We propose an implementation of the straight-line fit algorithm to evaluate data obtained as part of measurements of line structures, e.g. a grating line, which allows us to determine, at a conventional threshold value, the coordinates of the edges, the position and the width of its photometric profile as well as the related standard uncertainty contribution. These are derived for the (1 − α)100% confidence intervals with α [0, 1]. The implementation is demonstrated using data obtained by the PTB Nanometer Comparator (Fluegge and Köning 2001 Proc. SPIE 4401 275–83). The investigation revealed that large parts of the uncertainty of the position and the width of the line are due to the choice of the fit interval and the uncertainty of the determination of the minimum and maximum level of the ...

The Physikalisch-Technische Bundesanstalt (PTB) has substantially improved the quality of its local time scale UTC(PTB), which is the national realization of the international time reference Coordinated Universal Time (UTC). It serves as the basis for PTB's time services, for local clock comparisons and for international time comparisons. Since February 2010 UTC(PTB) has been realized using an active hydrogen maser (AHM) steered in frequency via a phase micro-stepper according to an algorithm which combines the frequency comparison data between the AHM and primary and commercial caesium clocks of PTB. Thereby the long-term stability and accuracy of PTB's primary clocks, in particular its fountain clock CSF1, were combined with the short-term frequency stability of the AHM. CSF1 data were used to calculate the steering on all but six days during 15 months. During the time between July 2010 and July 2011, the time difference between UTC(PTB) and UTC was always less than 6 ns and th...

The future mise en pratique for the realization of the kelvin will be founded on the melting temperatures of particular metal–carbon eutectic alloys as thermodynamic temperature references. However, at the moment there is no consensus on what should be taken as the melting temperature. An ideal melting or freezing curve should be a completely flat plateau at a specific temperature. Any departure from the ideal is due to shortcomings in the realization and should be accommodated within the uncertainty budget. However, for the proposed alloy-based fixed points, melting takes place over typically some hundreds of millikelvins. Including the entire melting range within the uncertainties would lead to an unnecessarily pessimistic view of the utility of these as reference standards. Therefore, detailed analysis of the shape of the melting curve is needed to give a value associated with some identifiable aspect of the phase transition. A range of approaches are or could be used; ...

The interfacial energy due to elastic micro-strains at the austenite–twinned martensite interface is calculated for the NiTi shape memory alloy undergoing cubic-to-monoclinic B2 ↔ B19' transformation. For each crystallographically distinct microstructure, an energetically favourable local shape of the interface is determined. The approach employs finite element computations and energy minimization with respect to shape parameters, taking into account elastic anisotropy of the phases and finite-strain kinematics. The effect of atomic-scale interfacial energy is studied.

In this study a model based on thermodynamics was derived to calculate the critical and stable sizes of various elemental catalyst nanoparticles (Mo, Fe, Co, Ni and Au) formed from their nanofilms for the growth of carbon nanotubes. In the first step, the modeling of heterogeneous transformation of films into nanoparticles was considered based on the size dependence of Gibbs free energy changes. At the second step, the reshaping of nanoparticles to nanorods was obtained based on the Laplace–Young equation. The proposed model was compared with the existing experimental data. The results of this study were in good agreement with the available experimental data.

We analyse the ideal shear resistances of 15 nonequivalent slip systems in β-Sn using first-principles density functional theory. From the ideal shear resistance and Schmid's law, the orientation dependence of active slip systems in a β-Sn single crystal subjected to uniaxial tension is investigated. We find that has the lowest ideal shear resistance among the 15 slip systems. Our calculations indicate that, depending on crystal orientation, uniaxial tension activates seven nonequivalent groups of slip systems. The active slip systems for [1 0 0] and [1 1 0] orientations determined in this study agree with the experimental results.

The evolution of permeability in Al–4.5 wt%Cu during equiaxed dendritic solidification has been determined through physical and numerical modelling for solid fractions from 0.35 to 0.8. Cast samples solidified with a variety of cooling rates and quenched at different stages during dendritic solidification were used to generate 3D geometries of solidifying microstructure using x-ray microtomography. The permeability was then characterized (i) physically by passing glycerin through large-scale analogues of the microstructure and (ii) numerically by solving the continuity and momentum equations for the corresponding unstructured meshes of the 3D geometries used for the physical models. The numerically determined values of permeability are in good agreement with those measured and within the scatter of related studies. The permeability results have been compared with the Carman–Kozeny expression to determine the value of the Carman–Kozeny constant. Moreover, the correlation of second...

Interatomic potentials for pure Li and the Mg–Li binary system have been developed based on the second nearest-neighbor modified embedded-atom method formalism. The potentials can describe various fundamental physical properties of pure Li (bulk, point defect, planar defect and thermal properties) and alloy behaviors (thermodynamic, structural and elastic properties) in reasonable agreement with experimental data or higher-level calculations. The applicability of the potential to atomistic investigations on the deformation behavior of Mg alloys and the effect of Li is demonstrated.

Achieving periodicity and size uniformity of quantum dots is significant in improving the performance of quantum dot based devices. An efficient way to control the size and arrangement of quantum dots is to employ a patterned substrate in quantum dot growth. In this paper, the composition, position and shape transition of quantum dots are considered to obtain the minimum energy of the system. The least-energy principle is used here to estimate the critical size of the patterned substrate for single quantum dot growth. Numerical results are in good agreement with experiment, which can help one to control the arrangement of quantum dots by projection of the patterned substrate.

We present a model-based estimation method to reconstruct the unmeasured membrane potential of neuronal populations from a single-channel electroencephalographic (EEG) measurement. We consider a class of neural mass models that share a general structure, specifically the models by Stam et al (1999 Clin. Neurophysiol. 110 1801–13), Jansen and Rit (1995 Biol. Cybern. 73 357–66) and Wendling et al (2005 J. Clin. Neurophysiol. 22 343). Under idealized assumptions, we prove the global exponential convergence of our filter. Then, under more realistic assumptions, we investigate the robustness of our filter against model uncertainties and disturbances. Analytic proofs are provided for all results and our analyses are further illustrated via simulations.