Search results for: equation modeling methods

Authors: Tadas Telksnys, Zenonas Navickas, Minvydas Ragulskis

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Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation.

Keywords: Hodgkin-Huxley equation, solitary solution, existence condition, operator method

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Authors: Honggang Qu, Yong Xu, Rongmei Liu, Zhenji Gao, Bin Wang

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Today's mining industry is advancing gradually toward digital and visual direction. The three-dimensional visualization geological modeling of mine is the digital characterization of mineral deposits and is one of the key technology of digital mining. Three-dimensional geological modeling is a technology that combines geological spatial information management, geological interpretation, geological spatial analysis and prediction, geostatistical analysis, entity content analysis and graphic visualization in a three-dimensional environment with computer technology and is used in geological analysis. In this paper, the three-dimensional geological modeling of an iron mine through the use of Surpac is constructed, and the weight difference of the estimation methods between the distance power inverse ratio method and ordinary kriging is studied, and the ore body volume and reserves are simulated and calculated by using these two methods. Compared with the actual mine reserves, its result is relatively accurate, so it provides scientific bases for mine resource assessment, reserve calculation, mining design and so on.

Keywords: three-dimensional geological modeling, geological database, geostatistics, block model

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Authors: Shittu Ahmed Tajudeen

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This study examines student-teachers’ attitude and intention towards cell-phone use for learning. The study involves one hundred and ninety (190) trainee teachers in one of the Institutes of Education in Nigeria. The data of the study was collected through a questionnaire on a rating of seven point likert-type Scale. The data collected was used to test the hypothesized model of the study using Structural Equation Modeling approach. The finding of the study revealed that Perceived Usefulness (PU), Perceived Ease of Use (PEU), Subjective Norm (SN) and Attitude significantly influence students’ intention towards adoption of cell-phone for learning. The study showed that perceived ease of use stands to be the strongest predictor of cell-phone use. The model of the study exhibits a good-fit with the data and provides an explanation on student- teachers’ attitude and intention towards cell-phone for learning.

Keywords: cell-phone, adoption, structural equation modeling, technology acceptance model

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Authors: Ranajay Bhowmick

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Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion

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Authors: Nara Guimarães, Marcelo Aquino Martorano, Douglas Gouvêa

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An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles.

Keywords: Cahn-Hilliard equation, miscibility gap, phase separation, dimensional domains

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Authors: Virendra J. Majarikar, Harikrishnan N. Unni

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This paper sets to demonstrate a modeling of electrokinetic mixing employing electroosmotic stationary and time-dependent microchannel using alternate zeta patches on the lower surface of the micromixer in a lab on chip microfluidic device. Electroosmotic flow is amplified using different 2D and 3D model designs with alternate and geometric zeta potential values such as 25, 50, and 100 mV, respectively, to achieve high concentration mixing in the electrokinetically-driven microfluidic system. The enhancement of electrokinetic mixing is studied using Finite Element Modeling, and simulation workflow is accomplished with defined integral steps. It can be observed that the presence of alternate zeta patches can help inducing microvortex flows inside the channel, which in turn can improve mixing efficiency. Fluid flow and concentration fields are simulated by solving Navier-Stokes equation (implying Helmholtz-Smoluchowski slip velocity boundary condition) and Convection-Diffusion equation. The effect of the magnitude of zeta potential, the number of alternate zeta patches, etc. are analysed thoroughly. 2D simulation reveals that there is a cumulative increase in concentration mixing, whereas 3D simulation differs slightly with low zeta potential as that of the 2D model within the T-shaped micromixer for concentration 1 mol/m³ and 0 mol/m³, respectively. Moreover, 2D model results were compared with those of 3D to indicate the importance of the 3D model in a microfluidic design process.

Keywords: COMSOL Multiphysics®, electrokinetic, electroosmotic, microfluidics, zeta potential

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Authors: Taehyun Kim, Hyunjoo Park, Taehyun Kim

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Since the rapid economic development, Korea has recently entered a period of low growth due to population decline and aging. Due to the urbanization around the metropolitan area and the hollowing of local cities, the ecological capacity of a city is decreasing while ecological footprints are increasing, requiring a compact space plan for maintaining urban functions. The purpose of this study is to analyze the relationship between urban spatial structure and residents' ecological footprints for sustainable spatial planning. To do this, we try to analyze the relationship between intra-urban spatial structure, such as net/gross density and service accessibility, and resident ecological footprints of food, housing, transportation, goods and services through survey and structural equation modeling. The results of the study will be useful in establishing an implementation plan for sustainable development goals (SDGs), especially for sustainable cities and communities (SDG 11) and responsible consumption and production (SDG 12) in the future.

Keywords: ecological footprint, structural equation modeling, survey, sustainability, urban spatial structure

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Authors: Itissam Abuiziah

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In several hydraulic systems, it is necessary to calculate the head losses which depend on the resistance flow friction factor in Darcy equation. Computing the resistance friction is based on implicit Colebrook-White equation which is considered as the standard for the friction calculation, but it needs high computational cost, therefore; several explicit approximation methods are used for solving an implicit equation to overcome this issue. It follows that the relative error is used to determine the most accurate method among the approximated used ones. Steel, cast iron and polyethylene pipe materials investigated with practical diameters ranged from 0.1m to 2.5m and velocities between 0.6m/s to 3m/s. In short, the results obtained show that the suitable method for some cases may not be accurate for other cases. For example, when using steel pipe materials, Zigrang and Silvester's method has revealed as the most precise in terms of low velocities 0.6 m/s to 1.3m/s. Comparatively, Halland method showed a less relative error with the gradual increase in velocity. Accordingly, the simulation results of this study might be employed by the hydraulic engineers, so they can take advantage to decide which is the most applicable method according to their practical pipe system expectations.

Keywords: Colebrook–White, explicit equation, friction factor, hydraulic resistance, implicit equation, Reynolds numbers

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Authors: Ih-Ching Hsu

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Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?

Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions

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Authors: S. Mousavian, F. Mousavian, V. Nikkhah Rashidabad

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Cubic equations of state like Redlich–Kwong (RK) EOS have been proved to be very reliable tools in the prediction of phase behavior. Despite their good performance in compositional calculations, they usually suffer from weaknesses in the predictions of saturated liquid density. In this research, RK equation was modified. The result of this study shows that modified equation has good agreement with experimental data.

Keywords: equation of state, modification, ammonia, genetic algorithm

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Authors: Palwinder Singh, Munish Sandhir, Tejinder Singh

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The ordinary differential equations (ODE) represent a natural framework for mathematical modeling of many real-life situations in the field of engineering, control systems, physics, chemistry and astronomy etc. Such type of differential equations can be solved by analytical methods or by numerical methods. If the solution is calculated using analytical methods, it is done through calculus theories, and thus requires a longer time to solve. In this paper, we compare the numerical accuracy of the solutions given by the three main types of one-step initial value solvers: Taylor’s Series Method, Euler’s Method and Runge-Kutta Fourth Order Method (RK4). The comparison of accuracy is obtained through comparing the solutions of ordinary differential equation given by these three methods. Furthermore, to verify the accuracy; we compare these numerical solutions with the exact solutions.

Keywords: Ordinary differential equations (ODE), Taylor’s Series Method, Euler’s Method, Runge-Kutta Fourth Order Method

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Authors: A. E. Kobryn

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We present both descriptive and predictive modeling of structural properties of blends of PCBM or organic-inorganic hybrid perovskites of the type CH3NH3PbX3 (X=Cl, Br, I) with P3HT, P3BT or squaraine SQ2 dye sensitizer, including adsorption on TiO2 clusters having rutile (110) surface. In our study, we use a methodology that allows computing the microscopic structure of blends on the nanometer scale and getting insight on miscibility of its components at various thermodynamic conditions. The methodology is based on the integral equation theory of molecular liquids in the reference interaction site representation/model (RISM) and uses the universal force field. Input parameters for RISM, such as optimized molecular geometries and charge distribution of interaction sites, are derived with the use of the density functional theory methods. To compare the diffusivity of the PCBM in binary blends with P3HT and P3BT, respectively, the study is complemented with MD simulation. A very good agreement with experiment and the reports of alternative modeling or simulation is observed for PCBM in P3HT system. The performance of P3BT with perovskites, however, seems as expected. The calculated nanoscale morphologies of blends of P3HT, P3BT or SQ2 with perovskites, including adsorption on TiO2, are all new and serve as an instrument in rational design of organic/hybrid photovoltaics. They are used in collaboration with experts who actually make prototypes or devices for practical applications.

Keywords: multiscale theory and modeling, nanoscale morphology, organic-inorganic halide perovskites, three dimensional distribution

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Authors: Zainab D. Abd Ali, Thamir H. Khalaf

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In this paper, the characteristics of electric discharge in gap between two (parallel-plate) dielectric plates are studies, the gap filled with Argon gas in atm pressure at ambient temperature, the thickness of gap typically less than 1 mm and dielectric may be up 10 cm in diameter. One of dielectric plates a sinusoidal voltage is applied with Rf frequency, the other plates is electrically grounded. The simulation in this work depending on Boltzmann equation solver in first few moments, fluid model and plasma chemistry, in one dimensional modeling. This modeling have insight into characteristics of Dielectric Barrier Discharge through studying properties of breakdown of gas, electric field, electric potential, and calculating electron density, mean electron energy, electron current density ,ion current density, total plasma current density. The investigation also include: 1. The influence of change in thickness of gap between two plates if we doubled or reduced gap to half. 2. The effect of thickness of dielectric plates. 3. The influence of change in type and properties of dielectric material (gass, silicon, Teflon).

Keywords: computational diagnostics, Boltzmann equation, electric discharge, electron density

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Authors: Benedict Barnes, Anthony Y. Aidoo

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A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard.

Keywords: divergence regularization method, Helmholtz equation, ill-posed inhomogeneous Cauchy boundary conditions

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Authors: Alireza Lohrasbi, Alireza Lavaei, Mohammadali M. Shahlaei

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The liquid flow and the free surface shape during the initial stage of dam breaking are investigated. A numerical scheme is developed to predict the wave of an unsteady, incompressible viscous flow with free surface. The method involves a two dimensional finite element (2D), in a vertical plan. The Naiver-Stokes equations for conservation of momentum and mass for Newtonian fluids, continuity equation, and full nonlinear kinematic free-surface equation were used as the governing equations. The mapping developed to solve highly deformed free surface problems common in waves formed during wave propagation, transforms the run up model from the physical domain to a computational domain with Arbitrary Lagrangian Eulerian (ALE) finite element modeling technique.

Keywords: dam break, Naiver-Stokes equations, free-surface flows, Arbitrary Lagrangian-Eulerian

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Authors: Nordila Ahmad, Thamer Mohammad, Bruce W. Melville, Zuliziana Suif

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Current methods for predicting local scour at wide bridge piers, were developed on the basis of laboratory studies and very limited scour prediction were tested with field data. Laboratory wide pier scour equation from previous findings with field data were presented. A wide range of field data were used and it consists of both live-bed and clear-water scour. A method for assessing the quality of the data was developed and applied to the data set. Three other wide pier-scour equations from the literature were used to compare the performance of each predictive method. The best-performing scour equation were analyzed using statistical analysis. Comparisons of computed and observed scour depths indicate that the equation from the previous publication produced the smallest discrepancy ratio and RMSE value when compared with the large amount of laboratory and field data.

Keywords: field data, local scour, scour equation, wide piers

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Authors: F. U. Rahman, R. Q. Zhang

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This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future.

Keywords: Green’s function, hydrogen atom, Lippmann Schwinger equation, radial wave

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Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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Authors: Hugo Daneluzzo, Christelle Rabbat, Alan Jean-Marie

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Water electrolysis is one of the most advanced technologies for producing hydrogen and can be easily combined with electricity from different sources. Under the influence of electric current, water molecules can be split into oxygen and hydrogen. The production of hydrogen by water electrolysis favors the integration of renewable energy sources into the energy mix by compensating for their intermittence through the storage of the energy produced when production exceeds demand and its release during off-peak production periods. Among the various electrolysis technologies, anion exchange membrane (AEM) electrolyser cells are emerging as a reliable technology for water electrolysis. Modeling and simulation are effective tools to save time, money, and effort during the optimization of operating conditions and the investigation of the design. The modeling and simulation become even more important when dealing with multiphysics dynamic systems. One of those systems is the AEM electrolysis cell involving complex physico-chemical reactions. Once developed, models may be utilized to comprehend the mechanisms to control and detect flaws in the systems. Several modeling methods have been initiated by scientists. These methods can be separated into two main approaches, namely equation-based modeling and graph-based modeling. The former approach is less user-friendly and difficult to update as it is based on ordinary or partial differential equations to represent the systems. However, the latter approach is more user-friendly and allows a clear representation of physical phenomena. In this case, the system is depicted by connecting subsystems, so-called blocks, through ports based on their physical interactions, hence being suitable for multiphysics systems. Among the graphical modelling methods, the bond graph is receiving increasing attention as being domain-independent and relying on the energy exchange between the components of the system. At present, few studies have investigated the modelling of AEM systems. A mathematical model and a bond graph model were used in previous studies to model the electrolysis cell performance. In this study, experimental data from literature were simulated using OpenModelica using bond graphs and mathematical approaches. The polarization curves at different operating conditions obtained by both approaches were compared with experimental ones. It was stated that both models predicted satisfactorily the polarization curves with error margins lower than 2% for equation-based models and lower than 5% for the bond graph model. The activation polarization of hydrogen evolution reactions (HER) and oxygen evolution reactions (OER) were behind the voltage loss in the AEM electrolyzer, whereas ion conduction through the membrane resulted in the ohmic loss. Therefore, highly active electro-catalysts are required for both HER and OER while high-conductivity AEMs are needed for effectively lowering the ohmic losses. The bond graph simulation of the polarisation curve for operating conditions at various temperatures has illustrated that voltage increases with temperature owing to the technology of the membrane. Simulation of the polarisation curve can be tested virtually, hence resulting in reduced cost and time involved due to experimental testing and improved design optimization. Further improvements can be made by implementing the bond graph model in a real power-to-gas-to-power scenario.

Keywords: hydrogen production, anion-exchange membrane, electrolyzer, mathematical modeling, multiphysics modeling

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Authors: Easa Ali Abbasi, Akbar Allahverdizadeh, Reza Jahangiri, Behnam Dadashzadeh

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Electrical current measurement is a suitable method for the performance determination of electrical devices. There are two contact and noncontact methods in this measuring process. Contact method has some disadvantages like having direct connection with wire which may endamage the system. Thus, in this paper, a bimorph piezoelectric cantilever beam which has a permanent magnet on its free end is used to measure electrical current in a noncontact way. In mathematical modeling, based on Galerkin method, the governing equation of the cantilever beam is solved, and the equation presenting the relation between applied force and beam’s output voltage is presented. Magnetic force resulting from current carrying wire is considered as the external excitation force of the system. The results are compared with other references in order to demonstrate the accuracy of the mathematical model. Finally, the effects of geometric parameters on the output voltage and natural frequency are presented.

Keywords: cantilever beam, electrical current measurement, forced excitation, piezoelectric

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Authors: Mohammed Kachtali, Imad Fenjiro, Jamal Alkarkouri

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Wind erosion is a serious environmental problem in arid and semi-arid regions. Indeed, wind erosion easily removes the finest particles of the soil surface, which also contribute to losing soil fertility. The siltation of infrastructures and cultivated areas and the negative impact on health are additional consequences of wind erosion. In Morocco, wind erosion constitutes the main factor of silting up in coast and Sahara. The aim of our study is to use an equation of wind erosion in order to estimate the soil loses by wind erosion in the coast of Gharb (North of Morocco). The used equation in our model includes the geographic data, climatic data of 30 years and edaphic data collected from area study which contained 11 crossing of 4 stations. Our results have shown that the values of wind erosion are higher and very different between some crossings (p < 0.001). This difference is explained by topography, soil texture, and climate. In conclusion, wind erosion is higher in Gharb coast and varies from station to another; this problem required several methods of control and mitigation.

Keywords: Gharb coast, modeling, silting, wind erosion

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Authors: Meruyert Zhassybayeva, Kuralay Yesmukhanova, Ratbay Myrzakulov

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Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found.

Keywords: Fokas-Lenells equation, integrability, soliton, the Hirota bilinear method

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Authors: Joseph Amponsah

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This research proposes an equation to predict and determine the momentum source equation term after factoring in the radial friction between the fluid and the blades and the impeller's propulsive power. This research aims to look at how CFD software can be used to predict the effect of flows in nuclear reactor stirred tanks through a momentum source equation and the concentration distribution of tracers that have been introduced in reactor tanks. The estimated findings, including the dimensionless concentration curves, power, and pumping numbers, dimensionless velocity profiles, and mixing times 4, were contrasted with results from tests in stirred containers. The investigation was carried out in Part I for vessels that were agitated by one impeller on a central shaft. The two types of impellers employed were an ordinary Rushton turbine and a 6-bladed 45° pitched blade turbine. The simulations made use of numerous reference frame techniques and the common k-e turbulence model. The impact of the grid type was also examined; unstructured, structured, and unique user-defined grids were looked at. The CFD model was used to simulate the flow field within the Rushton turbine nuclear reactor stirred tank. This method was validated using experimental data that were available close to the impeller tip and in the bulk area. Additionally, analyses of the computational efficiency and time using MRF and SM were done.

Keywords: Ansys fluent, momentum equation, CFD, prediction

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Authors: Hung-Jiun Chi, Cheng-En Tsai, Jia-Ying Tu

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Semi-active control of Magnetorheological (MR) dampers for vibration reduction of structural systems has received considerable attention in civil and earthquake engineering, because the effective stiffness and damping properties of MR fluid can change in a very short time in reaction to external loading, requiring only a low level of power. However, the inherent nonlinear dynamics of hysteresis raise challenges in the modeling and control processes. In order to control the MR damper, an innovative Duffing-like equation is proposed to approximate the hysteresis dynamics in a deterministic and systematic manner than previously has been possible. Then, the model-reference adaptive control technique based on the Duffing-like model and the Lyapunov method is discussed. Parameter identification work with experimental data is presented to show the effectiveness of the Duffing-like model. In addition, simulation results show that the resulting adaptive gains enable the MR damper force to track the desired response of the reference model satisfactorily, verifying the effectiveness of the proposed modeling and control techniques.

Keywords: magnetorheological damper, duffing equation, model-reference adaptive control, Lyapunov function, hysteresis

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Authors: Ognjen Vukovic

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Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research.

Keywords: Brownian motion, Chern-Simons theory, financial time series, econophysics

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Authors: Mohamed Arbi Khlifi, Badr M. Alshammari

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This paper discusses the general methods to saturation in the steady-state, two axis (d & q) frame models of synchronous machines. In particular, the important role of the magnetic coupling between the d-q axes (cross-magnetizing phenomenon), is demonstrated. For that purpose, distinct methods of saturation modeling of dumper synchronous machine with cross-saturation are identified, and detailed models synthesis in d-q axes. A number of models are given in the final developed form. The procedure and the novel models are verified by a critical application to prove the validity of the method and the equivalence between all developed models is reported. Advantages of some of the models over the existing ones and their applicability are discussed.

Keywords: cross-magnetizing, models synthesis, synchronous machine, saturated modeling, state-space vectors

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Authors: Benbiao Song, Yan Gao, Zhuo Liu

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Geostatistical modeling is the key technic for reservoir characterization, the quality of geological models will influence the prediction of reservoir performance greatly, but few studies have been done to quantify the factors impacting geostatistical reservoir modeling accuracy. In this study, 16 fluvial prototype models have been established to represent different geological complexity, 6 cases range from 16 to 361 wells were defined to reproduce all those 16 prototype models by different methodologies including SIS, object-based and MPFS algorithms accompany with different constraint parameters. Modeling accuracy ratio was defined to quantify the influence of each factor, and ten realizations were averaged to represent each accuracy ratio under the same modeling condition and parameters association. Totally 5760 simulations were done to quantify the relative contribution of each factor to the simulation accuracy, and the results can be used as strategy guide for facies modeling in the similar condition. It is founded that data density, geological trend and geological complexity have great impact on modeling accuracy. Modeling accuracy may up to 90% when channel sand width reaches up to 1.5 times of well space under whatever condition by SIS and MPFS methods. When well density is low, the contribution of geological trend may increase the modeling accuracy from 40% to 70%, while the use of proper variogram may have very limited contribution for SIS method. It can be implied that when well data are dense enough to cover simple geobodies, few efforts were needed to construct an acceptable model, when geobodies are complex with insufficient data group, it is better to construct a set of robust geological trend than rely on a reliable variogram function. For object-based method, the modeling accuracy does not increase obviously as SIS method by the increase of data density, but kept rational appearance when data density is low. MPFS methods have the similar trend with SIS method, but the use of proper geological trend accompany with rational variogram may have better modeling accuracy than MPFS method. It implies that the geological modeling strategy for a real reservoir case needs to be optimized by evaluation of dataset, geological complexity, geological constraint information and the modeling objective.

Keywords: fluvial facies, geostatistics, geological trend, modeling strategy, modeling accuracy, variogram

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Authors: Paschal A. Ochang, Emmanuel C. Oji

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The Duffing’s Equation is a second order system that is very important because they are fundamental to the behaviour of higher order systems and they have applications in almost all fields of science and engineering. In the biological area, it is useful in plant stem dependence and natural frequency and model of the Brain Crash Analysis (BCA). In Engineering, it is useful in the study of Damping indoor construction and Traffic lights and to the meteorologist it is used in the prediction of weather conditions. However, most Problems in real life that occur are non-linear in nature and may not have analytical solutions except approximations or simulations, so trying to find an exact explicit solution may in general be complicated and sometimes impossible. Therefore we aim to find out if it is possible to obtain one analytical fixed point to the non-linear ordinary equation using fixed point analytical method. We started by exposing the scope of the Duffing’s equation and other related works on it. With a major focus on the fixed point and fixed point iterative scheme, we tried different iterative schemes on the Duffing’s Equation. We were able to identify that one can only see the fixed points to a Damped Duffing’s Equation and not to the Undamped Duffing’s Equation. This is because the cubic nonlinearity term is the determining factor to the Duffing’s Equation. We finally came to the results where we identified the stability of an equation that is damped, forced and second order in nature. Generally, in this research, we approximate the solution of Duffing’s Equation by converting it to a system of First and Second Order Ordinary Differential Equation and using Fixed Point Iterative approach. This approach shows that for different versions of Duffing’s Equations (damped), we find fixed points, therefore the order of computations and running time of applied software in all fields using the Duffing’s equation will be reduced.

Keywords: damping, Duffing's equation, fixed point analysis, second order differential, stability analysis

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Authors: Marco Sewald

Abstract:

Comparing present to past the numbers of Americans expatriating U. S. citizenship have risen. Even though these numbers are small compared to the immigrants, U. S. citizens expatriations have historically been much lower, making the uptick worrisome. In addition, the published lists and numbers from the U.S. government seems incomplete, with many not counted. Different branches of the U. S. government report different numbers and no one seems to know exactly how big the real number is, even though the IRS and the FBI both track and/or publish numbers of Americans who renounce. Since there is no single explanation, anecdotal evidence suggests this uptick is caused by global tax law and increased compliance burdens imposed by the U.S. lawmakers on U.S. citizens abroad. Within a research project the question arose about the reasons why a constant growing number of U.S. citizens are expatriating – the answers are believed helping to explain the underlying governmental policy rational, leading to such activities. While it is impossible to locate former U.S. citizens to conduct a survey on the reasons and the U.S. government is not commenting on the reasons given within the process of expatriation, the chosen methodology is Structural Equation Modeling (SEM), in the first step by re-using current surveys conducted by different researchers within the population of U. S. citizens residing abroad during the last years. Surveys questioning the personal situation in the context of tax, compliance, citizenship and likelihood to repatriate to the U. S. In general SEM allows: (1) Representing, estimating and validating a theoretical model with linear (unidirectional or not) relationships. (2) Modeling causal relationships between multiple predictors (exogenous) and multiple dependent variables (endogenous). (3) Including unobservable latent variables. (4) Modeling measurement error: the degree to which observable variables describe latent variables. Moreover SEM seems very appealing since the results can be represented either by matrix equations or graphically. Results: the observed variables (items) of the construct are caused by various latent variables. The given surveys delivered a high correlation and it is therefore impossible to identify the distinct effect of each indicator on the latent variable – which was one desired result. Since every SEM comprises two parts: (1) measurement model (outer model) and (2) structural model (inner model), it seems necessary to extend the given data by conducting additional research and surveys to validate the outer model to gain the desired results.

Keywords: expatriation of U. S. citizens, SEM, structural equation modeling, validating

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Authors: Einav Srulovici, Michal Grinstein-Weiss, George Knafl, Linda Beeber, Shawn Kneipp, Barbara Mark

Abstract:

Background: The asset-building theoretical framework (ABTF) is acknowledged as the most complete framework thus far for depicting the relationships between asset accumulation (the stock of a household’s saved resources available for future investment) and health outcomes. Although the ABTF takes into consideration the reciprocal relationship between asset accumulation and health, no ABTF based study has yet examined this relationship. Therefore, the purpose of this study was to test the ABTF and psychological distress, focusing on the reciprocal relationship between assets accumulation and psychological distress. Methods: The study employed longitudinal data from 6,295 families from the 2001 and 2007 Panel Study of Income Dynamics data sets. Structural equation modeling (SEM) was used to test the reciprocal relationship between asset accumulation and psychological distress. Results: In general, the data displayed a good fit to the model. The longitudinal SEM found that asset accumulation significantly increased with a decreased in psychological distress over time, while psychological distress significantly increased with an increase in asset accumulation over time, confirming the existence of the hypothesized reciprocal relationship. Conclusions: Individuals who are less psychological distressed might have more energy to engage in activities, such as furthering their education or obtaining better jobs that are in turn associated with greater asset accumulation, while those who have greater assets may invest those assets in riskier investments, resulting in increased psychological distress. The confirmation of this reciprocal relationship highlights the importance of conducting longitudinal studies and testing the reciprocal relationship between asset accumulation and other health outcomes.

Keywords: asset-building theoretical framework, psychological distress, structural equation modeling, reciprocal relationship

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