Comparison of damping parameters based on the half-power bandwidth methods of viscous and hysteretic damping models

The half-power bandwidth method is usually used to calculate structural damping parameters by frequency response function (FRF). In this note, the half-power bandwidth methods for the displacement FRF, the velocity FRF, and the acceleration FRF are proposed based on viscous and hysteretic damping models, respectively. Comparison results show that the application conditions of half-power bandwidth methods for the displacement and acceleration FRFs are limited. They can only be used to calculate the small damping ratio/loss factor. The application condition of half-power bandwidth method for the velocity FRF is not limited. It can be used to calculate the large or small damping ratio/loss factor, which should be the first choice for calculating damping parameters. Besides, when the damping ratio is less than 0.2546 or the loss factor is less than 0.5658, the relative difference between the loss factor and twice the damping ratio is less than 10%. With the increase of the damping ratio or loss factor, the relative difference will increase rapidly, and the approximate relationship is no longer applicable.

CONTRIBUTION OF DRIFT AND DIFFUSION TO WATER CAPACITY DEIONIZATION

Drift and diffusion of ions in a cavity having the shape of oblate ellipsoid of revolution are considered. The obtained approximate relationship, between the time of drift and diffusion filling of deep cavity with ions, contains the applied voltage and the ratio of cavity size to the distance between electrodes. It shows that in the performed experiments with the device for water capacitive deionization the filling of electrodes by ions was carried out, mainly, due to diffusion.

True Cause for Multi-Layer Inductive Coils’ Sensitivity to Ambient Relative Humidity

For analyzing the properties of humidity-effect on the measurement of the inductance of multi-layer coils, a formula that establishes an approximate relationship between the coil’s inherent capacitance and interlayer parasitic capacitance has been derived. Such a derivation using the inductor’s equivalent circuit to include humidity effects clarifies the characterization of inductance, after more than half a century of neglect in the literature.

A semi-classical estimate for the q-parameter and decay time with Tsallis entropy of black holes in quantum geometry

In this letter, using the non-extensive entropy of Tsallis, we study some properties of the Schwarzschild black holes (BHs), based on the loop quantum gravity (LQG), some novel characteristics and results of the Schwarzschild BH can be obtained in Mejrhit and Ennadifi (Phys Lett B 794:45–49, 2019). Here we find that these findings are strikingly identical to ones obtained by Hawking and Page in anti-de Sitter space within the original of the Boltzmann entropy formula. By using the semi-classical estimate analysis on the energy at this minimum $$M_{min}$$ M min , an approximate relationship between the q and $$\gamma $$ γ parameters of BHs can be found, ($$q\approx \frac{\sqrt{3}\gamma }{\pi \ln 2}+1$$ q ≈ 3 γ π ln 2 + 1 ), which is remarkable approaching to q-parameters of cosmic ray spectra and quarks coalescing to hadrons in high energy.

Loss of life expectancy derived from a standardized mortality ratio in Denmark, Finland, Norway and Sweden

Aims: The standardized mortality ratio (SMR) is a widely used measure. A recent methodological study provided an accurate approximate relationship between an SMR and difference in lifetime expectancies. This study examines the usefulness of the theoretical relationship, when comparing historic mortality data in four Scandinavian populations. Methods: For Denmark, Finland, Norway and Sweden, data on mortality every fifth year in the period 1950 to 2010 were obtained. Using 1980 as the reference year, SMRs and difference in life expectancy were calculated. The assumptions behind the theoretical relationship were examined graphically. The theoretical relationship predicts a linear association with a slope, [Formula: see text], between log(SMR) and difference in life expectancies, and the theoretical prediction and calculated differences in lifetime expectancies were compared. We examined the linear association both for life expectancy at birth and at age 30. All analyses were done for females, males and the total population. Results: The approximate relationship provided accurate predictions of actual differences in lifetime expectancies. The accuracy of the predictions was better when age was restricted to above 30, and improved if the changes in mortality rate were close to a proportional change. Slopes of the linear relationship were generally around 9 for females and 10 for males. Conclusions: The theoretically derived relationship between SMR and difference in life expectancies provides an accurate prediction for comparing populations with approximately proportional differences in mortality, and was relatively robust. The relationship may provide a useful prediction of differences in lifetime expectancies, which can be more readily communicated and understood.

Relating the structure factors of two-dimensional materials in planar and spherical geometries

We derive an approximate relationship between the static structure factors of two-dimensional materials in planar and spherical geometries.

NNLO QCD corrections for Drell-Yan p ZT and $$ {\phi}_{{}^{\eta}}^{\ast } $$ observables at the LHC

Drell-Yan lepton pairs with finite transverse momentum are produced when the vector boson recoils against (multiple) parton emission(s), and is determined by QCD dynamics. At small transverse momentum, the fixed order predictions break down due to the emergence of large logarithmic contributions. This region can be studied via the p T Z distribution constructed from the energies of the leptons, or through the $$ {\phi}_{{}^{\eta}}^{\ast } $$ ϕ η ∗ distribution that relies on the directions of the leptons. For sufficiently small transverse momentum, the $$ {\phi}_{{}^{\eta}}^{\ast } $$ ϕ η ∗ observable can be measured experimentally with better resolution. We study the small p T Z and $$ {\phi}_{{}^{\eta}}^{\ast } $$ ϕ η ∗ distributions up to next-to-next-to-leading order (NNLO) in perturbative QCD. We compute the $$ {\phi}_{{}^{\eta}}^{\ast } $$ ϕ η ∗ distributions for the fully inclusive production of lepton pairs via Z/γ∗ to NNLO and normalise them to the NNLO cross sections for inclusive Z/γ∗ production. We compare our predictions with the $$ {\phi}_{{}^{\eta}}^{\ast } $$ ϕ η ∗ distribution measured by the ATLAS collaboration during LHC operation at 8 TeV. We find that at moderate to large values of $$ {\phi}_{{}^{\eta}}^{\ast } $$ ϕ η ∗ , the NNLO effects are positive and lead to a substantial improvement in the theory-data comparison compared to next-to-leading order (NLO). At small values of p T Z and $$ {\phi}_{{}^{\eta}}^{\ast } $$ ϕ η ∗ , the known large logarithmic enhancements emerge through and we identify the region where resummation is needed. We find an approximate relationship between the values of p T Z and $$ {\phi}_{{}^{\eta}}^{\ast } $$ ϕ η ∗ where the large logarithms emerge and find perturbative consistency between the two observables.

Spectrophotometric prediction of pre-colored fiber blends with a hybrid model based on artificial neural network and Stearns–Noechel model

The performance of the traditional color prediction model in the color prediction of colored fiber blends is usually not very satisfactory under a variety of conditions, due to the limitation of the trail data and the assumptions used for derivation. In contrast to the traditional model, artificial neural networks (ANN) have an excellent nonlinear mapping ability; however, they also have poor generalization ability if the training data are not sufficient. In this paper a hybrid model, called the Stearns–Noechel (S-N)–ANN model, is proposed, which combines the S-N model with the ANN model. This uses the S-N model first to build the approximate relationship between the recipe and spectrophotometric response of the color blends, followed by optimization with the ANN to achieve higher prediction accuracy and better practicability. Compared with the ANN model, the S-N–ANN model needs less training time with the same training data, yet achieves higher validation and correlation coefficients, indicating that the training of the S-N–ANN model is much easier. The average color difference of the predicted spectrum obtained with the S-N–ANN model was 0.86 CMC(2:1) unit, which was much lower than that obtained with either the ANN model (∼2.21) or the traditional S-N model (∼1.66), indicating that the S-N–ANN model is a more accurate method for the color prediction of colored fiber blends.