Lower Bounds to Eigenvalues for Vibrations and Buckling of Structures by Analytical Applications of a-priori Known Qualitative Information

Two methods to obtain lower bounds to eigenvalues are presented for cases which have equivalent minimum variational formulations. One method is an extension and elaboration of a theorem presented by the author in 1972, which affected the transfer of a weight function from one location to another over the physical system considered. The extension relies on information known a-priori about the exact solution of the problem, although the exact solution is not obtained. The other method is akin to the Rayleigh–Ritz method but yields lower bounds. The two methods are applied to various physical examples of vibrations and of buckling with rather good results. The application to other examples is direct and may be performed in a way quite similar to those examples shown.     

Multiple parallel cracks interaction problem inpiezoelectric ceramics

This paper has two goals. First, we propose the pseudo-traction–electric displacementmethod for solving the interaction problem of multiple parallel cracks in transversely isotropicpiezoelectric ceramics. Second, we present a fundamental understanding for the role that theelectric displacement loading plays in the interaction problem. Detailed comparisons between theresults under the compound mechanical–electric loading conditions and those derived underpurely mechanical loading conditions are performed. It is shown that the mechanical fractureparameters such as the stress intensity factors are no longer independent of the electric loading asthey would be in single crack problems. Quite contrary, the electric displacement loading has asignificant influence on the stress intensity factors, the total potential energy release rate and themechanical strain energy release rate. This important conclusion is mainly due to the interactioneffect, i.e., one of the multiple cracks releases the stresses and disturbs the electric fields near theother crack. It is also found that there are some special relative locations for the multiple parallelcracks at which the electric displacement loading has no effect on the Mode I stress intensityfactor. However, the mechanical strain energy release rate has no such a property.     

Towards predicting the encoding capability of MR fingerprinting sequences

Sequence optimization and appropriate sequence selection is still an unmet need in magnetic resonance fingerprinting (MRF). The main challenge in MRF sequence design is the lack of an appropriate measure of the sequence's encoding capability. To find such a measure, three different candidates for judging the encoding capability have been investigated: local and global dot-product-based measures judging dictionary entry similarity as well as a Monte Carlo method that evaluates the noise propagation properties of an MRF sequence. Consistency of these measures for different sequence lengths as well as the capability to predict actual sequence performance in both phantom and in vivo measurements was analyzed. While the dot-product-based measures yielded inconsistent results for different sequence lengths, the Monte Carlo method was in a good agreement with phantom experiments. In particular, the Monte Carlo method could accurately predict the performance of different flip angle patterns in actual measurements. The proposed Monte Carlo method provides an appropriate measure of MRF sequence encoding capability and may be used for sequence optimization.     

Combined experimental and computational study of W(II), Ru(II), Pt(IV) and Cu(I) amine and amido complexes using 15N NMR spectroscopy

Using 2D proton-coupled gHSQC pulse sequences in addition to 1D ¹⁵N NMR experiments of ¹⁵N labeled systems, ¹⁵N NMR chemical shifts of a range of transition metal amido and amine complexes were determined. Tungsten(II), ruthenium(II), platinum(IV) and copper(I) complexes with aniline and their anilido variants were studied and compared to free aniline, lithium anilido and anilinium tetrafluoroborate. Upon coordination of aniline to transition metals, upfield chemical shifts of 20–60 ppm were observed. Deprotonation of the amine complexes to form amido complexes resulted in downfield chemical shifts of 40–60 ppm for all of the complexes except for the tungsten d⁴ system. For the tungsten(II) complexes, the cationic aniline complex displayed a downfield shift of approximately 56 ppm relative to the neutral anilido complex. The change in chemical shift for amine to amido conversion is proposed to depend on the ability of the amido ligand to π-bond with the metal center, which influences the magnitude of the paramagnetic screening term.     

Fast gradient elution reversed-phase liquid chromatography with diode-array detection as a high-throughput screening method for drugs of abuse. II. Data analysis

In Part I of this work, we developed a method for the detection of drugs of abuse in biological samples based on fast gradient elution liquid-chromatography coupled with diode array spectroscopic detection (LC-DAD). In this part of the work, we apply the chemometric method of target factor analysis (TFA) to the chromatograms. This algorithm identifies the target compounds present in chromatograms based on a spectral library, resolves nearly co-eluting components, and differentiates between drugs with similar spectra. The ability to resolve highly overlapped peaks using the spectral data afforded by the DAD is what distinguishes the present method from conventional library searching methods. Our library has a mean list length (MLL) of 1.255 and a discriminating power of 0.997 when both retention index and spectral factors are considered. The algorithm compares a library of 47 different compounds of toxicological relevance to unknown samples and identifies which compounds are present based on spectral and retention index matching. The application of a corrected retention index for identification rather than raw retention times compensates for long-term and column-to-column retention time shifts and allows for the use of a single library of spectral and retention data. Training data sets were used to establish the search and identification parameters of the method. A validation data set of 70 chromatograms was used to calculate the sensitivity (correct identification of positives) and specificity (correct identification of negatives) of the method, which were found to be 92% and 94%, respectively.     

Efficient computation of steady solitary gravity waves

An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting nonlinear equation is solved via the Petviashvili iterative scheme. The computational results are compared to some existing approaches, such as Tanaka’s method and Fenton’s high-order asymptotic expansion. Several important integral quantities are computed for a large range of amplitudes. The integral representation of the velocity and acceleration fields in the bulk of the fluid is also provided.     

Effect of charged impurity correlations on transport in monolayer and bilayer graphene

We study both monolayer and bilayer graphene transport properties taking into account the presence of correlations in the spatial distribution of charged impurities. In particular we find that the experimentally observed sublinear scaling of the graphene conductivity can be naturally explained as arising from impurity correlation effects in the Coulomb disorder, with no need to assume the presence of short-range scattering centers in addition to charged impurities. We find that also in bilayer graphene, correlations among impurities induce a crossover of the scaling of the conductivity at higher carrier densities. We show that in the presence of correlation among charged impurities the conductivity depends nonlinearly on the impurity density n_i and can increase with n_i.     

Enhanced oxygen binding through surface mediated ionic bonds

Palladium clusters deposited on TiO₂ supports constitute important oxidation catalysts. Addition of O₂ in presence of deposited palladium clusters results in dissociated O atoms whose binding strength controls the activity of a catalytic oxidation reaction. Here we demonstrate how the presence of even remote Pd sites can more than double the energy required to remove surface O atoms from a surface. This unusual increase in binding is shown to originate in a Coulomb interaction between Pd^δ+ and O^δ? where the otherwise semiconducting support remains almost neutral acting to mediate a charge transfer from Pd to O sites. The O atoms supported on lattice Ti sites are further shown to form composite TiO motifs that can exchange sites with Pd atoms with a minimal energy, opening the pathway to Ti migration. This behavior is proposed to be linked to their identical valence pool containing d-states.     

Contact of a rigid cylinder indenting an elastic layer sliding over a rigid substrate

Details of the integral transform solution of the state of stress in a layer resting on but sliding over a rigid substrate, in the presence of interfacial friction, is studied. The free surface of the layer is subject to a localised contact, which is represented as a piecewise linear distribution of tractions, using the Bentall–Johnson procedure. The influence functions needed are derived and their properties discussed and compared with those already available for other interface conditions. Lastly, the procedure is applied to the problem of a shrink fit tyre which, under severe tyre/road tangential loading, can be ‘torn’ around the wheel (here, the substrate).     

DEA models for the explicit maximisation of relative efficiency

It has recently been demonstrated that incorporating weight bounds and other non-homogeneous restrictions in DEA models may lead to underestimation of the maximum relative efficiency of decision making units. This paper suggests a way of avoiding this by replacing the objective function in DEA models by the relative efficiency of the assessed unit and converting the resulting models to linear forms. An alternative approach based on incorporating weight restrictions in the recently introduced maximin DEA model is also considered. It is shown that imposing weight bounds in the maximin model is equivalent to imposing bounds on ratios of individual weights.