Search results for: amplification of angular speed differential

Authors: Riccardo Fratini, Riccardo Santini, Jacopo Serafini, Massimo Gennaretti, Stefano Panzieri

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This paper presents a nonlinear differential model, for a three-bladed horizontal axis wind turbine (HAWT) suited for control applications. It is based on a 8-dofs, lumped parameters structural dynamics coupled with a quasi-steady sectional aerodynamics. In particular, using the Euler-Lagrange Equation (Energetic Variation approach), the authors derive, and successively validate, such model. For the derivation of the aerodynamic model, the Greenbergs theory, an extension of the theory proposed by Theodorsen to the case of thin airfoils undergoing pulsating flows, is used. Specifically, in this work, the authors restricted that theory under the hypothesis of low perturbation reduced frequency k, which causes the lift deficiency function C(k) to be real and equal to 1. Furthermore, the expressions of the aerodynamic loads are obtained using the quasi-steady strip theory (Hodges and Ormiston), as a function of the chordwise and normal components of relative velocity between flow and airfoil Ut, Up, their derivatives, and section angular velocity ε˙. For the validation of the proposed model, the authors carried out open and closed-loop simulations of a 5 MW HAWT, characterized by radius R =61.5 m and by mean chord c = 3 m, with a nominal angular velocity Ωn = 1.266rad/sec. The first analysis performed is the steady state solution, where a uniform wind Vw = 11.4 m/s is considered and a collective pitch angle θ = 0.88◦ is imposed. During this step, the authors noticed that the proposed model is intrinsically periodic due to the effect of the wind and of the gravitational force. In order to reject this periodic trend in the model dynamics, the authors propose a collective repetitive control algorithm coupled with a PD controller. In particular, when the reference command to be tracked and/or the disturbance to be rejected are periodic signals with a fixed period, the repetitive control strategies can be applied due to their high precision, simple implementation and little performance dependency on system parameters. The functional scheme of a repetitive controller is quite simple and, given a periodic reference command, is composed of a control block Crc(s) usually added to an existing feedback control system. The control block contains and a free time-delay system eτs in a positive feedback loop, and a low-pass filter q(s). It should be noticed that, while the time delay term reduces the stability margin, on the other hand the low pass filter is added to ensure stability. It is worth noting that, in this work, the authors propose a phase shifting for the controller and the delay system has been modified as e^(−(T−γk)), where T is the period of the signal and γk is a phase shifting of k samples of the same periodic signal. It should be noticed that, the phase shifting technique is particularly useful in non-minimum phase systems, such as flexible structures. In fact, using the phase shifting, the iterative algorithm could reach the convergence also at high frequencies. Notice that, in our case study, the shifting of k samples depends both on the rotor angular velocity Ω and on the rotor azimuth angle Ψ: we refer to this controller as a spatial repetitive controller. The collective repetitive controller has also been coupled with a C(s) = PD(s), in order to dampen oscillations of the blades. The performance of the spatial repetitive controller is compared with an industrial PI controller. In particular, starting from wind speed velocity Vw = 11.4 m/s the controller is asked to maintain the nominal angular velocity Ωn = 1.266rad/s after an instantaneous increase of wind speed (Vw = 15 m/s). Then, a purely periodic external disturbance is introduced in order to stress the capabilities of the repetitive controller. The results of the simulations show that, contrary to a simple PI controller, the spatial repetitive-PD controller has the capability to reject both external disturbances and periodic trend in the model dynamics. Finally, the nominal value of the angular velocity is reached, in accordance with results obtained with commercial software for a turbine of the same type.

Keywords: wind turbines, aeroelasticity, repetitive control, periodic systems

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Authors: Abdelrahman Alghazali, Youssef Kassem, Hüseyin Çamur, Ozan Erenay

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Savonius is a drag type vertical axis wind turbine. Savonius wind turbines have a low cut-in speed and can operate at low wind speed. This makes it suitable for electricity or mechanical generation in low-power applications such as individual domestic installations. Therefore, the primary purpose of this work was to investigate the relationship between the type of Savonius rotor and the torque and mechanical power generated. And it was to illustrate how the type of rotor might play an important role in the prediction of mechanical power of wind turbine powered car. The main purpose of this paper is to predict and investigate the aerodynamic effects by means of velocity analysis on the performance of a wind turbine powered car by converting the wind energy into mechanical energy to overcome load that rotates the main shaft. The predicted results based on theoretical analysis were compared with experimental results obtained from literature. The percentage of error between the two was approximately around 20%. Prediction of the torque was done at a wind speed of 4 m/s, and an angular velocity of 130 RPM according to meteorological statistics in Northern Cyprus.

Keywords: mechanical power, torque, Savonius rotor, wind car

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Authors: T. Kobayashi, K. Shiba, T. Kaburagi, Y. Kurihara

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For the elderly living alone, falls can be a serious problem encountered in daily life. Some elderly people are unable to stand up without the assistance of a caregiver. They may become unconscious after a fall, which can lead to serious aftereffects such as hypothermia, dehydration, and sometimes even death. We treat the subject as an inverted pendulum and model its angle from the equilibrium position and its angular velocity. As the model is non-linear, we implement the filtering method with a particle filter which can estimate true states of the non-linear model. In order to evaluate the accuracy of the particle filter estimation results, we calculate the root mean square error (RMSE) between the estimated angle/angular velocity and the true values generated by the simulation. The experimental results give the highest accuracy RMSE of 0.0141 rad and 0.1311 rad/s for the angle and angular velocity, respectively.

Keywords: fall, microwave Doppler sensor, non-linear dynamics model, particle filter

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Authors: Tokuei Sako

Abstract:

The ground and low-lying singly-excited states of He and He-like atomic ions have been studied by the Full Configuration Interaction (FCI) method focusing on the angular correlation between two electrons in the studied systems. The two-electron angle density distribution obtained by integrating the square-modulus of the FCI wave function over the coordinates other than the interelectronic angle shows a distinct trend between the singlet-triplet pair of states for different values of the nuclear charge Zn. Further, both of these singlet and triplet distributions tend to show an increasingly stronger dependence on the interelectronic angle as Zn increases, in contrast to the well-known fact that the correlation energy approaches towards zero for increasing Zn. This controversial observation has been rationalized on the basis of the recently introduced concept of so-called conjugate Fermi holes.

Keywords: He-like systems, angular correlation, configuration interaction wave function, conjugate Fermi hole

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Authors: Seyed Ata Khalkhkali Sharifi, Gholamhossein Majzoubi, Farhad Abroush

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Developing mechanical properties of pure titanium has been reviewed in this paper by using ECAP process. At the first step of this article, the experimental samples were prepared as mentioned in the standards. Then pure grade 2 Ti was processed via equal-channel angular pressing (ECAp) for 2 passes following route-A at 400°C. After processing, the microstructural evolution, tensile, fatigue, hardness properties and wear behavior were investigated. Finally, the effect of ECAP process on these samples was analyzed. The results showed improvement in strength values with a slight decrease in ductility. The analysis on 30 points within the sample showed hardness increase in each pass. Also, it was concluded that fatigue properties were increased too.

Keywords: equal-channel angular pressing, titanium, mechanical behavior, engineering materials and applications

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Authors: Lev Idels, Arcady Ponosov

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Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others.

Keywords: delay equations, operator methods, stochastic noise, weak solutions

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Authors: Walid Wahballah, Taher Bazan, Fawzy Eltohamy

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One of the important functions of the satellite attitude control system is to provide the required pointing accuracy and attitude stability for optical remote sensing satellites to achieve good image quality. Although offering noise reduction and increased sensitivity, time delay and integration (TDI) charge coupled devices (CCDs) utilized in high-resolution satellites (HRS) are prone to introduce large amounts of pixel smear due to the instability of the line of sight. During on-orbit imaging, as a result of the Earth’s rotation and the satellite platform instability, the moving direction of the TDI-CCD linear array and the imaging direction of the camera become different. The speed of the image moving on the image plane (focal plane) represents the image motion velocity whereas the angle between the two directions is known as the drift angle (β). The drift angle occurs due to the rotation of the earth around its axis during satellite imaging; affecting the geometric accuracy and, consequently, causing image quality degradation. Therefore, the image motion velocity vector and the drift angle are two important factors used in the assessment of the image quality of TDI-CCD based optical remote sensing satellites. A model for estimating the image motion velocity and the drift angle in HRS is derived. The six satellite attitude control parameters represented in the derived model are the (roll angle φ, pitch angle θ, yaw angle ψ, roll angular velocity φ֗, pitch angular velocity θ֗ and yaw angular velocity ψ֗ ). The influence of these attitude parameters on the image quality is analyzed by establishing a relationship between the image motion velocity vector, drift angle and the six satellite attitude parameters. The influence of the satellite attitude parameters on the image quality is assessed by the presented model in terms of modulation transfer function (MTF) in both cross- and along-track directions. Three different cases representing the effect of pointing accuracy (φ, θ, ψ) bias are considered using four different sets of pointing accuracy typical values, while the satellite attitude stability parameters are ideal. In the same manner, the influence of satellite attitude stability (φ֗, θ֗, ψ֗) on image quality is also analysed for ideal pointing accuracy parameters. The results reveal that cross-track image quality is influenced seriously by the yaw angle bias and the roll angular velocity bias, while along-track image quality is influenced only by the pitch angular velocity bias.

Keywords: high-resolution satellites, pointing accuracy, attitude stability, TDI-CCD, smear, MTF

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Authors: Mohamed S. El-Asfoury, Ahmed Abdel-Moneim, Mohamed N. A. Nasr

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The current study uses finite element modeling to investigate and analyze a modified form of the from the conventional equal channel multi-angular pressing (ECMAP), using non-equal channels, on the workpiece material plastic deformation. The modified process non-equal channel multi-angular extrusion (NECMAE) is modeled using two-dimensional plane strain finite element model built using the commercial software ABAQUS. The workpiece material used is pure aluminum. The model was first validated by comparing its results to analytical solutions for single-pass equal channel angular extrusion (ECAP), as well as previously published data. After that, the model was used to examine the effects of different % of reductions of the area (for the second stage) on material plastic deformation, corner gap, and required the load. Three levels of reduction in the area were modeled; 10%, 30%, and 50%, and compared to single-pass and double-pass ECAP. Cases with a higher reduction in the area were found to have smaller corner gaps, higher and much uniform plastic deformation, as well as higher required loads. The current results are mainly attributed to the back pressure effects exerted by the second stage, as well as strain hardening effects experienced during the first stage.

Keywords: non-equal channel angular extrusion, multi-pass, sever plastic deformation, back pressure, Finite Element Modelling (FEM)

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Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

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An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

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Authors: Saeed Otarod

Abstract:

In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Lina Wu, Ye Li

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An equivalent relation between a harmonic form and a closed co-closed form is established on a complete non-compact manifold. This equivalence has been generalized for a differential k-form ω from Lq spaces to non-Lq spaces when q=2 in the context of p-balanced growth where p=2. Especially for a simple differential k-form on a complete non-compact manifold, the equivalent relation has been verified with the extended scope of q for from finite q-energy in Lq spaces to infinite q-energy in non-Lq spaces when with 2-balanced growth. Generalized Hadamard Theorem, Cauchy-Schwarz Inequality, and Calculus skills including Integration by Parts as well as Convergent Series have been applied as estimation techniques to evaluate growth rates for a differential form. In particular, energy growth rates as indicated by an appropriate power range in a selected test function lead to a balance between a harmonic differential form and a closed co-closed differential form. Research ideas and computational methods in this paper could provide an innovative way in the study of broadening Lq spaces to non-Lq spaces with a wide variety of infinite energy growth for a differential form.

Keywords: closed forms, co-closed forms, harmonic forms, L^q spaces, p-balanced growth, simple differential k-forms

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Dražen Cvitanić, Biljana Maljković

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This paper presents models for predicting operating speeds on tangent sections of two-lane rural roads developed on continuous speed data. The data corresponds to 20 drivers of different ages and driving experiences, driving their own cars along an 18 km long section of a state road. The data were first used for determination of maximum operating speeds on tangents and their comparison with speeds in the middle of tangents i.e. speed data used in most of operating speed studies. Analysis of continuous speed data indicated that the spot speed data are not reliable indicators of relevant speeds. After that, operating speed models for tangent sections were developed. There was no significant difference between models developed using speed data in the middle of tangent sections and models developed using maximum operating speeds on tangent sections. All developed models have higher coefficient of determination then models developed on spot speed data. Thus, it can be concluded that the method of measuring has more significant impact on the quality of operating speed model than the location of measurement.

Keywords: operating speed, continuous speed data, tangent sections, spot speed, consistency

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Authors: Mohammad Rahmani Rezaiyeh, Mojtaba Rahmani Rezaiyeh, Mehrdad Rahmani Rezaiyeh

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Smart speed bump is a new invention and I am invented it. Smart speed bump is a system that can change the position of speed bumps either active or passive in necessary situations. The basic system of smart speed bumps is based on a robotic system which includes mechanic, electronic and artificial intelligence. The smart speed bump is capable of smart decision making and can change its position by anticipating the peak of terrific hours. It can be noted to the advantages of this system such as preventing the waste of petrol while crossing speed bumps, traffic management, accelerating, flowing and securing traffic, reducing accidents and judicial records.

Keywords: invention, smart, robotic system, speed bump, traffic, management

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Ivan Balachin, Geanette Polanco, Jiang Xingliang, Hu Qin

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The problem of global warming raised up interest towards renewable energy sources. To reduce cost of wind energy is a challenge. Before building of wind park conditions such as: average wind speed, direction, time for each wind, probability of icing, must be considered in the design phase. Operation values used on the setting of control systems also will depend on mentioned variables. Here it is proposed a procedure to be include in the evaluation of the performance of a wind turbine, based on the amplitude of wind changes, the number of changes and their duration. A generic study case based on actual data is presented. Data analysing techniques were applied to model the power required for yaw system based on amplitude and data amount of wind changes. A theoretical model between time, amplitude of wind changes and angular speed of nacelle rotation was identified.

Keywords: field data processing, regression determination, wind turbine performance, wind turbine placing, yaw system losses

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Authors: Li-Ting Huang, Yu-Hsiang Shen, Cing-Ciao Ke, Sheng-Pin Tseng, Fan-Pin Tseng, Yu-Ching Ni, Chia-Yu Lin

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Chest radiography is the most common technique for the diagnosis and follow-up of pulmonary diseases. However, the lesions superimposed with normal structures are difficult to be detected in chest radiography. Chest tomosynthesis is a relatively new technique to obtain 3D section images from a set of low-dose projections acquired over a limited angular range. However, there are some limitations with chest tomosynthesis. Patients undergoing tomosynthesis have to be able to hold their breath firmly for 10 seconds. A digital tomosynthesis system with advanced reconstruction algorithm and high-stability motion mechanism was developed by our research group. The potential for the system to perform a bidirectional chest scan within 10 seconds is expected. The purpose of this study is to realize the influences of the scan speed on the image quality for our digital tomosynthesis system. The major factors that lead image blurring are the motion of the X-ray source and the patient. For the fore one, an experiment of imaging a chest phantom with three different scan speeds, which are 6 cm/s, 8 cm/s, and 15 cm/s, was proceeded to understand the scan speed influences on the image quality. For the rear factor, a normal SD (Sprague-Dawley) rat was imaged with it alive and sacrificed to assess the impact on the image quality due to breath motion. In both experiments, the profile of the ROIs (region of interest) and the CNRs (contrast-to-noise ratio) of the ROIs to the normal tissue of the reconstructed images was examined to realize the degradations of the qualities of the images. The preliminary results show that no obvious degradation of the image quality was observed with increasing scan speed, possibly due to the advanced designs for the hardware and software of the system. It implies that higher speed (15 cm/s) than that of the commercialized tomosynthesis system (12 cm/s) for the proposed system is achieved, and therefore a complete chest scan within 10 seconds is expected.

Keywords: chest radiography, digital tomosynthesis, image quality, scan speed

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

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

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Marinka K. Baghdasaryan, Siranush M. Muradyan, Avgen A. Gasparyan

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Analytical expressions of the current and angular errors, as well as the frequency characteristics of an induction converter describing the relation with its structural parameters, the core and winding characteristics are obtained. Based on estimation of the dependences obtained, a mathematical problem of parametric optimization is formulated which can successfully be used for investigation and diagnosing an induction converter.

Keywords: induction converters, magnetic circuit material, current and angular errors, frequency response, mathematical formulation, structural parameters

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Authors: Amani Alotaibi

Abstract:

3D printing has emerged as a pivotal technique for scaffold development, particularly in the field of bone tissue regeneration, due to its ability to customize scaffolds to fit complex geometries of bone defects. Among the various methods available, fused deposition modeling (FDM) is particularly promising as it avoids the use of solvents or toxic chemicals during fabrication. This study investigates the effects of three key parameters, extrusion temperature, screw rotational speed, and deposition speed, on the crystallization and mechanical properties of polycaprolactone (PCL) scaffolds. Three extrusion temperatures (70°C, 80°C, and 90°C), three screw speeds (10 RPM, 15 RPM, and 20 RPM), and three deposition speeds (8 mm/s, 10 mm/s, and 12 mm/s) were evaluated. The scaffolds were characterized using X-ray diffraction (XRD), differential scanning calorimetry (DSC), and tensile testing to assess changes in crystallinity and mechanical properties. Additionally, the scaffolds were analyzed for crystal size and biocompatibility. The results demonstrated that increasing the extrusion temperature to 80°C, combined with a screw speed of 15 RPM and a deposition speed of 10 mm/s, significantly improved the crystallinity, compressive modulus, and thermal resistance of the PCL scaffolds. These findings suggest that by fine-tuning basic 3D printing parameters, it is possible to modulate the structural and mechanical properties of the scaffold, thereby enhancing its suitability for bone tissue regeneration.

Keywords: 3D printing, polymer, scaffolds, tissue engineering, crystallization

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Authors: Zhan Chen, Wenquan Bi

Abstract:

This paper focuses on examining the strength of Midori against impossible differential attack. The Midori family of light weight block cipher orienting to energy-efficiency is proposed in ASIACRYPT2015. Using a 6-round property, the authors implement an 11-round impossible differential attack on Midori64 by extending two rounds on the top and three rounds on the bottom. There is enough key space to consider pre-whitening keys in this attack. An impossible differential path that minimises the key bits involved is used to reduce computational complexity. Several additional observations such as partial abort technique are used to further reduce data and time complexities. This attack has data complexity of 2 ⁶⁹·² chosen plaintexts, requires 2 ¹⁴·⁵⁸ blocks of memory and 2 ⁹⁴·⁷ 11- round Midori64 encryptions.

Keywords: cryptanalysis, impossible differential, light weight block cipher, Midori

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: Abtin Farokhipanah

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In recent years, analysis of structures is based on ductility design in contradictory to strength design in surveying earthquake effects on structures. ASCE07-10 code offers to intensify relative drifts calculated from a linear analysis with Cd which is called (Deflection Amplification Factor) to obtain the real relative drifts which can be calculated using nonlinear analysis. This lateral drift should be limited to the code boundaries. Calculation of this amplification factor for different structures, comparing with ASCE07-10 code and offering the best coefficient are the purposes of this research. Following our target, short and tall building steel structures with various earthquake resistant systems in linear and nonlinear analysis should be surveyed, so these questions will be answered: 1. Does the Response Modification Coefficient (R) have a meaningful relation to Deflection Amplification Factor? 2. Does structure height, seismic zone, response spectrum and similar parameters have an effect on the conversion coefficient of linear analysis to real drift of structure? The procedure has used to conduct this research includes: (a) Study on earthquake resistant systems, (b) Selection of systems and modeling, (c) Analyzing modeled systems using linear and nonlinear methods, (d) Calculating conversion coefficient for each system and (e) Comparing conversion coefficients with the code offered ones and concluding results.

Keywords: ASCE07-10 code, deflection amplification factor, earthquake engineering, lateral displacement of structures, response modification coefficient

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Authors: O. Acan, Y. Keskin

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In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: reduced differential transform method, adomian decomposition method, variational iteration method, homotopy analysis method

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Authors: K. Youssef, Ç. Hüseyin

Abstract:

The blades of a wind turbine have the most important job of any wind turbine component; they must capture the wind and convert it into usable mechanical energy. The objective of this work is to determine the mechanical power of single big C-section of vertical wind turbine for wind car in a two-dimensional model. The wind car has a vertical axis with 3 single big C-section blades mounted at an angle of 120°. Moreover, the three single big C-section blades are directly connected to wheels by using various kinds of links. Gears are used to convert the wind energy to mechanical energy to overcome the load exercised on the main shaft under low speed. This work allowed a comparison of drag characteristics and the mechanical power between the single big C-section blades with the previous work on 3 C-section and 3 double C-section blades for wind car. As a result obtained from the flow chart the torque and power curves of each case study are illustrated and compared with each other. In particular, drag force and torque acting on each types of blade was taken at an airflow speed of 4 m/s, and an angular velocity of 13.056 rad/s.

Keywords: blade, vertical wind turbine, drag characteristics, mechanical power

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