A statistical model of roundoff error for varying length floating-point arithmetic

A model is presented which explains the behavior of the roundoff error in a result quantity when computing precision is varied. A set of hypotheses concerning this a posteriori model is tested in a matrix inversion algorithm. The characteristics of the algorithms where the error model is valid are discussed. As an application of the model, the usual estimation procedure for roundoff error consisting of comparing the results computed in two different precisions is analyzed statistically.     

Inhibition of a palladium(II) catalyst upon formation of a di‐μ‐chloro complex: di‐μ‐chloro‐bis­[1,2‐bis­(di­phenyl­phosphino)­ethane‐P,P′]dipalladium(II) bis­(tetra­fluoro­borate) bis­(deutero­chloro­form) solvate

The title compound was formed upon slow evaporation of a solution of the solvated dicationic complex bis­(aceto­nitrile)­bis­[1,2‐bis­(di­phenyl‐phosphino)­ethane]­palladium(II) bis(tetra­fluoro­borate) in deuterated chloro­form. The dinucleur palladium complex forms triclinic crystals and there is an inversion center between the Pd atoms. Compared to the corresponding monomeric compound, the Cl—Pd—Cl angles decrease upon briding from 94.19 (7) to 86.96 (4)°.     

Effects of fibre-surface morphology on the mechanical properties of Porifera-inspired rubber-matrix composites

In this paper, mineralised organic fibre morphologies, inspired by the structures of Porifera (sponges) are correlated to the mechanical performance of fibre reinforced rubbers. The mineralised structures are rich in calcium carbonate and silica. These compounds nucleate and precipitate on the fibre surfaces yielding different morphologies as a function of mineral ion concentrations. Smaller mineralised precipitates manifestly improve the mechanical performance of composites while thicker precipitates enveloping the fibres give rise to inferior properties. Mechanisms and evidenced reasoning for these differences are reported herein.     

Influence of mesh deformation on the quality of large eddy simulations

The influence of mesh motion on the quality of large eddy simulation (LES) was studied in the present article. A three‐dimensional, turbulent pipe flow (Re_τ=360) was considered as a test case. Simulations with both stretching and static meshes were carried out in order to understand how mesh motion affects the turbulence statistics. The spatial filtering of static and moving mesh direct numerical simulation (DNS) data showed how an ideal LES would perform, while the comparison of DNS cases with static and moving meshes revealed that no significant numerical errors arise from the mesh motion when the simulation is fully resolved. The comparison of the filtered fields of the DNS with a moving mesh with the corresponding LES fields revealed different responses to mesh motion from different numerical approaches. A straightforward test was applied in order to verify that the moving mesh works consistently in LES: when the mesh is stretched in the streamwise direction, the moving mesh results should be in between the two extremal resolutions between which the mesh is stretched. Numerical investigations using four different LES approaches were carried out. In addition to the Smagorinsky model, three implicit LES approaches were used: linear interpolation (non‐dissipative), the Gamma limiter (dissipative), and the scale‐selective discretisation (slightly dissipative). The results indicate that while the Smagorinsky and the scale‐selective discretisation approaches produce results consistent with the resolution of the non‐static mesh, the implicit LES with linear interpolation or the Gamma scheme do not. Copyright © 2016 John Wiley & Sons, Ltd.     

Polarisation dependent Raman study of single-crystal nickel oxide

The magnetic domain structure and Raman scattering have been studied in NiO single-crystals with three different (100), (110) and (111) orientations. Twin-domain structure was observed in NiO(100) and NiO(110) single-crystals using cross-polarized optical microscopy. We found that the ratio of the two-magnon (at 1500 cm⁻¹) to the two-phonon (2LO, at 1100 cm⁻¹) Raman bands intensity is sensitive in a particular way to the type of the twin-domain pattern.     

A PCA study to determine how features in meteorite reflectance spectra vary with the samples’ physical properties

Meteorites have advanced our knowledge of processes in the Solar System with the application of high precision instruments here on Earth. The study of asteroids, the source of most meteorites, has in turn given us knowledge regarding the large scale evolution of the Solar System. Using the complementary information that asteroids and meteorites give us the story of our cosmic backyard can be more easily read. One efficient way to link meteorites to asteroids is by matching their respective reflectance spectra. There have been few convincing matches because of observational and scale differences as well as an incomplete knowledge of the light scattering physics involved. To better interpret the reflectance data we need to know the dependencies of the reflectance on physical properties and develop techniques for better comparisons of data sets. For these purposes we utilise our own measurements of 26 different meteorites together with spectra available on the NASA PDS.We find that normalisation of reflectance at a wavelength between 1.1 and 1.3 μm gives the closest match of spectra from meteorites common to both data sets. The depth of the spectra bands deepens by similar amounts for different types of surface texture alterations i.e. rock to sawn surface, rock to polished surface and rock to powdered surface. Principal Component Analysis (PCA) is able to easily place carbonaceous chondrites, ordinary chondrites and achondrites into distinct groups using their reflectance spectra. We track the variation of spectral features in principal component space by using a set of meteorite spectra synthesised from mineral and elemental spectra. A spectral agent that reduces the reflectance at all wavelengths is required, in addition to olivine, pyroxene and carbon, to generate a set of synthesised spectra to match the distribution of measured spectra, in principal component space.     

Virtual reality in posturography.

Balance dysfunctions are common, especially among elderly people. Present methods for the diagnosis and evaluation of severity of dysfuntion have limited value. We present a system that makes it easy to implement different visual and mechanical perturbations for clinical investigations of balance and visual-vestibular interaction. The system combines virtual reality visual stimulation with force platform posturography on a moving platform. We evaluate our contruction's utility in a classification task between 33 healthy controls and 77 patients with Ménière's disease, using a series of tests with different visual and mechanical stimuli. Responses of patients and controls differ significantly in parameters computed from stabilograms. We also show that the series of tests achieves a classification accuracy slightly over 80% between controls and patients.     

Acid-catalyzed hydrolyses of bridged bi- and tricyclic compounds-XII: Kinetics of hydration of 2-norbornenone,a special β,γ-unsaturated ketone

The reaction rates, activation parameters, solvent deuterium isotope effects, and dependences of rates on acid concentration measured for the hydration of 2-norbornenone and its four Me-substituted homologs in aqueous acid agree with the slow protonation of the CC double bond (A-S_E2 mechanism). Thus the mechanism differs from that reported for the isomerization (to α,β-unsaturated ketones) of unbridged β,γ-unsaturated ketones, e.g. 3-cycloalkenones and Δ⁵-3-ketosteroids, under catalysis by acid.