Search results for: Maxwell equations

Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa

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In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.

Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method

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Authors: Sofia N. Gonçalves, Duarte M. S. Albuquerque, José C. F. Pereira

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The energy transition is spurred by structural changes in energy demand, supply, and prices. Microwave technology was first proposed as a faster alternative for cooking food. It was found that food heated instantly when interacting with high-frequency electromagnetic waves. The dielectric properties account for a material’s ability to absorb electromagnetic energy and dissipate this energy in the form of heat. Many energy-intense industries could benefit from electromagnetic heating since many of the raw materials are dielectric at high temperatures. Limestone sedimentary rock is a dielectric material intensively used in the cement industry to produce unslaked lime. A numerical 3D model was implemented in COMSOL Multiphysics to study the limestone continuous processing under microwave heating. The model solves the two-way coupling between the Energy equation and Maxwell’s equations as well as the coupling between heat transfer and chemical interfaces. Complementary, a controller was implemented to optimize the overall heating efficiency and control the numerical model stability. This was done by continuously matching the cavity impedance and predicting the required energy for the system, avoiding energy inefficiencies. This controller was developed in MATLAB and successfully fulfilled all these goals. The limestone load influence on thermal decomposition and overall process efficiency was the main object of this study. The procedure considered the Verification and Validation of the chemical kinetics model separately from the coupled model. The chemical model was found to correctly describe the chosen kinetic equation, and the coupled model successfully solved the equations describing the numerical model. The interaction between flow of material and electric field Poynting vector revealed to influence limestone decomposition, as a result from the low dielectric properties of limestone. The numerical model considered this effect and took advantage from this interaction. The model was demonstrated to be highly unstable when solving non-linear temperature distributions. Limestone has a dielectric loss response that increases with temperature and has low thermal conductivity. For this reason, limestone is prone to produce thermal runaway under electromagnetic heating, as well as numerical model instabilities. Five different scenarios were tested by considering a material fill ratio of 30%, 50%, 65%, 80%, and 100%. Simulating the tube rotation for mixing enhancement was proven to be beneficial and crucial for all loads considered. When uniform temperature distribution is accomplished, the electromagnetic field and material interaction is facilitated. The results pointed out the inefficient development of the electric field within the bed for 30% fill ratio. The thermal efficiency showed the propensity to stabilize around 90%for loads higher than 50%. The process accomplished a maximum microwave efficiency of 75% for the 80% fill ratio, sustaining that the tube has an optimal fill of material. Electric field peak detachment was observed for the case with 100% fill ratio, justifying the lower efficiencies compared to 80%. Microwave technology has been demonstrated to be an important ally for the decarbonization of the cement industry.

Keywords: CFD numerical simulations, efficiency optimization, electromagnetic heating, impedance matching, limestone continuous processing

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Authors: Raphael de Oliveira Garcia, Samuel Rocha de Oliveira

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We have developed a new computer program in Fortran 90, in order to obtain numerical solutions of a system of Relativistic Magnetohydrodynamics partial differential equations with predetermined gravitation (GRMHD), capable of simulating the formation of relativistic jets from the accretion disk of matter up to his ejection. Initially we carried out a study on numerical methods of unidimensional Finite Volume, namely Lax-Friedrichs, Lax-Wendroff, Nessyahu-Tadmor method and Godunov methods dependent on Riemann problems, applied to equations Euler in order to verify their main features and make comparisons among those methods. It was then implemented the method of Finite Volume Centered of Nessyahu-Tadmor, a numerical schemes that has a formulation free and without dimensional separation of Riemann problem solvers, even in two or more spatial dimensions, at this point, already applied in equations GRMHD. Finally, the Nessyahu-Tadmor method was possible to obtain stable numerical solutions - without spurious oscillations or excessive dissipation - from the magnetized accretion disk process in rotation with respect to a central black hole (BH) Schwarzschild and immersed in a magnetosphere, for the ejection of matter in the form of jet over a distance of fourteen times the radius of the BH, a record in terms of astrophysical simulation of this kind. Also in our simulations, we managed to get substructures jets. A great advantage obtained was that, with the our code, we got simulate GRMHD equations in a simple personal computer.

Keywords: finite volume methods, central schemes, fortran 90, relativistic astrophysics, jet

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Authors: Roslinda Nazar, Amin Noor, Khamisah Jafar, Ioan Pop

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In this paper, the steady laminar three-dimensional boundary layer flow and heat transfer of a copper (Cu)-water nanofluid in the vicinity of a permeable shrinking flat surface in an otherwise quiescent fluid is studied. The nanofluid mathematical model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Dual solutions (upper and lower branch solutions) are found for the similarity boundary layer equations for a certain range of the suction parameter. A stability analysis has been performed to show which branch solutions are stable and physically realizable. The numerical results for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are obtained, presented and discussed in detail for a range of various governing parameters.

Keywords: heat transfer, nanofluid, shrinking surface, stability analysis, three-dimensional flow

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Authors: Arash Ghahraman, Gyula Bene

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The object of this study is to investigate the effect of viscosity on the propagation of free-surface waves in an incompressible viscous fluid layer of arbitrary depth. While we provide a more detailed study of properties of linear surface waves, the description of fully nonlinear waves in terms of KdV-like (Korteweg-de Vries) equations is discussed. In the linear case, we find that in shallow enough fluids, no surface waves can propagate. Even in any thicker fluid layers, propagation of very short and very long waves is forbidden. When wave propagation is possible, only a single propagating mode exists for any given horizontal wave number. The numerical results show that there can be two types of non-propagating modes. One type is always present, and there exist still infinitely many of such modes at the same parameters. In contrast, there can be zero, one or two modes belonging to the other type. Another significant feature is that KdV-like equations. They describe propagating nonlinear viscous surface waves. Since viscosity gives rise to a new wavenumber that cannot be small at the same time as the original one, these equations may not exist. Nonetheless, we propose a reasonable nonlinear description in terms of 1+1 variate functions that make possible successive approximations.

Keywords: free surface wave, water waves, KdV equation, viscosity

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Authors: Syukri Himran, Erwin Eka Putra, Nanang Roni

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This study explains the natural convection of viscous fluid flowing on semi-infinite vertical plate. A set of the governing equations describing the continuity, momentum and energy, have been reduced to dimensionless forms by introducing the references variables. To solve the problems, the equations are formulated by explicit finite-difference in time dependent form and computations are performed by Fortran program. The results describe velocity, temperature profiles both in transient and steady state conditions. An approximate value of heat transfer coefficient and the effects of Pr on convection flow are also presented.

Keywords: natural convection, vertical plate, velocity and temperature profiles, steady and unsteady

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Authors: Ahmed Alghurabi, Mysara Mohyaldinn, Shiferaw Jufar, Obai Younis, Abdullah Abduljabbar

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Erosion modeling equations were typically acquired from regulated experimental trials for solid particles entrained in single-phase or multi-phase flows. Evidently, those equations were later employed to predict the erosion damage caused by the continuous impacts of solid particles entrained in streamflow. It is also well-known that the particle impact angle and velocity do not change drastically in gas-sand flow erosion prediction; hence an accurate prediction of erosion can be projected. On the contrary, high-density fluid flows, such as water flow, through complex geometries, such as sand screens, greatly affect the sand particles’ trajectories/tracks and consequently impact the erosion rate predictions. Particle tracking models and erosion equations are frequently applied simultaneously as a method to improve erosion visualization and estimation. In the present work, computational fluid dynamic (CFD)-based erosion modeling was performed using a commercially available software; ANSYS Fluent. The continuous phase (water flow) behavior was simulated using the realizable K-epsilon model, and the secondary phase (solid particles), having a 5% flow concentration, was tracked with the help of the discrete phase model (DPM). To accomplish a successful erosion modeling, three erosion equations from the literature were utilized and introduced to the ANSYS Fluent software to predict the screen wire-slot velocity surge and estimate the maximum erosion rates on the screen surface. Results of turbulent kinetic energy, turbulence intensity, dissipation rate, the total pressure on the screen, screen wall shear stress, and flow velocity vectors were presented and discussed. Moreover, the particle tracks and path-lines were also demonstrated based on their residence time, velocity magnitude, and flow turbulence. On one hand, results from the utilized erosion equations have shown similarities in screen erosion patterns, locations, and DPM concentrations. On the other hand, the model equations estimated slightly different values of maximum erosion rates of the wire-wrapped screen. This is solely based on the fact that the utilized erosion equations were developed with some assumptions that are controlled by the experimental lab conditions.

Keywords: CFD simulation, erosion rate prediction, material loss due to erosion, water-sand flow

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Authors: X. Wang, J. S. Kuang

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The Fixed-angle Softened Truss Model with Tension-stiffening (FASTMT) has a superior performance in predicting the shear behaviour of reinforced concrete (RC) membrane elements, especially for the post-cracking behaviour. Nevertheless, massive computational work is inevitable due to the multiple transcendental equations involved in the stress-strain relationship. In this paper, an iterative root-finding technique is introduced to FASTMT for solving quickly the transcendental equations of the tension-stiffening effect of RC membrane elements. This fast FASTMT, which performs in MATLAB, uses the bisection method to calculate the tensile stress of the membranes. By adopting the simplification, the elapsed time of each loop is reduced significantly and the transcendental equations can be solved accurately. Owing to the high efficiency and good accuracy as compared with FASTMT, the fast FASTMT can be further applied in quick prediction of shear behaviour of complex large-scale RC structures.

Keywords: bisection method, FASTMT, iterative root-finding technique, reinforced concrete membrane

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Authors: T. Watanabe

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Combustion analysis of suspended sodium droplet is performed by solving numerically the Navier-Stokes equations and the energy conservation equations. The combustion model consists of the pre-ignition and post-ignition models. The reaction rate for the pre-ignition model is based on the chemical kinetics, while that for the post-ignition model is based on the mass transfer rate of oxygen. The calculated droplet temperature is shown to be in good agreement with the existing experimental data. The temperature field in and around the droplet is obtained as well as the droplet shape variation, and the present numerical model is confirmed to be effective for the combustion analysis.

Keywords: analysis, combustion, droplet, sodium

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Authors: Xuezhang Hou

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In the present paper, a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions is considered. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and spectral analysis and semigroup generation of the system operator is discussed. Subsequently, a sliding model control problem is proposed and investigated, and an equivalent control method is introduced and applied to the system. Finally, a significant result that the state of the system can be approximated by an ideal sliding mode under control in any accuracy is derived and examined.

Keywords: hyperbolic dynamic system, sliding model control, semigroup of linear operators, partial differential equations

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Authors: Md. S. Ansari, S. S. Motsa

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In this paper, an analysis has been made on the flow of non-Newtonian viscoelastic nanofluid over a linearly stretching sheet under the influence of uniform magnetic field. Heat transfer characteristics is analyzed taking into the effect of nonlinear radiation and non-uniform heat source/sink. Transport equations contain the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The relevant partial differential equations are non-dimensionalized and transformed into ordinary differential equations by using appropriate similarity transformations. The transformed, highly nonlinear, ordinary differential equations are solved by spectral local linearisation method. The numerical convergence, error and stability analysis of iteration schemes are presented. The effects of different controlling parameters, namely, radiation, space and temperature-dependent heat source/sink, Brownian motion, thermophoresis, viscoelastic, Lewis number and the magnetic force parameter on the flow field, heat transfer characteristics and nanoparticles concentration are examined. The present investigation has many industrial and engineering applications in the fields of coatings and suspensions, cooling of metallic plates, oils and grease, paper production, coal water or coal–oil slurries, heat exchangers’ technology, and materials’ processing and exploiting.

Keywords: magnetic field, nonlinear radiation, non-uniform heat source/sink, similar solution, spectral local linearisation method, Rosseland diffusion approximation

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Authors: Peña A. Roland R., Lozano P. Jean P.

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The waterflooding process is an enhanced oil recovery (EOR) method that appears tremendously successful. This paper shows the importance of the role of the numerical modelling of waterflooding and how to provide a better description of the fluid flow during this process. The mathematical model is based on the mass conservation equations for the oil and water phases. Rock compressibility and capillary pressure equations are coupled to the mathematical model. For discretizing and linearizing the partial differential equations, we used the Finite Volume technique and the Newton-Raphson method, respectively. The results of three scenarios for waterflooding in porous media are shown. The first scenario was estimating the water saturation in the media without rock compressibility and without capillary pressure. The second scenario was estimating the front of the water considering the rock compressibility and capillary pressure. The third case is to compare different fronts of water saturation for three fluids viscosity ratios without and with rock compressibility and without and with capillary pressure. Results of the simulation indicate that the rock compressibility and the capillary pressure produce changes in the pressure profile and saturation profile during the displacement of the oil for the water.

Keywords: capillary pressure, numerical simulation, rock compressibility, two-phase flow

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Authors: Partha P. Gopmandal, S. Bhattacharyya

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We investigate the thermal end effect on the pseudo-steady state behavior of the isotachophoretic transport of ionic species in a 2-D microchannel. Both ends of the channel are kept at a constant temperature which may lead to significant changes in electrophoretic migration speed. A mathematical model based on Nernst-Planck equations for transport of ions coupled with the equation for temperature field is considered. In addition, the charge conservation equations govern the potential field due to the external electric field. We have computed the equations for ion transport, potential and temperature in a coupled manner through the finite volume method. The diffusive terms are discretized via central difference scheme, while QUICK (Quadratic Upwind Interpolation Convection Kinematics) scheme is used to discretize the convective terms. We find that the thermal end effect has significant effect on the isotachophoretic (ITP) migration speed of the analyte. Our result shows that the ITP velocity for temperature dependent case no longer varies linearly with the applied electric field. A detailed analysis has been made to provide a range of the key parameters to minimize the Joule heating effect on ITP transport of analytes.

Keywords: finite volume method, isotachophoresis, QUICK scheme, thermal effect

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Authors: Julia Zimmerman, Gaurav Savant

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This study aims to evaluate the efficacy of the U.S. Army Corp of Engineers’ River Analysis System (HEC-RAS) application to modeling the hydraulics of estuaries. HEC-RAS has been broadly used for a variety of riverine applications. However, it has not been widely applied to the study of circulation in estuaries. This report details the model development and validation of a combined 1D/2D unsteady flow hydraulic model using HEC-RAS for estuaries and they are associated with tidally influenced rivers. Two estuaries, Galveston Bay and Delaware Bay, were used as case studies. Galveston Bay, a bar-built, vertically mixed estuary, was modeled for the 2005 calendar year. Delaware Bay, a drowned river valley estuary, was modeled from October 22, 2019, to November 5, 2019. Water surface elevation was used to validate both models by comparing simulation results to NOAA’s Center for Operational Oceanographic Products and Services (CO-OPS) gauge data. Simulations were run using the Diffusion Wave Equations (DW), the Shallow Water Equations, Eulerian-Lagrangian Method (SWE-ELM), and the Shallow Water Equations Eulerian Method (SWE-EM) and compared for both accuracy and computational resources required. In general, the Diffusion Wave Equations results were found to be comparable to the two Shallow Water equations sets while requiring less computational power. The 1D/2D combined approach was valid for study areas within the 2D flow area, with the 1D flow serving mainly as an inflow boundary condition. Within the Delaware Bay estuary, the HEC-RAS DW model ran in 22 minutes and had an average R² value of 0.94 within the 2-D mesh. The Galveston Bay HEC-RAS DW ran in 6 hours and 47 minutes and had an average R² value of 0.83 within the 2-D mesh. The longer run time and lower R² for Galveston Bay can be attributed to the increased length of the time frame modeled and the greater complexity of the estuarine system. The models did not accurately capture tidal effects within the 1D flow area.

Keywords: Delaware bay, estuarine hydraulics, Galveston bay, HEC-RAS, one-dimensional modeling, two-dimensional modeling

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Authors: Alexandra Andrade Brandão Soares, Paulo Batista Gonçalves

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Using a modal expansion that satisfies the boundary and continuity conditions and expresses the modal couplings characteristic of cylindrical shells in the nonlinear regime, the equations of motion are discretized using the Galerkin method. The resulting algebraic equations are solved by the Newton-Raphson method, thus obtaining the nonlinear frequency-amplitude relation. Finally, a parametric analysis is conducted to study the influence of the geometry of the shell, the gradient of the functional material and vibration modes on the degree and type of nonlinearity of the cylindrical shell, which is the main contribution of this research work.

Keywords: cylindrical shells, dynamics, functionally graded material, nonlinear vibrations

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Authors: Munawwar Mohabuth, Andrei Kotousov, Ching-Tai Ng

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On the basis of the finite deformation theory, the effect of homogeneous stress on the propagation of Lamb waves in an initially isotropic hyperelastic plate is analysed. The equations governing the propagation of small amplitude waves in the prestressed plate are derived using the theory of small deformations superimposed on large deformations. By enforcing traction free boundary conditions at the upper and lower surfaces of the plate, acoustoelastic dispersion equations for Lamb wave propagation are obtained, which are solved numerically. Results are given for an aluminum plate subjected to a range of applied stresses.

Keywords: acoustoelasticity, dispersion, finite deformation, lamb waves

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Authors: Sonia Sonia

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This paper presents a family of iterative scheme for solving nonlinear systems of equations which have wide application in sciences and engineering. The proposed iterative family is based upon some parameters which generates many different iterative schemes. This family is completely derivative free and uses first of divided difference operator. Moreover some numerical experiments are performed and compared with existing methods. Analysis of convergence shows that the presented family has fourth-order of convergence. The dynamical behaviour of proposed family and local convergence have also been discussed. The numerical performance and convergence region comparison demonstrates that proposed family is efficient.

Keywords: convergence, divided difference operator, nonlinear system, Newton's method

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Authors: Lloyd G. Allred

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The distribution of velocities of particles in plasma is a well understood discipline of plasma physics. Boltzmann’s law and the Maxwell-Boltzmann distribution describe the distribution of velocity of a particle in plasma as a function of mass and temperature. Particles with the same mass tend to have the same velocity. By expressing the same law in terms of energy alone, the author obtains a distribution independent of mass. In summary, for particles in plasma, the energies tend to equalize, independent of the masses of the individual particles. For high-energy plasma, the original law predicts velocities greater than the speed of light. If one uses Einstein’s formula for energy (E=mc²), then a relativistic correction is not required.

Keywords: cosmology, EMP, plasma physics, relativity

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Authors: M. Khoshab, M. J. Sedigh

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Dynamic systems, which in mathematical point of view are those governed by differential equations, are much more difficult to study and to predict their behavior in comparison with static systems which are governed by algebraic equations. Economical systems such as market are among complicated dynamic systems. This paper tries to adopt a very simple mathematical model for market and to study effect of supply and demand function on behavior of the market while the supply side experiences a lag due to production restrictions.

Keywords: dynamic system, lag on supply demand, market stability, supply demand model

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Authors: Saleh Elawgali

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Current spectrums of a four pole-pair, 400 kW induction machine were calculated for the cases of full symmetry and static eccentricity. The calculations involve integration of 93 electrical plus four mechanical ordinary differential equations. Electrical equations account for variable inductances affected by slotting and eccentricities. The calculations were followed by Fourier analysis of the stator currents in steady state operation. Zooms of the current spectrums, around the 50 Hz fundamental harmonic as well as of the main slot harmonic zone, were included. The spectrums included refer to both calculated and measured currents.

Keywords: diagnostic, harmonic, induction machine, spectrum

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Authors: Gonzalez Carlos, Martinez Fransisco

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There are various types of analysis that allow us to involve seismic phenomena that cause strong requirements for structures that are designed by society; one of them is a probabilistic analysis which works from prediction equations that have been created based on metadata seismic compiled in different regions. These equations form models that are used to describe the 5% damped pseudo spectra response for the various zones considering some easily known input parameters. The biggest problem for the creation of these models requires data with great robust statistics that support the results, and there are several places where this type of information is not available, for which the use of alternative methodologies helps to achieve adjustments to different models of seismic prediction.

Keywords: GMPM, 5% damped pseudo-response spectra, models of seismic prediction, PSHA

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Authors: Somveer Singh, Vineet Kumar Singh

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We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Maryam Ebrahimpour, Amir Ebrahimi

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This paper presents the steady-state amplitude analysis of MOS Colpitts oscillator with short channel device. The proposed method is based on a large signal analysis and the nonlinear differential equations that govern the oscillator circuit behaviour. Also, the short channel effects are considered in the proposed analysis and analytical equations for finding the steady-state oscillation amplitude are derived. The output voltage calculated from this analysis is in excellent agreement with simulations for a wide range of circuit parameters.

Keywords: colpitts oscillator, CMOS, electronics, circuits

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Authors: Fatemeh Nemati, Lucinda Leonard, Gwyn Lintern, Richard Thomson

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In this study, we will use modern numerical modeling approaches to estimate tsunami risks to the southern coast of British Columbia from landslides. Wave generation is to be simulated using the NHWAVE model, which solves the Navier-Stokes equations due to the more complex behavior of flow near the landslide source; far-field wave propagation will be simulated using the simpler model FUNWAVE_TVD with high-order Boussinesq-type wave equations, with a focus on the accurate simulation of wave propagation and regional- or coastal-scale inundation predictions.

Keywords: FUNWAVE-TVD, landslide-generated tsunami, NHWAVE, tsunami risk

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Authors: Chahid K. Ghaddar

Abstract:

The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: calculus, differential algebraic equations, solvers, spreadsheet

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Authors: Alireza Rafie Boldaji, Ahmad Saboonchi

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Chokes are commonly used in oil and gas production systems. A choke is a restriction basically designed to control flow rates of oil and gas wells, to prevent the downstream disturbances from propagating upstream (critical flow), and to protect the surface equipment facilities against slugging at high flowing pressures. There are different methods to calculate the multiphase flow rate, one of the multiphase flow measurement methods is the separation and measurement by on¬e-phaseFlow meter, another common method is the use of movable separator, their operations are very labor-intensive and costly. The current method used is based on the flow differential pressure on both sides of choke. Three groups of correlations describing two-phase flow through wellhead chokes were examined. The first group involved simple empirical equations similar to those of Gilbert, the second group comprised derived equations of two-phase flow incorporating PVT properties, and third group is computational method. In the article we calculate the flow of oil and gas through choke with simulation of this two phase flow bye computational fluid dynamic method, we use Ansys- fluent for this simulation and finally compared results of computational simulation whit empirical equations, the results show good agreement between experimental and numerical results.

Keywords: CFD, two-phase, choke, critical

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Authors: Hassan Youssef Mohamed

Abstract:

In this paper, we show new wave equations, and by using the equations, we concluded that the strong force and the weak force are not fundamental, but they are quantum effects for electromagnetism. This result is different from the current scientific understanding about strong and weak interactions at all. So, we introduce three evidences for our theory. First, we prove the asymptotic freedom phenomenon in the strong force by using our model. Second, we derive the nuclear shell model as an approximation of our model. Third, we prove that the leptons do not participate in the strong interactions, and we prove the short ranges of weak and strong interactions. So, our model is consistent with the current understanding of physics. Finally, we introduce the electron-positron model as the basic ingredients for protons, neutrons, and all matters, so we can study all particles interactions and nuclear interaction as many-body problems of electrons and positrons. Also, we prove the violation of parity conservation in weak interaction as evidence of our theory in the weak interaction. Also, we calculate the average of the binding energy per nucleon.

Keywords: new wave equations, the strong force, the grand unification theory, hydrogen atom, weak force, the nuclear shell model, the asymptotic freedom, electron-positron model, the violation of parity conservation, the binding energy

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Authors: Tala Toonsi, Marah Alagha, Lina Alnowaiser, Hala Rajab

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This report is about the Photomath app, which is an AI application that uses image recognition technology, specifically optical character recognition (OCR) algorithms. The (OCR) algorithm translates the images into a mathematical equation, and the app automatically provides a step-by-step solution. The application supports decimals, basic arithmetic, fractions, linear equations, and multiple functions such as logarithms. Testing was conducted to examine the usage of this app, and results were collected by surveying ten participants. Later, the results were analyzed. This paper seeks to answer the question: To what level the artificial intelligence features are accurate and the speed of process in this app. It is hoped this study will inform about the efficiency of AI in Photomath to the users.

Keywords: photomath, image recognition, app, OCR, artificial intelligence, mathematical equations.

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Authors: Saeed Otarod

Abstract:

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

Keywords: explicit, linear, differential, closed form

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Authors: Hasan Fatih Ertuğrul, Beytullah Okur, Huseyin Üvet, Kadir Erkan

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The objective of this paper is to analyze a 4-pole hybrid magnetic levitation system by using 3D finite element and analytical methods. The magnetostatic analysis of the system is carried out by using ANSYS MAXWELL-3D package. An analytical model is derived by magnetic equivalent circuit (MEC) method. The purpose of magnetostatic analysis is to determine the characteristics of attractive force and rotational torques by the change of air gap clearances, inclination angles and current excitations. The comparison between 3D finite element analysis and analytical results are presented at the rest of the paper.

Keywords: yoke hybrid electromagnet, 3D finite element analysis, magnetic levitation system, magnetostatic analysis

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