Search results for: wave equation

Authors: Jaime E. Munoz, Jose C. Arcos, Oscar E. Bautista, Ivan E. Campos

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The influence of slippage phenomenon over the destabilization and atomization mechanisms induced via surface acoustic waves on a Newtonian, millimeter-sized, drop deposited on a hydrophilic substrate is studied theoretically. By implementing the Navier-slip model and a lubrication-type approach into the equations which govern the dynamic response of a drop exposed to acoustic stress, a highly nonlinear evolution equation for the air-liquid interface is derived in terms of the acoustic capillary number and the slip coefficient. By numerically solving such an evolution equation, the Spatio-temporal deformation of the drop's free surface is obtained; in this context, atomization of the initial drop into micron-sized droplets is predicted at our numerical model once the acoustically-driven capillary waves reach a critical value: the instability length. Our results show slippage phenomenon at systems with partial and complete wetting favors the formation of capillary waves at the free surface, which traduces in a major volume of liquid being atomized in comparison to the no-slip case for a given time interval. In consequence, slippage at the wall possesses the capability to affect and improve the atomization rate for a drop exposed to a high-frequency acoustic field.

Keywords: capillary instability, lubrication theory, navier-slip condition, SAW atomization

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Authors: Khashayar Kazemzadeh, Mohammad Hanif Dasoomi

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According to the increasing volume of traffic, lane changing plays a crucial role in traffic flow. Lane changing in traffic depends on several factors including road geometrical design, speed, drivers’ behavioral characteristics, etc. A great deal of research has been carried out regarding these fields. Despite of the other significant factors, the drivers’ behavioral characteristics of lane changing has been emphasized in this paper. This paper has predicted the effective equation based on personal characteristics of lane changing by regression models.

Keywords: effective equation, lane changing, drivers’ behavioral characteristics, regression models

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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: Herlina Abdul Rahim, Javad Abbaszadeh, Ruzairi Abdul Rahim

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In this research, the non-invasive ultrasonic transmission tomography is investigated. In order to model the ultrasonic wave scattering for different thickness of metal pipes, two-dimensional (2D) finite element modeling (FEM) has been utilized. The wall thickness variation of the metal pipe and its influence on propagation of the ultrasonic pressure wave are explored in this paper, includes frequency analysing in order to find the maximum applicable frequency. The simulation results have been compared to experimental data and are shown to provide key insight for this well-defined experimental case by explaining the achieved reconstructed images from experimental setup. Finally, the experimental results which are useful for further investigation for the application of ultrasonic transmission tomography in industry are illustrated.

Keywords: ultrasonic transmission tomography, ultrasonic sensors, ultrasonic wave, non-invasive tomography, metal pipe

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Authors: A. R. Nezamabadi, M. Veiskarami

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This paper studies free vibration of simply supported functionally graded beams with piezoelectric layers based on the first order shear deformation theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. The governing equation is established. Resulting equation is solved using the Euler's equation. The effects of the constituent volume fractions, the influences of applied voltage on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: mechanical buckling, functionally graded beam, first order shear deformation theory, free vibration

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Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Illyas Isa, Mohamad Idris Saidin, Mustaffa Ahmad, Norhayati Hashim

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A highly selective and sensitive electrode for determination of trace amounts of Cu (II) using square wave anodic stripping voltammetry (SWASV) was proposed. The electrode was made of the paste of multiwall carbon nanotubes (MWCNT) and 2,6–diacetylpyridine-di-(1R)–(-)–fenchone diazine tetracarbonylmolybdenum(0) at 100:5 (w/w). Under optimal conditions the electrode showed a linear relationship with concentration in the range of 1.0 × 10–10 to 1.0 × 10– 6 M Cu (II) and limit of detection 8.0 × 10–11 M Cu (II). The relative standard deviation (n = 5) of response to 1.0 × 10–6 M Cu(II) was 0.036. The interferences of cations such as Ni(II), Mg(II), Cd(II), Co(II), Hg(II), and Zn(II) (in 10 and 100-folds concentration) are negligible except from Pb (II). Electrochemical impedance spectroscopy (EIS) showed that the charge transfer at the electrode-solution interface was favorable. Result of analysis of Cu(II) in several water samples agreed well with those obtained by inductively coupled plasma-optical emission spectrometry (ICP-OES). The proposed electrode was then recommended as an alternative to spectroscopic technique in analyzing Cu (II).

Keywords: chemically modified electrode, Cu(II), Square wave anodic stripping voltammetry, tetracarbonylmolybdenum(0)

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Authors: Hao Min Chuah, Tatsuya Yamazaki, Ryosui Iwasawa, Tatsumi Suto

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In recent years, with the advancement of digital technology, the movement to introduce so-called ICT (Information and Communication Technology), such as computer technology and network technology, to civil engineering construction sites and construction sites is accelerating. As part of this movement, attempts are being made in various situations to reproduce actual sites inside computers and use them for designing and construction planning, as well as for training inexperienced engineers. The installation of wave-dissipating blocks on coasts, etc., is a type of work that has been carried out by skilled workers based on their years of experience and is one of the tasks that is difficult for inexperienced workers to carry out on site. Wave-dissipating blocks are structures that are designed to protect coasts, beaches, and so on from erosion by reducing the energy of ocean waves. Wave-dissipating blocks usually weigh more than 1 t and are installed by being suspended by a crane, so it would be time-consuming and costly for inexperienced workers to train on-site. In this paper, therefore, a block installation simulator is developed based on Unity 3D, a game development engine. The simulator computes porosity. Porosity is defined as the ratio of the total volume of the wave breaker blocks inside the structure to the final shape of the ideal structure. Using the evaluation of porosity, the simulator can determine how well the user is able to install the blocks. The voxelization technique is used to calculate the porosity of the structure, simplifying the calculations. Other techniques, such as raycasting and box overlapping, are employed for accurate simulation. In the near future, the simulator will install an automatic block installation algorithm based on combinatorial optimization solutions and compare the user-demonstrated block installation and the appropriate installation solved by the algorithm.

Keywords: 3D simulator, porosity, user interface, voxelization, wave-dissipating blocks

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Authors: Chao-Qing Dai

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Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

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

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Authors: Masoud Ghermezi

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Studying the sheet metals is one of the most important research areas in the field of metal forming due to their extensive applications in the aerospace industries. A useful method for determining the forming limit of these materials and consequently preventing the rupture of sheet metals during the forming process is the use of the forming limit curve (FLC). In addition to specifying the forming limit, this curve also delineates a boundary for the allowed values of strain in sheet metal forming; these characteristics of the FLC along with its accuracy of computation and wide range of applications have made this curve the basis of research in the present paper. This study presents a new model that not only agrees with the results obtained from the above mentioned theory, but also eliminates its shortcomings. In this theory, like in the M-K theory, a thin sheet with an inhomogeneity as a gradient thickness reduction with a sinusoidal function has been chosen and subjected to two-dimensional stress. Through analytical evaluation, ultimately, a governing differential equation has been obtained. The numerical solution of this equation for the range of positive strains (stretched region) yields the results that agree with the results obtained from M-K theory. Also the solution of this equation for the range of negative strains (tension region) completes the FLC curve. The findings obtained by applying this equation on two alloys with the hardening exponents of 0.4 and 0.24 indicate the validity of the presented equation.

Keywords: sheet metal, metal forming, forming limit curve (FLC), M-K theory

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Authors: Alexander P. Smirnov, Sergey A. Matveev, Dmitry A. Zheltkov, Eugene E. Tyrtyshnikov

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We propose a new computational technique for multidimensional (multicomponent) Smoluchowski coagulation equation. Using low-rank approximations in Tensor Train format of both the solution and the coagulation kernel, we accelerate the classical finite-difference Runge-Kutta scheme keeping its level of accuracy. The complexity of the taken finite-difference scheme is reduced from O(N^2d) to O(d^2 N log N ), where N is the number of grid nodes and d is a dimensionality of the problem. The efficiency and the accuracy of the new method are demonstrated on concrete problem with known analytical solution.

Keywords: tensor train decomposition, multicomponent Smoluchowski equation, runge-kutta scheme, convolution

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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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: Maitri Dave

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Coronaviruses (CoV) is such infectious virus which has impacted globally in a more dangerous manner causing severe lung problems and leaving behind more serious diseases among the people. This pandemic has affected globally and created severe respiratory problems, and damaged the lungs. India has reported the first case of COVID-19 in January 2020. The first wave of COVID-19 took place from April to September of 2020. Soon after, a second peak is also noticed in the month of March 2021, which in turn becomes more dangerous due to a lack of supply of medical equipment. It created resource deficiency globally, specifically in India, where some necessary life-saving equipment like ventilators and oxygenators were not sufficient to cater to the demand-supply ratio effectively. Through carefully examining such a situation, India began to execute the process of vaccination in the month of January 2021 and successfully administered 25,46,71,259 doses of vaccines till now, which is only 15.5% of the total population while only 3.6% of the total population is fully vaccinated. India has authorized the British Oxford–AstraZeneca vaccine (Covishield), the Indian BBV152 (Covaxin) vaccine, and the Russian Sputnik V vaccine for emergency use. In the present study, we have collected all the data state wisely of both first and second wave and analyzed them using MS Excel Version 2019 and SPSS Statistics Version 26. Following the trends, we have predicted the characteristics of the upcoming third wave of COVID-19 and recommended some strategies, early actions, and measures that can be taken by the public health system in India to combat the third wave more effectively.

Keywords: COVID-19, vaccination, Covishiled, Coronavirus

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Authors: Shubham Jaiswal

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In the present article, a drive is taken to compute the solution of spatial fractional order advection-dispersion equation having source/sink term with given initial and boundary conditions. The equation is converted to a system of ordinary differential equations using second-kind shifted Chebyshev polynomials, which have finally been solved using finite difference method. The striking feature of the article is the fast transportation of solute concentration as and when the system approaches fractional order from standard order for specified values of the parameters of the system.

Keywords: spatial fractional order advection-dispersion equation, second-kind shifted Chebyshev polynomial, collocation method, conservative system, non-conservative system

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Authors: Moien Mojabi, Aurelien Hospital, Daniel Potts, Chris Young, Albert Leung

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The wave analysis is an integral part of the hydrotechnical assessment carried out during the permitting and design phases for coastal structures, such as marinas. This analysis aims in quantifying: i) the Suitability of the coastal structure design against Small Craft Harbour wave tranquility safety criterion; ii) Potential environmental impacts of the structure (e.g., effect on wave, flow, and sediment transport); iii) Mooring and dock design and iv) Requirements set by regulatory agency’s (e.g., WSA section 11 application). While a complex three-dimensional hydrodynamic modelling approach can be applied on large-scale projects, the need for an efficient and reliable wave analysis method suitable for smaller scale marina projects was identified. As a result, Tetra Tech has developed and applied an integrated analysis framework (hereafter TT approach), which takes the advantage of the state-of-the-art numerical models while preserving the level of simplicity that fits smaller scale projects. The present paper aims to describe the TT approach and highlight the key advantages of using this integrated framework in lake marina projects. The core of this methodology is made by integrating wind, water level, bathymetry, and structure geometry data. To respond to the needs of specific projects, several add-on modules have been added to the core of the TT approach. The main advantages of this method over the simplified analytical approaches are i) Accounting for the proper physics of the lake through the modelling of the entire lake (capturing real lake geometry) instead of a simplified fetch approach; ii) Providing a more realistic representation of the waves by modelling random waves instead of monochromatic waves; iii) Modelling wave-structure interaction (e.g. wave transmission/reflection application for floating structures and piles amongst others); iv) Accounting for wave interaction with the lakebed (e.g. bottom friction, refraction, and breaking); v) Providing the inputs for flow and sediment transport assessment at the project site; vi) Taking in consideration historical and geographical variations of the wind field; and vii) Independence of the scale of the reservoir under study. Overall, in comparison with simplified analytical approaches, this integrated framework provides a more realistic and reliable estimation of wave parameters (and its spatial distribution) in lake marinas, leading to a realistic hydrotechnical assessment accessible to any project size, from the development of a new marina to marina expansion and pile replacement. Tetra Tech has successfully utilized this approach since many years in the Okanagan area.

Keywords: wave modelling, wind-wave, extreme value analysis, marina

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Authors: Mohammad Reza Ebrahimi

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In new restructured power systems, swift fault detection is very important. The parallel transmission-lines are vastly used in this kind of power systems because of high amount of energy transferring. In this paper, a method based on the comparison of two schemes, i.e., i) maximum magnitude of travelling-wave (TW) energy ii) the instants of maximum energy occurrence at the circuits of parallel transmission-line is proposed. Using the travelling-wave of fault in order to faulted line identification this method has noticeable operation time. Moreover, the algorithm can cover for identification of faults as external or internal faults. For an internal fault, the exact location of the fault can be estimated confidently. A lot of simulations have been done with PSCAD/EMTDC to verify the performance of the proposed algorithm.

Keywords: travelling-wave, maximum energy, parallel transmission-line, fault location

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Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: Chao He, Shunhua Zhou, Peijun Guo

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The vast majority of existing underground railway lines consist of twin tunnels. In this paper, the dynamic interaction between two neighboring tunnels in a layered half-space is investigated by an analytical model. The two tunnels are modelled as cylindrical thin shells, while the soil in the form of a layered half-space with two cylindrical cavities is simulated by the elastic continuum theory. The transfer matrix method is first used to derive the relationship between the plane wave vectors in arbitrary layers and the source layer. Thereafter, the wave translation and transformation are introduced to determine the plane and cylindrical wave vectors in the source layer. The solution for the dynamic interaction between twin tunnels in a layered half-space is obtained by means of the compatibility of displacements and equilibrium of stresses on the two tunnel–soil interfaces. By coupling the proposed model with a fully track model, the train-induced vibrations from twin tunnels in a multi-layered half-space are investigated. The numerical results demonstrate that the existence of a neighboring tunnel has a significant effect on ground vibrations.

Keywords: underground railway, twin tunnels, wave translation and transformation, transfer matrix method

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Authors: Yuri Boiko, Iluju Kiringa, Tet Yeap

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We use modeling and simulation tools, to introduce a novel bias injection attack, named the ’Induced Pulsation Attack’, which targets Cyber Physical Systems with closed-loop controlled Brushless DC (BLDC) motor and Kalman filter driver in the feedback loop. This attack involves engaging a linear function with a constant gradient to distort the coefficient of the injected bias, which falsifies the Kalman filter estimates of the rotor’s angular speed. As a result, this manipulation interaction inside the control system causes periodic pulsations in a form of asymmetric sine wave of both current and voltage in the circuit windings, with a high magnitude. It is shown that by varying the gradient of linear function, one can control both the frequency and structure of the induced pulsations. It is also demonstrated that terminating the attack at any point leads to additional compensating effort from the controller to restore the speed to its equilibrium value. This compensation effort produces an exponentially decaying wave, which we call the ’attack withdrawal syndrome’ wave. The conditions for maximizing or minimizing the impact of the attack withdrawal syndrome are determined. Linking the termination of the attack to the end of the full period of the induced pulsation wave has been shown to nullify the attack withdrawal syndrome wave, thereby improving the attack’s covertness.

Keywords: cyber-attack, induced pulsation, bias injection, Kalman filter, BLDC motor, control system, closed loop, P- controller, PID-controller, saw-function, cyber-physical system

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Authors: Kajal K. Patel, M. N. Mehta, T. R. Singh

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When water is injected in oil formatted area in secondary oil recovery process the instability occurs near common interface due to viscosity difference of injected water and native oil. The governing equation gives rise to the non-linear partial differential equation and its solution has been obtained by Homotopy analysis method with appropriate guess value of the solution together with some conditions and standard relations. The solution gives the average cross-sectional area occupied by the schematic fingers during the occurs of instability phenomenon. The numerical and graphical presentation has developed by using Maple software.

Keywords: capillary pressure, homotopy analysis method, instability phenomenon, viscosity

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Authors: Chien-Lin Wang, Cha-Ling Ko, Tainsong Chen

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Pulse wave velocity (PWV) of blood flow provides important information of vessel property and blood pressure which can be used to assess cardiovascular disease. However, the above measurements need expensive equipment, such as Doppler ultrasound, MRI, angiography etc. The photoplethysmograph (PPG) signals are commonly utilized to detect blood volume changes. In this study, two infrared (IR) probes are designed and placed at a fixed distance from finger base and fingertip. An analog circuit with automatic gain adjustment is implemented to get the stable original PPG signals from above two IR probes. In order to obtain the time delay precisely between two PPG signals, we obtain the pulse transit time from the second derivative of the original PPG signals. To get a portable, wireless and low power consumption PWV measurement device, the low energy Bluetooth 4.0 (BLE) and the microprocessor (Cortex™-M3) are used in this study. The PWV is highly correlated with blood pressure. This portable device has potential to be used for continuous blood pressure monitoring.

Keywords: pulse wave velocity, photoplethysmography, portable device, biomedical engineering

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Authors: Clarinda Vitorino Nhangumbe, Ercília Sousa

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Weather derivatives are financial products used to cover non catastrophic weather events with a weather index as the underlying asset. The rainfall weather derivative pricing model is modeled based in the assumption that the rainfall dynamics follows Ornstein-Uhlenbeck process, and the partial differential equation approach is used to derive the convection-diffusion two dimensional time dependent partial differential equation, where the spatial variables are the rainfall index and rainfall depth. To compute the approximation solutions of the partial differential equation, the appropriate boundary conditions are suggested, and an explicit numerical method is proposed in order to deal efficiently with the different choices of the coefficients involved in the equation. Being an explicit numerical method, it will be conditionally stable, then the stability region of the numerical method and the order of convergence are discussed. The model is tested for real precipitation data.

Keywords: finite differences method, ornstein-uhlenbeck process, partial differential equations approach, rainfall derivatives

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Authors: S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, M. Suleiman

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The method of solving second order stiff ordinary differential equation (ODEs) that is based on backward differentiation formula (BDF) is considered in this paper. We derived the method by increasing the order of the existing method using an improved strategy in choosing the step size. Numerical results are presented to compare the efficiency of the proposed method to the MATLAB’s suite of ODEs solvers namely ode15s and ode23s. The method was found to be efficient to solve second order ordinary differential equation.

Keywords: backward differentiation formulae, block backward differentiation formulae, stiff ordinary differential equation, variable step size

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Authors: Ahmed A. El-Gindy, Elham S. El-Nashar, Abdallah Nafaa, Sameh El-Kafrawy

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The generation of energy from marine energy became one of the most preferable resources since it is a clean source and friendly to environment. Egypt has long shores along Mediterranean with important cities that need energy resources with significant wave energy. No detailed studies have been done on wave energy distribution in the Egyptian waters. The objective of this paper is to assess the energy wave power available in the Egyptian waters for the choice of the most suitable devices to be used in this area. This paper deals the characteristics and power of the offshore waves in the Egyptian waters. Since the field observations of waves are not frequent and need much technical work, the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis data in Mediterranean, with a grid size 0.75 degree, which is a relatively course grid, are considered in the present study for preliminary assessment of sea waves characteristics and power. The used data covers the period from 2012 to 2014. The data used are significant wave height (swh), mean wave period (mwp) and wave direction taken at six hourly intervals, at seven chosen stations, and at grid points covering the Egyptian waters. The wave power (wp) formula was used to calculate energy flux. Descriptive statistical analysis including monthly means and standard deviations of the swh, mwp, and wp. The percentiles of wave heights and their corresponding power are done, as a tool of choice of the best technology suitable for the site. The surfer is used to show spatial distributions of wp. The analysis of data at chosen 7 stations determined the potential of wp off important Egyptian cities. Offshore of Al Saloum and Marsa Matruh, the highest wp occurred in January and February (16.93-18.05) ± (18.08-22.12) kw/m while the lowest occurred in June and October (1.49-1.69) ± (1.45-1.74) kw/m. In front of Alexandria and Rashid, the highest wp occurred in January and February (16.93-18.05) ± (18.08-22.12) kw/m while the lowest occurred in June and September (1.29-2.01) ± (1.31-1.83) kw/m. In front of Damietta and Port Said, the highest wp occurred in February (14.29-17.61) ± (21.61-27.10) kw/m and the lowest occurred in June (0.94-0.96) ± (0.71-0.72) kw/m. In winter, the probabilities of waves higher than 0.8 m in percentage were, at Al Saloum and Marsa Matruh (76.56-80.33) ± (11.62-12.05), at Alexandria and Rashid (73.67-74.79) ± (16.21-18.59) and at Damietta and Port Said (66.28-68.69) ± (17.88-17.90). In spring, the percentiles were, at Al Saloum and Marsa Matruh, (48.17-50.92) ± (5.79-6.56), at Alexandria and Rashid, (39.38-43.59) ± (9.06-9.34) and at Damietta and Port Said, (31.59-33.61) ± (10.72-11.25). In summer, the probabilities were, at Al Saloum and Marsa Matruh (57.70-66.67) ± (4.87-6.83), at Alexandria and Rashid (59.96-65.13) ± (9.14-9.35) and at Damietta and Port Said (46.38-49.28) ± (10.89-11.47). In autumn, the probabilities were, at Al Saloum and Marsa Matruh (58.75-59.56) ± (2.55-5.84), at Alexandria and Rashid (47.78-52.13) ± (3.11-7.08) and at Damietta and Port Said (41.16-42.52) ± (7.52-8.34).

Keywords: distribution of sea waves energy, Egyptian Mediterranean waters, waves characteristics, waves power

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Authors: Raphael Zanella

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This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under the axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit march-in-time. The code is verified by space and time convergence tests using a manufactured solution. The solving of an example problem with an axisymmetric formulation is compared to that with a full-3D formulation. Both formulations lead to the same result, but the code based on the axisymmetric formulation is much faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest in using an axisymmetric formulation when it is possible.

Keywords: axisymmetric problem, continuous finite elements, heat equation, weak formulation

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Authors: Razieh Khalafi

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The brain is the information processing centre of the human body. Stimuli in the form of information are transferred to the brain and then brain makes the decision on how to respond to them. In this research, we propose a new partial differential equation which analyses the EEG signals and make a relationship between the incoming stimuli and the brain response to them. In order to test the proposed model, a set of external stimuli applied to the model and the model’s outputs were checked versus the real EEG data. The results show that this model can model the EEG signal well. The proposed model is useful not only for modelling of EEG signal in case external stimuli but it can be used for modelling of brain response in case of internal stimuli.

Keywords: brain, stimuli, partial differential equation, response, EEG signal

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Authors: Hind Mestouri

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The study and simulation of a millimeter wave antenna for 5G mobile communication systems is the topic of this paper. We present at the beginning the general aspects of the 5G technology. We recall the objectives of the 5G standard, its architecture, and the parameters that characterize it. The proposed antenna model is designed using the CST Microwave Studio simulation software. Numerous methods are used at all steps of the design procedures, such as theoretical calculation of parameters, declaration of parameter values, and evaluation of the antenna through the obtained results. Initially, we were interested in the design of an antenna array at the 10 GHz frequency. Afterward, we also simulated and presented an antenna array at 2.5 GHz. For each antenna designed, a parametric study was conducted to understand and highlight the role and effects of the various parameters in order to optimize them and achieve a final efficient structure. The obtained results using CST Microwave Studio showed that the characteristics of the designed antennas (bandwidth, gain, radiation pattern) satisfy the specifications of 5G mobile communications.

Keywords: 5G, antenna array, millimeter wave, 10 GHz, CST Microwave Studio

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Authors: Mohamed Elshobaki, Alessandro Valiani, Valerio Caleffi

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In this paper, we solve 1-D shallow water equation for sub-critical and super-critical water flow at junction. The water flow at junction has been studied for the last 50 years from the physical-hydraulic point of views and for numerical computations need more attention. For numerical simulation, we need to establish an inner boundary condition at the junction to avoid an oscillation which rise from the waves interactions at the junction. Indeed, we introduce a new boundary condition at the junction based on the mass conservation, total head, and the admissible wave relations between the flow parameters in the three branches to predict the water depths and discharges at the junction. These boundary conditions are valid for sub-critical flow and super-critical flow.

Keywords: numerical simulation, junction flow, sub-critical flow, super-critical flow

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Authors: Giacomo Ciani

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This paper reviews the impact of quantum noise on modern gravitational wave interferometers and explains how squeezed vacuum states are used to push the noise below the standard quantum limit. With the first detection of gravitational waves from a pair of colliding black holes in September 2015 and subsequent detections including that of gravitational waves from a pair of colliding neutron stars, the ground-based interferometric gravitational wave observatories LIGO and VIRGO have opened the era of gravitational-wave and multi-messenger astronomy. Improving the sensitivity of the detectors is of paramount importance to increase the number and quality of the detections, fully exploiting this new information channel about the universe. Although still in the commissioning phase and not at nominal sensitivity, these interferometers are designed to be ultimately limited by a combination of shot noise and quantum radiation pressure noise, which define an envelope known as the standard quantum limit. Despite the name, this limit can be beaten with the use of advanced quantum measurement techniques, with the use of squeezed vacuum states being currently the most mature and promising. Different strategies for implementation of the technology in the large-scale detectors, in both their frequency-independent and frequency-dependent variations, are presented, together with an analysis of the main technological issues and expected sensitivity gain.

Keywords: gravitational waves, interferometers, squeezed vacuum, standard quantum limit

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