Empirical Power Research Articles

Nanoindentation creep and stress relaxation tests of polycarbonate: Analysis of viscoelastic properties by different rheological models

Abstract Feedback-controlled nanoindentation with a Berkovich diamond tip has been used to perform creep and stress relaxation tests on polycarbonate at room temperature for a wide range of loads (10 – 30000 μN) and indentation depths (30 – 3000 nm). The creep compliance J(t) and relaxation modulus G(t) have been calculated from experimental data as a function of time in the range t = 0.1 – 100 (1000) s. The data are analysed by different rheological models which are compared: (1) the Burgers model, (2) the generalised Maxwell/generalised Kelvin model, and two empirical approaches: (3) a logarithmic model, and (4) a power law model. The Burgers model gives a poor description of the material behaviour since it assumes a steady-state flow of material which is not observed in the experimental time range. The generalised models yield a set of discrete relaxation- and retardation time constants. It is shown that these time constants do not correlate with specific molecular moving processes in the polymer, but are only one of several possible parameterisations of the creep and relaxation curves. Numerical differentiation of G(t) and J(t) shows that polycarbonate has continuous relaxation- and retardation time spectra, respectively, and the dynamic viscosity η(t) of the material increases linearly with time. The behaviour of polycarbonate is best represented by the empirical power law model, which allows optimum fit of creep/relaxation curves, relaxation and retardation time spectra and time-dependent viscosity.

Statistical Powers of Univariate Normality Tests: Comparative Analysis of 2016 Election Process in Uganda

The study conducted an empirical comparison of powers of the univariate normality tests using real data for consistency with simulated data. The main objective was to compare the empirical power of the normality tests using natural data for consistency. Six normality tests were selected from the Empirical Distribution Function (EDF), the Correlation and Regression family of normality tests and moment-based normality tests were considered in this study. From the EDF family of normality tests, the Kolmogorov-Smirnov test (Lilliefors correction) and Anderson-Darling normality tests were chosen. From the regression and correlation family of distributions, Shapiro-Wilk and Shapiro-Francia normality tests were chosen. Jaque-Bera and D’Agostino Pearson normality tests were chosen from the moment family of normality tests. The data adopted in this study comprised of the 2016 Uganda election results as cited by Solomon (2016). The analysis was done using a combination of different statistical packages (EXCEL, R and STATA). The data was gathered from the Uganda Electoral Commission website and cleaned using EXCEL package. After the data cleaning process, the data analysis was done using a combination of R (S-plus programing). The analysis involved writing computer programs that tested the data for normality of the different normality tests specified in the study. All the graphical visualizations were done in STATA. The results of the analysis indicate that S-W produced the most powerful results, followed by S-F, D-A, K-S, J-B and lastly A-D. The data thus indicates that the moment-based tests results are better than the EDF-based tests due to huge kurtosis and skewness statistics in the data. The study thus recommends that it is vital to deal with outliers before carrying out any further statistical tests, and the moment-based tests should be applied in the instances where the data is known to have instances of kurtosis and skewness.

A robust test statistic for independence in high dimensional data

The likelihood ratio test used to test complete independence cannot be used in high-dimensional data. In literature, many test statistics were proposed to cope with this problem. However, these statistics are sensitive to outliers. In this study, we suggest a test statistic that is not sensitive to outliers and can be used in high-dimensional data to test complete independence. We investigate the performance of our suggested statistic in terms of the empirical size and the empirical power by using three simulation studies and a real example dataset. And, we construct an R package to implement our proposed test statistic on real high-dimensional data in applications.

Dielectric and mechanical properties of CaCu3Ti3.925(Nb0.5Al0.5)0.075O12 & Al reinforced epoxy-composites (0–3) for embedded capacitor applications

CaCu3Ti3.925(Nb0.5Al0.5)0.075O12 [CCTNAO] ceramics were synthesized by microwave assisted solid state reaction technique. CCTNAO ceramics possessed room temperature (RT) dielectric constant (εr) ∼ 24,173 with tanδ ∼0.149 at 1 kHz frequency. Commercially available epoxy-resin, hardener, Al-powder along with CCTNAO powder were used to prepare epoxy based 0–3 composites. Maximum εr ∼33.37 with tanδ ∼0.107 at RT were obtained for 40 vol% CCTNAO loading in epoxy. For x = 0.2 in (1-x)[0.8 Epoxy-0.2 CCTNAO]-x Al Epoxy composites, highest εr ∼77.6 with tanδ ∼ 0.15 at 1 kHz frequency were observed. Increase in εr with the increase of Al filler content in composites is attributed to interfacial polarization and cluster formations. Different theoretical models were discussed to explain the dielectric properties of synthesized composites. Experimentally measured values of εeff were in close agreement with EMT model (n = 0.13) and Yamada Model (η = 7). An empirical proposed power law εeff = εm(1+x)n, with n ∼ 10 had a considerable agreement with the experimental results. Vickers hardness test study was carried out to ascertain the mechanical properties of the synthesized composites.

Sample size calculation in hierarchical factorial trials with unequal cluster sizes.

Motivated by a suicide prevention trial with hierarchical treatment allocation (cluster-level and individual-level treatments), we address the sample size requirements for testing the treatment effects as well as their interaction. We assume a linear mixed model, within which two types of treatment effect estimands (controlled effect and marginal effect) are defined. For each null hypothesis corresponding to an estimand, we derive sample size formulas based on large-sample z-approximation, and provide finite-sample modifications based on a t-approximation. We relax the equal cluster size assumption and express the sample size formulas as functions of the mean and coefficient of variation of cluster sizes. We show that the sample size requirement for testing the controlled effect of the cluster-level treatment is more sensitive to cluster size variability than that for testing the controlled effect of the individual-level treatment; the same observation holds for testing the marginal effects. In addition, we show that the sample size for testing the interaction effect is proportional to that for testing the controlled or the marginal effect of the individual-level treatment. We conduct extensive simulations to validate the proposed sample size formulas, and find the empirical power agrees well with the predicted power for each test. Furthermore, the t-approximations often provide better control of type I error rate with a small number of clusters. Finally, we illustrate our sample size formulas to design the motivating suicide prevention factorial trial. The proposed methods are implemented in the R package H2x2Factorial.

Conditional Test for Ultrahigh Dimensional Linear Regression Coefficients

This paper is concerned with a conditional test for regression coefficients in ultrahigh dimensional linear models. Conditioning on a subset of important predictors in the model, we test the overall significance of regression coefficients of the remaining ultrahigh dimensional predictors. We first propose a conditional U-statistic test (CUT) based on an estimated U-statistic for a high dimensional linear regression model and prove that its null asymptotic distribution is normal under some mild assumptions. However, the empirical power of the proposed test is inversely affected by the dimensionality of predictors. To this end, we further propose a two-stage CUT with screening (CUTS) procedure to reduce the dimensionality under the sparsity assumption and enhance the empirical power based on random data splitting strategy. In the first stage, we divide data randomly into two equal halves and apply the conditional sure independence screening to the first half to reduce the dimensionality; In the second stage, we apply the proposed CUT test to the second half. To eliminate the effect of random data splitting and further enhance the empirical power, we also develop a powerful ensemble algorithm based on multiple splitting strategy and prove that the family-wise error rate is asymptotically controlled at a given significance level. We demonstrate the excellent finite-sample performances of the proposed conditional test via Monte Carlo simulations and a real data analysis.

Can Nacar, Labor and Power in the Late Ottoman Empire. Tobacco Workers, Managers, and the State, 1872�1912

Can Nacar, Labor and Power in the Late Ottoman Empire. Tobacco Workers, Managers, and the State, 1872�1912

A Michaelis-Menten rate model for the electrodialysis of concentrated salts

• A modified Michaelis-Menten model is presented for electrodialysis (ED). • Kinetics with concentrated salts are different than at low salt concentrations. • Electrodialysis of concentrated salts appear to follow saturation kinetics. • A standard electrical resistance model failed to adequately model the process. • The chemistry of the electrode rinse solution impacts the process kinetics. Volt-Amp profiles are used to describe electrodialysis (ED) dynamics when the concentration of the diluate is equal to the concentration of the concentrate and both are at high concentration. A standard electronic model that treats the ED process as a series of resistors failed to describe the performance of a 10-cell pair, 200 cm 2 per membrane pilot electrodialysis unit treating 0.5–6% NaCl. The standard electronic model resulted in a regression coefficient of R 2 < 0.76 and underestimated the observed system resistance by 0.54 to 1.1 Ohms depending on the conductivity of the test water. However, if the overall process was treated as a saturated chemical reaction, such as a modified Michaelis-Menten function, the regression exceeded R 2 > 0.999. The current was plotted as a function of the conductivity of the salt at a constant conductivity of electrode rinse solution. Each curve was a function of the applied voltage. The value of the saturation coefficient for the system plots as {D sat } ∼ 22.1 mS/cm (2.21 S/m). The kinetic coefficient i MAX plotted as a linear function of the effective voltage at 25 °C (298°K). More importantly, a series of tests with a constant feed conductivity and with varied electrode rinse solution conductivity also plotted as Michaelis-Menten type curves. The saturation coefficient for the electrode rinse solution also fitted well to {E sat } ∼ 22.1 mS/cm (2.21 S/m) and the values for i MAX were also linear with respect to applied voltage. Overall, the results from 12 data sets follow the formula i = αβi MAX where α and β are the ratios of the conductivity of the fluid divided by the sum of the conductivity plus the saturation, e.g., for electrode rinse solution α = {E}/({E} + {E sat }) and for the electrode rinse β = {D}/({D} + {D sat }), indicating the co-dependence of the feedstock and electrode rinse in the overall process dynamics. This interpretation is in opposition to the standard modeling of ED where the process is viewed as a series of resistances and the electrode rinse resistance is usually determined to be negligible. These data suggest that the effects of saturated feedstock and saturated rinse solution, measured as current or ion transport, are inextricably co-dependent. Three full-batch test runs of between 7.2 and 9-hr duration using different initial feedstock and electrode rinse water conditions were analyzed to estimate the relative effects of diluate and concentrate concentration on the test results. A third saturation coefficient was introduced, γ = {C}/({C} + {C sat }) where the terms {C} and {C sat } represent the conductivity and the saturation coefficient of the concentrate. The model for long duration batch tests, including the different effects of the concentrate and diluate, is well represented by i = (αβ 0.8 γ 0.2 i MAX ). The empirical power coefficients, β 0.8 and γ 0.2 , indicate that the diluate conductivity carries more influence on the rate of the process than does the conductivity of the concentrate. The model has the potential to allow for the scale-up of the ED process using at most one adjustable parameter (the saturation coefficient of the membrane measured as mS/cm or S/cm). Michaelis-Menten kinetics and the modifications by others represent a rich literature on the modeling of different types of inhibition, topics of concern for membrane transport phenomenon.

Assessment of the Wind Energy Potential of Two Burundian Sites

1-year hourly wind speed data from two Burundian stations, namely Bujumbura and Muyinga, have been processed in this work to bring an efficient help for the planning and installation of wind energy conversion systems (WECS) at those localities. Mean seasonal and diurnal variations of wind direction and wind shear exponent have been derived. Two-parameter Weibull probability density functions (PDFs) fitting the observed monthly and annual wind speed relative frequency distributions have been implemented. As shown through three complementary statistical tests, the fitting technique was very satisfactory. A wind resource analysis at 10 m above ground level (AGL) has led to a mean power density at Bujumbura which is almost thirteen fold higher than at Muyinga. The use of the empirical power law to extrapolate wind characteristics at heights from 150 to 350 m AGL has shown that energy potential of hilltops around Muyinga was only suitable for small, individual scale wind energy applications. At the opposite, wind energy potential of ridge-tops and hilltops around Bujumbura has been found suitable for medium and large scale electricity production. For that locality and at those heights, energy outputs and capacity factors (CF or Cf) have been computed for ten selected wind turbines (WTs), together with costs of electricity (COE) using the present value of cost (PVC) method. Amongst those WTs, YDF-1500-87 and S95-2.1 MW have emerged as the best options for installation owing to their highest CF and lowest COE. Moreover, an analysis of those two quantities at monthly basis for YDF-1500-87 WT has led to its best performance in the dry season. Compared to the average present COE of household hydroelectricity consumption, results of this study have evidenced economical feasibility and benefit of WECS setting in selected Burundian sites in order to supplement traditional electricity sources.

Optimizing hybrid offshore wind farms for cost-competitive hydrogen production in Germany

Nearly 96% of the world's current hydrogen production comes from fossil-fuel-based sources, contributing to global greenhouse gas emissions. Hydrogen is often discussed as a critical lever in decarbonizing future power systems. Producing hydrogen using unsold offshore wind electricity may offer a low-carbon production pathway and emerging business model. This study investigates whether participating in an ancillary service market is cost competitive for offshore wind-based hydrogen production. It also determines the optimal size of a hydrogen electrolyser relative to an offshore wind farm. Two flexibility strategies for offshore wind farms are developed in this study: an optimal bidding strategy into ancillary service markets for offshore wind farms that build hydrogen production facilities and optimal sizing of Power-to-Hydrogen (PtH) facilities at wind farms. Using empirical European power market and wind generation data, the study finds that offshore-wind based hydrogen must participate in ancillary service markets to generate net positive revenues at current levels of wind generation to become cost competitive in Germany. The estimated carbon abatement cost of “green” hydrogen ranges between 187 EUR/tonCO2e and 265 EUR/tonCO2e. Allowing hydrogen producers to receive similar subsidies as offshore wind farms that produce only electricity could facilitate further cost reduction. Utilizing excess and intermittent offshore wind highlights one possible pathway that could achieve increasing returns on greenhouse gas emission reductions due to technological learning in hydrogen production, even under conditions where low power prices make offshore wind less competitive in the European electricity market.

Layer-Dependent Nonlinear Optical Properties of WS2, MoS2, and Bi2S3 Films Synthesized by Chemical Vapor Deposition.

Two-dimensional (2D) layered materials have shown layer-dependent optical properties in both linear optical and nonlinear optical (NLO) regimes due to prominent interlayer coupling and quantum confinement in an atomic scale. However, the NLO properties become more complicated as both saturable absorption (SA) and reverse saturable absorption (RSA) easily happen in 2D materials, which results in a significant challenge to understand the evolution of nonlinear absorption with layers. Motivated by this, chemical vapor-deposited chalcogenide compounds (WS2, MoS2, and Bi2S3) are used to investigate the pump intensity and layer number-dependent NLO properties. The values of nonlinear absorption coefficients of these chalcogenide compounds increase with the pump intensity by an 800 nm femtosecond laser, which can be described by an empirical power law function. The SA process due to the large transition probability of the ground state readily takes place in thick samples, while RSA occurs easily in thin samples due to the two-photon absorption (TPA). The transition from TPA to SA is deduced to occur at 13L-WS2, 15L-MoS2, and 5L-Bi2S3, which is related to the layer-dependent band gaps. Our results provide an efficient way to tune optical nonlinearities with a controlled layer number and to design corresponding NLO devices such as optical switches and saturable absorbers.

The goals of the Mongol invaders according to European sources of the middle of the XIII century. Part 2

The middle of the XIII century - the apogee of power of the unified Mongol Empire. In 1241-1242, the first, bloodiest and most destructive Mongol invasion into Europe took place. Certainly, it was vital for the Europeans to find an answer to the question: what did the invaders want, what goals did they pursue? In this article, the author shows that, due to the abundance of contradictory information and the acute lack of an objective understanding of the new enemy at first, European political and ecclesiastical figures attributed many goals to the Mongols (at least eighteen!), of which only three were fully confirmed - an attack on Russia, Poland, and Hungary, and the rest were either not realized for some reason, or arose in minds of the Europeans themselves. All these goals, identified in various official and unofficial European sources, mainly dating from the middle of the XIII century, are discussed here taking into account information from synchronous Eastern sources. Despite well-known ideas of a world-building monarchy, perhaps actually hatched by the Mongol khans, events in Europe suggest that their main goal there was to punish the Hungarian king Bela IV, who refused to hand over the Polovtsians hiding in Hungary to the Mongols.

The goals of the Mongol invaders according to European sources of the middle of the XIII century. Part 1

The middle of the XIII century - the apogee of power of the unified Mongol Empire. In 1241-1242, the first, bloodiest and most destructive Mongol invasion into Europe took place. Certainly, it was vital for the Europeans to find an answer to the question: what did the invaders want, what goals did they pursue? In this article, the author shows that, due to the abundance of contradictory information and the acute lack of an objective understanding of the new enemy at first, European political and ecclesiastical figures attributed many goals to the Mongols (at least eighteen!), of which only three were fully confirmed - an attack on Russia, Poland, and Hungary, and the rest were either not realized for some reason, or arose in minds of the Europeans themselves. All these goals, identified in various official and unofficial European sources, mainly dating from the middle of the XIII century, are discussed here taking into account information from synchronous Eastern sources. Despite well-known ideas of a world-building monarchy, perhaps actually hatched by the Mongol khans, events in Europe suggest that their main goal there was to punish the Hungarian king Bela IV, who refused to hand over the Polovtsians hiding in Hungary to the Mongols.

BHEP Class of Tests for Multivariate Normality: An Empirical Comparison

This paper compares the empirical power performances of eight tests for multivariate normality classified under Baringhaus-Henze-Epps-Pulley (BHEP) class of tests. The tests are compared under eight different alternative distributions. The result shows that the eight statistics have good control over type-I-error. Also, some tests are more sensitive to distributional differences with respect to their power performances than others. Also, some tests are generally more powerful than others. The generally most powerful ones are therefore recommended.

Power considerations for generalized estimating equations analyses of four-level cluster randomized trials.

In this article, we develop methods for sample size and power calculations in four-level intervention studies when intervention assignment is carried out at any level, with a particular focus on cluster randomized trials (CRTs). CRTs involving four levels are becoming popular in healthcare research, where the effects are measured, for example, from evaluations (level 1) within participants (level 2) in divisions (level 3) that are nested in clusters (level 4). In such multilevel CRTs, we consider three types of intraclass correlations between different evaluations to account for such clustering: that of the same participant, that of different participants from the same division, and that of different participants from different divisions in the same cluster. Assuming arbitrary link and variance functions, with the proposed correlation structure as the true correlation structure, closed-form sample size formulas for randomization carried out at any level (including individually randomized trials within a four-level clustered structure) are derived based on the generalized estimating equations approach using the model-based variance and using the sandwich variance with an independence working correlation matrix. We demonstrate that empirical power corresponds well with that predicted by the proposed method for as few as eight clusters, when data are analyzed using the matrix-adjusted estimating equations for the correlation parameters with a bias-corrected sandwich variance estimator, under both balanced and unbalanceddesigns.

Analysis of process efficiency in laser fusion cutting and some single- and multi-objective optimization aspects

For an efficient use of laser cutting technology, it is of great importance to analyze the impact of process parameters on different performance indicators, such as cut quality criteria, productivity criteria, costs as well as environmental performance criteria (energy and resource efficiency). Having this in mind, this study presents the experimental results of CO2 laser fusion cutting of AISI 304 stainless steel using nitrogen, with the aim of developing a semi-empirical mathematical model for the estimation of process efficiency as an important indicator of the achievable energy transfer efficiency in the cutting process. The model was developed by relating the theoretical power needed to melt the volume per unit time and used laser power, where the change of kerf width was modeled using an empirical power model in terms of laser cutting parameters such as laser power, cutting speed, and focus position. The obtained results indicated the dominant effect of the focus position on the change in process efficiency, followed by the cutting speed and laser power. In addition, in order to maximize process efficiency and simultaneously ensure high cut quality without dross formation, a laser cutting optimization problem with constraints was formulated and solved. Also, a multi-objective optimization problem aimed at simultaneous optimization of process efficiency and material removal rate was formulated and solved, where the determined set of Pareto non-dominated solutions was analyzed by using the entropy method and multi-criteria decision analysis method, that is, the Technique for Order of Preference by Similarity to Ideal Solution. The optimization results revealed that in order to enhance process efficiency and material removal rate, while ensuring high cut quality without dross formation, focusing the laser beam deep into the bulk of material is needed with particular trade-offs between laser power and cutting speed levels at high pressure levels of nitrogen.

Abnormal neural oscillations depicting excitatory‐inhibitory imbalance are distinctly associated with amyloid and tau depositions in Alzheimer's disease

AbstractBackgroundExcitation‐to‐inhibition (E/I) imbalance is believed to be a key contributor of synaptic and network degeneration in Alzheimer’s disease (AD)(Frere and Slutsky, 2018). Extensive preclinical research on transgenic animal models of AD have demonstrated neuronal and circuit level E/I imbalance mediated by amyloid‐beta (Aβ) and abnormally phosphorylated tau proteins (Harris et al., 2020; Palop and Mucke, 2016). However, the mechanisms of E/I imbalance leading to disrupted networks and their relationships to Aβ and tau in humans remain poorly understood.MethodIn this multimodal imaging study in patients with AD (n=20 AD patients; n=35 age‐matched controls; Table‐1), we first examined the spectral changes in oscillatory brain rhythms using magnetoencephalography and their relationships to tau and amyloid‐beta (Aβ) accumulation in PET imaging (flortaucipir and 11C‐PiB, for tau and Aβ, respectively). Next, we estimated parameters of a linear neural mass model (Raj et al., 2020) that best fit the observed spectra, and examined the relationships between model parameters for excitatory and inhibitory neural sub‐populations, and tau and Aβ accumulations.ResultWe found that neuronal hypoactivity was associated with tau while hyperactivity was associated with Aβ (Figure 1). We also demonstrated E/I imbalance in patients with AD, depicted as abnormal excitatory and inhibitory neuronal parameters in a linear neural mass model that reproduced the empirical macroscopic power spectra (Figure 2). The abnormal excitatory and inhibitory neuronal parameters showed distinct associations with tau and Aβ—higher tau correlated with a longer excitatory time‐constant, whereas higher Aβ correlated with a longer inhibitory time‐constant (Figure 3).ConclusionThe unique contribution of the collective finding in the current study is to demonstrate how abnormalities in the oscillatory power spectrum in AD is mechanistically linked to impaired function of excitatory and inhibitory neuronal populations that are in turn associated with tau and Aβ accumulations. Neural oscillations are modulators of rate and timing of neuronal spiking and have a key role in governing the neuronal excitability (Siegel et al., 2012). The multimodal neuroimaging in AD patients in the current study demonstrate how different frequency oscillations are distinctly affected by Aβ and tau, and offer new perspectives for network stabilizing therapies.

A RMT-based LM test for error cross-sectional independence in large heterogeneous panel data models*

This paper introduces a new test for error cross-sectional independence in large panel data models with exogenous regressors having heterogenous slope coefficients. The proposed statistic, LMRMT , is based on the Lagrange Multiplier (LM) principle and the sample correlation matrix of the model’s residuals. Since in large panels poorly estimates its population counterpart, results from Random Matrix Theory (RMT) are used to establish the high-dimensional limiting distribution of LMRMT under heteroskedastic normal errors and assuming that both the panel size N and the sample size grow to infinity in comparable magnitude. Simulation results show that is largely correctly sized (except for some small values of N and T). Further, the empirical size and power outcomes show robustness of our statistic to deviations from the assumptions of normality for the error terms and of strict exogeneity for the regressors. The test has comparable small sample properties to related tests in the literature which have been developed under different asymptotic theory.

A New Goodness of Fit Test for Multivariate Normality and Comparative Simulation Study

The testing of multivariate normality remains a significant scientific problem. Although it is being extensively researched, it is still unclear how to choose the best test based on the sample size, variance, covariance matrix and others. In order to contribute to this field, a new goodness of fit test for multivariate normality is introduced. This test is based on the mean absolute deviation of the empirical distribution density from the theoretical distribution density. A new test was compared with the most popular tests in terms of empirical power. The power of the tests was estimated for the selected alternative distributions and examined by the Monte Carlo modeling method for the chosen sample sizes and dimensions. Based on the modeling results, it can be concluded that a new test is one of the most powerful tests for checking multivariate normality, especially for smaller samples. In addition, the assumption of normality of two real data sets was checked.

Dielectric relaxation and scaling of AC conductivity observed in mixed valence perovskite Eu2CoMnO6

Monophasic and polycrystalline double perovskite Eu2CoMnO6 has been synthesized, and its structural characterization, frequency and temperature-dependent dielectric relaxation have been studied. Observed thermally activated dielectric relaxation was explained using the empirical Havriliak–Negami (HN) dielectric relaxation function with an estimated activation energy [Formula: see text] [Formula: see text] 0.22 eV and attempt frequency [Formula: see text] [Formula: see text] 2.46 × 109 Hz. The frequency-dependent AC conductivity data, over a wide range of temperature (100–325 K), followed the empirical universal power law behavior ([Formula: see text], [Formula: see text] is the constant exponent) showing two different frequency exponents, respectively, in the high- and low-temperature regions. The high-temperature ([Formula: see text] 275 K) conductivity data followed the continuous time random walk (CTRW) approximation model proposed by Dyre. However, this model failed to reproduce the observed conductivity spectra in the low-temperature side ([Formula: see text] 200 K). Interestingly, both the high- and low-temperatures’ conductivity data can be scaled to the master curve with suitably chosen scaling parameters.