Search results for: residual power series method

Authors: Zuhier Altawallbeh

Abstract:

This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Gebreegziabher Hailu

Abstract:

This paper presents the development of residual power series methods aimed at efficiently solving stiff differential equations, which pose significant challenges in numerical analysis due to their rapid changes in solution behavior. The RPSM is a numerical approach that generates polynomial-based approximate solutions without the need for linearization, discretization, or perturbation techniques, making it straightforward to implement and less prone to computational errors. We introduce an approach that utilizes power series expansions combined with residual minimization techniques to enhance convergence and stability. By analyzing the theoretical foundations of stiffness, we delve into the formulation of the residual power series method, detailing how it effectively captures the dynamics of stiff systems while maintaining computational efficiency. Numerical experiments demonstrate the method's superiority in terms of accuracy and computational cost when compared to traditional methods like implicit Runge-Kutta or multistep techniques. We also explore adaptive strategies within our framework to automatically adjust parameters based on the stiffness characteristics of the problem at hand. Ultimately, our findings contribute to the broader toolkit for tackling stiff differential equations, offering a robust alternative that promises to streamline computational workflows in various applied mathematics and engineering contexts.

Keywords: residual power series methods, stiff differential equoations, numerical approach, Runge Kutta methods

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Authors: Wiem Gadri

Abstract:

This study delves into the intriguing properties of Pisot and Salem numbers within the framework of formal Laurent series over finite fields, a domain where these numbers’ spectral charac-teristics, Λm(β) and lm(β), have yet to be fully explored. Utilizing a methodological approach that combines algebraic number theory with the analysis of power series, we extend the foundational work of Erdos, Joo, and Komornik to this new setting. Our research uncovers bounds for lm(β), revealing how these depend on the degree of the minimal polynomial of β and thus offering a novel characterization of Pisot and Salem formal power series. The findings significantly contribute to our understanding of these numbers, highlighting their distribution and properties in the context of formal power series. This investigation not only bridges number theory with formal power series analysis but also sets the stage for further interdisciplinary research in these areas.

Keywords: Pisot numbers, Salem numbers, formal power series, over a finite field

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Authors: D. Sersab, M. Aberkane

Abstract:

Residual stresses, in high-density polyethylene (HDPE) pipes, result from a nonhomogeneous cooling rate that occurs between the inner and outer surfaces during the extrusion process in manufacture. Most known methods of measurements to determine the magnitude and profile of the residual stresses in the pipe wall thickness are layer removal and ring slitting method. The combined layer removal and ring slitting methods described in this paper involves measurement of the circumferential residual stresses with minimal local disturbance. The existing methods used for pipe geometry (ring slitting method) gives a single residual stress value at the bore. The layer removal method which is used more in flat plate specimen is implemented with ring slitting method. The method permits stress measurements to be made directly at different depth in the pipe wall and a well-defined residual stress profile was consequently obtained.

Keywords: residual stress, layer removal, ring splitting, HDPE, wall thickness

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Authors: H. Gholami, M. Jalali Azizpour

Abstract:

For materials such as hard coating whose stresses state are difficult to obtain by a widely used method called high-speed hole-drilling method (ASTM Standard E837). It is important to develop a non contact method. This process itself imposes an additional stresses. The through thickness residual stress of st37 steel using elector-discharge was investigated. The strain gage and dynamic strain indicator used in all cases was FRS-2-11 rosette type and TML 221, respectively. The average residual stress in depth of 320 µm was -6.47 MPa.

Keywords: HVOF, residual stress, thermal spray, WC-Co

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Authors: Muhammet Emre Turan, Sait Özçelik, Yavuz Sun

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In railway rails, residual stress was measured and the values of residual stress were associated with hardness and micro structure in this study. At first, three rails as one meter long were taken and residual stresses were measured by cutting method according to the EN 13674-1 standardization. In this study, strain gauge that is an electrical apparatus was used. During the cutting, change in resistance in rail gave us residual stress value via computer program. After residual stress measurement, Brinell hardness distribution were performed for head parts of rails. Thus, the relationship between residual stress and hardness were established. In addition to that, micro structure analysis was carried out by optical microscope. The results show that, the micro structure and hardness value was changed with residual stress.

Keywords: residual stress, hardness, micro structure, rail, strain gauge

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Authors: Yong Sun, Vladimir Luzin, Zhen Qian, William J. T. Daniel, Mingxing Zhang, Shichao Ding

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The residual stresses in roll formed products are generally very high and un-predictable. This is due to the occurrence of redundant plastic deformation in roll forming process and it can cause various product defects. Although the residual stresses of a roll formed product consist of longitudinal and transverse residual stresses components, but the longitudinal residual stresses plays a key role to the product defects of a roll formed product and therefore, only the longitudinal residual stresses concerned by the roll forming scholars and engineers. However, how to inspect the residual stresses of a product quickly and economically as a routine operation is still a challenge. This paper introduces a residual stresses measurement method called slope cutting method to study the longitudinal residual stresses through layers geometrically to a roll formed products or a product with similar process such as a rolled sheet. The detailed measuring procedure is given and discussed. The residual stresses variation through the layer can be derived based on the variation of curvature in different layers and steps. The slope cutting method has been explored and validated by experimental study on a roll-formed square tube. The neutron diffraction method is applied to validate the accuracy of the newly proposed layering removal materials results. The two set results agree with each other very well and therefore, the method is expected to be a routine testing method to monitor the quality of a product been formed and that is a great impact to roll forming industry.

Keywords: roll forming, residual stress, measurement method, neutron diffraction

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Authors: L. Q. Yuan, J. Yang, A. Siddiqui

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A new regression uncertainty analysis methodology was applied to determine the uncertainties of the critical heat flux (CHF) power correlation for an advanced 43-element bundle design, which was developed by Canadian Nuclear Laboratories (CNL) to achieve improved economics, resource utilization and energy sustainability. The new methodology is considered more appropriate than the traditional methodology in the assessment of the experimental uncertainty associated with regressions. The methodology was first assessed using both the Monte Carlo Method (MCM) and the Taylor Series Method (TSM) for a simple linear regression model, and then extended successfully to a non-linear CHF power regression model (CHF power as a function of inlet temperature, outlet pressure and mass flow rate). The regression uncertainty assessed by MCM agrees well with that by TSM. An equation to evaluate the CHF power regression uncertainty was developed and expressed as a function of independent variables that determine the CHF power.

Keywords: CHF experiment, CHF correlation, regression uncertainty, Monte Carlo Method, Taylor Series Method

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Authors: N. Ravikumar, S. Krishnan, B. Yokeshkumar

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In present days, the power quality issues are increases due to non-linear loads like fridge, AC, washing machines, induction motor, etc. This power quality issues will affects the output voltages, output current, and output power of the total performance of the generator. This paper explains how to test the generator using the Fluke 435 II series power quality analyser. This Fluke 435 II series power quality analyser is used to measure the voltage, current, power, energy, total harmonic distortion (THD), current harmonics, voltage harmonics, power factor, and frequency. The Fluke 435 II series power quality analyser have several advantages. They are i) it will records output in analog and digital format. ii) the fluke analyzer will records at every 0.25 sec. iii) it will also measure all the electrical parameter at a time.

Keywords: THD, harmonics, power quality, TNEB, Fluke 435

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Authors: Lai Tzu-Hsuan, Lai Jung-Nien, Lin Jaung-Geng, Kao Shung-Te, Hsuan-Kuang Jung

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Background: Whether acupuncture therapy contributes to preserving residual renal function (RRF) remains largely unknown. This case series evidenced the potential beneficial effects of acupuncture for preserving RRF in five patients with the end-stage renal disease under hemodialysis (HD) treatment. Participants: Five patients on HD receiving eight sessions of weekly 30-min interdialytic acupuncture (Inter-A) with residual urine volume (rUV) and residual glomerular filtration rate (rGFR) recorded once every two weeks were included for analysis. Outcomes: Changes in rUV and rGFR calculated using 24-hour urine collection data were analyzed to assess RRF. Variations in hemoglobin, urea Kt/V and serum albumin levels measured monthly were analyzed to evaluate HD adequacy. Results: After eight Inter-A sessions, mean (standard deviation (SD)) rUV and rGFR increased from 612 (184) ml/day and 1.48 (.94) ml/min/1.73 m2 at baseline to 803(289) ml/day and 2.04(1.17) ml/min/1.73m2 at 2- and 4-week follow-up, respectively. The mean percentage difference increased by 31% in rUV and 38% in rGFR. Routine measurements on HD adequacy also showed improvement. Conclusions: Acupuncture might be an optional add-on treatment for HD population with poor control of water; however, further well-designed controlled trials are warranted.

Keywords: end-stage renal disease, hemodialysis, acupuncture, residual renal function, residual urine volume

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Authors: O. Abdelkhalek, A. Naimi, M. Rami, M. N. Tandjaoui, A. Kechich

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This paper deals with the active and reactive power flow analysis inside the unified power quality conditioner (UPQC) during several cases. The UPQC is a combination of shunt and series active power filter (APF). It is one of the best solutions towards the mitigation of voltage sags and swells problems on distribution network. This analysis can provide the helpful information to well understanding the interaction between the series filter, the shunt filter, the DC bus link and electrical network. The mathematical analysis is based on active and reactive power flow through the shunt and series active power filter. Wherein series APF can absorb or deliver the active power to mitigate a swell or sage voltage where in the both cases it absorbs a small reactive power quantity whereas the shunt active power absorbs or releases the active power for stabilizing the storage capacitor’s voltage as well as the power factor correction. The voltage sag and voltage swell are usually interpreted through the DC bus voltage curves. These two phenomena are introduced in this paper with a new interpretation based on the active and reactive power flow analysis inside the UPQC. For simplifying this study, a linear load is supposed in this digital simulation. The simulation results are carried out to confirm the analysis done.

Keywords: UPQC, Power flow analysis, shunt filter, series filter.

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Authors: Qian Zhao, Shi-Qi Liu, Bo Guo, Zhi-Jun Cheng, Xiao-Yue Wu

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Cold standby redundancy is considered to be an effective mechanism for improving system reliability and is widely used in industrial engineering. However, because of the complexity of the reliability structure, there is little literature studying on the residual life of cold standby system consisting of complex components. In this paper, a simulation method is presented to predict the residual life of k-out-of-n cold standby system. In practical cases, failure information of a system is either unknown, partly unknown or completely known. Our proposed method is designed to deal with the three scenarios, respectively. Differences between the procedures are analyzed. Finally, numerical examples are used to validate the proposed simulation method.

Keywords: cold standby system, k-out-of-n, residual life, simulation sampling

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Authors: Hesham A. Elkaranshawy, Amr M. Abdelrazek, Hosam M. Ezzat

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The system of ordinary nonlinear differential equations describing sliding velocity during impact with friction for a three-dimensional rigid-multibody system is developed. No analytical solutions have been obtained before for this highly nonlinear system. Hence, a power series solution is proposed. Since the validity of this solution is limited to its convergence zone, a suitable time step is chosen and at the end of it a new series solution is constructed. For a case study, the trajectory of the sliding velocity using the proposed method is built using 6 time steps, which coincides with a Runge-Kutta solution using 38 time steps.

Keywords: impact with friction, nonlinear ordinary differential equations, power series solutions, rough collision

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Authors: Pyung Soo Kim, Eung Hyuk Lee, Mun Suck Jang

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In the current paper, a residual generation filter with finite memory structure is proposed for fault detection. The proposed finite memory residual generation filter provides the residual by real-time filtering of fault vector using only the most recent finite observations and inputs on the window. It is shown that the residual given by the proposed residual generation filter provides the exact fault for noise-free systems. Finally, to illustrate the capability of the proposed residual generation filter, numerical examples are performed for the discretized DC motor system having the multiple sensor faults.

Keywords: residual generation filter, finite memory structure, kalman filter, fast detection

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Authors: Ahmad Awajan, Sadam Al Wadi

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In this study, a hybrid method based on Empirical Mode Decomposition and Holt-Winter (EMD-HW) is used to forecast Amman stock market data. First, the data are decomposed by EMD method into Intrinsic Mode Functions (IMFs) and residual components. Then, all components are forecasted by HW technique. Finally, forecasting values are aggregated together to get the forecasting value of stock market data. Empirical results showed that the EMD- HW outperform individual forecasting models. The strength of this EMD-HW lies in its ability to forecast non-stationary and non- linear time series without a need to use any transformation method. Moreover, EMD-HW has a relatively high accuracy comparing with eight existing forecasting methods based on the five forecast error measures.

Keywords: Holt-Winter method, empirical mode decomposition, forecasting, time series

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Authors: F. Husem, M. E. Turan, Y. Sun, H. Ahlatci, I. Tozlu

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Residual stress and fatigue crack growth rates are important to determine mechanical behavior of rails. This study aims to make relationship between residual stress and fatigue crack growth values in rails. For this purpose, three R260 quality rails (0.6-0.8% C, 0.6-1.25 Mn) were chosen. Residual stress of samples was measured by cutting method that is related in railway standard. Then samples were machined for fatigue crack growth test and analyze was completed according to the ASTM E647 standard which gives information about parameters of rails for this test. Microstructure characterizations were examined by Light Optic Microscope (LOM). The results showed that residual stress change with fatigue crack growth rate. The sample has highest residual stress exhibits highest crack growth rate and pearlitic structure can be seen clearly for all samples by microstructure analyze.

Keywords: residual stress, fatigue crack growth, R260, SEM, ASTM E647

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Authors: Qian Zhu, Shidong Nie, Bo Yang, Gang Xiong, Guoxin Dai

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GJ steel is a new type of high-performance structural steel which has been increasingly adopted in practical engineering. Q460GJ structural steel has a nominal yield strength of 460 MPa, which does not decrease significantly with the increase of steel plate thickness like normal structural steel. Thus, Q460GJ structural steel is normally used in medium-walled welded sections. However, research works on the residual stress in GJ steel members are few though it is one of the vital factors that can affect the member and structural behavior. This article aims to investigate the residual stresses in welded I-shaped sections fabricated from Q460GJ structural steel plates by experimental tests. A total of four full scale welded medium-walled I-shaped sections were tested by sectioning method. Both circular curve correction method and straightening measurement method were adopted in this study to obtain the final magnitude and distribution of the longitudinal residual stresses. In addition, this paper also explores the interaction between flanges and webs. And based on the statistical evaluation of the experimental data, a multilayer residual stress model is proposed.

Keywords: Q460GJ structural steel, residual stresses, sectioning method, welded medium-walled I-shaped sections

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Authors: M. Jalali Azizpour, H. Mohammadi Majd, A.R. Aboudi Asl, D. Sajedipour, V. Tawaf

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Sandblasting is a generally used surface treatment technique to improve the residual stress and adhesion of coatings to substrate. The goal of this work is to study the effect of temperature on the residual stress in sandblasting AISI1045 substrate. For this purpose a two dimensional axisymmetric model of shot impacting on an AISI 1045 disc was generated using ABAQUS version 6.10. The result shows for sandblasting temperature there is an optimum condition. In addition there are other effective factors that influence the fatigue life of parts.

Keywords: modeling, shot peen, residual stress, temperature

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Authors: Chen-Yin Kuo, Yung-Hsin Lee

Abstract:

Previous studies applying residual income valuation (RIV) model generally use panel data and single-equation model to forecast stock prices. Unlike these, this paper uses Taiwan longitudinal data to estimate multi-equation time-series models such as Vector Autoregressive (VAR), Vector Error Correction Model (VECM), and conduct out-of-sample forecasting. Further, this work assesses their forecasting performance by two instruments. In favor of extant research, the major finding shows that VECM outperforms other three models in forecasting for three stock sectors over entire horizons. It implies that an error correction term containing long-run information contributes to improve forecasting accuracy. Moreover, the pattern of composite shows that at longer horizon, VECM produces the greater reduction in errors, and performs substantially better than VAR.

Keywords: residual income valuation model, vector error correction model, out of sample forecasting, forecasting accuracy

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Authors: Xiang Jia, Zhijun Cheng

Abstract:

The residual lifetime of a product is the operation time between the current time and the time point when the failure happens. The residual lifetime estimation is rather important in reliability analysis. To predict the residual lifetime, it is necessary to assume or verify a particular distribution that the lifetime of the product follows. And the two-parameter Weibull distribution is frequently adopted to describe the lifetime in reliability engineering. Due to the time constraint and cost reduction, a life testing experiment is usually terminated before all the units have failed. Then the censored data is usually collected. In addition, other information could also be obtained for reliability analysis. The expert judgements are considered as it is common that the experts could present some useful information concerning the reliability. Therefore, the residual lifetime is estimated for Weibull distribution by fusing the censored data and expert judgements in this paper. First, the closed-forms concerning the point estimate and confidence interval for the residual lifetime under the Weibull distribution are both presented. Next, the expert judgements are regarded as the prior information and how to determine the prior distribution of Weibull parameters is developed. For completeness, the cases that there is only one, and there are more than two expert judgements are both focused on. Further, the posterior distribution of Weibull parameters is derived. Considering that it is difficult to derive the posterior distribution of residual lifetime, a sample-based method is proposed to generate the posterior samples of Weibull parameters based on the Monte Carlo Markov Chain (MCMC) method. And these samples are used to obtain the Bayes estimation and credible interval for the residual lifetime. Finally, an illustrative example is discussed to show the application. It demonstrates that the proposed method is rather simple, satisfactory, and robust.

Keywords: expert judgements, information fusion, residual lifetime, Weibull distribution

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Authors: M. Gazzah, B. Jaouachi, F. Sakli

Abstract:

This research focuses on the yarn-to-yarn and metal-to-fabric friction effects on the residual bagging behavior expressed by residual bagging height, volume and recovery of some denim fabrics. The results show, that both residual bagging height and residual bagging volume, which is determined using image analysis method, are significantly affected due to the most influential fabric parameter variations, the weft yarns density and the mean frictional coefficients. After the applied number of fatigue cycles, the findings revealed that the weft yarn rigidity contributes on fabric bagging behavior accurately. Among the tested samples, our results show that the elastic fabrics present a high recovery ability to give low bagging height and volume values.

Keywords: bagging recovery, denim fabric, metal-to-fabric friction, residual bagging height, yarn-to-yarn friction

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Authors: Danladi Ali, Onah Festus Iloabuchi

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In this paper, GSM signal strength was measured in order to detect the type of the signal fading phenomenon using one-dimensional multilevel wavelet residual method and neural network clustering to determine the average GSM signal strength received in the study area. The wavelet residual method predicted that the GSM signal experienced slow fading and attenuated with MSE of 3.875dB. The neural network clustering revealed that mostly -75dB, -85dB and -95dB were received. This means that the signal strength received in the study is a weak signal.

Keywords: one-dimensional multilevel wavelets, path loss, GSM signal strength, propagation, urban environment

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Authors: J. S. Savier

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Real power is the component power which is converted into useful energy whereas reactive power is the component of power which cannot be converted to useful energy but it is required for the magnetization of various electrical machineries. If the reactive power is compensated at the consumer end, the need for reactive power flow from generators to the load can be avoided and hence the overall power loss can be reduced. In this scenario, this paper presents a succinct method called JSS method for allocation of reactive power losses to consumers connected to radial distribution networks in a deregulated environment. The proposed method has the advantage that no assumptions are made while deriving the reactive power loss allocation method.

Keywords: deregulation, reactive power loss allocation, radial distribution systems, succinct method

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Authors: Meihua Fang, Tao Fei

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Post-processing can effectively improve the resistance to laser damage in multilayer films used in a high power laser system. In this work, HfO₂/SiO₂ multilayer films are prepared by e-beam evaporation and then β-ray irradiation is employed as the post-processing method. The particle irradiation affects the laser induced damage threshold (LIDT), which includes defects, surface roughness, packing density, and residual stress. The residual stress that is relaxed during irradiation changes from compressive stress into tensile stress. Our results indicate that appropriate tensile stress can improve LIDT remarkably. In view of the fact that LIDT rises from 8 J/cm² to 12 J/cm², i.e., 50% increase, after the film has been irradiated by 2.2×10¹³/cm² β-ray, the particle irradiation can be used as a controllable and desirable post-processing method to improve the resistance to laser induced damage.

Keywords: β-ray irradiation, multilayer film, residual stress, laser-induced damage threshold

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Authors: Ahmad Moussavi

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In this paper, we are concerned with the Jacobson semisimple skew inverse Laurent series rings R((x−1; α, δ)) and the skew Laurent power series rings R[[x, x−1; α]], where R is an associative ring equipped with an automorphism α and an α-derivation δ. Examples to illustrate and delimit the theory are provided.

Keywords: skew polynomial rings, Laurent series, skew inverse Laurent series rings

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Authors: M. A. Askari, M. A. Nazari, P. Perrier, Y. Payan

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Growth and remodeling of biological structures have gained lots of attention over the past decades. Determining the response of living tissues to mechanical loads is necessary for a wide range of developing fields such as prosthetics design or computerassisted surgical interventions. It is a well-known fact that biological structures are never stress-free, even when externally unloaded. The exact origin of these residual stresses is not clear, but theoretically, growth is one of the main sources. Extracting body organ’s shapes from medical imaging does not produce any information regarding the existing residual stresses in that organ. The simplest cause of such stresses is gravity since an organ grows under its influence from birth. Ignoring such residual stresses might cause erroneous results in numerical simulations. Accounting for residual stresses due to tissue growth can improve the accuracy of mechanical analysis results. This paper presents an original computational framework based on gradual growth to determine the residual stresses due to growth. To illustrate the method, we apply it to a finite element model of a healthy human face reconstructed from medical images. The distribution of residual stress in facial tissues is computed, which can overcome the effect of gravity and maintain tissues firmness. Our assumption is that tissue wrinkles caused by aging could be a consequence of decreasing residual stress and thus not counteracting gravity. Taking into account these stresses seems therefore extremely important in maxillofacial surgery. It would indeed help surgeons to estimate tissues changes after surgery.

Keywords: finite element method, growth, residual stress, soft tissue

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Authors: Mahdi Daghmhehci Firoozjaei, Minchang Kim, Dima Alhadidi

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In this paper, we present a power profiling model for smart grid consumers based on real time load data acquired smart meters. It profiles consumers’ power consumption behaviour using the dynamic time warping (DTW) clustering algorithm. Due to the invariability of signal warping of this algorithm, time-disordered load data can be profiled and consumption features be extracted. Two load types are defined and the related load patterns are extracted for classifying consumption behaviour by DTW. The classification methodology is discussed in detail. To evaluate the performance of the method, we analyze the time-series load data measured by a smart meter in a real case. The results verify the effectiveness of the proposed profiling method with 90.91% true positive rate for load type clustering in the best case.

Keywords: power profiling, user privacy, dynamic time warping, smart grid

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Authors: Arvind Dhingra, Ashwani Kumar Sharma

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Power quality is an important parameter for today’s consumers. Various custom power devices are in use to give a proper supply of power quality. Dynamic Voltage Restorer is one such custom power device. DVR is a static VAR device which is used for series compensation. It is a power electronic device that is used to inject a voltage in series and in synchronism to compensate for the sag in voltage. Inductive Loads are a major source of power quality distortion. The induction furnace is one such typical load. A typical induction furnace is used for melting the scrap or iron. At the time of starting the melting process, the power quality is distorted to a large extent especially with the induction of harmonics. DVR is one such approach to mitigate these harmonics. This paper is an attempt to overview the various control strategies being followed for control of power quality by using DVR. An overview of control of harmonics using DVR is also presented.

Keywords: DVR, power quality, harmonics, harmonic mitigation

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

Abstract:

A method to obtain analytic approximations for special function of interest in engineering and physics is described here. Each approximate function will be valid for every positive value of the variable and accuracy will be high and increasing with the number of parameters to determine. The general technique will be shown through an application to the modified Bessel function of order zero, I₀(x). The form and the calculation of the parameters are performed with the simultaneous use of the power series and asymptotic expansion. As in Padé method rational functions are used, but now they are combined with other elementary functions as; fractional powers, hyperbolic, trigonometric and exponential functions, and others. The elementary function is determined, considering that the approximate function should be a bridge between the power series and the asymptotic expansion. In the case of the I₀(x) function two analytic approximations have been already determined. The simplest one is (1+x²/4)⁻¹/⁴(1+0.24273x²) cosh(x)/(1+0.43023x²). The parameters of I₀(x) were determined using the leading term of the asymptotic expansion and two coefficients of the power series, and the maximum relative error is 0.05. In a second case, two terms of the asymptotic expansion were used and 4 of the power series and the maximum relative error is 0.001 at x≈9.5. Approximations with much higher accuracy will be also shown. In conclusion a new technique is described to obtain analytic approximations to some functions of interest in sciences, such that they have a high accuracy, they are valid for every positive value of the variable, they can be integrated and differentiated as the usual, functions, and furthermore they can be calculated easily even with a regular pocket calculator.

Keywords: analytic approximations, mathematical-physics applications, quasi-rational functions, special functions

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Authors: Naimi Abdelhamid, Othmane Abdelkhalek

Abstract:

With the current rise in the demand of electrical energy, present-day power systems which are large and complex, will continue to grow in both size and complexity. Flexible AC Transmission System (FACTS) controllers provide new facilities, both in steady state power flow control and dynamic stability control. Thyristor Controlled Series Capacitor (TCSC) is one of FACTS equipment, which is used for power flow control of active power in electric power system and for increase of capacities of transmission lines. In this paper, a Backstepping Power Flow Controller (BPFC) for TCSC in multimachine power system is developed and tested. The simulation results show that the TCSC proposed controller is capable of controlling the transmitted active power and improving the transient stability when compared with conventional PI Power Flow Controller (PIPFC).

Keywords: FACTS, thyristor controlled series capacitor (TCSC), backstepping, BPFC, PIPFC

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