Search results for: einstein field equations

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

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

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

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Authors: D. Pradeep Mitra, Prafulla

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

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

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Authors: Shyh Ming Chern

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

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

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Authors: Muhammad Asghar Saqib, Saad Saleem Khan, Syed Abdul Rahman Kashif

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In order to have higher efficiency, performance and reliability the regular monitoring of an electrical motor is required. This article presents a novel view of the air-gap magnetic field analysis of a switched reluctance motor under rotor cracks and rotor tilt along its shaft axis. The fault diagnosis is illustrated on the basis of a 3-D model of the motor using finite element analysis (FEA). The analytical equations of flux linkages have been used to determine the inductance. The results of the 3-D finite element analysis on a 6/4 switched reluctance motor (SRM) shows the variation of mutual inductance with the tilting of the rotor shaft and cracked rotor conditions. These results present useful information regarding the detection of shaft tilting and cracked rotors.

Keywords: switched reluctance motor, finite element analysis, cracked rotor, 3-D modelling of a srm

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Authors: Abdulatif Abdusalam, Mohamed Shaban

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In this paper, we consider the nonlinear pulse propagation through a nonuniform birefringent fiber Bragg grating (FBG) whose index modulation depth varies along the propagation direction. Here, the pulse propagation is governed by the nonlinear birefringent coupled mode (NLBCM) equations. To form the Bragg soliton outside the photonic bandgap (PBG), the NLBCM equations are reduced to the well known NLS type equation by multiple scale analysis. As we consider the pulse propagation in a nonuniform FBG, the pulse propagation outside the PBG is governed by inhomogeneous NLS (INLS) rather than NLS. We, then, discuss the formation of soliton in the FBG known as Bragg soliton whose central frequency lies outside but close to the PBG of the grating structure. Further, we discuss Bragg soliton compression due to a delicate balance between the SPM and the varying grating induced dispersion. In addition, Bragg soliton collision, Bragg soliton switching and possible logic gates have also been discussed.

Keywords: Bragg grating, non uniform fiber, non linear pulse

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Authors: Karen E. Supan

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Thermal degradation kinetics of switchgrass (Panicum virgatum) from the field, as well as in a pellet form, are presented. Thermogravimetric analysis tests were performed at heating rates of 10-40 K min⁻¹ in an inert atmosphere. The activation energy and the pre-exponential factor were calculated using the Ozawa/Flynn/Wall method as suggested by the ASTM Standard Test Method for Decomposition Kinetics by Thermogravimetry. Four stages were seen in the degradation: dehydration, active pyrolysis of hemicellulose, active pyrolysis of cellulose, and passive pyrolysis. The derivative mass loss peak for active pyrolysis of cellulose in the field-dried sample was much higher than the pelletized. The range of activation energy in the 0.15 – 0.70 conversion interval was 191 – 242 kJ mol⁻¹ for the field-dried and 130-192 kJ mol⁻¹ for the pellets. The highest activation energies were achieved at 0.50 conversion and were 242 kJ mol⁻¹ and 192 kJ mol⁻¹ for the field-dried and pellets, respectively. The thermal degradation and activation energies were comparable to switchgrass and other biomass reported in the literature.

Keywords: biomass, switchgrass, thermal degradation, thermogravimetric analysis

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Authors: Pius W. Molo Chin

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Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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Authors: Siva Kumar Reddy, Anwesha Mukherjee, Abha Misra

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Excellent energy absorption capability in carbon nanotubes (CNT) is shown in their bulk structure that behaves like super compressible foam. Furthermore, a tunable mechanical behavior of CNT foam is achieved using several methods like changing the concentration of precursors, polymer impregnation, non covalent functionalization of CNT microstructure etc. Influence of magnetic field on compressive behavior of magnetic CNT demonstrated an enhanced peak stress and energy absorption capability, which does not require any surface and structural modification of the foam. This presentation discusses the mechanical behavior of micro porous CNT foam that is impregnated in magnetic field responsive fluid. Magnetic particles are dispersed in a nonmagnetic fluid so that alignment of both particles and CNT could play a crucial role in controlling the stiffness of the overall structure. It is revealed that the compressive behavior of CNT foam critically depends on the fluid viscosity as well as magnetic field intensity. Both peak Stress and energy absorption in CNT foam followed a power law behavior with the increase in the magnetic field intensity. However, in the absence of magnetic field, both peak stress and energy absorption capability of CNT foam presented a linear dependence on the fluid viscosity. Hence, this work demonstrates the role magnetic filed in controlling the mechanical behavior of the foams prepared at nanoscale.

Keywords: carbon nanotubes, magnetic field, energy absorption capability and viscosity

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Authors: Xiaodong Wen, Lijuan Liu, Xinfeng Sun

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A high power electrodeless plasma thruster is being developed at Lanzhou Institute of Physics. In this thruster, a rotating magnetic field (RMF) driven by two radio-frequency coils which dephased by 90 degrees are applied both for propellant ionization and plasma acceleration. In the ionization stage, a very high azimuthal current can be driven by RMF and then makes plasma forms a field reversed configuration, namely self-confined plasmoid. Profoundly understanding the transport characteristics of the plasmoid in the following acceleration stage is the key to improve the thruster performances. In this paper, a 3D MHD model is established and the influences of the RMF and an applied magnetic field on the self-confined plasmoid acceleration are investigated. The simulation results show that, by applying a RMF with strength and frequency of 250 G and 370 kHz, the plasmoid can be accelerated to an average velocity of 17 km/s at the exit of the thruster.

Keywords: electric space propulsion, field reversed configuration, rotating magnetic field, transport phenomena

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Authors: Balgaisha Mukanova, Tolkyn Mirgalikyzy

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Theory of interpretation of electromagnetic fields studied in the electrical prospecting with direct current is mainly developed for the case of a horizontal surface observation. However in practice we often have to work in difficult terrain surface. Conducting interpretation without the influence of topography can cause non-existent anomalies on sections. This raises the problem of studying the impact of different shapes of ground surface relief on the results of electrical prospecting's research. This research examines the numerical solutions of the direct problem of electrical prospecting for two-dimensional and three-dimensional media, taking into account the terrain. The problem is solved using the method of integral equations. The density of secondary currents on the relief surface is obtained.

Keywords: ground surface relief, method of integral equations, numerical method, electromagnetic

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Authors: Taha Zakaraia Abdel Wahid

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The behavior of the unsteady non-equilibrium distribution function for a dilute gas under the effect of non-linear thermal radiation field is presented. For the best of our knowledge this is done for the first time at all. The distinction and comparisons between the unsteady perturbed and the unsteady equilibrium velocity distribution functions are illustrated. The equilibrium time for the dilute gas is determined for the first time. The non-equilibrium thermodynamic properties of the system (gas+the heated plate) are investigated. The results are applied to the Argon gas, for various values of radiation field intensity. 3D-Graphics illustrating the calculated variables are drawn to predict their behavior. The results are discussed.

Keywords: dilute gas, radiation field, exact solutions, travelling wave method, unsteady BGK model, irreversible thermodynamics, unsteady non-equilibrium distribution functions

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Authors: Dana S. Smith, Angela Goins, Shahnaz Savani

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Using a mixed-methods approach, this study explored costs to student wellbeing generated by the social work field practicum requirement. The project was conducted by faculty at a medium-sized university in the United States. Social work educators and field practicum instructors participated in interviews. Students and former students completed surveys on the topic. The data analysis revealed emotional burdens as well as threats to student wellbeing in association with the fieldwork required for those in pursuit of a social work degree. The study includes recommendations for anti-oppressive approaches for academic programs and implications for further research.

Keywords: emotional wellbeing, field practicum, mixed-methods, social justice

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Authors: Dana S. Smith, Angela Goins, Shahnaz Savani

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Using a mixed-methods approach, this study explored costs to student wellbeing generated by the social work field practicum requirement. The project was conducted by faculty at a medium sized university in the United States. Social work educators and field practicum instructors participated in interviews. Students and former students completed surveys on the topic. The data analysis revealed emotional burdens as well as threats to student wellbeing in association with the fieldwork required for those in pursuit of a social work degree. The study includes recommendations of anti-oppressive approaches for academic programs and implications for further research.

Keywords: emotional wellbeing, field practicum, mixed-methods, social justice

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Authors: C. Casini, V. Da Deppo, P. Zuppella, P. Chioetto, A. Slemer, F. Frassetto, M. Romoli, F. Landini, M. Pancrazzi, V. Andretta, E. Antonucci, A. Bemporad, M. Casti, Y. De Leo, M. Fabi, S. Fineschi, F. Frassati, C. Grimani, G. Jerse, P. Heinzel, K. Heerlein, A. Liberatore, E. Magli, G. Naletto, G. Nicolini, M.G. Pelizzo, P. Romano, C. Sasso, D. Spadaro, M. Stangalini, T. Straus, R. Susino, L. Teriaca, M. Uslenghi, A. Volpicelli

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Solar Orbiter, launched on February 9^th 2020, is an ESA/NASA mission conceived to study the Sun. The payload is composed of 10 instruments, among which there is the Metis coronagraph. A coronagraph aims at taking images of the solar corona: the occulter element simulates a total solar eclipse. This work presents some of the results obtained in the visible light band (580-640 nm) using a flat field panel source. The flat field panel gives a uniform illumination; consequently, it has been used during the on-ground calibration for several purposes: evaluating the response of each pixel of the detector (linearity); and characterizing the Field of View of the coronagraph. As a conclusion, a major result is the verification that the requirement for the Field of View (FoV) of Metis is fulfilled. Some investigations are in progress in order to verify that the performance measured on-ground did not change after launch.

Keywords: solar orbiter, Metis, coronagraph, flat field panel, calibration, on-ground, performance

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Authors: M. Kalbac, T. Verhagen, K. Drogowska, J. Vejpravova

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One- and two-dimensional carbon nano structures with sp2 hybridization of carbon atoms (single walled carbon nano tubes and graphene) are promising materials in future electronic and spintronics devices due to specific character of their electronic structure. In this paper, we present a comparative study of graphene and single-wall carbon nano tubes by Raman spectro-microscopy in strong magnetic field. This unique method allows to study changes in electronic band structure of the two types of carbon nano structures induced by a strong magnetic field.

Keywords: carbon nano structures, magnetic field, raman spectroscopy, spectro-microscopy

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Authors: Dawid Sołoducha, Tomasz Borowski, Marian Kordas, Rafał Rakoczy

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The magnetic field in the past few years became an important part of many studies. Magnetic field (MF) may be used to affect the process in many ways; for example, it can be used as a factor to stabilize the system. We can use MF to steer the operation, to activate or inhibit the process, or even to affect the vital activity of microorganisms. Using various types of magnetic field generators is always connected with the delivery of some heat to the system. Heat transfer is a very important phenomenon; it can influence the process positively and negatively, so it’s necessary to measure heat stream transferred from the place of generation and prevent negative influence on the operation. The aim of the presented work was to apply various types of magnetic fields and to measure heat transfer phenomena. The results were obtained by continuous measurement at several measuring points with temperature probes. Results were compilated in the form of temperature profiles. The study investigated the undetermined heat transfer in a custom system equipped with a magnetic field generator. Experimental investigations are provided for the explanation of the influence of the various type of magnetic fields on the heat transfer process. The tested processes are described by means of the criteria which defined heat transfer intensification under the action of magnetic field.

Keywords: heat transfer, magnetic field, undetermined heat transfer, temperature profile

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Authors: Manasa Kalla, Narasimha Raju Chebrolu, Ashok Chatterjee

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We have studied the quantum transport properties of a single molecular transistor in the presence of an external magnetic field using the Keldysh Green function technique. We also used the Anderson-Holstein-Caldeira-Leggett Model to describe the single molecular transistor that consists of a molecular quantum dot (QD) coupled to two metallic leads and placed on a substrate that acts as a heat bath. The phonons are eliminated by the Lang-Firsov transformation and the effective Hamiltonian is used to study the effect of an external magnetic field on the spectral density function, Tunneling Current, Differential Conductance and Spin polarization. A peak in the spectral function corresponds to a possible excitation. In the presence of a magnetic field, the spin-up and spin-down states are degenerate and this degeneracy is lifted by the magnetic field leading to the splitting of the central peak of the spectral function. The tunneling current decreases with increasing magnetic field. We have observed that even the differential conductance peak in the zero magnetic field curve is split in the presence electron-phonon interaction. As the magnetic field is increased, each peak splits into two peaks. And each peak indicates the existence of an energy level. Thus the number of energy levels for transport in the bias window increases with the magnetic field. In the presence of the electron-phonon interaction, Differential Conductance in general gets reduced and decreases faster with the magnetic field. As magnetic field strength increases, the spin polarization of the current is increasing. Our results show that a strongly interacting QD coupled to metallic leads in the presence of external magnetic field parallel to the plane of QD acts as a spin filter at zero temperature.

Keywords: Anderson-Holstein model, Caldeira-Leggett model, spin-polarization, quantum dots

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Authors: Chia-Jui Yu, Chien-Ju Chen, Jyun-Hao Liao, Chia-Ching Wu, Meng-Chyi Wu

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In this letter, we demonstrate high-performance AlGaN/GaN planar Schottky barrier diodes (SBDs) on the silicon substrate with field plate structure for increasing breakdown voltage V_B. A low turn-on resistance R_ON (3.55 mΩ-cm²), low reverse leakage current (< 0.1 µA) at -100 V, and high reverse breakdown voltage V_B (> 1.1 kV) SBD has been fabricated. A virgin SBD exhibited a breakdown voltage (measured at 1 mA/mm) of 615 V, and with the field plate technology device exhibited a breakdown voltage (measured at 1 mA/mm) of 1525 V (the anode–cathode distance was L_AC = 40 µm). Devices without the field plate design exhibit a Baliga’s figure of merit of V_B²/ R_ON = 60.2 MW/cm², whereas devices with the field plate design show a Baliga’s figure of merit of V_B²/ R_ON = 340.9 MW/cm² (the anode–cathode distance was L_AC = 20 µm).

Keywords: AlGaN/GaN heterostructure, silicon substrate, Schottky barrier diode (SBD), high breakdown voltage, Baliga’s figure-of-merit, field plate

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Authors: Bijay Kumar Sahoo

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An important feature of InₓGa₁-ₓN/GaN heterostructures is strong built-in polarization (BIP) electric field at the hetero-interface due to spontaneous (sp) and piezoelectric (pz) polarizations. The intensity of this electric field reaches several MV/cm. This field has profound impact on optical, electrical and thermal properties. In this work, the effect of BIP field on thermal conductivity of InₓGa₁-ₓN/GaN heterostructure has been investigated theoretically. The interaction between the elastic strain and built in electric field induces additional electric polarization. This additional polarization contributes to the elastic constant of InₓGa₁-ₓN alloy. This in turn modifies material parameters of InₓGa₁-ₓN. The BIP mechanism enhances elastic constant, phonon velocity and Debye temperature and their bowing constants in InₓGa₁-ₓN alloy. These enhanced thermal parameters increase phonon mean free path which boost thermal conduction process. The thermal conductivity (k) of InxGa1-xN alloy has been estimated for x=0, 0.1, 0.3 and 0.9. Computation finds that irrespective of In content, the room temperature k of InₓGa₁-ₓN/GaN heterostructure is enhanced by BIP mechanism. Our analysis shows that at a certain temperature both k with and without BIP show crossover. Below this temperature k with BIP field is lower than k without BIP; however, above this temperature k with BIP field is significantly contributed by BIP mechanism leading to k with BIP field become higher than k without BIP field. The crossover temperature is primary pyroelectric transition temperature. The pyroelectric transition temperature of InₓGa₁-ₓN alloy has been predicted for different x. This signature of pyroelectric nature suggests that thermal conductivity can reveal pyroelectricity in InₓGa₁-ₓN alloy. The composition dependent room temperature k for x=0.1 and 0.3 are in line with prior experimental studies. The result can be used to minimize the self-heating effect in InₓGa₁-ₓN/GaN heterostructures.

Keywords: built-in polarization, phonon relaxation time, thermal properties of InₓGa₁-ₓN /GaN heterostructure, self-heating

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Authors: Farzad Tofigh, Saeideh Najafi, Reza Heidari, Rashid Jamei

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In order to study the effects of magnetic field on the root system and growth of Phaseolus vulgaris, an experiment was conducted in 2012. The possible involvement of magnetic field (MF) pretreatment in physiological factors of Phaseolus vulgaris was investigated. Seeds were subjected to 10 days with 1.8 mT of magnetic field for 1h per day. MF pretreatment decreased the plant height, fresh and dry weight, length of root and length of shoot, Chlorophyll a, Chlorophyll b and carotenoid in 10 days old seedling. In addition, activity of enzymes such as Catalase and Guaiacol peroxidase was decreased due to MF exposure. Also, the total Protein and DPPH content of the treated by magnetic field was not significantly changed in compare to control groups, while the flavonoid, Phenol and prolin content of the treated of the treated by magnetic field was significantly changed in compare to control groups. Lateral branches of roots and secondary roots increased with MF. The results suggest that pretreatment of this MF plays important roles in changes in crop productivity. In all cases there was observed a slight stimulating effect of the factors examined. The growth dynamics were weakened. The plants were shorter. Moreover, the effect of a magnetic field on the crop of Phaseolus vulgaris and its structure was small.

Keywords: carotenoid, chlorophyll a, chlorophyll b, DPPH, enzymes, flavonoid, germination, growth, phenol, proline, protein, magnetic field

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Authors: Amin Hamrahi

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Near Field Communication (NFC) is one of the latest wireless communication technologies. NFC enables electronic devices to communicate in short range using the radio waves. NFC offers safe yet simple communication between electronic devices. This technology provides the fastest way to communicate two device with in a fraction of second. With NFC technology, communication occurs when an NFC-compatible device is brought within a few centimeters of another NFC device. NFC is an open-platform technology that is being standardized in the NFC Forum. NFC is based on and extends on RFID. It operates on 13.56 MHz frequency.

Keywords: near field communication, NFC technology, wireless communication technologies, NFC-compatible device, NFC, communication

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Authors: Sabiha Chouchane, Azzedine Hani, Jean-Paul Chopart, Alexandra Levesque

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The electrodeposition of Zn-Ni alloy is mostly studied for its high degree of corrosion and mechanical properties. In this work, the zinc–nickel alloy coatings elaborated from sulfate bath have been carried out under low and high applied magnetic field. The effect of alloy stuctural parameters upon corrosion behavior is studied. It has been found that the magnetically induced convection changes the phase composition, promoting the zinc phase in spite of the γ-Ni₅Zn₂₁. Low magnetic field acts also on the morphology of the deposits as a levelling agent and a refiner by lowering the deposit roughness Ra and the spot size. For alloy obtained with low magnetic field (up to 1T) superimposition, surface morphology modification has no significant influence on corrosion behavior whereas for low nickel content alloy, the modification of phase composition, induced by applied magnetic field, favours higher polarization resistance. When high magnetic field amplitude is involved (up to12T), the phase composition modifications are the same that for low applied B and the morphology is not largely modified. In this case, the hydrogen reduction current dramatically decreases that leads to a large shift of the corrosion potential. It is suggested that the surface reactivity of electrodeposited alloys depends on the magnetically induced convection that is efficient during the codeposition process.

Keywords: magnetic field, Zn-Ni alloy, corrosion, corrosive medium

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Authors: Mounir Adal, Baalal Azeddine, Afifi Moulay Larbi

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Numerical analysis is a branch of mathematics devoted to the development of iterative matrix calculation techniques. We are searching for operations optimization as objective to calculate and solve systems of equations of order n with time and energy saving for computers that are conducted to calculate and analyze big data by solving matrix equations. Furthermore, this scientific discipline is producing results with a margin of error of approximation called rates. Thus, the results obtained from the numerical analysis techniques that are held on computer software such as MATLAB or Simulink offers a preliminary diagnosis of the situation of the environment or space targets. By this we can offer technical procedures needed for engineering or scientific studies exploitable by engineers for water.

Keywords: numerical analysis methods, obstacles solving, engineering, simulation, numerical modeling, iteration, computer, MATLAB, water, underground, velocity

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Authors: Madhu Aneja, Sapna Sharma

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The water-based bioconvection of a nanofluid containing motile gyrotactic micro-organisms over nonlinear inclined stretching sheet has been investigated. The governing nonlinear boundary layer equations of the model are reduced to a system of ordinary differential equations via Oberbeck-Boussinesq approximation and similarity transformations. Further, the modified set of equations with associated boundary conditions are solved using Finite Element Method. The impact of various pertinent parameters on the velocity, temperature, nanoparticles concentration, density of motile micro-organisms profiles are obtained and analyzed in details. The results show that with the increase in angle of inclination δ, velocity decreases while temperature, nanoparticles concentration, a density of motile micro-organisms increases. Additionally, the skin friction coefficient, Nusselt number, Sherwood number, density number are computed for various thermophysical parameters. It is noticed that increasing Brownian motion and thermophoresis parameter leads to an increase in temperature of fluid which results in a reduction in Nusselt number. On the contrary, Sherwood number rises with an increase in Brownian motion and thermophoresis parameter. The findings have been validated by comparing the results of special cases with existing studies.

Keywords: bioconvection, finite element method, gyrotactic micro-organisms, inclined stretching sheet, nanofluid

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Authors: Teh Raihana Nazirah Roslan, Siti Zulaiha Ibrahim, Sharmila Karim

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A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

Keywords: Cox-Ingersoll-Ross model, equity warrants, Heston model, hybrid models, stochastic

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Authors: Krzysztof Pomorski

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In the given work we present universal mathematical framework for modeling of cattle farm system that can set and validate various hypothesis that can be tested against experimental data. The presented work is preliminary but it is expected to be valid tool for future deeper analysis that can result in new class of prediction methods allowing early detection of cow dieseaes as well as cow performance. Therefore the presented work shall have its meaning in agriculture models and in machine learning as well. It also opens the possibilities for incorporation of certain class of biological models necessary in modeling of cow behavior and farm performance that might include the impact of environment on the farm system. Particular attention is paid to the model of coupled oscillators that it the basic building hypothesis that can construct the model showing certain periodic or quasiperiodic behavior.

Keywords: coupled ordinary differential equations, cattle farm system, numerical methods, stochastic differential equations

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Authors: Damir Latypov

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A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

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Authors: Shun-Qi Zhang, Shu-Yang Zhang, Min Chen

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Applying strong electric field on piezoelectric actuators, on one hand very significant electroelastic material nonlinear effects will occur, on the other hand piezo plates and shells may undergo large displacements and rotations. In order to give a precise prediction of piezolaminated smart structures under large electric field, this paper develops a finite element (FE) model accounting for both electroelastic material nonlinearity and geometric nonlinearity with large rotations based on the first order shear deformation (FSOD) hypothesis. The proposed FE model is applied to analyze a piezolaminated semicircular shell structure.

Keywords: smart structures, piezolamintes, material nonlinearity, strong electric field

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Authors: Faruk Firat Çalim, Nurullah Karaca, Hakan Tacettin Türker

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In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: circular rod, out-of-plane free vibration analysis, transfer matrix method

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Authors: Fatemeh Yazdanmehr, Iulian Nistor

Abstract:

The scope of the current study is the evaluation of the electric field effect on electrostatic desalting mathematical modeling with laboratory data. This research study was focused on developing a model for an existing operation desalting unit of one of the Iranian heavy oil field with a 75 MBPD production capacity. The high temperature of inlet oil to dehydration unit reduces the oil recovery, so the mathematical modeling of desalter operation parameters is very significant. The existing production unit operating data has been used for the accuracy of the mathematical desalting plant model. The inlet oil temperature to desalter was decreased from 110 to 80°C, and the desalted electrical field was increased from 0.75 to 2.5 Kv/cm. The model result shows that the desalter parameter changes meet the water-oil specification and also the oil production and consequently annual income is increased. In addition to that, changing desalter operation conditions reduces environmental footprint because of flare gas reduction. Following to specify the accuracy of selected electrostatic desalter electrical field, laboratory data has been used. Experimental data are used to ensure the effect of electrical field change on desalter. Therefore, the lab test is done on a crude oil sample. The results include the dehydration efficiency in the presence of a demulsifier and under electrical field (0.75 Kv) conditions at various temperatures. Comparing lab experimental and electrostatic desalter mathematical model results shows 1-3 percent acceptable error which confirms the validity of desalter specification and operation conditions changes.

Keywords: desalter, electrical field, demulsification, mathematical modeling, water-oil separation

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