Search results for: dispersive wave equations

Authors: A. L. Qureshi, A. A. Mahessar, A. Baloch

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Flood wave propagation in river channel flow can be enunciated by nonlinear equations of motion for unsteady flow. However, it is difficult to find analytical solution of these complex non-linear equations. Hence, verification of the numerical model should be carried out against field data and numerical predictions. This paper presents the verification of developed finite element model applying for unsteady flow in the open channels. The results of a proposed model indicate a good matching with both Preissmann scheme and HEC-RAS model for a river reach of 29 km at both sites (15 km from upstream and at downstream end) for discharge hydrographs. It also has an agreeable comparison with the Preissemann scheme for the flow depth (stage) hydrographs. The proposed model has also been applying to forecast daily discharges at 400 km downstream from Sukkur barrage, which demonstrates accurate model predictions with observed daily discharges. Hence, this model may be utilized for predicting and issuing flood warnings about flood hazardous in advance.

Keywords: finite element method, Preissmann scheme, HEC-RAS, flood forecasting, Indus river

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Authors: Minas Balyan

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Nowadays X-ray nonlinear diffraction and nonlinear effects are investigated due to the presence of the third generation synchrotron sources and XFELs. X-ray third order nonlinear dynamical diffraction is considered as well. Using the nonlinear model of the usual visible light optics the third-order nonlinear Takagi’s equations for monochromatic waves and the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses are obtained by the author in previous papers. The obtained equations show, that even if the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero (forbidden reflection), the dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus, in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well-known Renninger effect takes place. In this work, the 'third order nonlinear Renninger effect' is considered theoretically.

Keywords: Bragg diffraction, nonlinear Takagi’s equations, nonlinear Renninger effect, third order nonlinearity

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Authors: Sudhir Kumar Tewatia, Kanishck Tewatia, Anttriksh Tewatia

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Advancements in soil consolidation are discussed, and further improvements are proposed with particular reference to Tewatia’s Y-Y’ Approach, which is called the Settlement versus Rate of Settlement Approach in consolidation. A branch of calculus named Y-Y' (or y versus dy/dx) is suggested (as compared to the common X-Y', x versus dy/dx, dy/dx versus x or Newton-Leibniz branch) that solves some complicated/unsolved theoretical and practical problems in physical sciences (Physics, Chemistry, Mathematics, Biology, and allied sciences) and engineering in an amazingly simple and short manner, particularly when independent variable X is unknown and X-Y' Approach can’t be used. Complicated theoretical and practical problems in 1D, 2D, 3D Primary and Secondary consolidations with non-uniform gradual loading and irregularly shaped clays are solved with elementary school level Y-Y' Approach, and it is interesting to note that in X-Y' Approach, equations become more difficult while we move from one to three dimensions, but in Y-Y' Approach even 2D/3D equations are very simple to derive, solve, and use; rather easier sometimes. This branch of calculus will have a far-reaching impact on understanding and solving the problems in different fields of physical sciences and engineering that were hitherto unsolved or difficult to be solved by normal calculus/numerical/computer methods. Some particular cases from soil consolidation that basically creeps and diffusion equations in isolation and in combination with each other are taken for comparison with heat transfer. The Y-Y’ Approach can similarly be applied in wave equations and other fields wherever normal calculus works or fails. Soil mechanics uses mathematical analogies from other fields of physical sciences and engineering to solve theoretical and practical problems; for example, consolidation theory is a replica of the heat equation from thermodynamics with the addition of the effective stress principle. An attempt is made to give them mathematical analogies.

Keywords: calculus, clay, consolidation, creep, diffusion, heat, settlement

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Authors: Zunnurain Ahmad

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This work presents design of a dual band antenna for the 5G communications in the millimeter wave band. As opposed to conventional patch antennas which are limited to single narrow band operation a shared aperture concept is utilized for this antenna. The patch aperture is coupled through two rectangular slots etched on a thin printed circuit board (100μm). The patch is elevated in air thus avoiding excitation of surface waves and minimizing dielectric losses at millimeter wave frequencies. With this approach the radiator can cover lower band of 28 GHz and upper band of 37/ 39 GHz dedicated for the fifth generation communications. The simulated radiation efficiency of the antenna stays above 90%.

Keywords: antenna, millimeter wave, 5G, 3D

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Authors: Chih-Chung Huang, Po-Hsun Peng

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Ultrasound transient elastography has become a valuable tool for many clinical diagnoses, such as liver diseases and breast cancer. The pathological tissue can be distinguished by elastography due to its stiffness is different from surrounding normal tissues. An ultrafast frame rate of ultrasound imaging is needed for transient elastography modality. The elastography obtained in the ultrafast system suffers from a low quality for resolution, and affects the robustness of the transient elastography. In order to overcome these problems, a coherent plane wave compounding technique has been proposed for conventional ultrasound system which the operating frequency is around 3-15 MHz. The purpose of this study is to develop a novel beamforming technique for high frequency ultrasound coherent plane-wave compounding imaging and the simulated results will provide the standards for hardware developments. Plane-wave compounding imaging produces a series of low-resolution images, which fires whole elements of an array transducer in one shot with different inclination angles and receives the echoes by conventional beamforming, and compounds them coherently. Simulations of plane-wave compounding image and focused transmit image were performed using Field II. All images were produced by point spread functions (PSFs) and cyst phantoms with a 64-element linear array working at 35MHz center frequency, 55% bandwidth, and pitch of 0.05 mm. The F number is 1.55 in all the simulations. The simulated results of PSFs and cyst phantom which were obtained using single, 17, 43 angles plane wave transmission (angle of each plane wave is separated by 0.75 degree), and focused transmission. The resolution and contrast of image were improved with the number of angles of firing plane wave. The lateral resolutions for different methods were measured by -10 dB lateral beam width. Comparison of the plane-wave compounding image and focused transmit image, both images exhibited the same lateral resolution of 70 um as 37 angles were performed. The lateral resolution can reach 55 um as the plane-wave was compounded 47 angles. All the results show the potential of using high-frequency plane-wave compound imaging for realizing the elastic properties of the microstructure tissue, such as eye, skin and vessel walls in the future.

Keywords: plane wave imaging, high frequency ultrasound, elastography, beamforming

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Authors: Johan Buermans, Kristel Crombé, Niek Desmet, Laura Dittrich, Andrei Goriaev, Yurii Kovtun, Daniel López-Rodriguez, Sören Möller, Per Petersson, Maja Verstraeten

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The International Thermonuclear Experimental Reactor (ITER) will rely on three sources of external heating to produce and sustain a plasma; Neutral Beam Injection (NBI), Ion Cyclotron Resonance Heating (ICRH), and Electron Cyclotron Resonance Heating (ECRH). ECRH is a way to heat the electrons in a plasma by resonant absorption of electromagnetic waves. The energy of the electrons is transferred indirectly to the ions by collisions. The electron cyclotron heating system can be directed to deposit heat in particular regions in the plasma (https://www.iter.org/mach/Heating). Electron Cyclotron Resonance Heating (ECRH) at the fundamental resonance in X-mode is limited by a low cut-off density. Electromagnetic waves cannot propagate in the region between this cut-off and the Upper Hybrid Resonance (UHR) and cannot reach the Electron Cyclotron Resonance (ECR) position. Higher harmonic heating is hence preferred in heating scenarios nowadays to overcome this problem. Additional power deposition mechanisms can occur above this threshold to increase the plasma density. This includes collisional losses in the evanescent region, resonant power coupling at the UHR, tunneling of the X-wave with resonant coupling at the ECR, and conversion to the Electron Bernstein Wave (EBW) with resonant coupling at the ECR. A more profound knowledge of these deposition mechanisms can help determine the optimal plasma production scenarios. Several ECRH experiments are performed on the TOroidally MAgnetized System (TOMAS) to identify the conditions for Electron Bernstein Wave (EBW) heating. Density and temperature profiles are measured with movable Triple Langmuir Probes in the horizontal and vertical directions. Measurements of the forwarded and reflected power allow evaluation of the coupling efficiency. Optical emission spectroscopy and camera images also contribute to plasma characterization. The influence of the injected power, magnetic field, gas pressure, and wave polarization on the different deposition mechanisms is studied, and the contribution of the Electron Bernstein Wave is evaluated. The TOMATOR 1D hydrogen-helium plasma simulator numerically describes the evolution of current less magnetized Radio Frequency plasmas in a tokamak based on Braginskii’s legal continuity and heat balance equations. This code was initially benchmarked with experimental data from TCV to determine the transport coefficients. The code is used to model the plasma parameters and the power deposition profiles. The modeling is compared with the data from the experiments.

Keywords: electron Bernstein wave, Langmuir probe, plasma characterization, TOMAS

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Authors: Steven D. P. Moore

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An electrical discharge in the air induces an electromagnetic (EM) wave capable of wireless transfer, reception, and conversion back into electrical discharge at a distant location. Following Norton’s ground wave principles, EM wave radiation (EMR) runs parallel to the Earth’s surface. Energy in an EMR wave can move through the air and be focused to create a spark at a distant location, focused by a receiver to generate a local electrical discharge. This local discharge can be amplified and stored but also has the propensity to initiate another EMR wave. In addition to typical EM waves, lightning is also associated with atmospheric events, trans-ionospheric pulse pairs, the most powerful natural EMR signal on the planet. With each lightning strike, regardless of global position, it generates naturally occurring pulse-pairs that are emitted towards space within a narrow cone. An EMR wave can self-propagate, travel at the speed of light, and, if polarized, contain vector properties. If this reflective pulse could be directed by design through structures that have increased probabilities for lighting strikes, it could theoretically travel near the surface of the Earth at light speed towards a selected receiver for local transformation into electrical energy. Through research, there are several influencing parameters that could be modified to model, test, and increase the potential for adopting this technology towards the goal of developing a global grid that utilizes natural sources of energy.

Keywords: electricity, sparkgap, wireless, electromagnetic

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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: Norazuwin Najihah Mat Tahir, Fuziyah Ishak, Seripah Awang Kechil

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The onset of the convective instability in the horizontal through flow of a power-law nanofluid saturated by porous layer heated from below under the influences of magnetic field are investigated in this study. The linear stability theory is used for the transformation of the partial differential equations to system of ordinary differential equations through infinitesimal perturbations, scaling, linearization and method of normal modes with two-dimensional periodic waves. The system is solved analytically for the closed form solution of the Rayleigh number by using the Galerkin-type weighted residuals method to investigate the onset of both traveling wave and oscillatory convection. The effects of the power-law index, Lewis number and Peclet number on the stability of the system were investigated. The Lewis number stabilizes while the power-law index and Peclet number destabilize the nanofluid system. The system in the presence of magnetic field is more stable than the system in the absence of magnetic field.

Keywords: convection, instability, magnetic field, nanofluid, power-law

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Authors: T. Bouchabchoub, A. Bendahmane, A. Haouriqui, N. Attou

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This paper presents simulation results of Forex predicting model equations in order to give approximately a prevision of interest rates. First, Hall-Taylor (HT) equations have been used with Taylor rule (TR) to adapt them to European and American Forex Markets. Indeed, initial Taylor Rule equation is conceived for all Forex transactions in every States: It includes only one equation and six parameters. Here, the model has been used with Hall-Taylor equations, initially including twelve equations which have been reduced to only three equations. Analysis has been developed on the following base macroeconomic variables: Real change rate, investment wages, anticipated inflation, realized inflation, real production, interest rates, gap production and potential production. This model has been used to specifically study the impact of an inflation shock on macroeconomic director interest rates.

Keywords: interest rate, Forex, Taylor rule, production, European Central Bank (ECB), Federal Reserve System (FED).

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Authors: Adetunji A. Adeyanju., Mathew O. Omeike, Johnson O. Adeniran, Biodun S. Badmus

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In this paper, we discuss certain conditions for uniform asymptotic stability and uniform ultimate boundedness of solutions to some systems of Aizermann-type of differential equations by means of second method of Lyapunov. In achieving our goal, some Lyapunov functions are constructed to serve as basic tools. The stability results in this paper, extend some stability results for some Aizermann-type of differential equations found in literature. Also, we prove some results on uniform boundedness and uniform ultimate boundedness of solutions of systems of equations study.

Keywords: Aizermann, boundedness, first order, Lyapunov function, stability

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Authors: Zuhier Altawallbeh

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

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

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Authors: Bruno Coelho Lima, Joao F.A. Martos, Paulo G. P. Toro, Israel S. Rego

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The shock tube is a ground-facility widely used in aerospace and aeronautics science and technology for studies on gas dynamic and chemical-physical processes in gases at high-temperature, explosions and dynamic calibration of pressure sensors. A shock tube in its simplest form is comprised of two separate tubes of equal cross-section by a diaphragm. The diaphragm function is to separate the two reservoirs at different pressures. The reservoir containing high pressure is called the Driver, the low pressure reservoir is called Driven. When the diaphragm is broken by pressure difference, a normal shock wave and non-stationary (named Incident Shock Wave) will be formed in the same place of diaphragm and will get around toward the closed end of Driven. When this shock wave reaches the closer end of the Driven section will be completely reflected. Now, the shock wave will interact with the boundary layer that was created by the induced flow by incident shock wave passage. The interaction between boundary layer and shock wave force the separation of the boundary layer. The aim of this paper is to make an analysis of influences of separation of the boundary layer in the reservoir pressure in the shock tube. A comparison among CDF (Computational Fluids Dynamics), experiments test and analytical analysis were performed. For the analytical analysis, some routines in Python was created, in the numerical simulations (Computational Fluids Dynamics) was used the Ansys Fluent, and the experimental tests were used T1 shock tube located in IEAv (Institute of Advanced Studies).

Keywords: boundary layer separation, moving shock wave, shock tube, transient simulation

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Authors: Fathi Alwafie

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In this paper we present the simulation of the propagation characteristics of the picocellular propagation channel environment. The first aim has been to find a correct description of the environment for received wave. The result of the first investigations is that the environment of the indoor wave significantly changes as we change the electric parameters of material constructions. A modified 3D ray tracing image method tool has been utilized for the coverage prediction. A detailed analysis of the dependence of the indoor wave on the wide-band characteristics of the channel: Root Mean Square (RMS) delay spread characteristics and mean excess delay, is also investigated.

Keywords: propagation, ray tracing, network, mobile computing

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Authors: María L. Jalón, Feargal Brennan

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A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response.

Keywords: non-stationary stochastic optimization, oscillating water, temporal variability, wave energy

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Authors: R. E. Fat-Helbary, A. A. Abdel-latief, M. S. Arfa, Alaa Mostafa

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The Egyptian Government proposed a general plan, aiming at constructing new settlements for Nubian in south Aswan in different places around Nasser Lake, one of these settlements in Kurkur area. The Nubian habitations in Wadi Kurkur are located around 30 km southwest of Aswan City. This area are affecting by near distance earthquakes from Kalabsha faults system. The shallow seismic refraction technique was conducted at the study area, to evaluate the soil and rock material quality and geotechnical parameters, in addition to the detection of the subsurface ground model under the study area. The P and S-wave velocities were calculated. The surface layer has P-wave, velocity ranges from 900 m/sec to 1625 m/sec and S-wave velocity ranges from 650 m/sec to 1400 m/sec. On the other hand the bedrock has P-wave velocity ranges from 1300 m/sec to 1980 m/sec and S-wave velocity ranges from 1050 m/sec to1725 m/sec. Measuring Vp and Vs velocities together with bulk density are calculated and used to extract the mechanical properties and geotechnical parameters of the foundation material at the study area. Output of this study is very important for solving the problems, which associated with the construction of various civil engineering purposes, for land use planning and for earthquakes resistant structure design.

Keywords: shallow seismic refraction technique, Kurkur area, p and s-wave velocities, geotechnical parameters, bulk density, Kalabsha faults

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Authors: Mustafa Ekici

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Natural convection is a basic process which is important in a wide variety of practical applications. In essence, a heated fluid expands and rises from buoyancy due to decreased density. Numerous papers have been written on natural or mixed convection in vertical ducts heated on the side. These equations have been proved to be valuable tools for the modelling of many phenomena such as fluid dynamics. Finding solutions to such equations or system of equations are in general not an easy task. We propose a method, which is called differential transform method, of solving a non-linear equations and compare the results with some of the other techniques. Illustrative examples shows that the results are in good agreement.

Keywords: differential transform method, momentum, energy equation, boundry value problem

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Authors: Fatemeh Sadat Sharifi

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In the present study, the capabilities of WAVEWATCH-III and MIKE21-SW for predicting the characteristics of wind waves in Hormuz Strait are evaluated. The GFS wind data (Global Forecast System) were derived. The bathymetry of gride with 2 arc-minute resolution, also were extracted from the ETOPO1. WAVEWATCH-III findings illustrate more valid prediction of wave features comparing to the MIKE-21 SW in deep water. Apparently, in shallow area, the MIKE-21 provides more uniformities with altimetry measurements. This may be due to the merits of the unstructured grid which are used in MIKE-21, leading to better representations of the coastal area. The findings on the direction of waves generated by wind in the modeling area indicate that in some regions, despite the increase in wind speed, significant wave height stays nearly unchanged. This is fundamental because of swift changes in wind track over the Strait of Hormuz. After discussing wind-induced waves in the region, the impact of instability of the surface layer on wave growth has been considered. For this purpose, the average monthly mean air temperature has been used. The results in cold months, when the surface layer is unstable, indicates an acceptable increase in the accuracy of prediction of the indicator wave height.

Keywords: numerical modeling, WAVEWATCH-III, Strait of Hormuz, MIKE21-SW

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Authors: Meziane Belkacem

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We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics.

Keywords: Physics, optics, nonlinear dynamics, chaos

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Authors: Haode Huo, Jingjing He, Rui Kang, Xuefei Guan

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This paper presents a study of Lamb wave damage diagnosis of composite delamination using instantaneous phase data. Numerical experiments are performed using the finite element method. Different sizes of delamination damages are modeled using finite element package ABAQUS. Lamb wave excitation and responses data are obtained using a pitch-catch configuration. Empirical mode decomposition is employed to extract the intrinsic mode functions (IMF). Hilbert–Huang Transform is applied to each of the resulting IMFs to obtain the instantaneous phase information. The baseline data for healthy plates are also generated using the same procedure. The size of delamination is correlated with the instantaneous phase change for damage diagnosis. It is observed that the unwrapped instantaneous phase of shows a consistent behavior with the increasing delamination size.

Keywords: delamination, lamb wave, finite element method, EMD, instantaneous phase

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Authors: Andriy Didenko, Zanin Kavazovic

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Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills.

Keywords: student project, Euler's method, spreadsheet, engineering education

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Authors: Chuan-Wen Liu, Min-Hsien Liu, Chung-Chieh Tai, Bing-Cheng Kuo, Cheng-Lung Chen, Huazhen Shen

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A recent surge in research on magnetic radar absorbing materials (RAMs) has presented researchers with new opportunities and challenges. This study was performed to gain a better understanding of the wave-absorbing phenomenon of magnetic RAMs. First, we hypothesized that the absorbing phenomenon is dependent on the particle shape. Using the Material Studio program and the micro-dot magnetic dipoles (MDMD) method, we obtained results from magnetic RAMs to support this hypothesis. The total MDMD energy of disk-like iron particles was greater than that of spherical iron particles. In addition, the particulate aggregation phenomenon decreases the wave-absorbance, according to both experiments and computational data. To conclude, this study may be of importance in terms of explaining the wave- absorbing characteristic of magnetic RAMs. Combining molecular dynamics simulation results and the theory of magnetization of magnetic dots, we investigated the magnetic properties of iron materials with different particle shapes and degrees of aggregation under external magnetic fields. The MDMD of the materials under magnetic fields of various strengths were simulated. Our results suggested that disk-like iron particles had a better magnetization than spherical iron particles. This result could be correlated with the magnetic wave- absorbing property of iron material.

Keywords: wave-absorbing property, magnetic material, micro-dot magnetic dipole, particulate aggregation

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Authors: Gaspar J. Machado, Stéphane Clain, Raphael Loubère

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The goal of the present work is to numerically study steady-state nonlinear hyperbolic equations in the context of the finite volume framework. We will consider the unidimensional Burgers' equation as the reference case for the scalar situation and the unidimensional Euler equations for the vectorial situation. We consider two approaches to solve the nonlinear equations: a time marching algorithm and a direct steady-state approach. We first develop the necessary and sufficient conditions to obtain the existence and unicity of the solution. We treat regular examples and solutions with a steady shock and to provide very-high-order finite volume approximations we implement a method based on the MOOD technology (Multi-dimensional Optimal Order Detection). The main ingredient consists in using an 'a posteriori' limiting strategy to eliminate non physical oscillations deriving from the Gibbs phenomenon while keeping a high accuracy for the smooth part.

Keywords: Euler equations, finite volume, MOOD, steady-state

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Authors: Richard Mitchell, Robert Mitchell, Thai Duong, Kyungbin Bae, Daegon Kim, Youngsub Lee, Inho Kim, Inho Park, Hyungseok Lee

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Although X-band radar is commonly used to measure the properties of ocean waves, the use of a higher frequency has several advantages, such as increased backscatter coefficient, better Doppler sensitivity, lower power, and a smaller package. A low-power Ku-band radar system was developed to demonstrate these advantages. It is fully coherent, and it interleaves short and long pulses to achieve a transmit duty ratio of 25%, which makes the best use of solid-state amplifiers. The range scales are 2 km, 4 km, and 8 km. The minimum range is 100 m, 200 m, and 400 m for the three range scales, and the range resolution is 4 m, 8 m, and 16 m for the three range scales. Measurements of the significant wave height, wavelength, wave period, and wave direction have been made using traditional 3D-FFT methods. Radar and ultrasonic sensor results collected over an extended period of time at a coastal site in South Korea are presented.

Keywords: measurement of ocean wave parameters, Ku-band radar, coherent radar, compact radar

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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: Zahid Ullah, Atlas Khan

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This research endeavors to explore the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. These equations hold significance in understanding complex physical systems like porous media flow, with applications spanning various branches of mathematics. The focus is on unraveling and analyzing regularity results to gain insights into the smoothness of solutions for these highly degenerate equations. Elliptic equations, fundamental in expressing and understanding diverse physical phenomena through partial differential equations (PDEs), are particularly adept at modeling steady-state and equilibrium behaviors. However, within the realm of elliptic equations, the subset of extremely degenerate cases presents a level of complexity that challenges traditional analytical methods, necessitating a deeper exploration of mathematical theory. While elliptic equations are celebrated for their versatility in capturing smooth and continuous behaviors across different disciplines, the introduction of degeneracy adds a layer of intricacy. Extremely degenerate elliptic equations are characterized by coefficients approaching singular behavior, posing non-trivial challenges in establishing classical solutions. Still, the exploration of extremely degenerate cases remains uncharted territory, requiring a profound understanding of mathematical structures and their implications. The motivation behind this research lies in addressing gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations. The study of extreme degeneracy is prompted by its prevalence in real-world applications, where physical phenomena often exhibit characteristics defying conventional mathematical modeling. Whether examining porous media flow or highly anisotropic materials, comprehending the regularity of solutions becomes crucial. Through this research, the aim is to contribute not only to the theoretical foundations of mathematics but also to the practical applicability of mathematical models in diverse scientific fields.

Keywords: elliptic equations, extremely degenerate, regularity results, partial differential equations, mathematical modeling, porous media flow

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Authors: Davood Yazdani Cherati, Hussein Hashemi Senejani

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In this paper, a convenient analytical solution for a system of coupled differential equations, derived from thermo-hydro-mechanical analysis of three-phase porous media such as unsaturated soils is developed. This kind of analysis can be used in various fields such as geothermal energy systems and seepage of leachate from buried municipal and domestic waste in geomaterials. Initially, a system of coupled differential equations, including energy, mass, and momentum conservation equations is considered, and an analytical method called AGM is employed to solve the problem. The method is straightforward and comprehensible and can be used to solve various nonlinear partial differential equations (PDEs). Results indicate the accuracy of the applied method for solving nonlinear partial differential equations.

Keywords: AGM, analytical solution, porous media, thermo-hydro-mechanical, unsaturated soils

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Authors: Jessada Tariboon

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In this article, using distribution kernel, we study the nonlinear equations with n-dimensional telegraph operator iterated k-times.

Keywords: telegraph operator, elementary solution, distribution kernel, nonlinear equations

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Authors: Trilok Mathur, Shivi Agarwal

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This paper deals with the solutions of fuzzy-fractional-order Riccati equations under Caputo-type fuzzy fractional derivatives. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhura difference and strongly generalized fuzzy differentiability. The Laplace-Adomian-Pade method is used for solving fractional Riccati-type initial value differential equations of fractional order. Moreover, we also displayed some examples to illustrate our methods.

Keywords: Caputo-type fuzzy fractional derivative, Fractional Riccati differential equations, Laplace-Adomian-Pade method, Mittag Leffler function

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Authors: Ruichong Zhang, Fadi Sawaged, Lotfi Gargab

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This paper introduces a wave-based approach for system identification of high-rise building structures with a pair of seismic recordings, which can be used to evaluate structural integrity and detect damage in post-earthquake structural condition assessment. The fundamental of the approach is based on wave features of generalized impulse and frequency response functions (GIRF and GFRF), i.e., wave responses at one structural location to an impulsive motion at another reference location in time and frequency domains respectively. With a pair of seismic recordings at the two locations, GFRF is obtainable as Fourier spectral ratio of the two recordings, and GIRF is then found with the inverse Fourier transformation of GFRF. With an appropriate continuous model for the structure, a closed-form solution of GFRF, and subsequent GIRF, can also be found in terms of wave transmission and reflection coefficients, which are related to structural physical properties above the impulse location. Matching the two sets of GFRF and/or GIRF from recordings and the model helps identify structural parameters such as wave velocity or shear modulus. For illustration, this study examines ten-story Millikan Library in Pasadena, California with recordings of Yorba Linda earthquake of September 3, 2002. The building is modelled as piecewise continuous layers, with which GFRF is derived as function of such building parameters as impedance, cross-sectional area, and damping. GIRF can then be found in closed form for some special cases and numerically in general. Not only does this study reveal the influential factors of building parameters in wave features of GIRF and GRFR, it also shows some system-identification results, which are consistent with other vibration- and wave-based results. Finally, this paper discusses the effectiveness of the proposed model in system identification.

Keywords: wave-based approach, seismic responses of buildings, wave propagation in structures, construction

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