Now showing items 21-40 of 787

    • BDF2 ADI orthogonal spline collocation method for the fractional integro-differential equations of parabolic type in three dimensions

      Yan, Yubin; Qiao, Leijie; Wang, Ruru; Hendy, Ahmed S.; Changsha University of Science and Technology; University of Chester; Ural Federal University; Benha University; Shanxi University (Elsevier, 2023-12-13)
      In this paper, we are concerned with constructing a fast and an efficient alternating direction implicit (ADI) scheme for the fractional parabolic integro-differential equations (FPIDE) with a weakly singular kernel in three dimensions (3D). Our constructed scheme is based on a second-order backward differentiation formula (BDF2) for temporal discretization, orthogonal spline collocation (OSC) method for spatial discretization and a second-order fractional quadrature rule proposed by Lubich for the Riemann-Liouville fractional integral. The stability and convergence of the constructed numerical scheme are derived. Finally, some numerical examples are given to illustrate the accuracy and validity of the BDF2 ADI OSC method. Based on the obtained results, the numerical results are in line with the theoretical ones.
    • Spatial discretization for stochastic semilinear superdiffusion driven by fractionally integrated multiplicative space-time white noise

      Yan, Yubin; Hoult, James; University of Chester (MDPI, 2023-12-06)
      We investigate the spatial discretization of a stochastic semilinear superdiffusion problem driven by fractionally integrated multiplicative space-time white noise. The white noise is characterized by its properties of being white in both space and time and the time fractional derivative is considered in the Caputo sense with an order $\alpha \in (1, 2)$. A spatial discretization scheme is introduced by approximating the space-time white noise with the Euler method in the spatial direction and approximating the second-order space derivative with the central difference scheme. By using the Green functions, we obtain both exact and approximate solutions for the proposed problem. The regularities of both the exact and approximate solutions are studied and the optimal error estimates that depend on the smoothness of the initial values are established. This paper builds upon the research presented in Mathematics. 2021. 9, 1917, where we originally focused on error estimates in the context of subdiffusion with $\alpha \in (0, 1)$. We extend our investigation to the spatial approximation of stochastic superdiffusion with $\alpha \in (1, 2)$ and place particular emphasis on refining our understanding of the superdiffusion phenomenon by analyzing the error estimates associated with the time derivative at the initial point.
    • High-order schemes based on extrapolation for semilinear fractional differential equation

      Yan, Yubin; Green, Charles; Pani, Amiya; Yang, Yuhui; LvLiang University; University of Chester; BITS-Pilani, K.K. Birla Goa Campus (Springer, 2023-12-11)
      By rewriting the Riemann–Liouville fractional derivative as Hadamard finite-part integral and with the help of piecewise quadratic interpolation polynomial approximations, a numerical scheme is developed for approximating the Riemann–Liouville fractional derivative of order α∈(1, 2). The error has the asymptotic expansion (d3τ3-α+d4τ4-α+d5τ5-α+⋯)+(d2∗τ4+d3∗τ6+d4∗τ8+⋯) at any fixed time tN=T, N∈Z+, where di, i=3, 4, … and di∗, i=2, 3, … denote some suitable constants and τ=T/N denotes the step size. Based on this discretization, a new scheme for approximating the linear fractional differential equation of order α∈(1, 2) is derived and its error is shown to have a similar asymptotic expansion. As a consequence, a high-order scheme for approximating the linear fractional differential equation is obtained by extrapolation. Further, a high-order scheme for approximating a semilinear fractional differential equation is introduced and analyzed. Several numerical experiments are conducted to show that the numerical results are consistent with our theoretical findings.
    • QSAR-driven screening uncovers and designs novel pyrimidine-4,6-diamine derivatives as potent JAK3 inhibitors

      Faris, Abdelmoujoud; Ibrahim, Ibrahim M.; Alnajjar, Radwan; Hadni, Hanine; Bhat, Mashooq Ahmad; Yaseen, Muhammad; Chakraborty, Souvik; Alsakhen, Nada; Shamkh, Israa M.; Mabood, Fazal; et al. (Taylor & Francis, 2023-12-07)
      This study presents a robust and integrated methodology that harnesses a range of computational techniques to facilitate the design and prediction of new inhibitors targeting the JAK3/STAT pathway. This methodology encompasses several strategies, including QSAR analysis, pharmacophore modeling, ADMET prediction, covalent docking, molecular dynamics (MD) simulations, and the calculation of binding free energies (MM/GBSA). An efficacious QSAR model was meticulously crafted through the employment of multiple linear regression (MLR). The initial MLR model underwent further refinement employing an artificial neural network (ANN) methodology aimed at minimizing predictive errors. Notably, both MLR and ANN exhibited commendable performance, showcasing R2 values of 0.89 and 0.95, respectively. The model's precision was assessed via leave-one-out cross-validation (CV) yielding a Q2 value of 0.65, supplemented by rigorous Y-randomization. , The pharmacophore model effectively differentiated between active and inactive drugs, identifying potential JAK3 inhibitors, and demonstrated validity with an ROC value of 0.86. The newly discovered and designed inhibitors exhibited high inhibitory potency, ranging from 6 to 8, as accurately predicted by the QSAR models. Comparative analysis with FDA-approved Tofacitinib revealed that the new compounds exhibited promising ADMET properties and strong covalent docking (CovDock) interactions. The stability of the new discovered and designed inhibitors within the JAK3 binding site was confirmed through 500 ns MD simulations, while MM/GBSA calculations supported their binding affinity. Additionally, a retrosynthetic study was conducted to facilitate the synthesis of these potential JAK3/STAT inhibitors. The overall integrated approach demonstrates the feasibility of designing novel JAK3/STAT inhibitors with robust efficacy and excellent ADMET characteristics that surpass Tofacitinib by a significant margin.
    • The recent development of protection coordination schemes based on inverse of AC microgrid: A review

      Alasali, Feras; Mustafa, Haytham; Saidi, Abdelaziz Salah; El‐Naily, Naser; Abeid, Salima; Holderbaum, William; Omran, Emad; Saad, Saad M.; The Hashemite University; College of Electrical and Electronics Technology-Benghazi; King Khalid University; University of Chester; University of Salford; Suez Canal Authority (Wiley Open Access, 2023-12-06)
      Integration of distributed generation systems and diversity of microgrid operations led to a change in the structure of the power system. Due to this conversion, new challenges have arisen when employing traditional overcurrent protection schemes. As a consequence, non‐classical protection schemes have attracted significant attention in the last few years. Engineers and scholars have proposed different non‐standard methods to increase the power protection system and ensure the highly selectivity performance. Although the non‐standard characteristics and their requirements, in general, have been outlined and analyzed in the available literature, protection coordination based on voltage current–time inverse, as a branch of non‐standard optimization methods, has not yet been thoroughly discussed, compared, or debated in detail. To close this gap, this review introduces a broad overview of recent research and developments of the voltage current–time inverse based protection coordination. Focuses on assessing the potential advantages and disadvantages of related studies and provide a classification and analysis of these studies. The future trends and some recommendations have been included in this review for improving fault detection sensitivity and coordination reliability.
    • A Comparative Study of Accuracy in Major Adaptive Filters for Motion Artefact Removal in Sleep Apnea Tests

      Chen, Yongrui; Zheng, Yurui; Johnson, Sam; Wiffen, Richard; Yang, Bin; University of Chester; Passion for Life Healthcare (Springer, 2023-12-05)
      Sleep apnoea is probably the most common respiratory disorder, respiration and blood oxygen saturation (SpO2) are major concerns in sleep apnoea and are also the two main parameters checked by Polysomnography (PSG, the gold standard for diagnosing sleep apnoea). In this study, we used a simple, non-invasive monitoring system based on photoplethysmography (PPG) to continuously monitor SpO2 and heart rate (HR) for individuals at home. Various breathing experiments were conducted to investigate the relationship between SpO2, HR, and apnoea under different conditions, where two techniques (empirical formula and customized formula) for calculating SpO2 and two methods (resting HR and instantaneous HR) for assessing HR were compared. Various adaptive filters were implemented to compare the effectiveness in removing motion artefacts (MA) during the tests. This study fills the gap in the literature by comparing the performance of different adaptive filters on estimating SpO2 and HR during apnoea. The results showed that up-down finger motion introduced more MA than left-right motion, and the errors in SpO2 estimation were increased as the frequency of movement was increased; due to the low sampling frequency features of these tests, the insertion of adaptive filter increased the noise in the data instead of eliminating the MA for SpO2 estimation; the normal least mean squares (NLMS) filter is more effective in removing MA in HR estimation than other filters.
    • Student perceptions of remote learning transitions in engineering disciplines during the COVID-19 pandemic: a cross-national study

      Behera, Amar Kumar; de Sousa, Ricardo Alves; Oleksik, Valentin; Dong, Jingyan; Fritzen, Daniel; University of Chester; University of Aveiro; Lucian Blaga University of Sibiu; North Carolina State University; SATC College, Criciuma (Taylor & Francis, 2022-06-06)
      This study captures student perceptions of the effectiveness of remote learning and assessment in two associated engineering disciplines, mechanical and industrial, during the COVID-19 pandemic in a cross-national study. A structured questionnaire with 24 items on a 5-point Likert scale was used. Parallel and exploratory factor analyses identified three primary subscales. The links between student perceptions and assessment outcomes were also studied. There was a clear preference for face-to-face teaching, with the highest for laboratories. Remote live lectures were preferred over recorded. Although students found the switch to remote learning helpful, group work and communication were highlighted as concern areas. Mean scores on subscales indicate a low preference for remote learning (2.23), modest delivery effectiveness (3.05) and effective digital delivery tools (3.61). Gender effects were found significant on all subscales, along with significant interactions with university and year-group. Preference for remote delivery of design-based modules was significantly higher than others.
    • Unconditionally stable and convergent difference scheme for superdiffusion with extrapolation

      Yan, Yubin; Yang, Jinping; Pani, Amiya; Green, Charles; University of Chester; Lvliang University; BITS-Pilani, KK Birla Goa Campus (Springer, 2023-11-23)
      Approximating the Hadamard finite-part integral by the quadratic interpolation polynomials, we obtain a scheme for approximating the Riemann-Liouville fractional derivative of order α∈(1, 2) and the error is shown to have the asymptotic expansion (d3τ3-α+d4τ4-α+d5τ5-α+⋯)+(d2∗τ4+d3∗τ6+d4∗τ8+⋯) at any fixed time, where τ denotes the step size and dl, l=3, 4, ⋯ and dl∗, l=2, 3, ⋯ are some suitable constants. Applying the proposed scheme in temporal direction and the central difference scheme in spatial direction, a new finite difference method is developed for approximating the time fractional wave equation. The proposed method is unconditionally stable, convergent with order O(τ3-α), α∈(1, 2) and the error has the asymptotic expansion. Richardson extrapolation is applied to improve the accuracy of the numerical method. The convergence orders are O(τ4-α) and O(τ2(3-α)), α∈(1, 2), respectively, after first two extrapolations. Numerical examples are presented to show that the numerical results are consistent with the theoretical findings.
    • PES-g-BST/PEEK composites modified by surface grafting with high dielectric tunability

      Liu, Shuhang; Peng, Mingyu; Xu, Xin; Guo, Yiting; Wu, Sichen; Xu, Jie; Baxter, Harry; Yang, Bin; Gao, Feng; Northwestern Polytechnical University; Honghui Hospital of Xi’an Jiaotong University; University of Chester
      Ceramic/polymer composites have been widely utilized due to their outstanding dielectric and mechanical properties. The interfacial bonding between ceramic and organic phases has a significant effect on the properties of composites. Therefore, enhancing the interfacial bond strength has become a hot issue. In this work, a chemically modified PES-g-BST/PEEK composite was prepared via cold-pressing sintering. The chemical bond was constructed to connect one end of PES (polyether sulfone) with BST (barium strontium titanate) and the other end with PEEK (polyether ether ketone) by using 4,4′-Diaminodiphenylsulfone (DDS), which enhanced the interface combination between ceramic fillers and organic phase. The influence of the surface grafting method and the amount of DDS on the microstructure and dielectric characteristics of the PES-g-BST/PEEK composite was investigated, and the amount of DDS was optimized. The permittivity, dielectric tunable efficiency, and dielectric tunability of the composites were improved. A chemically modified PES-g-BST/PEEK composite with improved dielectric properties and high dielectric tunability was obtained. The dielectric tunability amounts to 38.16 % under a 7 kV/mm bias, accompanied by a low dielectric constant of 14.5 and a dielectric loss of 0.076 (1 kHz). This work provides a way of enhancing the interface bonding of ceramic/polymer composites to improve dielectric tunability.
    • Quotients of the Highwater algebra and its cover

      Franchi, Clara; Mainardis, Mario; McInroy, Justin; Università Cattolica del Sacro Cuore; Università degli Studi di Udine; University of Chester (Elsevier, 2023-11-15)
      Primitive axial algebras of Monster type are a class of non-associative algebras with a strong link to finite (especially simple) groups. The motivating example is the Griess algebra, with the Monster as its automorphism group. A crucial step towards the understanding of such algebras is the explicit description of the 2-generated symmetric objects. Recent work of Yabe, and Franchi and Mainardis shows that any such algebra is either explicitly known, or is a quotient of the infinite-dimensional Highwater algebra H, or its characteristic 5 cover Ĥ. In this paper, we complete the classification of symmetric axial algebras of Monster type by determining the quotients of H and Ĥ. We proceed in a unified way, by defining a cover of H in all characteristics. This cover has a previously unseen fusion law and provides an insight into why the Highwater algebra has a cover which is of Monster type only in characteristic 5.
    • Measurement of interfacial shear stress in gas–liquid two-phase stratified flow

      Fang, Lide; Ge, Bin; Li, Zhixuan; Sun, Xuyang; Han, Bangbang; Faraj, Yousef; Zhao, Ning; Hebei University; National and Local Joint Engineering Research Center for Measuring Instruments and Systems; University of Chester (American Institute of Physics, 2023-10-26)
      Gas–liquid two-phase stratified flow exists in many industrial processes. Although the flow pattern is simple, the interfacial shear prediction of stratified flow is still the focus of the study. The calculation of the shear stress at the gas–liquid interface is closely related to the measurement of the void fraction and pressure drop of the stratified flow. In this study, a new method for the calculation of interfacial shear stress of gas–liquid two-phase stratified flow is proposed. Differential pressure measurement and planar laser-induced fluorescence technology are combined to obtain important parameters for stratified flow under low-speed flow conditions (Ql = 0.10–0.25 m3/h, Qg = 0.35–1.00 m3/h). The interfacial shear stress is successfully calculated using macroparameters. The uncertainty associated with the calculated parameters using the proposed method is 2.67%, and this study verifies the accuracy of the linear relationship. The method provides a new way to obtain the interfacial shear stress of gas–liquid stratified flow.
    • Three methods to measure the dissolution activation energy of cellulosic fibres using time-temperature superposition

      Liang, Yunhao; Ries, Michael; Hine, Peter; University of Leeds (Elsevier, 2022-04-28)
      Three methods are established to explore the dissolution kinetics of cellulosic fibres in the ionic liquid 1-ethyl-3-methyl-imidazolium acetate ([C2mim][OAc]), based on optical microscopic images of processed dried cellulose and cellulose hydrogels. The dissolution process for different times at various temperatures was analysed using time-temperature superposition, and from this the dissolution was found to follow an Arrhenius behaviour. Three values for the activation energy of dissolution were obtained from three different quantifying methods; these were found to agree, giving an average value of 73 ± 2 kJ/mol. A new method is developed to determine the swelling ratio of different regions of the processed cellulose samples, along with the different water volume fractions contained therein. The findings will be of interest to researchers making all cellulose composites and those studying the dissolution of cellulose by ionic liquids.
    • Pyrolysis activation energy of cellulosic fibres investigated by a method derived from the first order global model

      Liang, Yunhao; Hine, Peter; Ries, Michael; University of Leeds (Elsevier, 2022-12-30)
      The pyrolysis kinetics of cellulosic fibres, a natural cotton yarn (NCY) and a mercerized cotton yarn (MCY), has been explored with a modified first order global analysis method (FOG), via a series of non-isothermal experiments, using thermogravimetric analysis (TGA). The modified FOG analysis routine was developed to overcome discrepancy in heating rate and the difference between exact results and approximations in integrals. The intrinsic pyrolysis activation energy, with temperature range tending to zero, was found to be independent of heating rate and approximation used, giving average values of 153 ± 2 kJ/mol for NCY and 192 ± 7 kJ/mol for MCY. This proves the applicability of the reported analysis routine under the conducted TGA measurements. The reasons for different values were hypothesized to be the difference in chemical composition and crystalline structure. The findings provide a new approach in the investigation on pyrolysis kinetics of biomass and factors impacting their pyrolytic behaviour.
    • The weight enumerators of singly-even self-dual [88,44,14] codes and new binary self-dual [68,34,12] and [88,44,14] codes

      Gildea, Joe; Korban, Adrian; Roberts, Adam; Dundalk Institute of Technology; University of Chester (Elsevier, 2023-10-17)
      In this work, we focus on constructing binary self-dual [68, 34, 12] and [88, 44, 14] codes with new parameters in their weight enumerators. For this purpose, we present a new bordered matrix construction for self-dual codes which is derived as a modification of two known bordered matrix constructions. We provide the necessary conditions for the new construction to produce self-dual codes over finite commutative Frobenius rings of characteristic 2. We also construct the possible weight enumerators for singly-even self-dual [88, 44, 14] codes and their shadows as this has not been done in the literature yet. We employ the modified bordered matrix together with the well-known neighbour method to construct binary self-dual codes that could not be obtained from the other, known bordered matrix constructions. Many of the codes turn out to have parameters in their weight enumerators that were not known in the literature before.
    • Numerical Methods for Stochastic Allen-Cahn Equation and Stochastic Subdiffusion and Superdiffusion

      Yan, Yubin; Antonopoulou, Dimitra; Egwu, Bernard A. (University of Chester, 2023-04)
      In this Thesis, we consider the numerical solution of stochastic partial differential equations with particular interest on the Ɛ-dependent Allen-Cahn equation, and the stochastic time fractional partial differential equations in both subdiffusion and superdiffusion cases.
    • Strong approximation of stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise

      Yan, Yubin; Hu, Ye; Sarwar, Shahzad; University of Chester; Lvliang University; KingFahd University of Petroleum and Minerals (Wiley, 2023-09-03)
      Recently, Kovács et al. considered a Mittag‐Leffler Euler integrator for a stochastic semilinear Volterra integral‐differential equation with additive noise and proved the strong convergence error estimates [see SIAM J. Numer. Anal. 58(1) 2020, pp. 66‐85]. In this article, we shall consider the Mittag‐Leffler integrators for more general models: stochastic semilinear subdiffusion and superdiffusion driven by fractionally integrated additive noise. The mild solutions of our models involve four different Mittag‐Leffler functions. We first consider the existence, uniqueness and the regularities of the solutions. We then introduce the full discretization schemes for solving the problems. The temporal discretization is based on the Mittag‐Leffler integrators and the spatial discretization is based on the spectral method. The optimal strong convergence error estimates are proved under the reasonable assumptions for the semilinear term and for the regularity of the noise. Numerical examples are given to show that the numerical results are consistent with the theoretical results.
    • Identification of Disalicyloyl Curcumin as a Potential DNA Polymerase Inhibitor for Marek’s Disease Herpesvirus: A Computational Study Using Virtual Screening and Molecular Dynamics Simulations

      Cherif, Aziza; Basharat, Zarrin; Yaseen, Muhammad; Bhat, Mashooq Ahmad; Uddin, Imad; Ziedan, Noha; Mabood, Fazal; Sadfi-Zouaoui, Najla; Messaoudi, Abdelmonaem; Université de Tunis-El Manar; Alpha Genomics, Islamabad; University of Swat; King Saud University; University of Chester; Jendouba University (MDPI, 2023-09-12)
      Marek’s disease virus (MDV) is a highly contagious and persistent virus that causes T-lymphoma in chickens, posing a significant threat to the poultry industry despite the availability of vaccines. The emergence of new virulent strains has further intensified the challenge of designing effective antiviral drugs for MDV. In this study, our main objective was to identify novel antiviral phytochemicals through in silico analysis. We employed Alphafold to construct a three-dimensional (3D) structure of the MDV DNA polymerase, a crucial enzyme involved in viral replication. To ensure the accuracy of the structural model, we validated it using tools available at the SAVES server. Subsequently, a diverse dataset containing thousands of compounds, primarily derived from plant sources, was subjected to molecular docking with the MDV DNA polymerase model, utilizing AutoDock software V 4.2. Through comprehensive analysis of the docking results, we identified Disalicyloyl curcumin as a promising drug candidate that exhibited remarkable binding affinity, with a minimum energy of −12.66 Kcal/mol, specifically targeting the DNA polymerase enzyme. To further assess its potential, we performed molecular dynamics simulations, which confirmed the stability of Disalicyloyl curcumin within the MDV system. Experimental validation of its inhibitory activity in vitro can provide substantial support for its effectiveness. The outcomes of our study hold significant implications for the poultry industry, as the discovery of efficient antiviral phytochemicals against MDV could substantially mitigate the economic losses associated with this devastating disease.
    • Exploring Mixed Reality Level Design Workflows

      John, Nigel; Pop, Serban; Beever, Lee (University of Chester, 2023-03)
      The past decade has seen a continual increase in quality and capability of augmented reality (AR) and virtual reality (VR) devices. Due to this greater capability, there have been an influx of entertainment and serious games that have been developed for these systems. Yet, the current workflows for developing VR game levels for entertainment or serious games have remained the same, with developers using a game engine presented on a 2D screen with a traditional mouse and keyboard for input. This thesis explores the use of AR and VR technologies as part of level design workflows used to develop both entertainment and serious VR game levels. Two existing workflows were identified as areas that could be improved by integrating AR and VR technologies as part of the workflow. Whilst a third new workflow was developed which focused on enabling new experiences for players: Workflow 1: This workflow explored using AR to help create a digital map of an existing space to help improve realism and presence of a VR serious game environment. The initial focus was on improving the workflow for developers of serious game levels. Workflow 2: This workflow focused on improving entertainment VR game level creation through the development of a VR level editor. The focus was on improving the entertainment VR level design process for professional level designers. Workflow 3: This workflow enables new experiences by supporting substitutional reality (SR) level design for players through a mix of both AR and VR technologies. It enables players to develop their own entertainment game levels that support SR using consumer technology. Each of the three workflows are presented in this thesis along with results from multiple studies. Results from the studies show positive outcomes supporting each of the workflows.
    • Energy storage properties of samarium-doped bismuth sodium titanate-based lead-free ceramics

      Tang, Xuyao; Hu, Zimeng; Koval, Vladimir; Yang, Bin; Smith, Graham C.; Yan, Haixue; University of Chester (Elsevier, 2023-08-18)
      Due to worldwide environmental regulations, lead-free relaxors, namely Bi0.5Na0.5TiO3–6BaTiO3 (BNT-6BT) are being extensively studied as an alternative candidate for energy storage applications. Here, Sm was introduced at different A sites of the relaxor system; specifically, the Sm-doped BNT-6BT system was designed to replace Bi (BNT-Bi), Na (BNT-Na), and both the Bi and Na ions (BNT-BiNa) by Sm ions. It was found that the BNT-Bi sample possesses high piezoelectricity (d33=117.3 pC N-1), whereas the BNT-Na and BNT-BiNa ceramics show exceptionally high values of the energy storage density and efficiency. To define the energy storage performance, a new concept based on determining the recoverable energy storage intensity is proposed in the present work. This allows bypassing the high applied electric fields in determining the value of the energy storage density. An ultrahigh recoverable energy storage density (4.41 J cm-3), excellent energy storage efficiency (83.96%) and superhigh recoverable energy storage intensity (19.17×10-3 J kV-1 cm-2) were achieved in the BNT-BiNa ceramics simultaneously. Furthermore, the energy storage characteristics exhibit an excellent stability over a wide temperature range from 25 °C to 150 °C. Thus, the developed Sm-doped BNT-6BT ceramics show great potential for piezoelectric and high-power energy storage applications.
    • Broadband Dielectric Characterization of Carbon Black-Reinforced Natural Rubber

      Huang, Menglong; Tunnicliffe, Lewis B.; Liao, Shibai; Yang, Bin; Yan, Haixue; Busfield, James J. C.; Queen Mary University of London; University of Chester (Rubber Division, ACS, 2023-08-28)
      Natural rubber compounds reinforced with two different carbon blacks (N134 and N330) at various concentrations were characterized using very broadband dielectric spectroscopy from around 0.1 Hz to 0.3 THz using four different impedance and network analysis technologies. Percolation behavior was observed when the testing electrical frequency was below a certain range, which can be linked to the presence of percolated carbon black networks. When above a critical frequency level, the real part of AC conductivity or the permittivity tended to have a simple exponential relationship with the volume fraction of carbon black rather than a percolation-like behavior with the carbon black volume fraction and was no longer sensitive to carbon black networks. The AC conductivity derived via complex impedance was also strongly influenced by the choice of calculation model when the material was around or below the percolation threshold.