Search results for: coupled processes

Authors: Rahmat Purwoko, Bambang Riyanto Trilaksono

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This paper gives comparison of INS/GNSS architecture namely Loosely Coupled and Tightly Coupled using Hardware in the Loop Simulation in Guided Missile RKX-200 rocket model. INS/GNSS Tightly Coupled architecture requires pseudo-range, pseudo-range rate, and position and velocity of each satellite in constellation from GPS (Global Positioning System) measurement. The Loosely Coupled architecture use estimated position and velocity from GNSS receiver. INS/GNSS architecture also requires angular rate and specific force measurement from IMU (Inertial Measurement Unit). Loosely Coupled arhitecture designed using 15 states Kalman Filter and Tightly Coupled designed using 17 states Kalman Filter. Integration algorithm calculation using ECEF frame. Navigation System implemented Zedboard All Programmable SoC.

Keywords: kalman filter, loosely coupled, navigation system, tightly coupled

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Authors: Sun Zhe, Ruggero Micheletto

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The research of neural network is very important for the development of advanced next generation intelligent devices and the medical treatment. The most important part of the neural network research is the learning. The process of learning in our brain is essentially several adjustment processes of connection strength between neurons. It is very difficult to figure out how this mechanism works in the complex network and how the connection strength influences brain functions. For this reason, we made a model with only two coupled neurons and studied the influence of connection strength between them. To emulate the neuronal activity of realistic neurons, we prefer to use the Izhikevich neuron model. This model can simulate the neuron variables accurately and it’s simplicity is very suitable to implement on computers. In this research, the parameter ρ is used to estimate the correlation coefficient between spike train of two coupling neurons.We think the results is very important for figuring out the mechanism between synchronization of coupling neurons and synaptic plasticity. The result also presented the importance of the spike frequency adaptation in complex systems.

Keywords: neural networks, noise, stochastic processes, coupled neurons, correlation coefficient, synchronization, pacemaker, synaptic plasticity

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Authors: Kun-Peng Jin, Jin Liang, Ti-Jun Xiao

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In this work, we are concerned with the dynamic behaviors of solutions to some coupled systems with infinite memory, which consist of two partial differential equations where only one partial differential equation has damping. Such coupled systems are good mathematical models to describe the deformation and stress characteristics of some viscoelastic materials affected by temperature change, external forces, and other factors. By using the theory of operator semigroups, we give wellposedness results for the Cauchy problem for these coupled systems. Then, with the help of some auxiliary functions and lemmas, which are specially designed for overcoming difficulties in the proof, we show that the solutions of the coupled systems decay to zero in a strong way under a few basic conditions. The results in this dynamic analysis of coupled systems are generalizations of many existing results.

Keywords: dynamic analysis, coupled system, infinite memory, damping.

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Authors: Hyungsuk Han, Soohong Jeon, Chungwon Lee, YongHoon Kim

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When a rubber mount and flexible coupling are installed on the main engine, high torsional vibration can occur. The root cause of this high torsional vibration can be attributed to the lateral-torsional coupled vibration of the shaft system. Therefore, the lateral-torsional coupled vibration is investigated numerically after approximating the shaft system to a three-degrees-of-freedom Jeffcott rotor. To verify that the high torsional vibration is caused by the lateral-torsional coupled vibration, a test unit that can simulate this lateral-torsional coupled vibration occurring in the propulsion shaft is developed. Performing a vibration test with the test unit, it can be experimentally verified that the high torsional vibration occurring in the propulsion shaft of the particular ship was caused by the lateral-torsional coupled vibration.

Keywords: Jeffcott rotor, lateral-torsional coupled vibration, propulsion shaft, stability

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Authors: Suleiman Babani, Jazuli Sanusi Kazaure

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In this paper, two coupled-line couplers are designed and simulated using stripline technology. The coupled-line couplers (A and B) are designed with different values of coupling coefficient 6dB and 10dB respectively. Both of circuits have a coupled output port, a through output port and an isolated output port. Moreover, both circuits are tuned to function around 2.45 GHz. The design results are presented by simulation results obtained using ADS 2012.08 (Advanced Design System) software.

Keywords: ADS, coupled-line coupler, directional coupler, stripline

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Authors: Leyla Noroozbabaee, David Nickerson

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We introduce a modular, consistent, reusable bond graph model of the renal nephron’s proximal convoluted tubule (PCT), which can reproduce biological behaviour. In this work, we focus on ion and volume transport in the proximal convoluted tubule of the renal nephron. Modelling complex systems requires complex modelling problems to be broken down into manageable pieces. This can be enabled by developing models of subsystems that are subsequently coupled hierarchically. Because they are based on a graph structure. In the current work, we define two modular subsystems: the resistive module representing the membrane and the capacitive module representing solution compartments. Each module is analyzed based on thermodynamic processes, and all the subsystems are reintegrated into circuit theory in network thermodynamics. The epithelial transport system we introduce in the current study consists of five transport membranes and four solution compartments. Coupled dissipations in the system occur in the membrane subsystems and coupled free-energy increasing, or decreasing processes appear in solution compartment subsystems. These structural subsystems also consist of elementary thermodynamic processes: dissipations, free-energy change, and power conversions. We provide free and open access to the Python implementation to ensure our model is accessible, enabling the reader to explore the model through setting their simulations and reproducibility tests.

Keywords: Bond Graph, Epithelial Transport, Water Transport, Mathematical Modeling

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Authors: A. Chinig, J. Zbitou, A. Errkik, L. Elabdellaoui, A. Tajmouati, A. Tribak, M. Latrach

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This paper presents a new structure of microstrip band pass filter (BPF) based on coupled stepped impedance resonators. Each filter consists of two coupled stepped impedance resonators connected to microstrip feed lines. The coupled junction is utilized to connect the two BPFs to the antenna. This two band pass filters are designed and simulated to operate for the digital communication system (DCS) and Industrial Scientific and Medical (ISM) bands at 1.8 GHz and 2.45 GHz respectively. The proposed circuit presents good performances with an insertion loss lower than 2.3 dB and isolation between the two channels greater than 21 dB. The prototype of the optimized diplexer have been investigated numerically by using ADS Agilent and verified with CST microwave software.

Keywords: band pass filter, coupled junction, coupled stepped impedance resonators, diplexer, insertion loss, isolation

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Authors: Suad M. Abuzariba, Liang Chen, Saeed Hadjifaradji

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To evaluate the optical eye diagram due to polarization-mode dispersion (PMD), polarization-dependent loss (PDL), and chromatic dispersion (CD) for a system of highly mode coupled fiber with lumped section at any given optical pulse sequence we present an analytical modle. We found that with considering PDL and the polarization direction correlation between PMD and PDL, a system with highly mode coupled fiber with lumped section can have either higher or lower Q-factor than a highly mode coupled system with same root mean square PDL/PMD values. Also we noticed that a system of two highly mode coupled fibers connected together is not equivalent to a system of highly mode coupled fiber when fluctuation is considered

Keywords: polarization mode dispersion, polarization dependent loss, chromatic dispersion, optical eye diagram

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Authors: Salah Menouar, Sara Hassoul

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The dynamic of time-dependent three coupled oscillators is studied through an approach based on decoupling of them using the unitary transformation method. From a first unitary transformation, the Hamiltonian of the complicated original system is transformed to an equal but a simple one associated with the three coupled oscillators of which masses are unity. Finally, we diagonalize the matrix representation of the transformed hamiltonian by using a unitary matrix. The diagonalized Hamiltonian is just the same as the Hamiltonian of three simple oscillators. Through these procedures, the coupled oscillatory subsystems are completely decoupled. From this uncouplement, we can develop complete dynamics of the whole system in an easy way by just examining each oscillator independently. Such a development of the mechanical theory can be done regardless of the complication of the parameters' variations.

Keywords: schrödinger equation, hamiltonian, time-dependent three coupled oscillators, unitary transformation

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Authors: Irina E. Sukovataya, Oleg S. Sutormin, Valentina A. Kratasyuk

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Effect of viscosity of media on kinetic parameters of the coupled enzyme system NADH:FMN-oxidoreductase–luciferase was investigated with addition of organic solvents (glycerol and sucrose), because bioluminescent enzyme systems based on bacterial luciferases offer a unique and general tool for analysis of the many analytes and enzymes in the environment, research, and clinical laboratories and other fields. The possibility of stabilization and increase of activity of the coupled enzyme system NADH:FMN-oxidoreductase–luciferase activity in vicious aqueous-organic mixtures have been shown.

Keywords: coupled enzyme system of bioluminescence bacteria NAD(P)H:FMN-oxidoreductase–luciferase, glycerol, stabilization of enzymes, sucrose

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Authors: Hyun-Woo Jun, Tae-Chul Jeong, Huai-Cong Liu, Ju Lee

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The paper presents the electromagnetic-thermal flow coupled analysis of permanent magnet synchronous motor (PMSM) which has cooling channel in stator core for forced air cooling. Unlike the general PMSM design, to achieve ohmic loss reduction for high efficiency, cooling channel actively used in the stator core. Equivalent thermal network model was made to analyze the effect of the formation of the additional flow path in the core. According to the shape and position changing of the channel design, electromagnetic-thermal coupled analysis results were reviewed.

Keywords: coupled problems, electric motors, equivalent circuits, fluid flow, thermal analysis

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Authors: Rahil Samani, Saeed Soleimani, Ehsan Adib, Majid Pahlevani

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This paper presents an inverting high step-up DC/DC converter. Basically, this high step-up DC/DC converter is an appealing interface for solar applications. The proposed topology takes advantage of using coupled inductors. Due to the leakage inductances of these coupled inductors, the power MOSFET has the zero current switching (ZCS) condition, which results in decreased switching losses. This will substantially improve the overall efficiency of the power converter. Furthermore, employing coupled inductors has led to a higher voltage gain. Theoretical analysis and experimental results of a 100W 20V/220V prototype are presented to verify the superior performance of the proposed DC/DC converter.

Keywords: coupled inductors, high step-up DC/DC converter, zero-current switching, Cuk converter, SEPIC converter

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Authors: Jade Martínez-Llinàs, Pere Colet

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By exploring the possible dynamical regimes in a prototypical model for mutually delay-coupled OEOs, here it is shown that two mutually coupled non-identical OEOs, besides in- and out-of-phase square-waves, can generate stable square-wave pulses synchronized at a quarter of the period (T/4) in a broad parameter region. The key point to obtain T/4 solutions is that the two OEO operate with mixed feedback, namely with negative feedback in one and positive in the other. Furthermore, the coexistence of multiple solutions provides a large degree of flexibility for tuning the frequency in the GHz range without changing any parameter. As a result the two coupled OEOs system is good candidate to be implemented for information encoding as a high-capacity memory device.

Keywords: nonlinear optics, optoelectronic oscillators, square waves, synchronization

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Authors: Walid K. M. Bani Salameh, Hesham Ahmad, Mohammad Al-Shannag

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In Jordan having deficit atmospheric precipitation, an increase in water demand during summer months . Jordan can be regarded with a relatively high potential for waste water recycling and reuse. The main purpose of this paper was to investigate the removal of Total suspended solids (TSS) and chemical oxygen demand (COD) for olive mill waste water (OMW) by the electrocoagulation (EC) process. In the combination of electrocoagulation by using coupled iron–aluminum electrodes the optimum working pH was found to be in range 6. The efficiency of the electrocoagulation process allowed removal of TSS and COD about 82.5% and 47.5% respectively at 45 mA/cm2 after 70 minutes by using coupled iron–aluminum electrodes. These results showed that the optimum TSS and COD removal was obtained at the optimum experimental parameters such as current density, pH, and reaction time.

Keywords: olive mill wastewater, electrode, electrocoagulation (EC), TSS, COD

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Authors: Mohammad A. Bani-Khaled

Abstract:

In this work we use the Discrete Proper Orthogonal Decomposition transform to characterize the properties of coupled dynamics in thin-walled beams by exploiting numerical simulations obtained from finite element simulations. The outcomes of the will improve our understanding of the linear and nonlinear coupled behavior of thin-walled beams structures. Thin-walled beams have widespread usage in modern engineering application in both large scale structures (aeronautical structures), as well as in nano-structures (nano-tubes). Therefore, detailed knowledge in regard to the properties of coupled vibrations and buckling in these structures are of great interest in the research community. Due to the geometric complexity in the overall structure and in particular in the cross-sections it is necessary to involve computational mechanics to numerically simulate the dynamics. In using numerical computational techniques, it is not necessary to over simplify a model in order to solve the equations of motions. Computational dynamics methods produce databases of controlled resolution in time and space. These numerical databases contain information on the properties of the coupled dynamics. In order to extract the system dynamic properties and strength of coupling among the various fields of the motion, processing techniques are required. Time- Proper Orthogonal Decomposition transform is a powerful tool for processing databases for the dynamics. It will be used to study the coupled dynamics of thin-walled basic structures. These structures are ideal to form a basis for a systematic study of coupled dynamics in structures of complex geometry.

Keywords: coupled dynamics, geometric complexity, proper orthogonal decomposition (POD), thin walled beams

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Authors: Bouafia-Chergui Souâd, Chabani Malika, Bensmaili Aicha

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Water treatment and especially, medicament pollutants are nowadays important problems. Degradation of oxytetracycline was carried out using combined process of low-frequency ultrasound (US), ultraviolet irradiation and a catalyst. The effectiveness of the coupled processes has been evaluated by studying the effects of various operating parameters including initial OTC concentration, solution pH and catalyst mass. For the photolysis process, the monochromatic ultraviolet light wavelength utilized was 365 nm. The sonolysis experiments were performed with ultrasound at a frequency of 40 kHz. The heterogeneous photocatalysis was studied in the presence of TiO2. The processes were employed individually, and simultaneously to examine the details of the processes and to investigate the contribution of each process. Low UV intensity (12W), low pH and high mass of TiO2 conditions enhanced the sono-photocatalytic degradation of OTC. The results showed that the individual contribution sonochemical and photochemical reactions are very low, however, their coupling increases the degradation rate of 8 times compared to photolysis and 2 times compared to sonolysis. There is a synergistic effect between the two modes of radiation, UV and U.S. leading to 82.04% degradation yield. An application of these combined processes on the treatment of a real pharmaceutical wastewater was examined.

Keywords: sonolysis, photocatalysis, combined process, antibiotic

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Authors: Prashant Pandey

Abstract:

In the present article, an effective Laguerre collocation method is used to obtain the approximate solution of a system of coupled fractional-order non-linear reaction-advection-diffusion equation with prescribed initial and boundary conditions. In the proposed scheme, Laguerre polynomials are used together with an operational matrix and collocation method to obtain approximate solutions of the coupled system, so that our proposed model is converted into a system of algebraic equations which can be solved employing the Newton method. The solution profiles of the coupled system are presented graphically for different particular cases. The salient feature of the present article is finding the stability analysis of the proposed method and also the demonstration of the lower variation of solute concentrations with respect to the column length in the fractional-order system compared to the integer-order system. To show the higher efficiency, reliability, and accuracy of the proposed scheme, a comparison between the numerical results of Burger’s coupled system and its existing analytical result is reported. There are high compatibility and consistency between the approximate solution and its exact solution to a higher order of accuracy. The exhibition of error analysis for each case through tables and graphs confirms the super-linearly convergence rate of the proposed method.

Keywords: fractional coupled PDE, stability and convergence analysis, diffusion equation, Laguerre polynomials, spectral method

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Authors: Cem Çindaş, Serkan Şimşek

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In this paper, the study and design of a 3-dB 90° directional coupler operating in the S-band is proposed. The coupler employs symmetrical multi-section coupled lines designed in a stripline technique. Design is realized in AWR Design Environment and CST Microwave Studio. Using these two programs played a key role in attaining outcomes swiftly and precisely. The simulation results show that the coupler maintains amplitude consistency within ± 0.3 dB, isolation and reflection losses better than 16 dB, and phase difference between two output ports of 88º±0.6˚ in the 1.7 – 4.35 GHz range. This simulation results indicate an improvement is achieved in fractional bandwidth (FBW) performance around the center frequency of f0 = 3 GHz.

Keywords: coupled stripline, directional coupler, multi-section coupler, symmetrical coupler

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Authors: Mahdi Alkaeed, Adeel Ehsan

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Enterprise information systems (EIS) act as the backbone of organizations that belong to different domains. These systems not only play a major role in the efficient usage of resources and time but also throw light on the future roadmap for the enterprise. In today's rapidly expanding world of business and technology, enterprise systems from various heterogenous environments have to exchange information at some point, be it within the same organization or between different organizations. This reality strengthens the importance of interoperability between these systems, which is one of the key enablers of systems collaboration. Both information technology infrastructure and business processes have to be aligned with each other to achieve this effect. This will be difficult to attain if traditional tightly coupled architecture is used. Instead, a more loosely coupled service-oriented architecture has to be used. That would enable an effective interoperability level between different EIS. This paper discusses and presents the current work that has been done in the field of EIS interoperability. Along the way, it also discusses the challenges, solutions to tackle those challenges presented in the studied literature, and limitations, if any.

Keywords: enterprise systems interoperability, collaboration and integration, service-based architecture, open system architecture

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Authors: J. Vyas, R. Kazys, J. Sestoke

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Air-coupled ultrasonic is the contactless ultrasonic measurement approach which has become widespread for material characterization in Aerospace industry. It is always essential for the requirement of lightest weight, without compromising the durability. To archive the requirements, composite materials are widely used. This paper yields analysis of the air-coupled ultrasonics for composite materials such as CFRP (Carbon Fibre Reinforced Polymer) and GLARE (Glass Fiber Metal Laminate) and honeycombs for the design of modern aircrafts. Laser vibrometry could be the key source of characterization for the aerospace components. The air-coupled ultrasonics fundamentals, including principles, working modes and transducer arrangements used for this purpose is also recounted in brief. The emphasis of this paper is to approach the developed NDT techniques based on the ultrasonic guided waves applications and the possibilities of use of laser vibrometry in different materials with non-contact measurement of guided waves. 3D assessment technique which employs the single point laser head using, automatic scanning relocation of the material to assess the mechanical displacement including pros and cons of the composite materials for aerospace applications with defects and delaminations.

Keywords: air-coupled ultrasonics, contactless measurement, laser interferometry, NDT, ultrasonic guided waves

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Authors: Mingde Du, Dong Han

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A low profile, dual polarized, slot coupled patch antenna is designed and developed in this paper. The antenna has a measured bandwidth of 17.2% for return loss > 15 dB and pair ports isolation >23 dB. The gain of the antenna is over 10 dBi and the half power beam widths (HPBW) of the antenna are 80±3^o in the horizontal plane and 39±2^o in the vertical plane. The cross polarization discrimination (XPD) is less than 20 dB in HPBW. Within the operating band, the performances of good impedance match, high ports isolation, low cross polarization, and stable radiation patterns are achieved.

Keywords: dual polarized, patch antenna, slot coupled, base station antenna

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Authors: Kamel Al-Khaled

Abstract:

In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: Roderick Melnik, Sanjay Prabhakar

Abstract:

The relaxed state of graphene nanostructures due to externally applied tensile stress along both the armchair and zigzag directions are analyzed in detail. The results, obtained with the Finite Element Method (FEM), demonstrate that the amplitude of ripple waves in such nanostructures increases with temperature. Details of the multi-scale multi-physics computational procedure developed for this analysis are also provided.

Keywords: nanostructures, modeling, coupled processes, computer-aided design, nanotechnological applications

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Authors: J. V. Gonzalez Fernandez, T. Mozume, S. Gozu, A. Lastras Martinez, L. F. Lastras Martinez, J. Ortega Gallegos, R. E. Balderas Navarro

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We report on a theoretical-experimental study of photoreflectance anisotropy (PRA) spectroscopy of coupled double quantum wells. By probing the in-plane interfacial optical anisotropies, we demonstrate that PRA spectroscopy has the capacity to detect and distinguish layers with quantum dimensions. In order to account for the experimental PRA spectra, we have used a theoretical model at k=0 based on a linear electro-optic effect through a piezoelectric shear strain.

Keywords: coupled double quantum well (CDQW), linear electro-optic (LEO) effect, photoreflectance anisotropy (PRA), piezoelectric shear strain

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Authors: Abdelatif Gadoum, Djilali Benyoucef, Mouloudj Hadj, Alla Eddine Toubal Maamar, Mohamed Habib Allah Lahoual

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Hydrogen occurs naturally in the form of chemical compounds, most often in water and hydrocarbons. The main objective of this study is 2D modeling of hydrogen production in inductively coupled plasma in methane at low pressure. In the present model, we include the motions and the collisions of both neutral and charged particles by considering 19 species (i.e in total ; neutrals, radicals, ions, and electrons), and more than 120 reactions (electron impact with methane, neutral-neutral, neutral-ions and surface reactions). The results show that the rate conversion of methane reach 90% and the hydrogen production is about 30%.

Keywords: hydrogen production, inductively coupled plasma, fluid model, methane plasma

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Authors: Azher Jameel, Ghulam Ashraf Harmain

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In the recent years, the enriched techniques like the extended finite element method, the element free Galerkin method, and the Coupled finite element-element free Galerkin method have found wide application in modeling different types of discontinuities produced by cracks, contact surfaces, and bi-material interfaces. The extended finite element method faces severe mesh distortion issues while modeling large deformation problems. The element free Galerkin method does not have mesh distortion issues, but it is computationally more demanding than the finite element method. The coupled FE-EFGM proves to be an efficient numerical tool for modeling large deformation problems as it exploits the advantages of both FEM and EFGM. The present paper employs the coupled FE-EFGM to model large elastoplastic deformations in bi-material engineering components. The large deformation occurring in the domain has been modeled by using the total Lagrangian approach. The non-linear elastoplastic behavior of the material has been represented by the Ramberg-Osgood model. The elastic predictor-plastic corrector algorithms are used for the evaluation stresses during large deformation. Finally, several numerical problems are solved by the coupled FE-EFGM to illustrate its applicability, efficiency and accuracy in modeling large elastoplastic deformations in bi-material samples. The results obtained by the proposed technique are compared with the results obtained by XFEM and EFGM. A remarkable agreement was observed between the results obtained by the three techniques.

Keywords: XFEM, EFGM, coupled FE-EFGM, level sets, large deformation

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Authors: H. Kazemi Esfeh, V. Akbari, M. Ehdaei, T. N. G. Borhani, A. Shamiri, M. Najafi

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In an industrial fluidized bed polymerization reactor, particle size distribution (PSD) plays a significant role in the reactor efficiency evaluation. The computational fluid dynamic (CFD) models coupled with population balance equation (CFD-PBM) have been extensively employed to investigate the flow behavior in the poly-disperse multiphase fluidized bed reactors (FBRs) utilizing ANSYS Fluent code. In this study, an existing CFD-PBM/ DQMOM coupled modeling framework has been used to highlight its potential to analyze the industrial-scale gas phase polymerization reactor. The predicted results reveal an acceptable agreement with the observed industrial data in terms of pressure drop and bed height. The simulated results also indicate that the higher particle growth rate can be achieved for bigger particles. Hence, the 2D CFD-PBM/DQMOM coupled model can be used as a reliable tool for analyzing and improving the design and operation of the gas phase polymerization FBRs.

Keywords: computational fluid dynamics, population balance equation, fluidized bed polymerization reactor, direct quadrature method of moments

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Authors: Yacine Arioua

Abstract:

In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Caputo-type Katugampola fractional differential equations with integral boundary conditions. Based upon a contraction mapping principle, Schauders fixed point theorems, some new existence and uniqueness results of solutions for the given problems are obtained. For application, some examples are given to illustrate the usefulness of our main results.

Keywords: fractional differential equations, coupled system, Caputo-Katugampola derivative, fixed point theorems, existence, uniqueness

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Authors: Chungkuk Jin, Moo-Hyun Kim, HeonYong Kang

Abstract:

A surface riding (SR) wave energy converter (WEC) is designed and its feasibility and performance are numerically simulated by the author-developed floater-mooring-magnet-electromagnetics fully-coupled dynamic analysis computer program. The biggest advantage of the SR-WEC is that the performance is equally effective even in low sea states and its structural robustness is greatly improved by simply riding along the wave surface compared to other existing WECs. By the numerical simulations and actuator testing, it is clearly demonstrated that the concept works and through the optimization process, its efficiency can be improved.

Keywords: computer simulation, electromagnetics fully-coupled dynamics, floater-mooring-magnet, optimization, performance evaluation, surface riding, WEC

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Authors: Adriano Valdes-Gomez, Francisco Javier Sevilla

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We devise a numerical algorithm to simulate the diffusion of a Brownian particle restricted to the surface of a three-dimensional sphere when the particle is under the effects of an external potential that is coupled linearly. It is obtained using elementary geometry, yet, it converges, in the weak sense, to the solutions to the Smoluchowski equation. Rotations on the sphere, which are the analogs of linear displacements in euclidean spaces, are calculated using algebraic operations and then by a proper scaling, which makes the algorithm efficient and quite simple, especially to what may be the short-time propagator approach. Our findings prove that the global effects of curvature are taken into account in both dynamic and stationary processes, and it is not restricted to work in configuration space, neither restricted to the overdamped limit. We have generalized it successfully to simulate the Kramers or the Ornstein-Uhlenbeck process, where it is necessary to work directly in phase space, and it may be adapted to other two dimensional surfaces with non-constant curvature.

Keywords: diffusion on the sphere, Fokker-Planck equation on the sphere, non equilibrium processes on the sphere, numerical methods for diffusion on the sphere

Procedia PDF Downloads 148