase space arguments for processes involving spin flips. We close by reviewing the evidence for the existence of the intermediate regime in experiments on weakly spin-polarized ³ He and ³ He– ⁴ He mixtures.     

Whole-body vibration experienced by haulage truck operators in surface mining operations: A comparison of various analysis methods utilized in the prediction of health risks

Whole body vibration (WBV) was measured on eight surface haulage trucks in three size classes (35, 100, 150 ton haul capacities). Vibration was measured at the seat/operator interface in accordance with the ISO 2631-1 standard during 1 h of normal operation. Highest acceleration readings were observed in the z-axis (vertical). Estimated equivalent daily exposure values in the range of 0.44–0.82 ms^?2 were observed using the frequency-weighted r.m.s method and 8.7–16.4 ms^?1.75 using the vibration dose value method. Assessment was carried out using ISO 2631-1 and 2631-5. Operators of surface haulage trucks are regularly exposed to WBV levels that exceed safety limits as dictated by the ISO 2631-1 standard. However, according to ISO 2631-5 the probability of an adverse health effect remains low. These findings confirm an apparent disagreement between the two analysis methods.     

Accuracy estimate and optimization techniques for SimRank computation

The measure of similarity between objects is a very useful tool in many areas of computer science, including information retrieval. SimRank is a simple and intuitive measure of this kind, based on a graph-theoretic model. SimRank is typically computed iteratively, in the spirit of PageRank. However, existing work on SimRank lacks accuracy estimation of iterative computation and has discouraging time complexity. In this paper, we present a technique to estimate the accuracy of computing SimRank iteratively. This technique provides a way to find out the number of iterations required to achieve a desired accuracy when computing SimRank. We also present optimization techniques that improve the computational complexity of the iterative algorithm from O(n ⁴) in the worst case to min(O(nl), O(n ³/ log₂ n)), with n denoting the number of objects, and l denoting the number object-to-object relationships. We also introduce a threshold sieving heuristic and its accuracy estimation that further improves the efficiency of the method. As a practical illustration of our techniques, we computed SimRank scores on a subset of English Wikipedia corpus, consisting of the complete set of articles and category links.