Taylor Series Approximation Research Articles

A Taylor Series Approximation Model for Characterizing the Output Resistance of a GFET

A Taylor Series Approximation Model for Characterizing the Output Resistance of a GFET

Finite Element Analysis in The Investigation of Methods to Model AC Resistance in A Coated Conductor

In our electricity dependent and rapidly automated society, the manipulation and usage of electricity to transmit energy is of significant prevalence. In particular, the application of current in high frequency transformers, inductors and motor generators presents a unique efficiency problem: The loss of energy through the spiking of effective resistance intrinsically related to the skin and proximity effects of an AC current. By the usage of Finite Element Analysis (FEA) in the simulative investigation of various variables on AC resistance, this paper seeks to provide insights into how coated conductors might offer advantages over the standard conductor in certain conditions, thus guiding future design and application in high-efficiency electronics. The papers findings reveal that adding a layer of coating with a lower conductivity than the core material could offer reduced energy losses up to the point when the skin depth matches the coating’s thickness. Moreover, the study explored the influence of the coating’s conductivity, suggesting that an increased conductivity of the coating material could further minimize copper losses, albeit with the trade-off of potentially higher costs. The study concludes with a Taylor Series approximation of the relationship between AC resistance and frequency using simulative data.

Accurate EVSI Estimation for Nonlinear Models Using the Gaussian Approximation Method.

The expected value of sample information (EVSI) measures the expected benefits that could be obtained by collecting additional data. Estimating EVSI using the traditional nested Monte Carlo method is computationally expensive, but the recently developed Gaussian approximation (GA) approach can efficiently estimate EVSI across different sample sizes. However, the conventional GA may result in biased EVSI estimates if the decision models are highly nonlinear. This bias may lead to suboptimal study designs when GA is used to optimize the value of different studies. Therefore, we extend the conventional GA approach to improve its performance for nonlinear decision models. Our method provides accurate EVSI estimates by approximating the conditional expectation of the benefit based on 2 steps. First, a Taylor series approximation is applied to estimate the conditional expectation of the benefit as a function of the conditional moments of the parameters of interest using a spline, which is fitted to the samples of the parameters and the corresponding benefits. Next, the conditional moments of parameters are approximated by the conventional GA and Fisher information. The proposed approach is applied to several data collection exercises involving non-Gaussian parameters and nonlinear decision models. Its performance is compared with the nested Monte Carlo method, the conventional GA approach, and the nonparametric regression-based method for EVSI calculation. The proposed approach provides accurate EVSI estimates across different sample sizes when the parameters of interest are non-Gaussian and the decision models are nonlinear. The computational cost of the proposed method is similar to that of other novel methods. The proposed approach can estimate EVSI across sample sizes accurately and efficiently, which may support researchers in determining an economically optimal study design using EVSI. The Gaussian approximation method efficiently estimates the expected value of sample information (EVSI) for clinical trials with varying sample sizes, but it may introduce bias when health economic models have a nonlinear structure.We introduce the spline-based Taylor series approximation method and combine it with the original Gaussian approximation to correct the nonlinearity-induced bias in EVSI estimation.Our approach can provide more precise EVSI estimates for complex decision models without sacrificing computational efficiency, which can enhance the resource allocation strategies from the cost-effective perspective.

Correspondence Analysis for Assessing Departures from Perfect Symmetry Using the Cressie–Read Family of Divergence Statistics

Recently, Beh and Lombardo (2022, Symmetry, 14, 1103) showed how to perform a correspondence analysis on a two-way contingency table where Bowker’s statistic lies at the numerical heart of this analysis. Thus, we showed how this statistic could be used to visually identify departures from perfect symmetry. Interestingly, Bowker’s statistic is a special case of the symmetry version of the Cressie–Read family of divergence statistics. Therefore, this paper presents a new framework for visually assessing departures from perfect symmetry using a second-order Taylor series approximation of the Cressie–Read family of divergence statistics.

Comprehensive design strategy of the NSD–TMD controlled system with closed-form frequency-amplitude solutions

A negative stiffness device (NSD) utilizing pre-compressed helical springs has been integrated with diverse vibration control techniques. Recently, the incorporation of NSD has been proposed to enhance the efficacy of a tuned mass damper (TMD) controlled system. This study introduces two design strategies for the NSD–TMD system, which functions either as a TMD with an adjustable operating bandwidth or as a pure non-linear energy sink. First, the non-linear force of NSD was expressed in a Taylor series approximation form incorporating a negative linear stiffness and a positive cubic stiffness term. Second, the equations of motion were formulated, and closed-form solutions were derived using the complexification–averaging method. The accuracy of the Taylor series approximation was substantiated within a specified range through a comparison of force–displacement curves. Third, the accuracy of the dynamic closed-form solutions was affirmed by comparing the amplitude–frequency curves with the numerical simulations. For a case study, an actual timber pedestrian bridge with decaying natural frequency was selected, and the two design strategies were examined individually. The vibration control performance of the TMD and NSD–TMD was also comparatively analyzed. The assessment focused on the peak force transmissibility value and the effective operating frequency bandwidth. Results highlighted a notable enhancement in operational performance, particularly for primary structures exhibiting diminishing modal frequencies. In a TMD-controlled system, the efficacy of vibration control deteriorates and may even amplify the dynamic response when a modal frequency shift occurs in the primary structure. Conversely, both design strategies of NSD–TMD can achieve lower transmissibility and broaden the operating bandwidth.

Analysis of parabolic trough solar collector thermal efficiency with application of a graphene oxide nanosheet‐based nanofluid

AbstractNowadays, clean energy production and reconciliation with nature is one of the best solutions known to rectify the global warming issue. Solar energy, as a clean and green one, has recently been drawing scientists' attention to itself more than ever. Applying parabolic trough solar collectors (PTSCs) is one of the state‐of‐the‐art ways to extract energy from the sun. As one of the most interesting research topics, the thermal efficiency enhancement of PTSCs is studied. The current study demonstrates how the thermal efficiency of PTSCs is enhanced through the application of graphene oxide (GO) nanosheets, as an inexpensive nanomaterial with superb thermal conductivity and unique structure, in thermal oil, namely, Behran oil, as heat transfer fluid, within the effective volume fraction range of 0.05. The above‐mentioned analysis is based on the theoretical calculations performed through a mathematical model based on the Taylor series approximation. All the calculations are performed with respect to a PTSC unit of a solar–thermal power plant situated in Shiraz, Iran, as the research case study. In addition, the Nan et al. model is used to analytically predict how the increase in the volume fraction of GO nanosheets raises the thermal conductivity and consequently increases the convection heat transfer coefficient of the nanofluid, leading to the thermal efficiency enhancement of PTSCs. The results reveal a maximum thermal efficiency of 71.10% for the volume fraction of 0.05. In comparison to the thermal efficiency of the real‐world case‐study mentioned above with pure thermal oil, that is, 67.71%, the thermal efficiency enhancement by about 5.5%, is achieved. Moreover, it is discussed how the thermal efficiency achieved from GO nanosheets surpasses the ones obtained from the application of particle shape nanomaterials, or carbon nanotubes in the same conditions.

Study of the Bias of the Initial Phase Estimation of a Sinewave of Known Frequency in the Presence of Phase Noise.

The estimation of the parameters of a sinusoidal signal is of paramount importance in various applications in the fields of sensors, signal processing, parameter estimation, and device characterization, among others. The presence, in the measurement system, of non-ideal phenomena such as additive noise in the signals, phase noise in the stimulus generation, jitter in the sampling system, frequency error in the experimental setup, among others, leads to increased uncertainty and bias in the estimated quantities obtained by least squares methods and those derived from them. Therefore, from a metrological point of view, it is important to be able to theoretically predict and quantify those uncertainties in order to properly design the measurement system and its parameters, such as the number of samples to acquire or the stimulus signal amplitude to use to minimize the uncertainty in the estimated values. Previous works have shown that the presence of these non-ideal phenomena leads to increased uncertainty and bias in the estimation of the sinewave amplitude. The present work complements this knowledge by focusing specifically on the effect of phase noise and sampling jitter in the bias of the initial phase estimation of a sinusoidal signal of known frequency (three‑parameter sine fitting procedure). A theoretical derivation of the bias of initial phase estimation that takes into consideration the presence of phase noise in the sinewave is presented. Since a Taylor series approximation was used where only the first term was retained, it was necessary to validate the analytical derivations with numerical simulations using a Monte Carlo type of procedure. This process was applied to different conditions regarding the phase noise standard deviation, initial phase value, and number of samples. It is concluded that, in most scenarios, initial phase estimation using sine fitting is unbiased in the presence of phase noise or jitter. It is shown, however, that in cases of extremely high phase noise standard deviation and a very low number of samples, a bias occurs.

Constraint free physics-informed machine learning for micromagnetic energy minimization

We introduce a novel method for micromagnetic energy minimization which uses physics-informed neural networks to find a magnetic configuration which minimizes the Gibbs Free energy functional without the need of any constraint optimization framework. The Cayley transform is applied to a neural network to assure that the model output lives on the Lie group of rotation matrices SO(3). For the stray field computation we use the splitting ansatz of Garcia-Cervera and Roma together with a hard constraint extreme learning machine in combination with a Taylor series approximation for very accurate evaluation of the single layer potential which only requires a very coarse discretization of the surface. Further, we present a modeling framework for constructive solid geometry which uses R-functions to exactly satisfy essential boundary conditions arising in the course of stray field computation. This framework can be applied to many other areas of interest. Our method shows promising results on the NIST μMAG Standard Problem #3, and is also applied to compute the demagnetization process of a hard magnetic Nd2Fe14B cube.

CMISR: Circular medical image super-resolution

Classical methods of medical image super-resolution (MISR) utilize open-loop architecture with implicit under-resolution (UR) unit and explicit super-resolution (SR) unit. The UR unit can always be given, assumed, or estimated, while the SR unit is elaborately designed according to various SR algorithms. The closed-loop feedback mechanism is widely employed in current MISR approaches and can efficiently improve their performance. The feedback mechanism may be divided into two categories: local feedback and global feedback. Therefore, this paper proposes a global feedback-based closed-cycle framework, circular MISR (CMISR), with unambiguous UR and advanced SR elements. Mathematical model and closed-loop equation of CMISR are built. Mathematical proof with Taylor-series approximation indicates that CMISR has zero recovery error in steady-state. In addition, CMISR holds plug-and-play characteristic that fuses model-based and learning-based approaches and can be established on any existing MISR algorithms. Five CMISR algorithms are respectively proposed based on the state-of-the-art open-loop MISR algorithms. Experimental results with three scale factors and on three open medical image datasets show that CMISR is superior to MISR in reconstruction performance and is particularly suited to medical images with strong edges or intense contrast.

A Class of Population Mean Estimators in Stratified Random Sampling: A Case Study on Fine Particulate Matter in the North of Thailand

Residents of Thailand’s upper northern have been facing hazardous air quality with the amount of fine particulate matter rising several times higher than the standards of the World Health Organization for many years which is classified as a level that severely affects public health. The dust problem is an urgent issue in Thailand that needs to be solved. Assessment of pollution data in advance can help the Thai government in planning to abolish and prevent ongoing dust problems for Thai citizens. A new class of population mean estimators is proposed under stratified random sampling. The bias and mean square error of the proposed estimators are studied using a Taylor series approximation. A simulation study and an application to air pollution data in the north of Thailand to investigate the performance of the estimators. The results from the air pollution data in the north of Thailand present that the proposed estimators offer the highest efficiency concerning others.

Fractional programming for Stackelberg game under type-2 fuzzy environment

This study intends to present a Stackelberg game model for design of the fractional type-2 fuzzy programming. In achieving this aspiration, we develop a probabilistic fuzzy multi-objective fractional linear programming where the entire parameters are of type-2 fuzzy numbers apart from the right-hand side of the constraints are follow Weibull distribution. In the projected approach, the membership function allied with each objective function is generated by using the first-order Taylor series approximation and converted into a single objective function by assuming the weights of the objective functions are equal. Type conversion is made in two ways by existing methods, and using stochastic programming, the probabilistic constraints are transformed into a deterministic form. The accessible model incorporates the non-linear programming viewpoint of the decision-maker and is solved with the help of intuitionistic fuzzy programming (IFS). A comparison study on the optimum results by genetic algorithm (GA) and particle swarm optimization (PSO) with the LINGO 15.0 iterative scheme is offered to resolve the created bi-level programming problem (BLPP) in the course of the Stackelberg game. To make obvious the feasibility of the projected representation and solution methodology, realistic data are measured and results are presented through several discussions.

Interacting Multiple Model Estimators for Fault Detection in a Magnetorheological Damper.

This paper proposes a novel estimator for the purpose of fault detection and diagnosis. The interacting multiple model (IMM) strategy is effective for estimating the behaviour of systems with multiple operating modes. Each mode corresponds to a distinct mathematical model and is subject to a filtering process. This paper applies various model-based filters in combination with the IMM strategy. One such estimator employs the recently introduced extended sliding innovation filter (ESIF) known as the IMM-ESIF. The ESIF is an extension of the sliding innovation filter for nonlinear systems based on the sliding mode concept. In the presence of modeling uncertainties, the ESIF has been proven to be more robust compared to methods such as the extended Kalman filter (EKF). The novel IMM-ESIF strategy is also compared with the IMM strategy, which incorporates the unscented Kalman filter (UKF), referred to herein as IMM-UKF. While EKF uses Taylor series approximation to linearize the system model, the UKF uses sigma point to calculate the system's mean and covariance. The methods were applied to an experimental magnetorheological (MR) damper setup, which was designed for testing control and estimation theory. Magnetorheological dampers exhibit a diverse array of applications in the automotive and aerospace sectors, with particular relevance to attenuating vibrations through adaptive suspension systems. Applied to a magnetorheological (MR) damper with distinct operating modes determined by the damper's current, the results showcase the effectiveness of IMM-ESIF. In mixed operational conditions, IMM-ESIF demonstrates a notable 80% to 90% reduction in estimation error compared to its counterparts. Furthermore, it exhibits a 4% to 5% enhancement in correctly classifying operational modes, establishing IMM-ESIF as a promising and efficient alternative for adaptive estimation in electromechanical systems. The improved accuracy in estimating the system's behaviour, even amidst uncertainties and mixed operational scenarios, signifies the potential of IMM-ESIF to significantly enhance the overall robustness and efficiency of estimations.

Numerical treatment of Burgers' equation based on weakly L-stable generalized time integration formula with the NSFD scheme

In this study, we present a weakly L-stable convergent time integration formula of order N1>3 (N1∈Z is odd) to solve Burgers' equation. The time integration formula for the initial value problem w′(t)=f(t,w),w(t0)=η0 is formulated using backward explicit Taylor series approximation of order (N1−1) and Hermite approximation polynomial of order (N1−2). We convert the Burgers' equation into the initial value problem using the nonstandard finite difference scheme for spatial derivatives and implement the derived integration formula. The nonstandard finite difference scheme makes it possible to choose several denominator functions. The method's convergence, stability and truncation error are also discussed. To show the correctness and effectiveness of the proposed technique, we present numerical solutions, ‖e‖2 and ‖e‖∞ error norms in several tables and figures. Additionally, the numerical outcomes are compared with the results of some existing techniques and exact solutions.

Tension spline approach to singularly perturbed delay differential equations involving large delay

To solve the singlularly perturbed delay differential equations of convection type, spline in tension technique is used. Taylor series approximation is used to tackle the first order derivative term involved in the problem and finally a tridiagonal scheme is obtained, which is then solved by Thomas algorithm. An example is illustrated to show the method's applicability and it is solved numerically for different values of perturbation parameter. The maximum absolute errors and rate of convergence are given in tables and it is seen that our method is of first order convergent.

Iterative Approach for Traffic Assignment with Capacity Limits using Taylor Series Approximation

This study presents a method for reaching user equilibrium in network traffic assignment problems with capacity constraints. The presented approach minimizes each user’s own travel time using a gradient-based algorithm based on the Taylor series. The algorithm is shown to converge efficiently to user equilibrium after a limited number of iterations. A numerical example is provided to demonstrate the effectiveness of the presented approach, and comparisons are made with other algorithms available in the literature. The obtained results show that the presented method is capable of reaching user equilibrium for capacity network traffic assignment problems.

Controlling periodic Fano resonances of quantum acoustic waves with a giant atom coupled to a microwave waveguide

Nanoscale Fano resonances, with applications from telecommunications to ultra-sensitive biosensing, have prompted extensive research. We demonstrate that a superconducting qubit, jointly coupled to microwave waveguides and an inter-digital transducer composite device, can exhibit acoustic Fano resonances. Our analytical framework, leveraging the Taylor series approximation, elucidates the origins of these quantum acoustic resonances with periodic Fano-like interference. By analyzing the analytical Fano parameter, we demonstrate that the Fano resonances and their corresponding Fano widths near the resonance frequency of a giant atom can be precisely controlled and manipulated by adjusting the time delay. Moreover, not just the near-resonant Fano profiles, but the entire periodic Fano resonance features can be precisely modulated from Lorentz, Fano to quasi-Lorentz shapes by tuning the coupling strength of the microwave waveguide. Our analytical framework offers insights into the control and manipulation of periodic Fano resonances in quantum acoustic waves, thereby presenting significant potential for applications such as quantum information processing, sensing, and communication.

POLYNOMIAL UTILITY

We approximate the utility function by polynomial series and solve the related dynamic portfolio optimization problems. We study the quality of the Taylor and Bernstein series approximation in response to the points and degrees of the expansions and generalize from earlier expansions applied to portfolio optimization. The issue of time inconsistency, arising from a dynamically adapted center of the expansion, is approached by equilibrium theory. We present new ways of constructing polynomial utility functions and study their pitfalls and potentials. In the numerical study, we focus on two specific utility functions: For power utility, access to the optimal portfolio allows for a complete illustration of the approximations; for the S-shaped utility function of prospect theory, the use of equilibrium theory allows for approximating the solution to the (obviously interesting but yet unsolved) case of current wealth as a dynamic reference point.

VaR Estimation with Quantum Computing Noise Correction Using Neural Networks

In this paper, we present the development of a quantum computing method for calculating the value at risk (VaR) for a portfolio of assets managed by a finance institution. We extend the conventional Monte Carlo algorithm to calculate the VaR of an arbitrary number of assets by employing random variable algebra and Taylor series approximation. The resulting algorithm is suitable to be executed in real quantum computers. However, the noise affecting current quantum computers renders them almost useless for the task. We present a methodology to mitigate the noise impact by using neural networks to compensate for the noise effects. The system combines the output from a real quantum computer with the neural network processing. The feedback is used to fine tune the quantum circuits. The results show that this approach is useful for estimating the VaR in finance institutions, particularly when dealing with a large number of assets. We demonstrate the validity of the proposed method with up to 139 assets. The accuracy of the method is also proven. We achieved an error of less than 1% in the empirical measurements with respect to the parametric model.

Approximate water vertical infiltration extremum path in unsaturated soils

According to the principle of stationary action, water vertically infiltrates unsaturated soils along an infiltration-duration extremum path with linear deviation. The solution of the Euler–Lagrange equation with appropriate boundary conditions yields a linear relationship between the moisture diffusion function and the ratio of the spatial location to the wetting front distance. By integrating the law of mass conservation at the boundary, the temporal evolution of the wetting front is implicitly derived. A linear term is introduced to compensate for the deviation in calculating the position of the wetting front owing to the Taylor series approximation. Based on the representation of the diffusion function in relation to the boundary diffusivity, the spatial location and the position of the wetting front, a direct way to determine hydraulic conductivity is presented. Unlike existing methods, the proposed approach involves fewer hypotheses and is more theoretically robust. Moreover, the material parameters in the proposed approach have a clear physical meaning and can be explicitly determined. Using the Brooks–Corey hydraulic function, the evolution and distribution characteristics of the water content are explicitly determined, while the advancing wetting front is implicitly represented. The results of the proposed solution for different types of soil are in agreement with these numerical and analytical solutions.

Local Convergence of Two Fifth Order Algorithms with Hölder Continuity Assumptions

In order to estimate the solution of the zero for the nonlinear systems, we conduct the local convergence investigation in this paper. In contrast to the Lipschitz condition used in the preceding study, we have used the Hölder continuity requirement. Additionally, we use a derivative approximation to take the derivative free iterative technique with the same order. A computed radius of convergence balls based on the Hölder constant is also provided. No Taylor's series approximation on a higher order Fréchet derivate is used in this investigation. To broaden the relevance of our work, a comparison of convergence ball radii is also provided. This highlights the uniqueness of this paper.