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A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this paper we extend the diffusive logistic model with unknown moving front to the random scenario by assuming that the involved parameters have a finite degree of randomness. The resulting mathematical model becomes a random free boundary partial differential problem and it is addressed numerically combining the finite difference method with two approaches for the treatment of the moving front. Firstly, we propose a front-fixing transformation, reshaping the original random free boundary domain into a fixed deterministic one. A second approach is using the front-tracking method to capture the evolution of the moving front adapted to the random framework. Statistical moments of the approximating solution stochastic process and the stochastic moving boundary solution are calculated by the Monte Carlo technique. Qualitative numerical analysis establishes the stability and positivity conditions. Numerical examples are provided to compare both approaches, study the spreading-vanishing dichotomy, prove qualitative properties of the schemes and show the numerical convergence. [ABSTRACT FROM AUTHOR]

This paper is a computational bifurcation analysis of a non-linear partial differential equation (PDE) characterizing equilibrium configurations in Micro electromechanical Systems (MEMS). MEMS are engineering systems that utilize electrostatic forces to actuate elastic surfaces. The potential equilibrium states of MEMS are described by solutions of a singularly perturbed elliptic nonlinear PDE. We develop a numerical method which couples a finite element approximation with mesh refinement to a pseudo arc-length continuation algorithm to numerically obtain bifurcation diagrams in the physically relevant two dimensional scenario. Several geometries, including a unit disk, square, and annulus, are studied to understand the behavior of the system over a range of domains and parameter regimes. We find that solution multiplicity, and importantly the potential for bistability in the system, depends sensitively on the parameters. In the annulus domain, symmetry breaking bifurcations are located and asymmetric solution branches are tracked. This work significantly extends the envelope for numerical characterization of equilibrium states in microscopic electrostatic contact problems relating to MEMS. [ABSTRACT FROM AUTHOR]

Purpose: The paper proposes an efficient and insightful approach for solving neutral delay differential equations (NDDE) with high-frequency inputs. This paper aims to overcome the need to use a very small time step when high frequencies are present. High-frequency signals abound in communication circuits when modulated signals are involved. Design/methodology/approach: The method involves an asymptotic expansion of the solution and each term in the expansion can be determined either from NDDE without oscillatory inputs or recursive equations. Such an approach leads to an efficient algorithm with a performance that improves as the input frequency increases. Findings: An example shall indicate the salient features of the method. Its improved performance shall be shown when the input frequency increases. The example is chosen as it is similar to that in literature concerned with partial element equivalent circuit (PEEC) circuits (Bellen et al., 1999). Its structure shall also be shown to enable insights into the behaviour of the system governed by the differential equation. Originality/value: The method is novel in its application to NDDE as arises in engineering applications such as those involving PEEC circuits. In addition, the focus of the method is on a technique suitable for high-frequency signals. [ABSTRACT FROM AUTHOR]

In this paper, we construct an improved Implicit–Explicit (IMEX) numerical scheme based on the conservation form of the advection–diffusion equations and study the numerical stability of the method in case of a nonlinear advection–diffusion Lotka–Volterra model. The classical numerical methods might be unsuitable for providing accurate numerical results for advection–diffusion problem in which advection dominates diffusion. An improved numerical scheme is proposed, which can preserve the positivity for arbitrary stepsizes. The convergence, boundedness, existence and uniqueness of the numerical solutions are investigated in paper. A threshold value denoted by R 0 Δ x , is introduced in the stability analysis. It is shown that the numerical semi-trivial equilibrium is locally asymptotically stable if R 0 Δ x < 1 and unstable if R 0 Δ x > 1. Moreover, the limiting behaviors of the threshold value are exhibited. Finally, some numerical simulations are given to confirm the conclusions. [ABSTRACT FROM AUTHOR]

Purpose: The susceptible-infectious-susceptible (SIS) infectious disease models without spatial heterogeneity have limited applications, and the numerical simulation without considering models' global existence and uniqueness of classical solutions might converge to an impractical solution. This paper aims to develop a robust and reliable numerical approach to the SIS epidemic model with spatial heterogeneity, which characterizes the horizontal and vertical transmission of the disease. Design/methodology/approach: This study used stability analysis methods from nonlinear dynamics to evaluate the stability of SIS epidemic models. Additionally, the authors applied numerical solution methods from diffusion equations and heat conduction equations in fluid mechanics to infectious disease transmission models with spatial heterogeneity, which can guarantee a robustly stable and highly reliable numerical process. The findings revealed that this interdisciplinary approach not only provides a more comprehensive understanding of the propagation patterns of infectious diseases across various spatial environments but also offers new application directions in the fields of fluid mechanics and heat flow. The results of this study are highly significant for developing effective control strategies against infectious diseases while offering new ideas and methods for related fields of research. Findings: Through theoretical analysis and numerical simulation, the distribution of infected persons in heterogeneous environments is closely related to the location parameters. The finding is suitable for clinical use. Originality/value: The theoretical analysis of the stability theorem and the threshold dynamics guarantee robust stability and fast convergence of the numerical solution. It opens up a new window for a robust and reliable numerical study. [ABSTRACT FROM AUTHOR]

In this paper, we propose an effective Chebyshev–Picard iteration (CPI) method for solving delay differential equations with a constant delay. This approach adopts the Chebyshev series to represent the solution and improves the accuracy of the solution by successive Picard iterations. The CPI method is implemented in a matrix–vector form efficiently without matrix inversion. We also present a multi-interval CPI method for solving long-term simulation problems. Further, the convergence of the CPI method is analyzed by evaluating the eigenvalues of the coefficient matrices of the iteration. Several numerical experiments including both the linear and nonlinear systems with delay effects are presented to demonstrate the high accuracy and efficiency of the CPI method by comparison with the classic methods. [ABSTRACT FROM AUTHOR]

The acquisition of drinking water is discussed in this paper by three-dimensional modeling of a solar desalination plant focusing on renewable energies. The reservoir of the desalination plant contains aluminum nanoparticles with a constant weight percent. A layer of n-Eicosane phase change material (PCM) with various thicknesses is used at the bottom of the desalination plant reservoir. The objective of the present paper is to examine the entropy generation, including frictional, thermal, and total entropy generation in the flow of steam and air inside the desalination plant and the use of the PCM layer. The angle of the glass changes from 10 to 45°, and the thickness of the PCM layer varies during the day. The nanofluid flow is assumed to be two-phase, and the finite element method (FEM) is employed to solve the equations using COMSOL software. The results show that increasing the glass angle enhances the frictional entropy generation, and decreases the thermal entropy generation. Using PCM with a thickness of 50 mm reduces the thermal entropy generation in the steam, especially in the afternoon. The amount of PMC thickness changes the total entropy generation in the PMC. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of the paper is the simulation of nonuniform transmission lines. Design/methodology/approach: The method involves a Magnus expansion and a numerical Laplace transform. The method involves a judicious arrangement of the governing equations so as to enable efficient simulation. Findings: The results confirm an effective and efficient numerical solver for inclusion of nonuniform transmission lines in circuit simulation. Originality/value: The work combines a Magnus expansion and numerical Laplace transform algorithm in a novel manner and applies the resultant algorithm for the effective and efficient simulation of nonuniform transmission lines. [ABSTRACT FROM AUTHOR]

The PVT solar collectors can produce the thermal energy and power in a same frame. The improvement of the PVT's efficiency leads to reducing the system size and capital costs. To this end, this paper studied the irreversibilities of the Al 2 O 3 Cu/water hybrid nanofluid (NF) in a PVT solar collector considering two single and double serpentine channels (SS and DS). The influences of Re and nanoparticle concentration (φ) on the thermal and frictional entropy generation rates (S ˙ t h and S ˙ f r) were investigated and the thermal, electrical and overall exergy efficiencies (ψ th , ψ e , ψ ov) of the PVT with SS and DS channels were compared and discussed. Based on the results, the DS channel exhibited S ˙ f r of almost 75 % lower than SS channel due to lower nanofluid inlet velocities and velocity gradients. In addition, S ˙ t h for the DS channel is nearly 65 % lower and 26 % higher than that for the SS channel at Re numbers of 500 and 2000, respectively. Besides, the Re escalation from 500 to 2000 intensifies S ˙ f r by almost 94 % at different φs in the SS and DS channels. The increase in φ from 0 % to 1 % escalates S ˙ f r by almost 99.98 % times for two configuration regardless of the Re number. ψ th of the DD channel is nearly 14.5 % and 12.77 % higher than that of the SS channel at Re s of 500 and 2000, respectively. Besides, ψ e of the PVT with the DS channel is 2.36 % higher than that with SS channel at Re =500 at four studied φs. Moreover, the maximum ψ e for the PVT with the DS and SS were obtained as 22.29 % and 21.28 %, respectively, which are associated with Re =1500 and φ=0.25 %. Additionally, a predictive model was presented to determine the total entropy generation rate based in the Re and φ as the inputs. [ABSTRACT FROM AUTHOR]

This paper studied the heat transfer and entropy generation rate of water-Fe 3 O 4 magnetic nanofluid flow inside three twisted tubes with square, triangular, and elliptical cross-sections at the absence and presence of a magnetic field (MF) effect for Reynolds number (Re) range of 400–800, pitch distance (P s) range of 25–75 mm as well as the nanoparticle concentration (φ) range of 1%, 2%, and 4%. Based on the results, the increase in Re from 400 to 800 escalated convective heat transfer coefficient (h) by 33.98% (or 4.66%), 23.97% (or 18.46%) and 31.36% (or 20.91%) in the square, triangular, and elliptical twisted tubes, respectively, under the absence (or presence) of the MF. At P =50 mm and φ=2%, the MF improved h by 21–45%, 21–26%, and 0–16% within the Re range of 400–800 for the square, triangular, and elliptical twisted tubes, respectively. Nearly 60% and 50% pressure drop observed as Re escalated from 400 to 800 in the absence and presence of the MF, respectively. The highest performance evaluation criterion (PEC) (i.e. 1.45) and the lowest PEC (i.e. 0.91) were obtained for the square twisted tube at Re =400 and elliptical tube at Re = 800, respectively. The highest and lowest PEC of the square twisted tube (i.e. 1.88 and 1.45) at Re =400 were observed for P =50 mm and φs of 4% and 2%, respectively. In the presence of the MF effect, nearly 37–48% (or 32–35%) increase in the S ˙ f r (or S ˙ t h) were obtained at P s of 25–75 mm against the cases without the MF effect. [ABSTRACT FROM AUTHOR]

In this paper, a novel COVID-19 reaction–diffusion model with virus mutation and media coverage is investigated. First, the solution's uniform boundedness for the system is established. Then, the basic reproduction numbers for ordinary and mutant viruses spread in heterogeneous environments are defined. Furthermore, the endemic equilibrium's asymptotic distribution for the system is explored. In addition, when one diffusion coefficient tends to zero and the other diffusion coefficients are greater than zero and fixed, the solution of the system will asymptotically approach endemic equilibrium. Next, a theoretical analysis of how high-frequency media coverage affects the development of the COVID-19 epidemic is conducted. Theoretical research shows that high-frequency media coverage will lead to the disappearance of the disease. Meantime, global sensitivity analysis on the basic reproduction numbers R 01 and R 02 are performed. Finally, theoretical simulations and instance predictions are carried out. Because of the complexity of the Shanghai epidemic and changes in management and control, the infection rates β 1 (t) , β 2 (t) are given in the form of a piecewise function with more practical significance, and they are used to predict the epidemic trend of COVID-19 in Shanghai. Through a series of numerical simulations and analysis, the key indicators of the Shanghai COVID-19 epidemic are as follows : (1) The basic reproduction numbers in the early, middle, and late stages of COVID-19 are R ¯ 0 (1 : 34) = 0. 9152 , R ¯ 0 (35 : 49) = 3. 1476 , and R ¯ 0 (50 : 140) = 0. 6547 , respectively; (2) This epidemic round in Shanghai will peak at 3,270 new daily confirmed cases on the 49th day (April 15); (3) The final size of the epidemic will reach 63,470 confirmed cases; (4) This round of COVID-19 epidemic in Shanghai, China, is expected to be fully cleared in late June to early July. The above conclusions are basically consistent with the facts. Of course, with the rise in temperature and strict control, the epidemic situation in Shanghai, China, is expected to be cleared earlier. Our results provide new ideas for preventing and controlling the COVID-19 epidemic. • A reaction–diffusion model with virus mutation and media coverage is proposed. • The asymptotic properties of endemic equilibrium with small diffusion are explored. • Global sensitivity analysis for R 01 and R 02 and are performed. • Applying piecewise functions β 1 (t) , β 2 (t) , to predict the Shanghai COVID-19 epidemic. • Key indicators of COVID-19, such as R 0 , peak, final scale, clear time are obtained. [ABSTRACT FROM AUTHOR]

In a recent paper [H. Dong, J. Tang, and X. Mao, SIAM J. Control Optim., 2022], the stability of delayed feedback control of Lévy noise driven stochastic delay hybrid systems is discussed. Notably, the system assumes the absence of the neutral term and imposes the classical linear growth condition on the jump coefficients. This work aims to close the gap by imposing the superlinearly growing jump coefficients for a class of highly nonlinear neutral stochastic delay hybrid systems with Lévy noise (NSDHSs-LN), where neutral-term implies that the systems depend on derivatives with delays in addition to the present and past states. We first show the existence and uniqueness theorem of the solution to the highly nonlinear NSDHSs-LN under the local Lipschitz condition, along with the moment boundedness and finiteness of the solution. We then demonstrate the moment exponential stability and almost sure exponential stability of highly nonlinear NSDHSs-LN through a variable-delay feedback control function and Lyapunov functionals. Finally, we apply our results to a concrete stabilization problem of a coupled oscillator-pendulum system with Lévy noise, and some numerical analyses are presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Purpose: Detection of low-frequency pressures such as heart rate in the range of 1 Hz is one of the applications of low-frequency resonator. In this paper, the structure of the resonator is in the form of a plate, whose mathematical model has been extracted according to past works and is reported. Design/methodology/approach: This paper presents an electromechanical microresonator that can be used as an ultra-low-frequency pressure sensor. It is very important to choose the right material for the sensors to have the optimal conditions. In this work, by proposing the innovative use of polytetrafluoroethylene material with low stiffness coefficient, the necessary conditions are provided to reduce the vibration frequency of the resonator. Findings: The proposed design is simulated with the help of COMSOL, and its results are compared with the results of the mathematical model, which are very close to each other. Therefore, by inferring the results, the authors can rely on accurate simulations and finalize the similar designs with full confidence before fabrication. Originality/value: There are important advantages regarding the geometry of the proposed design structure that is the possibility of detecting a pressure of 1 Pa only with voltages less than 2 V. On the other hand, the pull-in effect causes very low frequencies to be achieved in detection with the help of the proposed resonator. Also, the linear and nonlinear behavior of the resonator by applying different pressures has been studied and reported to find the appropriate operating range of the resonator and its limitations. [ABSTRACT FROM AUTHOR]

The application of V-cut twisted tape turbulator inserted in the absorber tube of a photovoltaic thermal (PVT) system was investigated through a 3-D numerical analysis. The objective was to determine the effect of turbulator pitch distance (50 mm, 77 mm, and 100 mm) and Re number (500, 1000, 1500, and 2000) on the PVT energy and exergy performances. The results were compared with those obtained for the absorber tube without turbulator. Our findings demonstrated that the pressure drop and PV temperature, respectively, escalates and diminishes by 78–84% and 5.69–6.68% for the case with turbulator (pitch of 100 mm) as Re increases from 500 to 2000. In consequence, the overall energy efficiency and overall exergy efficiency improve by 15.76–14.27% and 12.01–8.68%, respectively, for the increase in Re within the studied range. In addition, the application of turbulator with a pitch of 100 mm improves the overall energy and exergy efficiencies of the PVT system by 3.04–7.70% and 4.03–13.08% at the Re range of 500–2000 as compared to the without turbulator case. Moreover, the greatest useful thermal and electrical efficiencies were obtained for the PVT with turbulator pitch of 100 mm and at Re =2000, which yields the highest overall thermal and exergy efficiencies of 75.46% and 16.34%, respectively. Furthermore, RSM technique is utilized to obtain a model for the overall energy and exergy efficiencies versus Re and P. [ABSTRACT FROM AUTHOR]

Recently, the long time numerical simulation of PDEs with weak nonlinearity (or small potentials) becomes an interesting topic. In this paper, for the Klein–Gordon–Schrödinger equation (KGSE) with a small coupling constant ɛ ∈ (0 , 1 ] , we proposed a time-splitting Fourier pseudo-spectral (TSFP) scheme by reformulating the KGSE into a coupled nonlinear Schrödinger system (CNLSS). Through rigorous error analysis, we establish improved error bounds for the scheme at O (h m + ɛ τ 2) up to the long time at O (1 / ɛ) where h is the mesh size and τ is the time step, respectively, and m depends on the regularity conditions. Compared with the results of existing numerical analysis, our analysis has the advantage of showing the long time numerical errors for the KGSE with the small coupling constant. The tools for error analysis mainly include the mathematical induction and the standard energy method as well as the regularity compensation oscillation (RCO) technique which has been developed recently. The numerical experiments support our theoretical analysis. Our scheme is novel because that to the best of our knowledge there has not been any TSFP scheme and any relevant long time analysis for the KGSE. [ABSTRACT FROM AUTHOR]

In this paper, an element-free Galerkin (EFG) method is developed for the numerical analysis of the time-fractional subdiffusion equation. By using the L 2 − 1 σ formula to approximate the Caputo fractional derivative, a second-order accurate scheme is proposed to achieve temporal discretization. Then, time-independent integer-order boundary value problems are formed, and a stabilized EFG method is applied to establish the discretize linear algebraic systems. Error of the proposed meshless method is proved theoretically. Numerical results show the convergence and effectiveness of the method. [ABSTRACT FROM AUTHOR]

The price of a barrier option is often computed numerically. Due to the path dependency, the convergence rate of such numerical approximation is generally of order 1 / 2. In this paper, we show that the convergence order can be achieved at 1 under certain condition. This confirms a numerical analysis done previously by the third author with others. We consider the case where the underlying process is a Brownian motion with drift. The price of a barrier option coincides with the price of a vanilla option of the "symmetrized" diffusion, which has a discontinuous drift. The symmetrized diffusion is then approximated by a Markov chain and the corresponding option price is calculated. This approximation to the barrier option is shown to have a convergence order of 1 under some mild condition on the initial value of the process and the payoff function. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to establish the mathematical model and solve the complex calculation multi-field coupling problem for an electromagnetic overhead transmission line galloping excitation test system. Design/methodology/approach: An electromagnetic excitation test system is introduced. To calculate the vibration response of the transmission line, a transient coupled finite element model containing electromagnetic repulsive mechanism and transmission line system was established. Considering the advantages of Newmark-ß algorithm and fourth-order Runge–Kutta algorithm, the two algorithms are combined to solve the model. Compared with the simulation results of existing commercial finite element software, the accuracy of the calculation model of electromagnetic force and wire vibration response are verified. Findings: Comparison results show that the proposed calculation model can accurately obtain the force of electromagnetic mechanism and the vibration response of the overhead power lines, and improve the calculation efficiency. The calculation results show that vibration under electromagnetic excitation presents a double half-wave mode, and the galloping amplitude varies according to the charging voltage. Originality/value: This paper built the transient simulation model for a galloping test system. The Newmark-ß algorithm and the fourth-order Runge–Kutta algorithm are used to solve the model. The research results are of great significance for the actual galloping test system design. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the numerical analysis of Fitzhugh–Nagumo (FHN) reaction–diffusion equations. The properties of numerical solutions of a semi-discrete and fully-practical piecewise linear finite element technique are provided. Moreover, for a semi-discrete and fully discrete finite element approximation, we establish a priori estimates and error bounds. We also introduce the results of some numerical examples in one and two dimensions, which confirm the theoretical findings of this paper. [ABSTRACT FROM AUTHOR]

Purpose: The variational principle views a complex problem in an energy way, it gives good physical understanding of an iteration method, and the variational-based numerical methods always have a conservation scheme with a fast convergent rate. The purpose of this paper is to establish a variational principle for a fractal nano/microelectromechanical (N/MEMS) system. Design/methodology/approach: This paper begins with an approximate variational principle in literature for the studied problem, and a genuine variational principle is obtained by the semi-inverse method. Findings: The semi-inverse method is a good mathematical tool to the search for a genuine fractal variational formulation for the N/MEMS system. Research limitations/implications: The established variational principle can be used for both analytical and numerical analyses of the N/MEMS systems, and it can be extended to some more complex cases. Practical implications: The variational principle can be used for variational-based finite element methods and energy-based analytical methods. Originality/value: The new and genuine variational principle is obtained. This paper discovers the missing piece of the puzzle for the establishment of a variational principle from governing equations for a complex problem by the semi-inverse method. The new variational theory opens a new direction in fractal MEMS systems. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we introduce a notion of a t-filter on residuated lattices which is a generalization of several special types of filters. We provide some basic properties of t-filters and show how particular results about special types of filters (e.g. Extension property, Triple of equivalent characteristics, and Quotient characteristics) are uniformly covered by this simple general framework. [Copyright &y& Elsevier]

Purpose: This paper aims to propose a new unified and non-ideal switch model for analysis of switching circuits. Design/methodology/approach: The model has a single unified structure that includes all possible states (on, off) of the switches. The analysis with the proposed switch model requires only one topology and uses the single system equation regardless of states of switches. Moreover, to improve accuracy, the model contains the on-state resistance and capacitive effect of switches. The system equations and the states of switches are updated by control variables, used in the model. Findings: There are no restrictions on circuit topology and switch connections. Switches can be internally and externally controlled. The non-ideal nature of the model allows the switch to be modeled more realistically and eliminates the drawbacks of the ideal switch concept. After modeling with the proposed switch model, a linear circuit is obtained. Two examples related to switching circuits are included into the study. The results confirm the accuracy of the model. Originality/value: This paper contributes a different switch model for analysis of switching converters to the literature. The main advantage of the model is that it has a unified and non-ideal property. With the proposed switch model, the transient events, like voltage spikes and high-frequency noises, caused by inductor and capacitor elements at switching instants can be observed properly. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to elaborate the method and algorithm for the analysis of the influence of temperature on back electromotive force (BEMF) waveforms in a line start permanent magnet synchronous motor (LSPMSM). Design/methodology/approach: The paper presents a finite element analysis of temperature influence on BEMF and back electromotive coefficient in a LSPMSM. In this paper, a two-dimensional field model of coupled electromagnetic and thermal phenomena in the LSPMSM was presented. The influence of temperature on magnetic properties of the permanent magnets as well as on electric and thermal properties of the materials has been taken into account. Simulation results have been compared to measurements. The selected results have been presented and discussed. Findings: The simulations results are compared with measurements to confirm the adequacy of this approach to the analysis of coupled electromagnetic-thermal problems. Originality/value: The paper offers appropriate author's software for the transient and steady-state analysis of coupled electromagnetic and thermal problems in LSPMS motor. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to investigate the influences of dimple location on the heat transfer performance of a pin fin-dimpled channel with upright/curved/inclined pin fins under stationary and rotating conditions. Design/methodology/approach: Numerical methods based on a realizable k-ε turbulent model are used to conduct this study. Three kinds of pin fins (upright, curved, inclined) and three dimple locations (front, middle, behind) are studied for Ro varying from 0 to 0.5. Findings: On the whole, pin fin plays a dominated role in heat transfer performance compared to dimple. The heading path and interaction of the longitudinal secondary flow and jet-like flow critically affect heat transfer performance. The formation, development and impingement of jet-like flow and longitudinal secondary flow are significantly affected by dimple locations. Dimple at behind position shows the poorest heat transfer enhancement. Originality/value: This study is an extend of another previous study in which an innovative curved pin fin is proposed. The originality of this paper is to evaluate the heat transfer performance for the combined cooling structure of dimple and pin fin, which will provide original and useful application and experience for turbine blade design. [ABSTRACT FROM AUTHOR]

Conventional data compression schemes aim at implementing a trade-off between the rate required to represent the compressed data and the resulting distortion between the original and reconstructed data. However, in more and more applications, what is desired is not reconstruction accuracy but the quality of the realization of a certain task by the receiver. In this paper, the receiver task is modeled by an optimization problem whose parameters have to be compressed by the transmitter. Motivated by applications such as the smart grid, this paper focuses on a goal function which is of L p -norm-type. The aim is to design the precoding, quantization, and decoding stages such that the maximum of the goal function obtained with the compressed version of the parameters is as close as possible to the maximum obtained without compression. The numerical analysis, based on real smart grid signals, clearly shows the benefits of the proposed approach compared to the conventional distortion-based compression paradigm. • General framework for designing compression methods for the L p norm minimization problem. • Novel linear and nonlinear transformation schemes by taking into account the performance degradation in terms of the L p norm induced by model reduction. • Tailor the quantization rule to be goal-oriented by considering the impact of the precoding and the final use of the compressed data. • Evaluation of the proposed coding schemes with a real dataset and show the significant performance improvement compared to existing conventional transformation and quantization techniques. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the numerical representation of the linearly implicit Euler method for an age-structured HIV infection model with a general transmission mechanism. We first define the basic reproduction number of the continuous model, and present the stability results of the equilibriums. For the numerical process, we establish the solvability of the system and the non-negativity and convergence of numerical solutions. In the analysis of the long-term dynamical behavior, this paper mainly focus on the existence of the infection equilibrium determined by the numerical reproduction number R 0 Δ t. To overcome the difficulty caused by the complexity of epidemic transmission mechanisms, the 1-order convergence analysis of numerical basic reproduction numbers R 0 Δ t is implemented by using the properties of the fundamental solution matrix. By a comparison principle, we show that the disease-free equilibrium is globally asymptotically stable if R 0 Δ t < 1. Moreover, for R 0 Δ t > 1 , a unique numerical endemic equilibrium exists, which converges to the exact one, is locally asymptotically stable. Hence, numerical processes visually represent the dynamic properties of nonlinear age-structured HIV models. Finally, some numerical experiments demonstrate the verification and the efficiency of our results. • The age-structured HIV model with general transmission is reviewed. • The exact basic reproduction number is recalled. • The linearly implicit Euler method is implemented to the model. • The theoretical and numerical threshold dynamics are investigated. • The convergence of the basic reproduction numbers is proved for general case. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the high-order approximation of a class of SPDEs with cubic nonlinearity driven by multiplicative noise with the help of the amplitude equations. The highlight of our work is the provision of approximate solutions with enhanced accuracy. Precisely, previous researches primarily concentrated on deriving approximate solutions via the first-order amplitude equations. However, this paper constructs approximate solutions by utilizing both first-order and second-order amplitude equations. And, we rigorously prove that such approximate solutions enjoy improved convergence property. To further illustrate our demonstration intuitively, we apply our main theorem to stochastic Allen–Cahn equation and present a numerical analysis. • The high-order amplitude equations of SPDEs with multiplicative noise is obtained. • The provision of approximate solutions with enhanced accuracy is given. • The approximate solutions enjoy improved convergence property is rigorously proved. • Applications and numerical analysis to stochastic Allen–Cahn equation are presented. [ABSTRACT FROM AUTHOR]

This paper analyses the generalised collocation Trefftz method which allows to combine the advantages of the T -Trefftz and MFS. The initial idea of the method is to approximate the solution with a linear combination of many basis functions with many source points. The application of only one source point with nonsingular basis function allows for set up linearly independent set. On the other hand, using logarithmic and negative power bases for the source points enables better control over quality of the solution. The validity of the proposed method is conducted for the potential problem in a two-dimensional simply and doubly connected domain without using the domain decomposition. [ABSTRACT FROM AUTHOR]

In this paper, thermally induced vibrations of beams made of functionally graded materials (FGMs) subjected to cooling shocks are investigated. It is considered that the beam has been made of a mixture of stainless steel (SUS 304) and low-carbon steel (AISI 1020). To model the displacement field, the third-order beam theory, known as the Reddy beam theory (RBT), is used. Material properties depend on temperature and distribution of materials, and this dependence is modeled through the temperature and the location of materials along the thickness direction. Considering the uncoupled thermoelasticity theory, the temperature distribution is obtained using a one-dimensional Fourier-type transient heat conduction equation, and the equations of motion governing the higher-order beam are derived utilizing Hamilton's principle. Solving the equations is done numerically; the generalized differential quadrature method (GDQM) is employed to approximate the spatial derivatives, and the Newton-Raphson scheme is applied to linearize the equations. In addition, for approximation of the time derivatives, the Newmark method is utilized. Subsequently, the effects of various parameters on the non-dimensional lateral deflection of the higher-order beam considering two different types of thermal loading are investigated. A comprehensive parametric study is conducted to study the effects of important parameters including beam thickness, thermal load rapidity time, the amount of applied load, and the FG parameter. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to further advance the multiple space/time subdomain framework with model reduction. Existing linear multistep (LMS) methods that are second-order time accurate, and useful for practical applications, have a significant limitation. They do not account for separable controllable numerical dissipation of the primary variables. Furthermore, they have little or no significant choices of altogether different algorithms that can be integrated in a single analysis to mitigate numerical oscillations that may occur. In lieu of such limitations, under the generalized single-step single-solve (GS4) umbrella, several of the deficiencies are circumvented. Design/methodology/approach: The GS4 framework encompasses a wide variety of LMS schemes that are all second-order time accurate and offers controllable numerical dissipation. Unlike existing state-of-art, the present framework permits implicit–implicit and implicit–explicit coupling of algorithms via differential algebraic equations (DAE). As further advancement, this study embeds proper orthogonal decomposition (POD) to further reduce model sizes. This study also uses an iterative convergence check in acquiring sufficient snapshot data to adequately capture the physics to prescribed accuracy requirements. Simple linear/nonlinear transient numerical examples are presented to provide proof of concept. Findings: The present DAE-GS4-POD framework has the flexibility of using different spatial methods and different time integration algorithms in altogether different subdomains in conjunction with the POD to advance and improve the computational efficiency. Originality/value: The novelty of this paper is the addition of reduced order modeling features, how it applies to the previous DAE-GS4 framework and the improvement of the computational efficiency. The proposed framework/tool kit provides all the needed flexibility, robustness and adaptability for engineering computations. [ABSTRACT FROM AUTHOR]

The paper deals with the numerical positivity, convergence and dynamical behaviors (including extinction and persistence) for stochastic SIR model. For the real significance of the numerical analysis on stochastic SIR model, a linearly implicit Euler method with truncated Wiener process is introduced. The numerical positivity is obtained by the truncated Wiener process, which is the basis for the investigation of convergence and dynamical behavior. The numerical dynamical behavior is obtained by an exponential presentation for the nonlinear stochastic stability function and the large number theorem for martingale, which reproduces the existing theoretical results of exact solution. Finally, numerical examples are given to validate our numerical results for stochastic SIR model. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to present a procedure for approximating DC operating points of nonlinear circuits. The presented approach can also be applied in case of multiple DC operating points. Design/methodology/approach: A generalized Carleman linearization is used, which transforms an algebraic nonlinear equation into an equivalent infinite-dimensional linear system. In general, no close-form solution can be given for the infinite-dimensional linear system. Hence, the infinite-dimensional linear system is approximated by a finite one over a predefined interval using a self-consistent technique. The presented procedure allows to approximate all possible DC operating points within a predefined interval. To isolate all DC operating points, the initial interval is gradually divided into subintervals. Findings: It is shown that the presented approach is not restricted to the polynomial case and allows to approximate all DC operating points. The presented approach can be applied in case of multiple DC operating points and does not depend on the domain of attraction of the DC operating points. Originality/value: A new procedure for the approximation of DC operating points of nonlinear circuits based on a generalized Carleman linearization is presented. This approach can be applied in case of multiple DC operating points and is independent of the domain of attraction. Further, this generalized approach is not restricted to the polynomial case and can be applied to a variety of circuits. [ABSTRACT FROM AUTHOR]

Time-varying problems frequently arise in the territories of science and engineering, and most of the time-varying problems can be described by dynamic matrix equations. As a powerful tool for solving dynamic matrix equations, the zeroing neural network (ZNN) develops fast in recent years. Convergence and robustness are two main performance indicators of the ZNN model. However, the development of the ZNN is focused on the improvement of its convergence in the past, and its robustness to noises is rarely considered. In order to achieve fast convergence and robustness of the ZNN model, a novel activation function (NAF) is presented in this paper. Based on the NAF, a noise-tolerant parameter-variable ZNN (NTPVZNN) model for solving dynamic Sylvester matrix equations (DSME) is realized, and its fixed-time convergence and robustness to noises are verified by rigorous mathematical analysis and numerical simulation results. Besides, two examples of electrical circuit currents computing and robotic manipulator trajectory tracking using the proposed NTPVZNN model in noisy environment further demonstrates its practical application ability. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to present the principle of virtual air gap inductance and the design of a voltage regulation device based on this principle. The authors provide a comprehensive analysis of this specific application that consists of locally saturating the magnetic circuit of the voltage regulator to modify its global properties. This saturation is created by a direct current flowing in a small auxiliary coil inserted in the specific area of the magnetic circuit to saturate this zone. Design/methodology/approach: Analytical calculation and finite elements simulations are used to optimize the device for a specific application tied to the supply of electrical ovens in metallurgic usage. Experimental results are presented at the end of the paper. Findings: The experimental results presented in this paper are in concordance with the analytical calculation and with the finite element simulations for different operation points. The difficulty of the study of the virtual air gap comes mainly from the nonlinearity of the phenomena because the principle is based on a local and controllable saturation of the magnetic circuit. Originality/value: The originality of the paper concerns the introduction of virtual air gap principle in a specific industrial application. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to introduce a non-invasive and convenient method to detect a life-threatening disease called aortic dissection. A Bayesian inference based on enhanced multi-sensors impedance cardiography (ICG) method has been applied to classify signals from healthy and sick patients. Design/methodology/approach: A 3D numerical model consisting of simplified organ geometries is used to simulate the electrical impedance changes in the ICG-relevant domain of the human torso. The Bayesian probability theory is used for detecting an aortic dissection, which provides information about the probabilities for both cases, a dissected and a healthy aorta. Thus, the reliability and the uncertainty of the disease identification are found by this method and may indicate further diagnostic clarification. Findings: The Bayesian classification shows that the enhanced multi-sensors ICG is more reliable in detecting aortic dissection than conventional ICG. Bayesian probability theory allows a rigorous quantification of all uncertainties to draw reliable conclusions for the medical treatment of aortic dissection. Originality/value: This paper presents a non-invasive and reliable method based on a numerical simulation that could be beneficial for the medical management of aortic dissection patients. With this method, clinicians would be able to monitor the patient's status and make better decisions in the treatment procedure of each patient. [ABSTRACT FROM AUTHOR]

This paper proposes to utilize intentional time delays as part of controllers to improve the damping of electromechanical oscillations of power systems. Through stability theory, the control parameter settings for which these delays in Power System Stabilizers (PSSs) improve the small signal stability of a power system are systematically identified, including the key parameter settings for which stability regions in the parameter plane remain connected for effective operation. The paper shows that PSSs with two control channels can be effectively designed to achieve best damping characteristics for a wide range of delays. Analytical results are presented on the One-Machine Infinite-Bus (OMIB) electromechanical power system model. To demonstrate the opportunities in more realistic dynamic models, our results are then implemented via numerical analysis on the IEEE standard 14-bus system. [ABSTRACT FROM AUTHOR]

This paper addresses and experimentally demonstrates a programmable linear equation solver by analog computation. A set of differential equations using transconductance devices directly translated from circuit theory converges to the linear equation solution. These energy-efficient analog techniques are experimentally demonstrated in a configurable analog platform. The resulting analog linear equation solution circuits are effectively analog filters. The paper analyzes the algorithmic issues and analog numerical analysis issues, including accuracy, convergence time, and the interpretation of condition number for analog solutions. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to propose a precise turbulence model for automobile aerodynamics simulation, which can predict flow separation and reattachment phenomena more accurately. Design/methodology/approach: As the results of wake flow simulation with commonly used turbulence models are unsatisfactory, by introducing a nonlinear Reynolds stress term and combining the detached Eddy simulation (DES) model, this paper proposes a nonlinear-low-Reynolds number (LRN)/DES turbulence model. The turbulence model is verified in a backward-facing step case and applied in the flow field analysis of the Ahmed model. Several widely applied turbulence models are compared with the nonlinear-LRN/DES model and the experimental data of the above cases. Findings: Compared with the experimental data and several turbulence models, the nonlinear-LRN/DES model gives better agreement with the experiment and can predict the automobile wake flow structures and aerodynamic characteristics more accurately. Research limitations/implications: The nonlinear-LRN/DES model proposed in this paper suffers from separation delays when simulating the separation flows above the rear slant of the Ahmed body. Therefore, more factors need to be considered to further improve the accuracy of the model. Practical implications: This paper proposes a turbulence model that can more accurately simulate the wake flow field structure of automobiles, which is valuable for improving the calculation accuracy of the aerodynamic characteristics of automobiles. Originality/value: Based on the nonlinear eddy viscosity method and the scale resolved simulation, a nonlinear-LRN/DES turbulence model including the nonlinear Reynolds stress terms for separation and reattachment prediction, as well as the wake vortex structure prediction is first proposed. [ABSTRACT FROM AUTHOR]

The present paper performed a numerical study on two-phase nanofluid (NFs) flow in a circular heatsink for cooling several LEDs. The heatsink is symmetrically designed and has two inlets and four outlets. Six heat sources or LEDs are placed on the circumference of a circle and a heat source is also mounted in the center of the heatsink. By varying the diameter of the circle, the side length of the heat sources, and the input velocity of the NFs, one may estimate the values of thermal resistance (THR), temperature uniformity (TUY) on the heatsink, heat transfer coefficient (HTC), and pressure drop in the heatsink. The finite element and two-phase mixture method are utilized for NFs simulations. It demonstrate that the heat source placed in the middle has a lower temperature than other heat sources. The results are most significantly affected by changing the NFs' velocity. The value of dimensionless temperature increases and subsequently decreases as the sides of the heat sources get longer. The dimensionless temperature first decreases and then increases as the distance between the heat sources and the heatsink's center increases. The amount of THR is high when the heat sources' side length or velocity values are large. [ABSTRACT FROM AUTHOR]

In this paper, we focus on develop high-order and structure-preserving numerical algorithm for the two-dimensional nonlinear space fractional Schrödinger equations. By constructing a new generating function, we obtain a fourth-order numerical differential formula and use it to approximate the spatial Riesz derivative, while the Crank–Nicolson method is applied for the time derivative. Based on the energy method, the conservation, solvability and convergence of the numerical algorithm are proved. Finally, some numerical examples are used to verify the correctness of the theoretical analysis and the validity of the numerical algorithm. [ABSTRACT FROM AUTHOR]

Artificial upwelling by the use of airlift pump is regarded as an effective way in utilizing deep ocean water and actualizing ocean fertilization. This paper focuses on numerical analysis of steady air–water two-phase flow in a vertical pipe of an airlift system based on one-dimensional multi-fluid model. The depth distributions of 6 physical quantities such as volumetric fractions and axial velocities of two phases, air density and pressure are calculated by solving the governing equations or by integrating the vector form of nonhomogeneous ordinary differential equation for two-phase flow interval. Upon successful verification of the present numerical model through a comparison with precedent theoretical and experimental results in case of a vertical pipe with length of 7.86 m, the model is extended to the case of artificial upwelling from water depth of 2000 m. The effects of submerged depth of air–water mixer on the pumped amount of water and the depth distributions of 6 physical quantities are considered. • This paper is concerned with numerical analysis of steady air–water two-phase flow in a vertical pipe of an airlift system to lift deep ocean water. • The depth distributions of 6 physical quantities such as volumetric fractions and axial velocities of two phases, air density and pressure are obtained from one-dimensional multi-fluid model. • The present model can be applied to predict the performance of airlift pump for lifting deep ocean water and the depth distributions of 6 physical quantities in axial direction. [ABSTRACT FROM AUTHOR]

Purpose: Heuristic algorithms have been widely used in different types of optimization problems. Their unique features in terms of running time and flexibility have made them superior to deterministic algorithms. To accurately compare different heuristic algorithms in solving optimization problems, the final optimal solution needs to be known. Existing deterministic methods such as Exhaustive Search and Integer Linear Programming can provide the final global optimal solution for small-scale optimization problems. However, as the system grows the number of calculations and required memory size incredibly increases, so applying existing deterministic methods is no longer possible for medium and large-scale systems. The purpose of this paper is to introduce a novel deterministic method with short running time and small memory size requirement for optimal placement of Micro Phasor Measurement Units (µPMUs) in radial electricity distribution systems to make the system completely observable. Design/methodology/approach: First, the principle of the method is explained and the observability of the system is analyzed. Then, the algorithm's running time and memory usage when applying on some of the modified versions of the Institute of Electrical and Electronics Engineers 123-node test feeder are obtained and compared with those of its deterministic counterparts. Findings: Because of the innovative method of step-by-step placement of µPMUs, a unique method is developed. Simulation results elucidate that the proposed method has unique features of short running time and small memory size requirements. Originality/value: While the mathematical background of the observability study of electricity distribution systems is very well-presented in the referenced papers, the proposed step-by-step placement method of µPMUs, which shrinks unobservable parts of the system in each step, is not discussed yet. The presented paper is directly applicable to typical problems in the field of power systems. [ABSTRACT FROM AUTHOR]

Memristors are widely used to construct multi-scroll/wing chaotic systems with complex dynamics. However, the generation of a multi-scroll/wing attractor is typically not induced by the memristor but depends on other nonlinear functions in the system, which does not take advantage of the unique features of the memristor for chaos-based applications. To address this issue, the present paper introduces a memristor coupling (MC) method to construct a novel memristive Sprott A system (MSAS) through coupling a flux-controlled memristor with multi-piecewise linear memductance into the chaotic Sprott A system. From theoretical analysis and numerical simulations, the MSAS is shown to be able to generate any number of multi-type hidden attractors, including multi-one-scroll, multi-double-scroll and multi-double-wing hidden attractors. In addition, it has two kinds of multistabilities, that is, heterogeneous multistability and homogeneous multistability. Based on these unique properties, different numbers of coexisting heterogeneous hidden attractors and coexisting homogeneous hidden attractors are derived respectively by switching the memristor initial states. These interesting dynamical properties are comprehensively investigated using nonlinear analysis tools. Furthermore, hardware experiments are implemented to demonstrate the feasibility of the MSAS and the effectiveness of the MC method. Finally, a new pseudo-random number generator (PRNG) is proposed to explore the practical applications of the MSAS. Performance evaluation results verify the high-quality randomness of the designed PRNG. [ABSTRACT FROM AUTHOR]

This study addresses the accuracy of stochastic simulations performed in Two-Dimensional Stochastic Neural Fields (2D-SNFs) with the infinite signal transmission speed and in the presence of external stimuli input. The numerical method in use belongs to the family of Galerkin-kind spectral approximations to Two-Dimensional Stochastic Neural Field Equations (2D-SNFEs). It translates the partial integro-differential fashion of such models into a large system of ordinary Stochastic Differential Equations (SDEs). Eventually, these SDEs are integrated approximately by the Euler–Maruyama scheme of the strong convergence order 0.5. In this paper, we devise a different-order approximate solution to the SNFE models at hand and look at the difference of such stochastic simulations on average for evaluating the consistency of the Euler–Maruyama-based numerical solution derived. The error committed in the 2D-SNFE-numerical-integration-scheme under study becomes available in our research. The other issue of particular attention and interest is hidden state reconstructions rooted in the 2D-SNFE approximations and incomplete noisy measurements of the membrane potential fulfilled at some user-assigned space positions and time instants. This statement leads to high-dimensional prediction and filtering problems to be solved. Here, we implement the Extended Kalman Filtering (EKF) approach, but accommodate it to our 2D-SNFE-oriented data assimilation scheme of huge size because of the two-dimensional manner of the stochastic process models in use. A sound performance of the newly-devised hidden state estimation technique is observed and exposed on a challenging 2D-SNFE example of computational neuroscience in Matlab. [ABSTRACT FROM AUTHOR]

In this paper, the Tsallis entropy based novel uncertainty relations on vector signals and matrix signals in terms of sparse representation are deduced for the first time. These new uncertainty bounds are not only related with the entropy parameter, but also related with the vector length, the min non-zero correlation between standard orthogonal basis and the given signals, the max correlation between the two given orthogonal basis and even the eigenvalues along with eigenvectors. Especially, the relationship between uncertainty bounds and matrix eigenvalues is discussed as well, as discloses the new interesting interpretation on sparse representation. In addition, the theoretical analysis and numerical examples have been shown to verify these newly proposed uncertainty principles, e.g., under the case of special parameters of Tsallis entropy, the uncertainty bound reaches its peak value for the sparsest representation of matrix (i.e., only one eigenvalue is not zero). Moreover, various numerical relations between uncertainty bounds and Tsallis entropy parameters are shown in perceptual form, as maybe give us the possible enlightenment or guidance in future sparse representation analysis. [ABSTRACT FROM AUTHOR]

This paper is devoted to develop a truly meshless numerical procedure for the fully non-linear analysis of sloshing phenomenon in an arbitrary-shape tank. For this purpose, the potential theory is considered as a liquid sloshing model, and the Lagrangian form of kinematic and dynamic boundary conditions in a moving coordinate system fixed to the tank is used to accurately capture the free surface. The multi-quadric radial basis function (MQ-RBF) augmented with the polynomial terms is employed to determine RBF-FD weights on neighboring nodes surrounding the center point for the spatial derivatives. These weight coefficients are used to solve both boundary value problems for velocity and acceleration potential. Compared with mash-based methods, the present method has the advantage of being easy to construct and flexible in dealing with the moving boundary problems. The free surface elevations, hydrodynamic pressure, and first-order natural sloshing frequencies have been reported for various geometries tanks under horizontal excitations at resonance and non-resonance cases. Fairly satisfactory agreement is observed in the numerical results and exiting results, especially for free surface elevation and first-order natural sloshing frequency. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to deal with characterisation of the thermal performance of a hybrid tubular and cavity solar thermal receiver. Design/methodology/approach: The coupled optical-flow-thermal analysis is carried out on the proposed receiver design. Modelling is performed in two and three dimensions for estimating heat loss by natural convection for an upward-facing cavity. Heat loss obtained in two dimensions by solving coupled continuity, momentum and energy equation inside the cavity domain is compared with the loss obtained using an established Nusselt number correlation for realistic receiver performance prediction. Findings: It is found that radiation emission from a heated cavity wall to the ambient is the dominant mode of heat loss from the receiver. The findings recommend that fluid flow path must be designed adjacent to the surface exposed to irradiation of concentrated flux to limit conduction heat loss. Research limitations/implications: On-sun experimental tests need to be performed to validate the numerical study. Practical implications: Numerical analysis of receivers provides guidelines for effective and efficient solar thermal receiver design. Social implications: Pressurised air receivers designed from this method can be integrated with Brayton cycles using air or supercritical carbon-dioxide to run a turbine generating electricity using a solar heat source. Originality/value: The present paper proposes a novel method for coupling the flux map from ray-tracing analysis and using it as a heat flux boundary condition for performing coupled flow and heat transfer analysis. This is achieved using affine transformation implemented using extrusion coupling tool from COMSOL Multiphysics software package. Cavity surface natural convection heat transfer coefficient is obtained locally based on the surface temperature distribution. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to propose and establish a set of new benchmark models to investigate and confidently validate the modeling and prediction of total stray-field loss inside magnetic and non-magnetic components under harmonics-direct current (HDC) hybrid excitations. As a new member-set (P21e) of the testing electromagnetic analysis methods Problem 21 Family, the focus is on efficient analysis methods and accurate material property modeling under complex excitations. Design/methodology/approach: This P21e-based benchmarking covers the design of new benchmark models with magnetic flux compensation, the establishment of a new benchmark measurement system with HDC hybrid excitation, the formulation of the testing program (such as defined Cases I–V) and the measurement and prediction of material properties under HDC hybrid excitations, to test electromagnetic analysis methods and finite element (FE) computation models and investigate the electromagnetic behavior of typical magnetic and electromagnetic shields in electrical equipment. Findings: The updated Problem 21 Family (V.2021) can now be used to investigate and validate the total power loss and the different shielding performance of magnetic and electromagnetic shields under various HDC hybrid excitations, including the different spatial distributions of the same excitation parameters. The new member-set (P21e) with magnetic flux compensation can experimentally determine the total power loss inside the load-component, which helps to validate the numerical modeling and simulation with confidence. The additional iron loss inside the laminated sheets caused by the magnetic flux normal to the laminations must be correctly modeled and predicted during the design and analysis. It is also observed that the magnetic properties (B27R090) measured in the rolling and transverse directions with different direct current (DC) biasing magnetic field are quite different from each other. Research limitations/implications: The future benchmarking target is to study the effects of stronger HDC hybrid excitations on the internal loss behavior and the microstructure of magnetic load components. Originality/value: This paper proposes a new extension of Problem 21 Family (1993–2021) with the upgraded excitation, involving multi-harmonics and DC bias. The alternating current (AC) and DC excitation can be applied at the two sides of the model's load-component to avoid the adverse impact on the AC and DC power supply and investigate the effect of different AC and DC hybrid patterns on the total loss inside the load-component. The overall effectiveness of numerical modeling and simulation is highlighted and achieved via combining the efficient electromagnetic analysis methods and solvers, the reliable material property modeling and prediction under complex excitations and the precise FE computation model using partition processing. The outcome of this project will be beneficial to large-scale and high-performance numerical modeling. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to use a fractional constitutive model with a nonlocal velocity gradient for replacing the nonlinear constitutive model to characterize its complex rheological behavior, where non-linear characteristics exist, for example, the inherent viscous behavior of the crude oil. The feasibility and flexibility of the fractional model are tested via a case study of non-Newtonian fluid. The finite element method is non-Newtonian used to numerically solve both momentum equation and energy equation to describe the fluid flow and convection heat transfer process. Design/methodology/approach: This paper provides a comprehensive theoretical and numerical study of flow and heat transfer of non-Newtonian fluids in a pipe based on the fractional constitutive model. Contrary to fractional order a, the rheological property of non-Newtonian fluid changes from shear-thinning to shear-thickening with the increase of power-law index n, therefore the flow and heat transfer are hindered to some extent. Findings: This paper discusses two dimensionless parameters on flow regime and thermal patterns, including Reynolds number (Re) and Nusselt number (Nu) in evaluating the flow rate and heat transfer rate. Analysis results show that the viscosity of the non-Newtonian fluid decreases with the rheological index (order α) increasing. While large fractional (order α) corresponds to the enhancement of heat transfer capacity. Research limitations/implications: First, it is observed that the increase of the Re results in an increase of the local Nusselt number (Nul). It means the heat transfer enhancement ratio increases with Re. Meanwhile, the increasement of the Nul indicating the enhancement in the heat transfer coefficient, produces a higher speed flow of crude oil. Originality/value: This study presents a new numerical investigation on characteristics of steady-state pipe flow and forced convection heat transfer by using a fractional constitutive model. The influences of various non-dimensional characteristic parameters of fluid on the velocity and temperature fields are analyzed in detail. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to investigate the circuit analysis differential equations, which play an important role in the field of electrical and electronic engineering, and it was necessary to propose a very simple and direct method to obtain approximate solutions for the linear or non-linear differential equations, which should be simple for engineers to understand. Design/methodology/approach: This paper introduces a simple novel Maclaurin series method (MSM) to propose an approximate novel solution in the area of circuit analysis for linear and non-linear differential equations. These equations describe the alternating current circuit of the resistor–capacitor, which evaluates the effect of non-linear current resistance. Linear and non-linear differential equations are evaluated as a computational analysis to assist the research, which reveals that the MSM is incredibly simple and effective. Findings: Simulation findings indicate that the achieved proposed solution using the novel suggested approach is identical to the exact solutions mentioned in the literature. As the Maclaurin series is available to all non-mathematicians, this paper reflects mostly on theoretical implementations of the numerous circuit problems that occur in the field of electrical engineering. Originality/value: A very simple and efficient method has been proposed in this paper, which is very easy to understand for even non-mathematicians such as engineers. The paper introduced a method of the Maclaurin series to solve non-linear differential equations resulting from the study of the circuits. The MSM mentioned here will be a useful tool in areas of physical and engineering anywhere the problem of the circuits is studied. [ABSTRACT FROM AUTHOR]