The importance of anisotropic Coulomb interaction in LaMnO3

In low-temperature anti-ferromagnetic LaMnO3, strong and localized electronic interactions among Mn 3d electrons prevent a satisfactory description from standard local density and generalized gradient approximations in density functional theory calculations. Here we show that the strong on-site electronic interactions are described well only by using direct and exchange corrections to the intra-orbital Coulomb potential. Only DFT+U calculations with explicit exchange corrections produce a balanced picture of electronic, magnetic and structural observables in agreement with experiment. To understand the reason, a rewriting of the functional form of the +U corrections is presented that leads to a more physical and transparent understanding of the effect of these correction terms. The approach highlights the importance of Hund’s coupling (intra-orbital exchange) in providing anisotropy across the occupation and energy eigenvalues of the Mn d states. This intra-orbital exchange is the key to fully activating the Jahn-Teller distortion, reproducing the experimental band gap and stabilizing the correct magnetic ground state in LaMnO3. The best parameter values for LaMnO3 within the DFT(PBEsol)+U framework are determined to be U = 8 eV and J = 1.9 eV.

Missing steps in a staircase: a qualitative study of the perspectives of key stakeholders on the use of adaptive designs in confirmatory trials

Background Despite the promising benefits of adaptive designs (ADs), their routine use, especially in confirmatory trials, is lagging behind the prominence given to them in the statistical literature. Much of the previous research to understand barriers and potential facilitators to the use of ADs has been driven from a pharmaceutical drug development perspective, with little focus on trials in the public sector. In this paper, we explore key stakeholders’ experiences, perceptions and views on barriers and facilitators to the use of ADs in publicly funded confirmatory trials. Methods Semi-structured, in-depth interviews of key stakeholders in clinical trials research (CTU directors, funding board and panel members, statisticians, regulators, chief investigators, data monitoring committee members and health economists) were conducted through telephone or face-to-face sessions, predominantly in the UK. We purposively selected participants sequentially to optimise maximum variation in views and experiences. We employed the framework approach to analyse the qualitative data. Results We interviewed 27 participants. We found some of the perceived barriers to be: lack of knowledge and experience coupled with paucity of case studies, lack of applied training, degree of reluctance to use ADs, lack of bridge funding and time to support design work, lack of statistical expertise, some anxiety about the impact of early trial stopping on researchers’ employment contracts, lack of understanding of acceptable scope of ADs and when ADs are appropriate, and statistical and practical complexities. Reluctance to use ADs seemed to be influenced by: therapeutic area, unfamiliarity, concerns about their robustness in decision-making and acceptability of findings to change practice, perceived complexities and proposed type of AD, among others. Conclusions There are still considerable multifaceted, individual and organisational obstacles to be addressed to improve uptake, and successful implementation of ADs when appropriate. Nevertheless, inferred positive change in attitudes and receptiveness towards the appropriate use of ADs by public funders are supportive and are a stepping stone for the future utilisation of ADs by researchers.

Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential

For a particular family of long-range potentials V, we prove that the eigenvalues of the indefinite Sturm–Liouville operator A = sign(x)(−Δ+V(x)) accumulate to zero asymptotically along specific curves in the complex plane. Additionally, we relate the asymptotics of complex eigenvalues to the two-term asymptotics of the eigenvalues of associated self-adjoint operators.

Electronic structure of point defects in controlled self-doping of the TiO2 (110) surface: Combined photoemission spectroscopy and density functional theory study

Point defects in metal oxides such as TiO2 are key to their applications in numerous technologies. The investigation of thermally induced nonstoichiometry in TiO2 is complicated by the difficulties in preparing and determining a desired degree of nonstoichiometry. We study controlled self-doping of TiO2 by adsorption of 1/8 and 1/16 monolayer Ti at the (110) surface using a combination of experimental and computational approaches to unravel the details of the adsorption process and the oxidation state of Ti. Upon adsorption of Ti, x-ray and ultraviolet photoemission spectroscopy (XPS and UPS) show formation of reduced Ti. Comparison of pure density functional theory (DFT) with experiment shows that pure DFT provides an inconsistent description of the electronic structure. To surmount this difficulty, we apply DFT corrected for on-site Coulomb interaction (DFT+U) to describe reduced Ti ions. The optimal value of U is 3 eV, determined from comparison of the computed Ti 3d electronic density of states with the UPS data. DFT+U and UPS show the appearance of a Ti 3d adsorbate-induced state at 1.3 eV above the valence band and 1.0 eV below the conduction band. The computations show that the adsorbed Ti atom is oxidized to Ti2+ and a fivefold coordinated surface Ti atom is reduced to Ti3+, while the remaining electron is distributed among other surface Ti atoms. The UPS data are best fitted with reduced Ti2+ and Ti3+ ions. These results demonstrate that the complexity of doped metal oxides is best understood with a combination of experiment and appropriate computations.

Surface and interstitial Ti diffusion at the rutile TiO2(110) surface

Diffusion of Ti through the TiO2 (110) rutile surface plays a key role in the growth and reactivity of TiO2. To understand the fundamental aspects of this important process, we present an analysis of the diffusion of Ti adspecies at the stoichiometric TiO2(110) surface using complementary computational methodologies of density functional theory corrected for on-site Coulomb interactions (DFT+U) and a charge equilibration (QEq) atomistic potential to identify minimum energy pathways. We find that diffusion of Ti from the surface to subsurface (and vice versa) follows an intersticialcy exchange mechanism, involving exchange of surface Ti with the 6-fold coordinated Ti below the bridging oxygen rows. Diffusion in the subsurface between layers also follows an interstitialcy mechanism. The diffusion of Ti is discussed in light of continued attempts to understand the re-oxidation of non-stoichiometric TiO2(110) surfaces.

Later Pleistocene evolution of the Exe valley: a chronostratigraphic model of terrace formation and its implications for Palaeolithic archaeology

This paper presents the first systematic chronostratigraphic study of the river terraces of the Exe catchment in South West England and a new conceptual model for terrace formation in unglaciated basins with applicability to terrace staircase sequences elsewhere. The Exe catchment lay beyond the maximum extent of Pleistocene ice sheets and the drainage pattern evolved from the Tertiary to the Middle Pleistocene, by which time the major valley systems were in place and downcutting began to create a staircase of strath terraces. The higher terraces (8-6) typically exhibit altitudinal overlap or appear to be draped over the landscape, whilst the middle terraces show greater altitudinal separation and the lowest terraces are of a cut and fill form. The terrace deposits investigated in this study were deposited in cold phases of the glacial-interglacial Milankovitch climatic cycles with the lowest four being deposited in the Devensian Marine Isotope Stages (MIS) 4-2. A new cascade process-response model is proposed of basin terrace evolution in the Exe valley, which emphasises the role of lateral erosion in the creation of strath terraces and the reworking of inherited resistant lithological components down through the staircase. The resultant emergent valley topography and the reworking of artefacts along with gravel clasts, have important implications for the dating of hominin presence and the local landscapes they inhabited. Whilst the terrace chronology suggested here is still not as detailed as that for the Thames or the Solent System it does indicate a Middle Palaeolithic hominin presence in the region, probably prior to the late Wolstonian Complex or MIS 6. This supports existing data from cave sites in South West England.

A simple analysis of thermodynamic properties for classical plasmas: I. theory

By eliminating the short range negative divergence of the Debye–Hückel pair distribution function, but retaining the exponential charge screening known to operate at large interparticle separation, the thermodynamic properties of one-component plasmas of point ions or charged hard spheres can be well represented even in the strong coupling regime. Predicted electrostatic free energies agree within 5% of simulation data for typical Coulomb interactions up to a factor of 10 times the average kinetic energy. Here, this idea is extended to the general case of a uniform ionic mixture, comprising an arbitrary number of components, embedded in a rigid neutralizing background. The new theory is implemented in two ways: (i) by an unambiguous iterative algorithm that requires numerical methods and breaks the symmetry of cross correlation functions; and (ii) by invoking generalized matrix inverses that maintain symmetry and yield completely analytic solutions, but which are not uniquely determined. The extreme computational simplicity of the theory is attractive when considering applications to complex inhomogeneous fluids of charged particles.

Complex formation in solutions of oppositely charged polyelectrolytes at different polyion compositions and salt content

The formation of complexes in solutions containing positively charged polyions (polycations) and a variable amount of negatively charged polyions (polyanions) has been investigated by Monte Carlo simulations. The polyions were described as flexible chains of charged hard spheres interacting through a screened Coulomb potential. The systems were analyzed in terms of cluster compositions, structure factors, and radial distribution functions. At 50% charge equivalence or less, complexes involving two polycations and one polyanion were frequent, while closer to charge equivalence, larger clusters were formed. Small and neutral complexes dominated the solution at charge equivalence in a monodisperse system, while larger clusters again dominated the solution when the polyions were made polydisperse. The cluster composition and solution structure were also examined as functions of added salt by varying the electrostatic screening length. The observed formation of clusters could be rationalized by a few simple rules.

A Monte Carlo study of solutions of oppositely charged polyelectrolytes

The formation of complexes appearing in solutions containing oppositely charged polyelectrolytes has been investigated by Monte Carlo simulations using two different models. The polyions are described as flexible chains of 20 connected charged hard spheres immersed in a homogenous dielectric background representing water. The small ions are either explicitly included or their effect described by using a screened Coulomb potential. The simulated solutions contained 10 positively charged polyions with 0, 2, or 5 negatively charged polyions and the respective counterions. Two different linear charge densities were considered, and structure factors, radial distribution functions, and polyion extensions were determined. A redistribution of positively charged polyions involving strong complexes formed between the oppositely charged polyions appeared as the number of negatively charged polyions was increased. The nature of the complexes was found to depend on the linear charge density of the chains. The simplified model involving the screened Coulomb potential gave qualitatively similar results as the model with explicit small ions. Finally, owing to the complex formation, the sampling in configurational space is nontrivial, and the efficiency of different trial moves was examined.

Microcontroller-based peak current mode control using digital slope compensation

Microcontroller-based peak current mode control of a buck converter is investigated. The new solution uses a discrete time controller with digital slope compensation. This is implemented using only a single-chip microcontroller to achieve desirable cycle-by-cycle peak current limiting. The digital controller is implemented as a two-pole, two-zero linear difference equation designed using a continuous time model of the buck converter and a discrete time transform. Subharmonic oscillations are removed with digital slope compensation using a discrete staircase ramp. A 16 W hardware implementation directly compares analog and digital control. Frequency response measurements are taken and it is shown that the crossover frequency and expected phase margin of the digital control system match that of its analog counterpart.

Within, but not between hands interactions in vibrotactile detection thresholds reflect somatosensory receptive field organization

Detection of a tactile stimulus on one finger is impaired when a concurrent stimulus (masker) is presented on an additional finger of the same or the opposite hand. This phenomenon is known to be finger-specific at the within-hand level. However, whether this specificity is also maintained at the between-hand level is not known. In four experiments, we addressed this issue by combining a Bayesian adaptive staircase procedure (QUEST) with a two-interval forced choice (2IFC) design in order to establish threshold for detecting 200ms, 100Hz sinusoidal vibrations applied to the index or little fingertip of either hand (targets). We systematically varied the masker finger (index, middle, ring, or little finger of either hand), while controlling the spatial location of the target and masker stimuli. Detection thresholds varied consistently as a function of the masker finger when the latter was on the same hand (Experiments 1 and 2), but not when on different hands (Experiments 3 and 4). Within the hand, detection thresholds increased for masker fingers closest to the target finger (i.e., middle>ring when the target was index). Between the hands, detection thresholds were higher only when the masker was present on any finger as compared to when the target was presented in isolation. The within hand effect of masker finger is consistent with the segregation of different fingers at the early stages of somatosensory processing, from the periphery to the primary somatosensory cortex (SI). We propose that detection is finger-specific and reflects the organisation of somatosensory receptive fields in SI within, but not between the hands.