Search results for: bi-conjugate gradient stabilized method

Authors: Mehran Naghizaderokni, Asscar Janalizadechobbasty

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This paper explores probabilistic method for assessing the liquefaction potential of sandy soils. The current simplified methods for assessing soil liquefaction potential use a deterministic safety factor in order to determine whether liquefaction will occur or not. However, these methods are unable to determine the liquefaction probability related to a safety factor. A solution to this problem can be found by reliability analysis.This paper presents a reliability analysis method based on the popular certain liquefaction analysis method. The proposed probabilistic method is formulated based on the results of reliability analyses of 190 field records and observations of soil performance against liquefaction. The results of the present study show that confidence coefficient greater and smaller than 1 does not mean safety and/or liquefaction in cadence for liquefaction, and for assuring liquefaction probability, reliability based method analysis should be used. This reliability method uses the empirical acceleration attenuation law in the Chalos area to derive the probability density distribution function and the statistics for the earthquake-induced cyclic shear stress ratio (CSR). The CSR and CRR statistics are used in continuity with the first order and second moment method to calculate the relation between the liquefaction probability, the safety factor and the reliability index. Based on the proposed method, the liquefaction probability related to a safety factor can be easily calculated. The influence of some of the soil parameters on the liquefaction probability can be quantitatively evaluated.

Keywords: liquefaction, reliability analysis, chalos area, civil and structural engineering

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Authors: B. Bouadjemia, M. Houaria, S. Haida, Y. B. Idriss, A, Akham, M. Matouguia, A. Gasmia, T. Lantria, S. Bentataa

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It have investigated the structural, optoelectronic, elastic and thermodynamic properties of KGeX₃ (X = F, Cl and Br) using the density functional theory (DFT) with generalized gradient approximation (GGA) for potential exchange correlation. The modified Becke-Johnson (mBJ-GGA) potential approximation is also used for calculating the optoelectronic properties of the material.The results show that the band structure of the metalloid halide perovskites KGeX₃ (X = F, Cl and Br) have a semiconductor behavior with direct band gap at R-R direction, the gap energy values for each compound as following: 2.83, 1.27 and 0.79eV respectively. The optical properties, such as real and imaginary parts of the dielectric functions, refractive index, reflectivity and absorption coefficient, are investigated. As results, these compounds are competent candidates for optoelectronic and photovoltaic devices in this range of the energy spectrum.

Keywords: density functional theory (DFT), semiconductor behavior, metalloid halide perovskites, optical propertie and photovoltaic devices

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Authors: Donggun Lee, Q-Han Park

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Due to its coarse grid, the Pseudo-Spectral Time Domain (PSTD) method has advantages against the Finite Difference Time Domain (FDTD) method in terms of memory requirement and operation time. However, since the efficiency of parallelization is much lower than that of FDTD, PSTD is not a useful method for a large-scale electromagnetic simulation in a parallel platform. In this paper, we propose the parallelization technique of the hybrid PSTD-FDTD (HPF) method which simultaneously possesses the efficient parallelizability of FDTD and the quick speed and low memory requirement of PSTD. Parallelization cost of the HPF method is exactly the same as the parallel FDTD, but still, it occupies much less memory space and has faster operation speed than the parallel FDTD. Experiments in distributed memory systems have shown that the parallel HPF method saves up to 96% of the operation time and reduces 84% of the memory requirement. Also, by combining the OpenMP library to the MPI library, we further reduced the operation time of the parallel HPF method by 50%.

Keywords: FDTD, hybrid, MPI, OpenMP, PSTD, parallelization

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Authors: Menouar Hanafi

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The original function of the process of platforming is to develop heavy naphtha (HSRN), coming from the atmospheric unit of distillation with a weak octane number (NO=44), to obtain a mixture of fuels â number octane raised by catalytically supporting specific groups of chemical reactions. The installation is divided into two sections: Section hydrobon. Section platforming. The rafinat coming from the bottom of column 12C2 to feed the section platforming, is divided into two parts whose flows are controlled and mixed with gas rich in hydrogen. Bottom of the column, we obtain stabilized reformat which is aspired by there pump to ensure the heating of the column whereas a part is sent towards storage after being cooled by the air cooler and the condenser. In catalytic catalyst of reforming, there is voluntarily associated a hydrogenating function-dehydrogenating, brought by platinum deposited, with an acid function brought by the alumina support (Al 2 0 3). The mechanism of action of this bifunctional catalyst depends on the severity of the operation, of the quality of the load and the type of catalyst. The catalyst used in the catalytic process of reforming is a very elaborate bifunctional catalyst whose performances are constantly improved thanks to the experimental research supported on an increasingly large comprehension of the phenomena. The American company Universel 0i1 petroleum (UOP) marketed several series of bimetallic catalysts such as R16, R20, R30, and R62 consisted Platinum/Rhenium on an acid support consisted the alumina added with a halogenous compound (chlorine).

Keywords: platforming, amelioration, octane number, catalyst

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Authors: Safia Akram

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In this article, the effects of peristaltic transport with double-diffusive convection in nanofluids through an asymmetric channel with different waveforms is presented. Mathematical modelling for two-dimensional and two directional flows of a Jeffrey fluid model along with double-diffusive convection in nanofluids are given. Exact solutions are obtained for nanoparticle fraction field, concentration field, temperature field, stream functions, pressure gradient and pressure rise in terms of axial and transverse coordinates under the restrictions of long wavelength and low Reynolds number. With the help of computational and graphical results the effects of Brownian motion, thermophoresis, Dufour, Soret, and Grashof numbers (thermal, concentration, nanoparticles) on peristaltic flow patterns with double-diffusive convection are discussed.

Keywords: nanofluid particles, peristaltic flow, Jeffrey fluid, magnetic field, asymmetric channel, different waveforms

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Authors: Elysia Barker, Jian Guo Zhou, Ling Qian, Steve Decent

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A method of modelling topography used in the simulation of riverbeds is proposed in this paper, which removes the need for datapoints and measurements of physical terrain. While complex scans of the contours of a surface can be achieved with other methods, this requires specialised tools, which the proposed method overcomes by using fractional Brownian motion (FBM) as a basis to estimate the real surface within a 15% margin of error while attempting to optimise algorithmic efficiency. This removes the need for complex, expensive equipment and reduces resources spent modelling bed topography. This method also accounts for the change in topography over time due to erosion, sediment transport, and other external factors which could affect the topography of the ground by updating its parameters and generating a new bed. The lattice Boltzmann method (LBM) is used to simulate both stationary and steady flow cases in a side-by-side comparison over the generated bed topography using the proposed method and a test case taken from an external source. The method, if successful, will be incorporated into the current LBM program used in the testing phase, which will allow an automatic generation of topography for the given situation in future research, removing the need for bed data to be specified.

Keywords: bed topography, FBM, LBM, shallow water, simulations

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Authors: Seyed Sadegh Naseralavi

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This paper presents a Kernel parallelization equation for damage identification in structures under unknown periodic excitations. Herein, the dynamic differential equation of the motion of structure is viewed as a mapping from displacements to external forces. Utilizing this viewpoint, a new method for damage detection in structures under periodic loads is presented. The developed method requires only two periods of load. The method detects the damages without finding the input loads. The method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering the concept, kernel parallelization equation (KPE) is derived for damage detection under unknown periodic loads. The method is verified for a case study under periodic loads.

Keywords: Kernel, unknown periodic load, damage detection, Kernel parallelization equation

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Authors: Eyasu Gemech, Kassa Michael, Mulugeta Atnafu

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A non-equivalent group's quasi-experiment research was conducted at Wolkite University to investigate MATLAB supported learning and students' conceptual understanding in learning Applied Mathematics II using four different comparative instructional approaches: MATLAB supported traditional lecture method, MATLAB supported collaborative method, only collaborative method, and only traditional lecture method. Four intact classes of mechanical engineering groups 1 and 2, garment engineering and textile engineering students were randomly selected out of eight departments. The first three departments were considered as treatment groups and the fourth one 'Textile engineering' was assigned as a comparison group. The departments had 30, 29, 35 and 32 students respectively. The results of the study show that there is a significant mean difference in students' conceptual understanding between groups of students learning through MATLAB supported collaborative method and the other learning approaches. Students who were learned through MATLAB technology-supported learning in combination with collaborative method were found to understand concepts of functions of two variables better than students learning through the other methods of learning. These, hence, are informative of the potential approaches universities would follow for a better students’ understanding of concepts.

Keywords: MATLAB supported collaborative method, MATLAB supported learning, collaborative method, conceptual understanding, functions of two variables

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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: Amenaghawon Clement Osemwinyen

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The Activity, Student-centred, Experiment, Improvisation - Plan, Do, See, Improve (ASEI-PDSI) method championed by the Strengthening Mathematics And Science Education (SMASE) - Nigeria Project is an attempt to improve the quality of mathematics, which has consistently declined over the years in both public primary and secondary schools across the country. The study thus assessed the ASEI-PDSI method on students’ attitudes and achievement in junior secondary schools (JSS) mathematics in FCT-Abuja. A survey research design was adopted, and 100 mathematics teachers using a stratified random sampling method were used for the study. The data were collected using structured questionnaires and analyzed using descriptive statistics. The findings showed that the ASEI-PDSI method had significantly improved the attitudes of students toward mathematics. The study also revealed that the ASEI-PDSI method significantly influenced junior secondary school (JSS) students’ mathematics achievement. Amongst the recommendations were that teachers should be encouraged to adopt the ASEI-PDSI method in teaching and learning mathematics in order to create a mathematically stimulating classroom environment which could advertently influence junior secondary school (JSS) students’ attitude and academic performance in mathematics. Also, regular in-service training programs should be organized by stakeholders (government and other interest groups) so as to improve the teaching strategies of teachers, mostly as they affect the ASEI-PDSI method.

Keywords: achievement, ASEI-PDSI method, attitude, mathematics, SMASE

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Authors: Heng Han, Zhilei Liang, Xiangong Zhou

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In this paper, the finite element method is used to study the temperature field of the main cable of the suspension bridge, and the calculation method of the average temperature of the cross-section of the main cable suitable for the construction control of the cable system is proposed; By comparing and analyzing the temperature field of the main cable with five diameters, a reasonable diameter limit for calculating the average temperature of the cross section of the main cable by finite element method is proposed. The results show that the maximum error of this method is less than 1℃, which meets the requirements of construction control accuracy; For the main cable with a diameter greater than 400mm, the surface temperature measuring points combined with the finite element method shall be used to calculate the average cross-section temperature.

Keywords: suspension bridge, main cable, temperature field, finite element

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Authors: Yuyan Yi, Jingyi Zheng, Nedret Billor

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Independent component analysis (ICA) is one of the most commonly used blind source separation (BSS) techniques for signal pre-processing, such as noise reduction and feature extraction. The main parameter in the ICA method is the number of independent components (IC). Although there have been several methods for the determination of the number of ICs, it has not been given sufficient attentionto this important parameter. In this study, wereview the mostused methods fordetermining the number of ICs and providetheir advantages and disadvantages. Further, wepropose an improved version of column-wise ICAByBlock method for the determination of the number of ICs.To assess the performance of the proposed method, we compare the column-wise ICAbyBlock with several existing methods through different ICA methods by using simulated and real signal data. Results show that the proposed column-wise ICAbyBlock is an effective and stable method for determining the optimal number of components in ICA. This method is simple, and results can be demonstrated intuitively with good visualizations.

Keywords: independent component analysis, optimal number, column-wise, correlation coefficient, cross-validation, ICAByblock

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Authors: T. Zergoug, S. E. H. Abaidia, A. Nedjar, M. Y. Mokeddem

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Physical properties of uranium di-nitride (UN2) were investigated in detail using first principles calculations based on density functional theory. To treat the strong correlation effects caused by 5f Uranium valence electrons, on-site Coulomb interaction correction via the Hubbard-like term, U (DFT+U) was employed. The UN2 structural, mechanical and thermodynamic properties were calculated within DFT and Various U of DFT+U approach. The Perdew–Burke–Ernzerhof (PBE.5.2) version of the generalized gradient approximation (GGA) is used to describe the exchange-correlation with the projector-augmented wave (PAW) pseudo potentials. A comparative study shows that results are improved by using the Hubbard formalism for a certain U value correction like the structural parameter. For some physical properties the variation versus Hubbard U is strong like Young modulus but for others it is weakly noticeable such as the density of state (DOS) or bulk modulus. We noticed also that up from U=7.5 eV, elastic results become not conform to the cubic cell elastic criteria since the C44 values turn out to be negative.

Keywords: uranium diNitride, UN2, DFT+U, elastic properties

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Authors: Wenjuan Du

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The phase compensation method was proposed based on the concept of the damping torque analysis (DTA). It is a method for the design of a PSS (power system stabilizer) to suppress local-mode power oscillations in a single-machine infinite-bus power system. This paper presents the application of the phase compensation method for the design of a PSS in a multi-machine power system. The application is achieved by examining the direct damping contribution of the stabilizer to the power oscillations. By using linearized equal area criterion, a theoretical proof to the application for the PSS design is presented. Hence PSS design in the paper is an example of stable tending control by localized method.

Keywords: phase compensation method, power system small-signal stability, power system stabilizer

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Authors: Rudra Vaghela, P. K. Kulkarni

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The aim of the present research was to develop oral Amphotericin B (AmB) nanocrystals (Nc) grafted with suitable ligand in order to enhance drug transport across the intestinal epithelial barrier and subsequently, active uptake by macrophages. AmB Nc were prepared by liquid anti-solvent precipitation technique (LAS). Poloxamer 188 was used to stabilize the prepared AmB Nc and grafted with mannose for actively targeting M cells in Peyer’s patches. To prevent shedding of the stabilizer and ligand, N,N’-Dicyclohexylcarbodiimide (DCC) was used as a cross-linker. The prepared AmB Nc were characterized for particle size, PDI, zeta potential, X-ray diffraction (XRD) and surface morphology using scanning electron microscope (SEM) and evaluated for drug content, in vitro drug release and cell uptake studies using caco-2 cells. The particle size of stabilized AmB Nc grafted with WGA was in the range of 287-417 nm with negative zeta potential between -18 to -25 mV. XRD studies revealed crystalline nature of AmB Nc. SEM studies revealed that ungrafted AmB Nc were irregular in shape with rough surface whereas, grafted AmB Nc were found to be rod-shaped with smooth surface. In vitro drug release of AmB Nc was found to be 86% at the end of one hour. Cellular studies revealed higher invasion and uptake of AmB Nc towards caco-2 cell membrane when compared to ungrafted AmB Nc. Our findings emphasize scope on developing oral delivery system for passively targeting M cells in Peyer’s patches.

Keywords: leishmaniasis, amphotericin b nanocrystals, macrophage targeting, LAS technique

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Authors: Savvas Varitis, Panagiotis Kavouras, George Kaimakamis, Eleni Pavlidou, George Vourlias, Konstantinos Chrysafis, Philomela Komninou, Theodoros Karakostas

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Tannery industry produces high quantities of chromium containing waste which also have high organic content. Processing of this waste is important since the organic content is above the disposal limits and the containing trivalent chromium could be potentially oxidized to hexavalent in the environment. This work aims to fabricate new vitreous and glass ceramic materials which could incorporate the tannery waste in stabilized form either for safe disposal or for the production of useful materials. Tannery waste was incinerated at 500oC in anoxic conditions so most of the organic content would be removed and the chromium remained trivalent. Glass forming agents SiO2, Na2O and CaO were mixed with the resulting ash in different proportions with decreasing ash content. Considering the low solubility of Cr in silicate melts, the mixtures were melted at 1400oC and/or 1500oC for 2h and then casted on a refractory steel plate. The resulting vitreous products were characterized by X-Ray Diffraction (XRD), Differential Thermal Analysis (DTA), Scanning and Transmission Electron Microscopy (SEM and TEM). XRD reveals the existence of Cr2O3 (eskolaite) crystallites embedded in a glassy amorphous matrix. Such crystallites are not formed under a certain proportion of the waste in the ash-vitrified material. Reduction of the ash proportion increases chromium content in the silicate matrix. From these glassy products, glass-ceramics were produced via different regimes of thermal treatment.

Keywords: chromium containing tannery ash, glass ceramic materials, thermal processing, vitrification

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Authors: Renata L. C. Leão, João E. Nascimento, Natalia C. E. S. Nascimento, Elaine S. Vasconcelos, Mércia L. Oliveira

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The quality control procedures of a radiopharmaceutical include the assessment of its chemical purity. The method suggested by international pharmacopeias consists of a thin layer chromatographic run. In this paper, the method proposed by the United States Pharmacopeia (USP) is compared to a direct method to determine the final concentration of aminopolyether in Fludeoxyglucose (¹⁸F-FDG) preparations. The approach (no chromatographic run) was achieved by placing the thin-layer chromatography (TLC) plate directly on an iodine vapor chamber. Both methods were validated and they showed adequate results to determine the concentration of aminopolyether in ¹⁸F-FDG preparations. However, the direct method is more sensitive, faster and simpler when compared to the reference method (with chromatographic run), and it may be chosen for use in routine quality control of ¹⁸F-FDG.

Keywords: chemical purity, Kryptofix 222, thin layer chromatography, validation

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Authors: Haniye Dehestani, Yadollah Ordokhani

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In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: collocation method, fractional partial differential equations, legendre-laguerre functions, pseudo-operational matrix of integration

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Authors: Andrey V. Timofeev

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An adaptive nonparametric method is proposed for stable real-time detection of seismoacoustic sources in multichannel C-OTDR systems with a significant number of channels. This method guarantees given upper boundaries for probabilities of Type I and Type II errors. Properties of the proposed method are rigorously proved. The results of practical applications of the proposed method in a real C-OTDR-system are presented in this report.

Keywords: guaranteed detection, multichannel monitoring systems, change point, interval estimation, adaptive detection

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Authors: Md. Fazlul Karim, Ahmad Izani Md. Ismail, Mohammed Ashaque Meah

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This paper focuses on the development of a 2-D Boundary Fitted and Nested Grid (BFNG) model to compute the tsunami propagation of Indonesian tsunami 2004 along the coastal region of Penang in Peninsular Malaysia. In the presence of a curvilinear coastline, boundary fitted grids are suitable to represent the model boundaries accurately. On the other hand, when large gradient of velocity within a confined area is expected, the use of a nested grid system is appropriate to improve the numerical accuracy with the least grid numbers. This paper constructs a shallow water nested and orthogonal boundary fitted grid model and presents computational results of the tsunami impact on the Penang coast due to the Indonesian tsunami of 2004. The results of the numerical simulations are compared with available data.

Keywords: boundary fitted nested model, tsunami, Penang Island, 2004 Indonesian Tsunami

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Authors: Wataru Nakamura, Tomoaki Hashimoto, Liang-Kuang Chen

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This paper provides a state estimation method for automatic control systems of nonlinear vehicle dynamics. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. In general, all the state variables of control systems are not precisedly known, because those variables are observed through output sensors and limited parts of them might be only measurable. Hence, automatic control systems must incorporate some type of state estimation. It is needed to establish a state estimation method for nonlinear vehicle dynamics with restricted measurable state variables. For this purpose, unscented Kalman filter method is applied in this study for estimating the state variables of nonlinear vehicle dynamics. The objective of this paper is to propose a state estimation method using unscented Kalman filter for nonlinear vehicle dynamics. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: state estimation, control systems, observer systems, nonlinear systems

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Authors: Nizar Tayem, AbuMuhammad Moinuddeen, Ahmed A. Hussain, Redha M. Radaydeh

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This research paper introduces an approach for estimating the direction of arrival (DOA) of multiple RF noncoherent sources in a uniform linear array (ULA). The proposed method utilizes a Capon-like estimation algorithm and incorporates LU decomposition to enhance the accuracy of DOA estimation while significantly reducing computational complexity compared to existing methods like the Capon method. Notably, the proposed method does not require prior knowledge of the number of sources. To validate its effectiveness, the proposed method undergoes validation through both software simulations and practical experimentation on a prototype testbed constructed using a software-defined radio (SDR) platform and GNU Radio software. The results obtained from MATLAB simulations and real-time experiments provide compelling evidence of the proposed method's efficacy.

Keywords: DOA estimation, real-time validation, software defined radio, computational complexity, Capon's method, GNU radio

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Authors: L. Giraudet, O. Simonetti, G. de Tournadre, N. Dumelié, B. Clarenc, F. Reisdorffer

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In this paper we intend to give a comprehensive view of the saturation misbehavior of thin film transistors (TFTs) based on disordered semiconductors, such as most organic TFTs, and its link to the field activation of the mobility. Experimental evidence of the field activation of the mobility is given for disordered semiconductor based TFTs, when reducing the gate length. Saturation misbehavior is observed simultaneously. Advanced transport models have been implemented in a quasi-2D numerical TFT simulation software. From the numerical simulations it is clearly established that field activation of the mobility alone cannot explain the saturation misbehavior. Evidence is given that high longitudinal field gradient at the drain end of the channel is responsible for an excess charge accumulation, preventing saturation. The two combined effects allow reproducing the experimental output characteristics of short channel TFTs, with S-shaped characteristics and saturation failure.

Keywords: mobility field activation, numerical simulation, OTFT, saturation failure

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Authors: Young Hee Geum

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We propose the numerical method defined by xn+1 = xn − λ[f(xn − μh(xn))/]f'(xn) , n ∈ N, and determine the control parameter λ and μ to converge cubically. In addition, we derive the asymptotic error constant. Applying this proposed scheme to various test functions, numerical results show a good agreement with the theory analyzed in this paper and are proven using Mathematica with its high-precision computability.

Keywords: asymptotic error constant, iterative method, multiple root, root-finding

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Authors: Yun Chol Kang, Myong Nam Kong, Nam Chol Yu, Jin Sim Kim, Un Yong Paek, Song Ho Kim

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This study focuses on the calculating approach of the thermal conductivity of 8 mol% yttria-stabilized zirconia (8YSZ) in different relative humidity corresponding to low water contents. When water content in 8YSZ is low, water droplets can accumulate in the neck regions. We assume that spherical water droplets are randomly located in the neck regions formed by grains and surrounded by the pores. Based on this, a new hypothetical pore constituted by air and water is proposed using the microstructural modeling. We consider 8YSZ is a two-phase material constituted by the solid region and the hypothetical pore region where the water droplets are penetrated in the pores, randomly. The results showed that the thermal conductivity of the hypothetical pore is calculated using the parallel resistance for low water contents, and the effective thermal conductivity of 8YSZ material constituted by solid and hypothetical pore in different relative humidities using EMPT. When the numbers of water layers on the surface of 8YSZ are less than 1.5, the proposed approach gives a good interpretation of the experimental results. When the theoretical value of the number of water layers on 8YSZ surface is 1, the water content is not enough to cover the internal solid surface completely. The proposed approach gives a better interpretation of the experimental results in different relative humidities that numbers of water layers on the surface of 8YSZ are less than 1.5.

Keywords: 8YSZ, microstructure, thermal conductivity, relative humidity

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Authors: Marcin Sowa

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The paper discusses the subinterval-based numerical method for fractional derivative computations. It is now referred to by its acronym – SubIval. The basis of the method is briefly recalled. The ability of the method to be applied in time stepping solvers is discussed. The possibility of implementing a time step size adaptive solver is also mentioned. The solver is tested on a transient circuit example. In order to display the accuracy of the solver – the results have been compared with those obtained by means of a semi-analytical method called gcdAlpha. The time step size adaptive solver applying SubIval has been proven to be very accurate as the results are very close to the referential solution. The solver is currently able to solve FDE (fractional differential equations) with various derivative orders for each equation and any type of source time functions.

Keywords: numerical method, SubIval, fractional calculus, numerical solver, circuit analysis

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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: Bing Chen, Xiang Ni, Eric Li

Abstract:

With the population ageing, the number of patients suffering from chronic diseases is increasing, among which stroke is a high incidence for the elderly. In addition, there is a gradual increase in the number of patients with orthopedic or neurological conditions such as spinal cord injuries, nerve injuries, and other knee injuries. These diseases are chronic, with high recurrence and complications, and normal walking is difficult for such patients. Nowadays, robotic knee exoskeletons have been developed for individuals with knee impairments. However, the currently available robotic knee exoskeletons are generally developed with heavyweight, which makes the patients uncomfortable to wear, prone to wearing fatigue, shortening the wearing time, and reducing the efficiency of exoskeletons. Some lightweight materials, such as carbon fiber and titanium alloy, have been used for the development of robotic knee exoskeletons. However, this increases the cost of the exoskeletons. This paper illustrates the design of a new ultra-light and ultra-stiff truss type of lattice structure. The lattice structures are arranged in a fan shape, which can fit well with circular arc surfaces such as circular holes, and it can be utilized in the design of rods, brackets, and other parts of a robotic knee exoskeleton to reduce the weight. The metamaterial is formed by continuous arrangement and combination of small truss structure unit cells, which changes the diameter of the pillar section, geometrical size, and relative density of each unit cell. It can be made quickly through additive manufacturing techniques such as metal 3D printing. The unit cell of the truss structure is small, and the machined parts of the robotic knee exoskeleton, such as connectors, rods, and bearing brackets, can be filled and replaced by gradient arrangement and non-uniform distribution. Under the condition of satisfying the mechanical properties of the robotic knee exoskeleton, the weight of the exoskeleton is reduced, and hence, the patient’s wearing fatigue is relaxed, and the wearing time of the exoskeleton is increased. Thus, the efficiency and wearing comfort, and safety of the exoskeleton can be improved. In this paper, a brief description of the hardware design of the prototype of the robotic knee exoskeleton is first presented. Next, the design of the ultra-light and ultra-stiff truss type of lattice structures is proposed, and the mechanical analysis of the single-cell unit is performed by establishing the theoretical model. Additionally, simulations are performed to evaluate the maximum stress-bearing capacity and compressive performance of the uniform arrangement and gradient arrangement of the cells. Finally, the static analysis is performed for the cell-filled rod and the unmodified rod, respectively, and the simulation results demonstrate the effectiveness and feasibility of the designed ultra-light and ultra-stiff truss type of lattice structures. In future studies, experiments will be conducted to further evaluate the performance of the designed lattice structures.

Keywords: additive manufacturing, lattice structures, metamaterial, robotic knee exoskeleton

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Authors: A. M. Sagir

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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

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

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Authors: Hadi S. Hosseini, Larry A. Taber

Abstract:

In the embryo, heart is initially a simple tubular structure that undergoes complex morphological changes as it transforms into a four-chambered pump. This work focuses on mechanisms that create heart tube (HT). The early embryo is composed of three relatively flat primary germ layers called endoderm, mesoderm, and ectoderm. Precardiac cells located within bilateral regions of the mesoderm called heart fields (HFs) fold and fuse along the embryonic midline to create the HT. The right and left halves of this plate fold symmetrically to bring their upper edges into contact along the midline, where they fuse. In a region near the fusion line, these layers then separate to generate the primitive HT and foregut, which then extend vertically. The anterior intestinal portal (AIP) is the opening at the caudal end of the foregut, which descends as the HT lengthens. The biomechanical mechanisms that drive this folding are poorly understood. Our central hypothesis is that folding is caused by differences in growth between the endoderm and mesoderm while subsequent extension is driven by contraction along the AIP. The feasibility of this hypothesis is examined using experiments with chick embryos and finite-element modeling (FEM). Fertilized white Leghorn chicken eggs were incubated for approximately 22-33 hours until appropriate Hamburger and Hamilton stage (HH5 to HH9) was reached. To inhibit contraction, embryos were cultured in media containing blebbistatin (myosin II inhibitor) for 18h. Three-dimensional models were created using ABAQUS (D. S. Simulia). The initial geometry consists of a flat plate including two layers representing the mesoderm and endoderm. Tissue was considered as a nonlinear elastic material with growth and contraction (negative growth) simulated using a theory, in which the total deformation gradient is given by F=F^*.G, where G is growth tensor and F* is the elastic deformation gradient tensor. In embryos exposed to blebbistatin, initial folding and AIP descension occurred normally. However, after HFs partially fused to create the upper part of the HT, fusion, and AIP descension stopped, and the HT failed to grow longer. These results suggest that cytoskeletal contraction is required only for the later stages of HT formation. In the model, a larger biaxial growth rate in the mesoderm compared to the endoderm causes the bilayered plate to bend ventrally, as the upper edge moves toward the midline, where it 'fuses' with the other half . This folding creates the upper section of the HT, as well as the foregut pocket bordered by the AIP. After this phase completes by stage HH7, contraction along the arch-shaped AIP pulls the lower edge of the plate downward, stretching the two layers. Results given by model are in reasonable agreement with experimental data for the shape of HT, as well as patterns of stress and strain. In conclusion, results of our study support our hypothesis for the creation of the heart tube.

Keywords: heart tube formation, FEM, chick embryo, biomechanics

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