Summability of Connected Correlation Functions of Coupled Lattice Fields

We consider two nonindependent random fields \(\psi \) and \(\phi \) defined on a countable set Z. For instance, \(Z=\mathbb {Z}^d\) or \(Z=\mathbb {Z}^d\times I\), where I denotes a finite set of possible “internal degrees of freedom” such as spin. We prove that, if the cumulants of \(\psi \) and \(\phi \) enjoy a certain decay property, then all joint cumulants between \(\psi \) and \(\phi \) are \(\ell _2\)-summable in the precise sense described in the text. The decay assumption for the cumulants of \(\psi \) and \(\phi \) is a restricted \( \ell _1\) summability condition called \(\ell _1\)-clustering property. One immediate application of the results is given by a stochastic process \(\psi _t(x)\) whose state is \(\ell _1\)-clustering at any time t: then the above estimates can be applied with \(\psi =\psi _t\) and \(\phi =\psi _0\) and we obtain uniform in t estimates for the summability of time-correlations of the field. The above clustering assumption is obviously satisfied by any \(\ell _1\)-clustering stationary state of the process, and our original motivation for the control of the summability of time-correlations comes from a quest for a rigorous control of the Green–Kubo correlation function in such a system. A key role in the proof is played by the properties of non-Gaussian Wick polynomials and their connection to cumulants     

The temperature-dependent electrical transport properties of liquid Sn using pseudopotential theory

We present the calculations of electrical resistivity, thermo-electric power and thermal conductivity based on the self-consistent approximation. The pseudopotential due to Hasegawa et al. [J. Non-Cryst. Solids 117/118, 300 (1990) M. Hasegawa, K. Hoshino, M. Watabe, and H. Young, J. Non-Cryst. Solids 117/118, 300 (1990).[Crossref], [Web of Science ®] , [Google Scholar]] for full electron–ion interaction, which is valid for all electrons and contains the repulsive delta function to achieve the necessary s-pseudisation, was used in the calculation. Temperature dependence of structure factor is achieved through temperature-dependent potential parameter in the pair-potential. The outcome of the present study is discussed in the light of other such results and with predictions of Wiedemann and Franz law up to moderately high temperature. Specially, high-temperature resistivity data necessitates the careful investigation of electron energy dispersion close to the Fermi level and possible metal to non-metal transition while going from dense-fluid to low density-fluid state. In the absence of experimental data at high temperature, these findings may serve as future guideline.     

Software support for the Nordtest method of measurement uncertainty evaluation

Software support for the Nordtest method of measurement uncertainty evaluation is described. According to the Nordtest approach, the combined measurement uncertainty is broken down into two main components??the within-laboratory reproducibility (intermediate precision) s _Rw and the uncertainty due to possible laboratory bias u(bias). Both of these can be conveniently estimated from validation and quality control data, thus significantly reducing the need for performing dedicated experiments for estimating detailed uncertainty contributions and thereby making uncertainty estimation easier for routine laboratories. An additional merit of this uncertainty estimation approach is that it reduces the danger of underestimating the uncertainty, which continues to be a problem at routine laboratories. The described software tool??MUkit (measurement uncertainty kit)??fully reflects the versatility of the Nordtest approach: it enables estimating the uncertainty components from different types of data, and the data can be imported using a variety of means such as different laboratory data systems and a dedicated web service as well as manual input. Prior to the development of the MUkit software, a laboratory survey was carried out to identify the needs of laboratories related to uncertainty estimation and other quality assurance procedures, as well as their needs for a practical tool for the calculation of measurement uncertainty.     

Characterization of quenched-in vacancies in Fe–Al alloys

Physical and mechanical properties of Fe–Al alloys are strongly influenced by atomic ordering and point defects. In the present work positron lifetime (LT) measurements combined with slow positron implantation spectroscopy (SPIS) were employed for an investigation of quenched-in vacancies in Fe–Al alloys with the Al content ranging from 18 to 49 at.%. The interpretation of positron annihilation data was performed using ab-initio   theoretical calculations of positron parameters. Quenched-in defects were identified as Fe-vacancies. It was found that the lifetime of positrons trapped at quenched-in defects increases with increasing Al content due to an increasing number of Al atoms surrounding the Fe vacancies. The concentration of quenched-in vacancies strongly increases with increasing Al content from ≈10⁻⁵$\approx {10}^{-5}$ in Fe₈₂Al₁₈${\mathrm{Fe}}_{82}{\mathrm{Al}}_{18}$ (i.e. the alloy with the lowest Al content studied) up to ≈10⁻¹$\approx {10}^{-1}$ in Fe₅₁Al₄₉${\mathrm{Fe}}_{51}{\mathrm{Al}}_{49}$ (i.e. the alloy with the highest Al content studied in this work).     

Coherence-polarization mixing in resonance gratings

We show, using rigorous diffraction theory, that resonance gratings can be used to transfer partial spatial correlation to partial polarization even if the incident light beam is fully polarized. The phenomenon is based on the fact that either of the two orthogonal polarization components can be coupled into the leaky waveguide mode, leading to a strong phase delay, while the other one is reflected without being coupled into the grating. Numerical demonstrations are based on a Gaussian Schell-model beam and a grating analysis performed by rigorous Fourier modal method.     

Variation of magnetic properties in heat treated and ball milled Fe3Al alloy

The magnetic properties of three samples of Fe₃Al—as melted and annealed, high energy ball milled and milled sample followed by annealing—have been studied using a combination of X-ray diffraction, Transmission electron microscopy, room temperature ⁵⁷Fe M?ssbauer spectroscopy and DC magnetization. The different magnetic contributions in the M?ssbauer spectra have been explained in terms of the nearest neighbour Al configuration of Fe. These correlate well to the bulk magnetic properties determined by DC magnetization. High temperature DC magnetization studies show the presence of antiferromagnetic contributions from grain boundaries in the ball milled, nano sized sample.     

Paramagnetic aluminium β-diketiminate

The β-diketiminate ligand framework is shown to undergo reduction to form a neutral main group radical stabilized by spiroconjugation of the unpaired electron over the group 13 element centre. The synthesized paramagnetic complex was characterized by EPR spectroscopy and computational chemistry.     

Slow mappings of finite distortion

We examine mappings of finite distortion from Euclidean spaces into Riemannian manifolds. We use integral type isoperimetric inequalities to obtain Liouville type growth results under mild assumptions on the distortion of the mappings and the geometry of the manifolds.