Search results for: nonlinear Takagi’s equations

Authors: Pei-Jyun Hsieh, Cheng-Hsuan Li, Bor-Chen Kuo

Abstract:

For hyperspectral image classification, feature reduction is an important pre-processing for avoiding the Hughes phenomena due to the difficulty for collecting training samples. Hence, lots of researches developed feature selection methods such as F-score, HSIC (Hilbert-Schmidt Independence Criterion), and etc., to improve hyperspectral image classification. However, most of them only consider the class separability in the original space, i.e., a linear class separability. In this study, we proposed a nonlinear class separability measure based on kernel trick for selecting an appropriate feature subset. The proposed nonlinear class separability was formed by a generalized RBF kernel with different bandwidths with respect to different features. Moreover, it considered the within-class separability and the between-class separability. A genetic algorithm was applied to tune these bandwidths such that the smallest with-class separability and the largest between-class separability simultaneously. This indicates the corresponding feature space is more suitable for classification. In addition, the corresponding nonlinear classification boundary can separate classes very well. These optimal bandwidths also show the importance of bands for hyperspectral image classification. The reciprocals of these bandwidths can be viewed as weights of bands. The smaller bandwidth, the larger weight of the band, and the more importance for classification. Hence, the descending order of the reciprocals of the bands gives an order for selecting the appropriate feature subsets. In the experiments, three hyperspectral image data sets, the Indian Pine Site data set, the PAVIA data set, and the Salinas A data set, were used to demonstrate the selected feature subsets by the proposed nonlinear feature selection method are more appropriate for hyperspectral image classification. Only ten percent of samples were randomly selected to form the training dataset. All non-background samples were used to form the testing dataset. The support vector machine was applied to classify these testing samples based on selected feature subsets. According to the experiments on the Indian Pine Site data set with 220 bands, the highest accuracies by applying the proposed method, F-score, and HSIC are 0.8795, 0.8795, and 0.87404, respectively. However, the proposed method selects 158 features. F-score and HSIC select 168 features and 217 features, respectively. Moreover, the classification accuracies increase dramatically only using first few features. The classification accuracies with respect to feature subsets of 10 features, 20 features, 50 features, and 110 features are 0.69587, 0.7348, 0.79217, and 0.84164, respectively. Furthermore, only using half selected features (110 features) of the proposed method, the corresponding classification accuracy (0.84168) is approximate to the highest classification accuracy, 0.8795. For other two hyperspectral image data sets, the PAVIA data set and Salinas A data set, we can obtain the similar results. These results illustrate our proposed method can efficiently find feature subsets to improve hyperspectral image classification. One can apply the proposed method to determine the suitable feature subset first according to specific purposes. Then researchers can only use the corresponding sensors to obtain the hyperspectral image and classify the samples. This can not only improve the classification performance but also reduce the cost for obtaining hyperspectral images.

Keywords: hyperspectral image classification, nonlinear feature selection, kernel trick, support vector machine

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Authors: Mohamad Amin Amini, Mehdi Poursha

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Nonlinear response history analysis (NL-RHA) is a robust analytical tool for estimating the seismic demands of structures responding in the inelastic range. However, because of its conceptual and numerical complications, the nonlinear static procedure (NSP) is being increasingly used as a suitable tool for seismic performance evaluation of structures. The conventional pushover analysis methods presented in various codes (FEMA 356; Eurocode-8; ATC-40), are limited to the first-mode-dominated structures, and cannot take higher modes effect into consideration. Therefore, since more than a decade ago, researchers developed enhanced pushover analysis procedures to take higher modes effect into account. The main objective of this study is to propose an enhanced invariant lateral displacement distribution to take higher modes effect into consideration in performing a displacement-based pushover analysis, whereby a set of laterally applied displacements, rather than forces, is monotonically applied to the structure. For this purpose, the effect of different parameters such as the spectral displacement of ground motion, the modal participation factor, and the effective modal participating mass ratio on the lateral displacement distribution is investigated to find the best distribution. The major simplification of this procedure is that the effect of higher modes is concentrated into a single invariant lateral load distribution. Therefore, only one pushover analysis is sufficient without any need to utilize a modal combination rule for combining the responses. The invariant lateral displacement distribution for pushover analysis is then calculated by combining the modal story displacements using the modal combination rules. The seismic demands resulting from the different procedures are compared to those from the more accurate nonlinear response history analysis (NL-RHA) as a benchmark solution. Two structures of different heights including 10 and 20-story special steel moment resisting frames (MRFs) were selected and evaluated. Twenty ground motion records were used to conduct the NL-RHA. The results show that more accurate responses can be obtained in comparison with the conventional lateral loads when the enhanced modal lateral displacement distributions are used.

Keywords: displacement-based pushover, enhanced lateral load distribution, higher modes effect, nonlinear response history analysis (NL-RHA)

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Authors: Alireza Abdikian

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By assuming a quantum relativistic degenerate electron-positron (e-p) plasma media, the nonlinear acoustic solitary propagation in the presence of the stationary ions for neutralizing the plasma background of bounded cylindrical geometry was investigated. By using the standard reductive perturbation technique with cooperation the quantum hydrodynamics model for the e-p fluid, the spherical Kadomtsev-Petviashvili equation was derived for small but finite amplitude waves and was given the solitary wave solution for the parameters relevant for dense astrophysical objects such as white dwarf stars. By using a suitable coordinate transformation and using improved F-expansion technique, the SKP equation can be solved analytically. The numerical results reveal that the relativistic effects lead to propagate the electrostatic bell shape structures and by increasing the relativistic effects, the amplitude and the width of the e-p acoustic solitary wave will decrease.

Keywords: Electron-positron plasma, Acoustic solitary wave, Relativistic plasmas, the spherical Kadomtsev-Petviashvili equation

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Authors: M. Najafi, S. Bab, F. Rahimi Dehgolan

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The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations.

Keywords: super harmonic resonances, non-linear vibration, axially moving beam, Galerkin method

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Authors: Gebreegziabher Hailu

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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: Djemai Bara, Mohamed Faouzi Mahboub, Djamila Bennaceur-Doumaz

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In this work, the role of the preformed plasma created on the front face of a target, irradiated by a high intensity short pulse laser, in the framework of ion acceleration process, modeled by Target Normal Sheath Acceleration (TNSA) mechanism, is studied. This plasma is composed of cold ions governed by fluid equations and non-thermal & trapped with densities represented by a "Cairns-Gurevich" equation. The self-similar solution of the equations shows that electronic trapping and the presence of non-thermal electrons in the pre-plasma are both responsible in ion acceleration as long as the proportion of energetic electrons is not too high. In the case where the majority of electrons are energetic, the electrons are accelerated directly by the ponderomotive force of the laser without the intermediate of an accelerating plasma wave.

Keywords: Cairns-Gurevich Equation, ion acceleration, plasma expansion, pre-plasma

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Authors: George Mahalu

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The Chua diode has been configured over time in various ways, using electronic structures like as operational amplifiers (OAs) or devices with gas or semiconductors. When discussing the use of semiconductor devices, tunnel diodes (Esaki diodes) are most often considered, and more recently, transistorized configurations such as lambda diodes. The paper-work proposed here uses in the modeling a lambda diode type configuration consisting of two Junction Field Effect Transistors (JFET). The original scheme is created in the MULTISIM electronic simulation environment and is analyzed in order to identify the conditions for the appearance of evolutionary unpredictability specific to nonlinear dynamic systems with chaos-induced behavior. The chaotic deterministic oscillator is one autonomous type, a fact that places it in the class of Chua’s type oscillators, the only significant and most important difference being the presence of a nonlinear device like the one mentioned structure above. The chaotic behavior is identified both by means of strange attractor-type trajectories and visible during the simulation and by highlighting the hypersensitivity of the system to small variations of one of the input parameters. The results obtained through simulation and the conclusions drawn are useful in the further research of ways to implement such constructive electronic solutions in theoretical and practical applications related to modern small signal amplification structures, to systems for encoding and decoding messages through various modern ways of communication, as well as new structures that can be imagined both in modern neural networks and in those for the physical implementation of some requirements imposed by current research with the aim of obtaining practically usable solutions in quantum computing and quantum computers.

Keywords: chaos, lambda diode, strange attractor, nonlinear system

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Authors: Feng Yang

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Machine learning (ML), especially deep learning (DL), has been extensively applied to many applications in recently years and gained great success in solving different problems, including scientific problems. However, conventional ML/DL methodologies are purely data-driven which have the limitations, such as need of ample amount of labelled training data, lack of consistency to physical principles, and lack of generalizability to new problems/domains. Recently, there is a growing consensus that ML models need to further take advantage of prior knowledge to deal with these limitations. Physics-informed machine learning, aiming at integration of physics/domain knowledge into ML, has been recognized as an emerging area of research, especially in the recent 2 to 3 years. In this work, physics-informed ML, specifically physics-informed neural network (NN), is employed and implemented to estimate the displacements at x, y, z directions in a solid mechanics problem that is controlled by equilibrium equations with boundary conditions. By incorporating the physics (i.e. the equilibrium equations) into the learning process of NN, it is showed that the NN can be trained very efficiently with a small set of labelled training data. Experiments with different settings of the NN model and the amount of labelled training data were conducted, and the results show that very high accuracy can be achieved in fulfilling the equilibrium equations as well as in predicting the displacements, e.g. in setting the overall displacement of 0.1, a root mean square error (RMSE) of 2.09 × 10−4 was achieved.

Keywords: deep learning, neural network, physics-informed machine learning, solid mechanics

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Authors: Huai-Cong Liu，Tae Chul Jeong，Ju Lee

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This paper describes characteristic analysis of a synchronous reluctance motor (SynRM)’s rotor with the Multi-segment and Multi-layer structure. The magnetic-saturation phenomenon in SynRM is often appeared. Therefore, when modeling analysis of SynRM the calculation of nonlinear magnetic field needs to be considered. An important influence factor on the convergence process is how to determine the relative permeability. An improved method, which ensures the calculation, is convergence by linear iterative method for saturated magnetic field. If there are inflection points on the magnetic curve,an optimum convergence method of solution for nonlinear magnetic field was provided. Then the equivalent magnetic circuit is calculated, and d,q-axis inductance can be got. At last, this process is applied to design a 7.5Kw SynRM and its validity is verified by comparing with the result of finite element method (FEM) and experimental test data.

Keywords: SynRM, magnetic-saturation, magnetic circuit, analytical modeling

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Authors: Abdi Ammar, Ouazir Youcef, Laissaoui Abdelmalek

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In this work, an approach based on transmission lines theory is presented. It is exploited for the calculation of overvoltage created by direct impacts of lightning waves on a guard cable of an overhead high-voltage line. First, we show the theoretical developments leading to the propagation equation, its discretization by finite difference time domain method (FDTD), and the resulting linear algebraic equations, followed by the calculation of the linear parameters of the line. The second step consists of solving the transmission lines system of equations by the FDTD method. This enabled us to determine the spatio-temporal evolution of the induced overvoltage.

Keywords: lightning surge, transient overvoltage, eddy current, FDTD, electromagnetic compatibility, ground wire

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Authors: M. M. Atashi, P. Malekzadeh

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A first known formulation for the out-of-plane free vibration analysis of functionally graded (FG) circular curved beams in thermal environment and with temperature dependent material properties is presented. The formulation is based on the first order shear deformation theory (FSDT), which includes the effects of shear deformation and rotary inertia due to both torsional and flexural vibrations. The material properties are assumed to be temperature dependent and graded in the direction normal to the plane of the beam curvature. The equations of motion and the related boundary conditions, which include the effects of initial thermal stresses, are derived using the Hamilton’s principle. Differential quadrature method (DQM), as an efficient and accurate numerical method, is adopted to solve the thermoelastic equilibrium equations and the equations of motion. The fast rate of convergence of the method is investigated and the formulations are validated by comparing the results in the limit cases with the available solutions in the literature for isotropic circular curved beams. In addition, for FG circular curved beams with soft simply supported edges, the results are compared with the obtained exact solutions. Then, the effects of temperature rise, boundary conditions, material and geometrical parameters on the natural frequencies are investigated.

Keywords: out of plane, free vibration, curved beams, functionally graded, thermal environment

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Authors: Edward J. Kansa, Pavel Holoborodko

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Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

Keywords: partial differential equations, Meshfree radial basis functions, , no restrictions on spatial dimensions, Extended arithmetic precision.

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Authors: Camille A. Issa, Omar Masri

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In the study, the commercial finite element software Abaqus was used to develop a three-dimensional nonlinear finite element model capable of simulating the pull-out test of reinforcing bars from underwater concrete. The results of thirty-two pull-out tests that have different parameters were implemented in the software to study the effect of the concrete cover, the bar size, the use of stirrups, and the compressive strength of concrete. The interaction properties used in the model provided accurate results in comparison with the experimental bond-slip results, thus the model has successfully simulated the pull-out test. The results of the finite element model are used to better understand and visualize the distribution of stresses in each component of the model, and to study the effect of the various parameters used in this study including the role of the stirrups in preventing the stress from reaching to the sides of the specimens.

Keywords: pull-out test, bond strength, underwater concrete, nonlinear finite element analysis, abaqus

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Authors: Elena M. Kopteva, Pavlina Jaluvkova, Zdenek Stuchlik

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In spite of the numerous attempts to close the discussion about the influence of cosmological expansion on local gravitationally bounded systems, this question arises in literature again and again and remains still far from its final resolution. Here one of the main problems is the problem of obtaining a physically adequate model of strongly gravitating object immersed in non-static cosmological background. Such objects are usually called ‘cosmological’ black holes and are of great interest in wide set of cosmological and astrophysical areas. In this work the set of new exact solutions of the Einstein equations is derived for the flat space that generalizes the known Lemaitre-Tolman-Bondi solution for the case of nonzero pressure. The solutions obtained are pretending to describe the black hole immersed in nonstatic cosmological background and give a possibility to investigate the hot problems concerning the effects of the cosmological expansion in gravitationally bounded systems, the structure formation in the early universe, black hole thermodynamics and other related problems. It is shown that each of the solutions obtained contains either the Reissner-Nordstrom or the Schwarzschild black hole in the central region of the space. It is demonstrated that the approach of the mass function use in solving of the Einstein equations allows clear physical interpretation of the resulting solutions, that is of much benefit to any their concrete application.

Keywords: exact solutions of the Einstein equations, cosmological black holes, generalized Lemaitre-Tolman-Bondi solutions, nonzero pressure

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Authors: Weihua Ruan, Kuan-Chou Chen

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This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.

Keywords: Hamilton-Jacobi-Bellman equations, infinite-horizon differential games, continuous and discrete state variables, political-economy models

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Authors: M. S. H. Chowdhury, Ishak Hashim

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In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the classical Adomian decomposition method (ADM) and the multi-stage Adomian decomposition method (MADM). The MADM is a technique adapted from the standard Adomian decomposition method (ADM) where standard ADM is converted into a hybrid numeric-analytic method called the multistage ADM (MADM). The MADM is tested for several examples. Comparisons with an explicit Runge-Kutta-type method (RK) and the classical ADM demonstrate the limitations of ADM and promising capability of the MADM for solving stiff initial value problems (IVPs).

Keywords: stiff system of ODEs, Runge-Kutta Type Method, Adomian decomposition method, Multistage ADM

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Authors: Tehreem Fatima, Enjun Xia

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The research investigates the relationship between total oil consumption and transport oil consumption, GDP, oil price, and oil reserve in order to forecast future oil demand in China. Annual time series data is used over the period of 1980 to 2015, and for this purpose, an oil demand function is estimated by applying structural time series model (STSM). The technique also uncovers the Underline energy demand trend (UEDT) for China oil demand and GDP, oil reserve, oil price and UEDT are considering important drivers of China oil demand. The long-run elasticity of total oil consumption with respect to GDP and price are (0.5, -0.04) respectively while GDP, oil reserve, and price remain (0.17; 0.23; -0.05) respectively. Moreover, the Estimated results of long-run elasticity of transport oil consumption with respect to GDP and price are (0.5, -0.00) respectively long-run estimates remain (0.28; 37.76;-37.8) for GDP, oil reserve, and price respectively. For both model estimated underline energy demand trend (UEDT) remains nonlinear and stochastic and with an increasing trend of (UEDT) and based on estimated equations, it is predicted that China total oil demand somewhere will be 9.9 thousand barrel per day by 2025 as compare to 9.4 thousand barrel per day in 2015, while transport oil demand predicting value is 9.0 thousand barrel per day by 2020 as compare to 8.8 thousand barrel per day in 2015.

Keywords: china, forecasting, oil, structural time series model (STSM), underline energy demand trend (UEDT)

Procedia PDF Downloads 283

Authors: Alireza Toloei, Ahmad R. Saffary, Reza Ghasemi

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Due to the growing need for energy and limited fossil resources, the use of renewable energy, particularly wind is strongly favored. We all wind energy can’t be saved. Betz law, 59% of the total kinetic energy of the wind turbine is extracting. Therefore turbine control to achieve maximum performance and maintain stable conditions seem necessary. In this article, we plan for a horizontal axis wind turbine variable-speed variable-pitch nonlinear controller to obtain maximum output power. The model presented in this article, including a wide range of wind turbines are horizontal axis. However, the parameters used in this model is from Vestas V29 225 kW wind turbine. We designed second order sliding mode controller, which was robust in the face of changes in wind speed and it eliminated chattering by using of super twisting algorithm. Finally, using MATLAB software to simulate the results we considered the accuracy of the simulation results.

Keywords: non linear controller, robust, sliding mode, kinetic energy

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Authors: E. Keramaris, V. Kanakoudis

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In this study the water flow in an open channel over a sharp-crested weir is investigated experimentally. For this reason a series of laboratory experiments were performed in an open channel with a sharp-crested weir. The maximum head expected over the weir, the total upstream water height and the downstream water height of the impact in the constant bed of the open channel were measured. The discharge was measured using a tank put right after the open channel. In addition, the discharge and the upstream velocity were also calculated using already known equations. The main finding is that the relative error percentage for the majority of the experimental measurements is ± 4%, meaning that the calculation of the discharge with a sharp-crested weir gives very good results compared to the numerical results from known equations.

Keywords: sharp-crested weir, weir height, flow measurement, open channel flow

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Authors: Yanrong Song, Zikai Dong, Runqin Xu, Jinrong Tian, Kexuan Li

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Nonlinear polarization rotation (NPR) technique has become one of the main techniques to achieve mode-locked fiber lasers for its compactness, implementation, and low cost. In this paper, we demonstrate a compact mode-locked Yb-doped fiber laser based on NPR technique in the all normal dispersion (ANDi) regime. In the laser cavity, there are no physical filter and polarization controller in laser cavity. Mode-locked pulse train is achieved in ANDi regime based on NPR technique. The fiber birefringence induced filtering effect is the mainly reason for mode-locking. After that, an extra 20 m long single-mode fiber is inserted in two different positions, dissipative soliton operation and noise like pulse operations are achieved correspondingly. The nonlinear effect is obviously enhanced in the noise like pulse regime and broadband spectrum generated owing to enhanced stimulated Raman scattering effect. When the pump power is 210 mW, the central wavelength is 1030 nm, and the corresponding 1st order Raman scattering stokes wave generates and locates at 1075 nm. When the pump power is 370 mW, the 1st and 2nd order Raman scattering stokes wave generate and locate at 1080 nm, 1126 nm respectively. When the pump power is 600 mW, the Raman continuum is generated with cascaded multi-order stokes waves, and the spectrum extends to 1188 nm. The total flat spectrum is from 1000nm to 1200nm. The maximum output average power and pulse energy are 18.0W and 14.75nJ, respectively.

Keywords: fiber laser, mode-locking, nonlinear polarization rotation, Raman scattering

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Authors: Yang Liu

Abstract:

Reinforced concrete (RC) shear wall structures are one of the most popular and efficient structural forms for medium- and high-rise buildings to resist the action of earthquake loading. Thus, it is of great significance to evaluate the seismic demands of the RC shear walls. In this paper, the application of the extend spectrum-based pushover analysis (ESPA) method on the seismic evaluation of the shear wall structure is presented. The ESPA method includes a nonlinear consecutive pushover analysis procedure and a linear elastic modal response analysis procedure to consider the combination of modes in both elastic and inelastic cases. It is found from the results of case study that the ESPA method can predict the seismic performance of shear wall structures, including internal forces and deformations very well.

Keywords: reinforced concrete shear wall, seismic performance, high mode effect, nonlinear analysis

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Authors: Dmitry V. Fomichev, Vladimir V. Solonin

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This paper presents the findings from a numerical simulation of the flow in 37-rod fuel assembly models spaced by a double-wire trapezoidal wrapping as applied to the BREST-OD-300 experimental nuclear reactor. Data on a high static pressure distribution within the models, and equations for determining the fuel bundle flow friction factors have been obtained. Recommendations are provided on using the closing turbulence models available in the ANSYS Fluent. A comparative analysis has been performed against the existing empirical equations for determining the flow friction factors. The calculated and experimental data fit has been shown. An analysis into the experimental data and results of the numerical simulation of the BREST-OD-300 fuel rod assembly hydrodynamic performance are presented.

Keywords: BREST-OD-300, ware-spaces, fuel assembly, computation fluid dynamics

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Authors: Radoslaw Pytlak, Damian Suski

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The aim of the paper is to provide a computational tool for planning a haemodialysis process. It is shown that optimization methods can be used to obtain the most effective treatment focused on removing both urea and phosphorus during the process. In order to achieve that, the IV–compartment model of phosphorus kinetics is applied. This kinetics model takes into account a rebound phenomenon that can occur during haemodialysis and results in a hybrid model of the process. Furthermore, vector fields associated with the model equations are such that it is very likely that using the most intuitive objective functions in the planning problem could lead to solutions which include sliding motions. Therefore, building computational tools for solving the problem of planning a haemodialysis process has required constructing numerical algorithms for solving optimal control problems with hybrid systems. The paper concentrates on minimum time control of hybrid systems since this control objective is the most suitable for the haemodialysis process considered in the paper. The presented approach to optimal control problems with hybrid systems is different from the others in several aspects. First of all, it is assumed that a hybrid system can exhibit sliding modes. Secondly, the system’s motion on the switching surface is described by index 2 differential–algebraic equations, and that guarantees accurate tracking of the sliding motion surface. Thirdly, the gradients of the problem’s functionals are evaluated with the help of adjoint equations. The adjoint equations presented in the paper take into account sliding motion and exhibit jump conditions at transition times. The optimality conditions in the form of the weak maximum principle for optimal control problems with hybrid systems exhibiting sliding modes and with piecewise constant controls are stated. The presented sensitivity analysis can be used to construct globally convergent algorithms for solving considered problems. The paper presents numerical results of solving the haemodialysis planning problem.

Keywords: haemodialysis planning process, hybrid systems, optimal control, sliding motion

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Authors: Mohammad Reza Ameri, Ali Massumi, Behnam Mahboubi

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The performance of masonry infilled frames during the past earthquakes shows that the infill panels play a major role as earthquake-resistant elements. The present study examines the influence of infill panels on seismic behavior of RC frame structures. For this purpose, several low- and mid-rise RC frames (two-, four-, seven-, and ten story) were numerically investigated. Reinforced masonry infill panels were then placed within the frames and the models were subjected to several nonlinear incremental static and dynamic analyses. The results of analyses showed that the use of reinforced masonry infill panels in RC frame structures can have beneficial effects on structural performance. It was confirmed that the use of masonry infill panels results in an increment in strength and stiffness of the framed buildings, followed by a reduction in displacement demand for the structural systems.

Keywords: reinforced masonry infill panels, nonlinear static analysis, incremental dynamic analysis, low-rise reinforced concrete frames, mid-rise reinforced concrete frames

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Authors: Shivani Singla, Om Prakash Pandey, Gopi Sharma

Abstract:

Metallic nanoparticle doped glasses has lead to rapid development in the field of optics. Large third order non-linearity, ultrafast time response, and a wide range of resonant absorption frequencies make these metallic nanoparticles more important in comparison to their bulk material. All these properties are highly dependent upon the size, shape, and surrounding environment of the nanoparticles. In a quest to find a suitable material for optical applications, several efforts have been devoted to improve the properties of such glasses in the past. In the present study, bismuth borate glass doped with different size gold nanoparticles (AuNPs) has been prepared using the conventional melt-quench technique. Synthesized glasses are characterized by X-ray diffraction (XRD) and Fourier Transformation Infrared spectroscopy (FTIR) to observe the structural modification in the glassy matrix with the variation in the size of the AuNPs. Glasses remain purely amorphous in nature even after the addition of AuNPs, whereas FTIR proposes that the main structure contains BO₃ and BO₄ units. Field emission scanning electron microscopy (FESEM) confirms the existence and variation in the size of AuNPs. Differential thermal analysis (DTA) depicts that prepared glasses are thermally stable and are highly suitable for the fabrication of optical fibers. The nonlinear optical parameters (nonlinear absorption coefficient and nonlinear refractive index) are calculated out by using the Z-scan technique with a Ti: sapphire laser at 800 nm. It has been concluded that the size of the nanoparticles highly influences the structural thermal and optical properties system.

Keywords: bismuth borate glass, different size, gold nanoparticles, nonlinearity

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Authors: Raphael Zanella, Todd A. Oliver, Karl W. Schulz

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This work deals with the finite element approximation of axisymmetric compressible flows with swirl velocity. We are interested in problems where the flow, while weakly dependent on the azimuthal coordinate, may have a strong azimuthal velocity component. We describe the approximation of the compressible Navier-Stokes equations with H1-conformal spaces of axisymmetric functions. The weak formulation is implemented in a C++ solver with explicit time marching. The code is first verified with a convergence test on a manufactured solution. The verification is completed by comparing the numerical and analytical solutions in a Poiseuille flow case and a Taylor-Couette flow case. The code is finally applied to the problem of a swirling subsonic air flow in a plasma torch geometry.

Keywords: axisymmetric problem, compressible Navier-Stokes equations, continuous finite elements, swirling flow

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Authors: Abdelhafid Zenati, Mohamed Tadjine

Abstract:

The mathematical formulation of biomedical problems is an important phase to understand and predict the dynamic of the controlled population. In this paper we perform a stability analysis of a coupled model for healthy and cancerous cells dynamics in Acute Myeloid Leukemia, this represents our first aim. Second, we illustrate the effect of the interconnection between healthy and cancer cells. The PDE-based model is transformed to a nonlinear distributed state space model (delay system). For an equilibrium point of interest, necessary and sufficient conditions of global asymptotic stability are given. Thus, we came up to give necessary and sufficient conditions of global asymptotic stability of the origin and the healthy situation and control of the dynamics of normal hematopoietic stem cells and cancerous during myelode Acute leukemia. Simulation studies are given to illustrate the developed results.

Keywords: distributed delay, global stability, modelling, nonlinear models, PDE, state space

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Authors: D. Pradeep Mitra, Prafulla

Abstract:

Looking to the word propellant-less system it makes us to believe that it is an impossible one, but this paper demonstrates the use of microwaves to create a system which makes impossible to be possible, it means a propellant-less propulsion system using microwaves. In these thrusters, microwaves are radiated into a sealed parabolic cavity through a waveguide, which act on the surface of the cavity and follow the axis of the thrusters to produce thrust. The advantages of these thrusters are: (1) Producing thrust without propellant; without erosion, wear, and thermal stress from the hot exhaust gas; and at the same time increasing quality. (2) If the microwave output power is stable, the performance of thrusters is not affected by its working environment. This paper is demonstrated from general maxwell equations. These equations are used to create the mathematical model of the thrusters. These mathematical model helps us to calculate the Q factor and calculate the approximate thrust which would be generated in the system.

Keywords: propellant less, microwaves, parabolic wave guide, propulsion system

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Authors: Juhee Lee, Yongjun Lee

Abstract:

In designing a low-energy-consuming buildings, the heat transfer through a large glass or wall becomes critical. Multiple layers of the window glasses and walls are employed for the high insulation. The gravity driven air flow between window glasses or wall layers is a natural heat convection phenomenon being a key of the heat transfer. For the first step of the natural heat transfer analysis, in this study the development and application of a finite volume method for the numerical computation of viscous incompressible flows is presented. It will become a part of the natural convection analysis with high-order scheme, multi-grid method, and dual-time step in the future. A finite volume method based on a fully-implicit second-order is used to discretize and solve the fluid flow on unstructured grids composed of arbitrary-shaped cells. The integrations of the governing equation are discretised in the finite volume manner using a collocated arrangement of variables. The convergence of the SIMPLE segregated algorithm for the solution of the coupled nonlinear algebraic equations is accelerated by using a sparse matrix solver such as BiCGSTAB. The method used in the present study is verified by applying it to some flows for which either the numerical solution is known or the solution can be obtained using another numerical technique available in the other researches. The accuracy of the method is assessed through the grid refinement.

Keywords: finite volume method, fluid flow, laminar flow, unstructured grid

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Authors: Shyh Ming Chern

Abstract:

Cubic equations of state (EoS), popular due to their simple mathematical form, ease of use, semi-theoretical nature and, reasonable accuracy are normally fitted to vapor-liquid equilibrium P-v-T data. As a result, They often show poor accuracy in the region near and above the critical point. In this study, the performance of the renowned Peng-Robinson (PR) and Patel-Teja (PT) EoS’s around the critical area has been examined against the P-v-T data of water. Both of them display large deviations at critical point. For instance, PR-EoS exhibits discrepancies as high as 47% for the specific volume, 28% for the enthalpy departure and 43% for the entropy departure at critical point. It is shown that incorporating P-v-T data of the supercritical region into the retuning of a cubic EoS can improve its performance above the critical point dramatically. Adopting a retuned acentric factor of 0.5491 instead of its genuine value of 0.344 for water in PR-EoS and a new F of 0.8854 instead of its original value of 0.6898 for water in PT-EoS reduces the discrepancies to about one third or less.

Keywords: equation of state, EoS, supercritical water, SCW

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