Search results for: dual integral equations

Authors: Elvis Adam Alhassan, Kaiyu Tian, Akos Konadu, Ernest Zamanah, Michael Jackson Adjabui, Ibrahim Justice Musah, Esther Agyeiwaa Owusu, Emmanuel K. A. Agyeman

Abstract:

In this paper, how to solve simultaneous equations using the Elvis improved method is shown. The Elvis improved method says; to make one variable in the first equation the subject; make the same variable in the second equation the subject; equate the results and simplify to obtain the value of the unknown variable; put the value of the variable found into one equation from the first or second steps and simplify for the remaining unknown variable. The difference between our Elvis improved method and the substitution method is that: with Elvis improved method, the same variable is made the subject in both equations, and the two resulting equations equated, unlike the substitution method where one variable is made the subject of only one equation and substituted into the other equation. After describing the Elvis improved method, findings from 100 secondary students and the views of 5 secondary tutors to demonstrate the effectiveness of the method are presented. The study's purpose is proved by hypothetical examples.

Keywords: simultaneous equations, substitution method, elimination method, graphical method, Elvis improved method

Procedia PDF Downloads 87

Authors: Carolina Payares-Asprino

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Dual-phase duplex stainless steel comprised of ferrite and austenite has shown high strength and corrosion resistance in many aggressive environments. Joining duplex alloys is challenging due to several embrittling precipitates and metallurgical changes during the welding process. The welding parameters strongly influence the quality of a weld joint. Therefore, it is necessary to quantify the weld bead’s integral properties as a function of welding parameters, especially when part of the weld bead is removed through a machining process due to aesthetic reasons or to couple the elements in the in-service structure. The present study uses the existing stress-strain model to predict the stress-strain curves for duplex stainless-steel welds under different welding conditions. Having mathematical expressions that predict the shape of the stress-strain curve is advantageous since it reduces the experimental work in obtaining the tensile test. In analysis and design, such stress-strain modeling simplifies the time of operations by being integrated into calculation tools, such as the finite element program codes. The elastic zone and the plastic zone of the curve can be defined by specific parameters, generating expressions that simulate the curve with great precision. There are empirical equations that describe the stress-strain curves. However, they only refer to the stress-strain curve for the stainless steel, but not when the material is under the welding process. It is a significant contribution to the applications of duplex stainless steel welds. For this study, a 3x3 matrix with a low, medium, and high level for each of the welding parameters were applied, giving a total of 27 weld bead plates. Two tensile specimens were manufactured from each welded plate, resulting in 54 tensile specimens for testing. When evaluating the four models used to predict the stress-strain curve in the welded specimens, only one model (Rasmussen) presented a good correlation in predicting the strain stress curve.

Keywords: duplex stainless steels, modeling, stress-stress curve, tensile test, welding

Procedia PDF Downloads 137

Authors: Fayad Ghawbar

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The significance of the Multiple Input Multiple Output (MIMO) system in the 5G wireless communication system is essential to enhance channel capacity and provide a high data rate resulting in a need for dual-polarization in vertical and horizontal. Furthermore, size reduction is critical in a MIMO system to deploy more antenna elements requiring a compact, low-profile design. A compact dual-band 4-MIMO antenna system has been presented in this paper with pattern and polarization diversity. The proposed single antenna structure has been designed using two antenna layers with a C shape in the front layer and a partial slot with a U-shaped cut in the ground to enhance isolation. The single antenna is printed on an FR4 dielectric substrate with an overall size of 18 mm×18 mm×1.6 mm. The 4-MIMO antenna elements were printed orthogonally on an FR4 substrate with a size dimension of 36 × 36 × 1.6 mm3 with zero edge-to-edge separation distance. The proposed compact 4-MIMO antenna elements resonate at 3.4-3.6 GHz and 4.8-5 GHz. The s-parameters measurement and simulation results agree, especially in the lower band with a slight frequency shift of the measurement results at the upper band due to fabrication imperfection. The proposed design shows isolation above -15 dB and -22 dB across the 4-MIMO elements. The MIMO diversity performance has been evaluated in terms of efficiency, ECC, DG, TARC, and CCL. The total and radiation efficiency were above 50 % across all parameters in both frequency bands. The ECC values were lower than 0.10, and the DG results were about 9.95 dB in all antenna elements. TARC results exhibited values lower than 0 dB with values lower than -25 dB in all MIMO elements at the dual-bands. Moreover, the channel capacity losses in the MIMO system were depicted using CCL with values lower than 0.4 Bits/s/Hz.

Keywords: compact antennas, MIMO antenna system, 5G communication, dual band, ECC, DG, TARC

Procedia PDF Downloads 118

Authors: Arun Goel

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Prediction of maximum local scour is necessary for the safety and economical design of the bridges. A number of equations have been developed over the years to predict local scour depth using laboratory data and a few pier equations have also been proposed using field data. Most of these equations are empirical in nature as indicated by the past publications. In this paper, attempts have been made to compute local depth of scour around bridge pier in dimensional and non-dimensional form by using linear regression, simple regression and SVM (Poly and Rbf) techniques along with few conventional empirical equations. The outcome of this study suggests that the SVM (Poly and Rbf) based modeling can be employed as an alternate to linear regression, simple regression and the conventional empirical equations in predicting scour depth of bridge piers. The results of present study on the basis of non-dimensional form of bridge pier scour indicates the improvement in the performance of SVM (Poly and Rbf) in comparison to dimensional form of scour.

Keywords: modeling, pier scour, regression, prediction, SVM (Poly and Rbf kernels)

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Authors: H. M. Al-Qassem, L. Cheng, Y. Pan

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In this paper we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log(deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Among key ingredients of our methods are an L¹→L² estimate and extrapolation.

Keywords: oscillatory singular integral, rough kernel, singular integral, Orlicz spaces, Block spaces, extrapolation, L^{p} boundedness

Procedia PDF Downloads 328

Authors: Piret Pernik

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Based on strategic, operational, and technical analysis of the ongoing armed conflict in Ukraine, this paper will examine the opportunities and risks of using small commercial drones (dual-use unmanned aerial vehicles, UAV) for military purposes. The paper discusses the opportunities and risks in the information domain, encompassing both cyber and electromagnetic interference and attacks. The paper will draw conclusions on a possible strategic impact to the battlefield outcomes in the modern armed conflicts by the widespread use of dual-use UAVs. This article will contribute to filling the gap in the literature by examining based on empirical data cyberattacks and electromagnetic interference. Today, more than one hundred states and non-state actors possess UAVs ranging from low cost commodity models, widely are dual-use, available and affordable to anyone, to high-cost combat UAVs (UCAV) with lethal kinetic strike capabilities, which can be enhanced with Artificial Intelligence (AI) and Machine Learning (ML). Dual-use UAVs have been used by various actors for intelligence, reconnaissance, surveillance, situational awareness, geolocation, and kinetic targeting. Thus they function as force multipliers enabling kinetic and electronic warfare attacks and provide comparative and asymmetric operational and tactical advances. Some go as far as argue that automated (or semi-automated) systems can change the character of warfare, while others observe that the use of small drones has not changed the balance of power or battlefield outcomes. UAVs give considerable opportunities for commanders, for example, because they can be operated without GPS navigation, makes them less vulnerable and dependent on satellite communications. They can and have been used to conduct cyberattacks, electromagnetic interference, and kinetic attacks. However, they are highly vulnerable to those attacks themselves. So far, strategic studies, literature, and expert commentary have overlooked cybersecurity and electronic interference dimension of the use of dual use UAVs. The studies that link technical analysis of opportunities and risks with strategic battlefield outcomes is missing. It is expected that dual use commercial UAV proliferation in armed and hybrid conflicts will continue and accelerate in the future. Therefore, it is important to understand specific opportunities and risks related to the crowdsourced use of dual-use UAVs, which can have kinetic effects. Technical countermeasures to protect UAVs differ depending on a type of UAV (small, midsize, large, stealth combat), and this paper will offer a unique analysis of small UAVs both from the view of opportunities and risks for commanders and other actors in armed conflict.

Keywords: dual-use technology, cyber attacks, electromagnetic warfare, case studies of cyberattacks in armed conflicts

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Authors: M. Y. Waziri, M. A. Aliyu

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The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

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Authors: Hongkui Li, Tongli Lu , Jianwu Zhang

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This paper focuses on developing an estimation method of clutch drag torque in wet DCT. The modelling of clutch drag torque is investigated. As the main factor affecting the clutch drag torque, dynamic viscosity of oil is discussed. The paper proposes an estimation method of clutch drag torque based on recursive least squares by utilizing the dynamic equations of gear shifting synchronization process. The results demonstrate that the estimation method has good accuracy and efficiency.

Keywords: clutch drag torque, wet DCT, dynamic viscosity, recursive least squares

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Authors: F. M. Ali, R. Nazar, N. M. Arifin, I. Pop

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In this paper, the problem of unsteady stagnation-point flow and heat transfer induced by a shrinking sheet in the presence of radiation effect is studied. The transformed boundary layer equations are solved numerically by the shooting method. The influence of radiation, unsteadiness and shrinking parameters, and the Prandtl number on the reduced skin friction coefficient and the heat transfer coefficient, as well as the velocity and temperature profiles are presented and discussed in detail. It is found that dual solutions exist and the temperature distribution becomes less significant with radiation parameter.

Keywords: heat transfer, radiation effect, shrinking sheet unsteady flow

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Authors: S. Habibi, T. E. Guarcia, A. Megueni, A. Ziadi, L. Aminallah, A. S. Bouchikhi

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The characterization of the microstructure of Dual Phase steel in various low-carbon, with a yield stress between 400 and 900 MPa were conducted .In order to assess the mechanical properties of steel, we examined the influence of their chemical compositions interictal and heat treatments (austenite + ferrite area) on their micro structures. In this work, we have taken a number of commercial DP steels, micro structurally characterized and used the conventional tensile testing of these steels for mechanical characterization.

Keywords: characterization, construction in civil engineering, micro structure, tensile DP steel

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Authors: Meruyert Zhassybayeva, Kuralay Yesmukhanova, Ratbay Myrzakulov

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Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found.

Keywords: Fokas-Lenells equation, integrability, soliton, the Hirota bilinear method

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Authors: S. B. Provost, Hossein Zareamoghaddam

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A univariate density approximation technique whereby the derivative of the logarithm of a density function is assumed to be expressible as a rational function is introduced. This approach which extends Pearson’s curve system is solely based on the moments of a distribution up to a determinable order. Upon solving a system of linear equations, the coefficients of the polynomial ratio can readily be identified. An explicit solution to the integral representation of the resulting density approximant is then obtained. It will be explained that when utilised in conjunction with sample moments, this methodology lends itself to the modelling of ‘big data’. Applications to sets of univariate and bivariate observations will be presented.

Keywords: density estimation, log-density, moments, Pearson's curve system

Procedia PDF Downloads 252

Authors: Jason Sheng-Hong Tsai, Faezeh Ebrahimzadeh, Min-Ching Chung, Shu-Mei Guo, Leang-San Shieh, Tzong-Jiy Tsai, Li Wang

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In this paper, we first construct a new state and disturbance estimator using discrete-time proportional plus integral observer to estimate the system state and the unknown external disturbance for the discrete-time system with an input-to-output direct-feedthrough term. Then, the generalized optimal linear quadratic digital tracker design is applied to construct a proportional plus integral observer-based tracker for the system with an unknown external disturbance to have a desired tracking performance. Finally, a numerical simulation is given to demonstrate the effectiveness of the new application of our proposed approach.

Keywords: non-minimum phase system, optimal linear quadratic tracker, proportional plus integral observer, state and disturbance estimator

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Authors: Arcady Ponosov, Ramazan Kadiev

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Input-to-State Stability (ISS) is widely used in deterministic control theory but less known in the stochastic case. Roughly speaking, the theory explains when small perturbations of the right-hand sides of the system on the entire semiaxis cause only small changes in the solutions of the system, again on the entire semiaxis. This property is crucial in many applications. In the report, we explain how to define and study ISS for systems of linear stochastic differential equations with or without delays. The central result connects ISS with the property of Lyapunov stability. This relationship is well-known in the deterministic setting, but its stochastic version is new. As an application, a method of studying asymptotic Lyapunov stability for stochastic delay equations is described and justified. Several examples are provided that confirm the efficiency and simplicity of the framework.

Keywords: asymptotic stability, delay equations, operator methods, stochastic perturbations

Procedia PDF Downloads 146

Authors: M. Nosik, I. Rymanova, N. Adamovich, S. Sevostyanihin, K. Ryzhov, Y. Kuimova, A. Kravtchenko, N. Sergeeva, A. Sobkin

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HIV and Tuberculosis (TB) infections each speed the other's progress. HIV-infection increases the risk of TB disease. At the same time, TB infection is associated with clinical progression of HIV-infection. HIV+TB co-infected patients are also at higher risk of acquiring new opportunistic infections. An important feature of disease progression and clinical outcome is the innate and acquired immune responses. HIV and TB, however, have a spectrum of dysfunctions of the immune response. As cytokines play a crucial role in the immunopathology of both infections, it is important to study immune interactions in patients with dual infection HIV+TB. Plasma levels of proinflammatory cytokines IL-2, IFN-γ and immunoregulating cytokines IL-4, IL-10 were evaluated in 75 patients with dual infection HIV+TB, 58 patients with HIV monoinfection and 50 patients with TB monoinfection who were previously naïve for HAART. The decreased levels of IL-2, IFN-γ, IL-4 and IL-10 were observed in patients with dual infection HIV+TB in comparison with patients who had only HIV or TB which means the profound suppression of Th1 and Th2 cytokine secretion. Thus, those cytokines could possibly serve as immunological markers of progression of HIV-infection in patients with TB.

Keywords: HIV, tuberculosis (TB), HIV associated with TB, Th1/ Th2 cytokine expression

Procedia PDF Downloads 331

Authors: Nader Parsazadeh

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The variety of bed sediment load relationships, insufficient information and data, and the influence of river conditions make the selection of an optimum relationship for a given river extremely difficult. Hence, in order to select the best formulae, the bed load equations should be evaluated. The affecting factors need to be scrutinized, and equations should be verified. Also, re-evaluation may be needed. In this research, sediment bed load of Dez Dam at Tal-e Zang Station has been studied. After reviewing the available references, the most common formulae were selected that included Meir-Peter and Muller, using MS Excel to compute and evaluate data. Then, 52 series of already measured data at the station were re-measured, and the sediment bed load was determined. 1. The calculated bed load obtained by different equations showed a great difference with that of measured data. 2. r difference ratio from 0.5 to 2.00 was 0% for all equations except for Nilsson and Shields equations while it was 61.5 and 59.6% for Nilsson and Shields equations, respectively. 3. By reviewing results and discarding probably erroneous measured data measurements (by human or machine), one may use Nilsson Equation due to its r value higher than 1 as an effective equation for estimating bed load at Tal-e Zang Station in order to predict activities that depend upon bed sediment load estimate to be determined. Also, since only few studies have been conducted so far, these results may be of assistance to the operators and consulting companies.

Keywords: bed load, empirical relation ship, sediment, Tale Zang Station

Procedia PDF Downloads 342

Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

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The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: closed surfaces, high-order approachs, numerical solutions, reaction-diffusion systems

Procedia PDF Downloads 339

Authors: Ophir Nave

Abstract:

In our research, we present the concept of singularly perturbed vector field (SPVF) method, and its application to thermal explosion of diesel spray combustion. Given a system of governing equations, which consist of hidden Multi-scale variables, the SPVF method transfer and decompose such system to fast and slow singularly perturbed subsystems (SPS). The SPVF method enables us to understand the complex system, and simplify the calculations. Later powerful analytical, numerical and asymptotic methods (e.g method of integral (invariant) manifold (MIM), the homotopy analysis method (HAM) etc.) can be applied to each subsystem. We compare the results obtained by the methods of integral invariant manifold and SPVF apply to spray droplets combustion model. The research deals with the development of an innovative method for extracting fast and slow variables in physical mathematical models. The method that we developed called singular perturbed vector field. This method based on a numerical algorithm applied to global quasi linearization applied to given physical model. The SPVF method applied successfully to combustion processes. Our results were compared to experimentally results. The SPVF is a general numerical and asymptotical method that reveals the hierarchy (multi-scale system) of a given system.

Keywords: polydisperse spray, model reduction, asymptotic analysis, multi-scale systems

Procedia PDF Downloads 191

Authors: J. Sharon Mano Pappu, Sathyanarayana N. Gummadi

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Growth of Debaryomyces nepalensis on mixed substrates in batch culture follows diauxic pattern of completely utilizing glucose during the first exponential growth phase, followed by an intermediate lag phase and a second exponential growth phase consuming xylose. The present study deals with the development of cybernetic mathematical model for prediction of xylitol production and yield. Production of xylitol from xylose in batch fermentation is investigated in the presence of glucose as the co-substrate. Different ratios of glucose and xylose concentrations are assessed to study the impact of multi substrate on production of xylitol in batch reactors. The parameters in the model equations were estimated from experimental observations using integral method. The model equations were solved simultaneously by numerical technique using MATLAB. The developed cybernetic model of xylose fermentation in the presence of a co-substrate can provide answers about how the ratio of glucose to xylose influences the yield and rate of production of xylitol. This model is expected to accurately predict the growth of microorganism on mixed substrate, duration of intermediate lag phase, consumption of substrate, production of xylitol. The model developed based on cybernetic modelling framework can be helpful to simulate the dynamic competition between the metabolic pathways.

Keywords: co-substrate, cybernetic model, diauxic growth, xylose, xylitol

Procedia PDF Downloads 299

Authors: Davood Yazdani Cherati, Ali Pak, Mehrdad Jafarzadeh

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This research contains the formulation of a two-dimensional analytical solution to transient heat, and moisture flow in a semi-infinite unsaturated soil environment under the influence of daily temperature changes. For this purpose, coupled energy conservation and mass fluid continuity equations governing hydrothermal behavior of unsaturated soil media are presented in terms of temperature and volumetric moisture content. In consideration of the soil environment as an infinite half-space and by linearization of the governing equations, Laplace–Fourier transformation is conducted to convert differential equations with partial derivatives (PDEs) to ordinary differential equations (ODEs). The obtained ODEs are solved, and the inverse transformations are calculated to determine the solution to the system of equations. Results indicate that heat variation induces moisture transport in both horizontal and vertical directions.

Keywords: analytical solution, heat conduction, hydrothermal analysis, laplace–fourier transformation, two-dimensional

Procedia PDF Downloads 186

Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

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The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L2. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: analytical regularization method, electromagnetic theory evolutionary equations of time-domain, TM Field

Procedia PDF Downloads 467

Authors: Raoudane Bouziyan, Kawser Mohammad Tawhid

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Microstrip antennas are low in profile, light in weight, conformable in structure and are now developed for many applications. The main difficulty of the microstrip antenna is its narrow bandwidth. Several modern applications like satellite communications, remote sensing, and multi-function radar systems will find it useful if there is dual-band antenna operating from a single aperture. Some applications require covering both transmitting and receiving frequency bands which are spaced apart. Providing multiple antennas to handle multiple frequencies and polarizations becomes especially difficult if the available space is limited as with airborne platforms and submarine periscopes. Dual band operation can be realized from a single feed using slot loaded or stacked microstrip antenna or two separately fed antennas sharing a common aperture. The former design, when used in arrays, has certain limitations like complicated beam forming or diplexing network and difficulty to realize good radiation patterns at both the bands. The second technique provides more flexibility with separate feed system as beams in each frequency band can be controlled independently. Another desirable feature of a dual band antenna is easy adjustability of upper and lower frequency bands. This thesis presents investigation of a new dual-band antenna, which is a hybrid of microstrip and waveguide radiating elements. The low band radiator is a Shorted Annular Ring (SAR) microstrip antenna and the high band radiator is an aperture antenna. The hybrid antenna is realized by forming a waveguide radiator in the shorted region of the SAR microstrip antenna. It is shown that the upper to lower frequency ratio can be controlled by the proper choice of various dimensions and dielectric material. Operation in both linear and circular polarization is possible in either band. Moreover, both broadside and conical beams can be generated in either band from this antenna element. Finite Element Method based software, HFSS and Method of Moments based software, FEKO were employed to perform parametric studies of the proposed dual-band antenna. The antenna was not tested physically. Therefore, in most cases, both HFSS and FEKO were employed to corroborate the simulation results.

Keywords: FEKO, HFSS, dual band, shorted annular ring patch

Procedia PDF Downloads 375

Authors: Mahmood Otadi, Maryam Mosleh

Abstract:

The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: A. M. Sagir

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The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software.

Keywords: block method, first order ordinary differential equations, linear multistep, self-starting

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Authors: Prodromos E. Atlamazoglou

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The method of moments combined with the method of symmetrical components is used for the analysis of interstitial hyperthermia applicators. The basis and testing functions are both piecewise sinusoids, qualifying our technique as a Galerkin one. The dielectric coatings are modeled by equivalent volume polarization currents, which are simply related to the conduction current distribution, avoiding in that way the introduction of additional unknowns or numerical integrations. The results of our method for a four dipole circular array, are in agreement with those already published in literature for a same hyperthermia configuration. Apart from being accurate, our approach is more general, more computationally efficient and takes into account the coupling between the antennas.

Keywords: hyperthermia, integral equations, insulated antennas, method of symmetrical components

Procedia PDF Downloads 236

Authors: Dong Sang Yoo

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We consider nonlinear uncertain systems such that a priori information of the uncertainties is not available. For such systems, we assume that the upper bound of the uncertainties is represented as a Fredholm integral equation of the first kind and we propose an adaptation law that is capable of estimating the upper bound and design a continuous robust control which renders nonlinear uncertain systems ultimately bounded.

Keywords: adaptive control, estimation, Fredholm integral, uncertain system

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Authors: Sara Mahesar, Saleem M. Chandio, Hira Soomro

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Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method.

Keywords: conventional Newton’s method, modified Newton’s method, order of convergence, system of nonlinear equations

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Authors: Chao-Qing Dai

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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: N. Fusun Oyman Serteller

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In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations

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Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid

Procedia PDF Downloads 282