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Articles 31 - 60 of 355

Full-Text Articles in Engineering

Research On Flexible Job-Shop Dynamic Scheduling Based On Game Theory, Yichen You, Wang Yan, Zhicheng Ji Nov 2021

Research On Flexible Job-Shop Dynamic Scheduling Based On Game Theory, Yichen You, Wang Yan, Zhicheng Ji

Journal of System Simulation

Abstract: To quickly and effectively respond to the machine fault disturbance events in Flexible Job-shop Scheduling Problem (FJSP), a flexible job-shop dynamic scheduling based on game theory is established. A pre-scheduling scheme is generated under Non-Dominated Sort Genetic Algorithm-Ⅱ (NSGA-Ⅱ) algorithm which introduces self-adapted crossover operators to improve the population diversity. For FJSP dynamic scheduling with machine fault, a multi-stage complete information game model is built to better balance the stability and robustness indicators and respond quickly to the machine fault, in which the stability and robustness indicators are mapped to the game players, and a hybrid Nash Equilibrium which …


Stability Analysis In Central America’S Power Grid, Sergio Sunley Aug 2021

Stability Analysis In Central America’S Power Grid, Sergio Sunley

International Programs

Finding the source of instability is key in ensuring an electric power grid proper functioning. This poster shows the results obtained from a stability analysis performed in Central America’s power grid in order to find the source of instability of that grid.


Numerical Stability Analysis For Independent Modal Vibration Suppression Of A Fluid-Conveying Pipe Using A Piezoelectric Inertia Actuator, Yih-Hwang Lin, Jui-Lung Chen, Chih-Liang Chu, Yau-Kun Tsai Aug 2021

Numerical Stability Analysis For Independent Modal Vibration Suppression Of A Fluid-Conveying Pipe Using A Piezoelectric Inertia Actuator, Yih-Hwang Lin, Jui-Lung Chen, Chih-Liang Chu, Yau-Kun Tsai

Journal of Marine Science and Technology

This study deals with numerical stability analysis for independent modal vibration suppression of a fluid-conveying pipe using a piezoelectric inertia actuator (PIA). The stability issue of the approach as proposed by the pioneer developers is addressed. The approach utilizes an infinite control weight for one component of the modal control input and results in a severe control spillover problem for the complex mode controlled, easily leading to closed loop instability even for open loop stable systems. The stability of the system depends on how the left eigenvector is normalized for transforming the original coupled equations to the decoupled ones in …


Digital Cutting Force Modeling For Milling Operations, Timothy T. No Aug 2021

Digital Cutting Force Modeling For Milling Operations, Timothy T. No

Doctoral Dissertations

Process improvement in milling through improved understanding of machining dynamics is an on-going research endeavor. The objective of this project is to advance digital modeling of the milling process by incorporating tool-specific geometry in the machining analysis. Structured light scanning will be used to perform tool geometry measurements and produce a 3D model. The 3D model data will include the spatial location of the cutting edges, as well as the rake and relief profiles from the tool cross section. The rake and relief profiles will be imported, together with the work material flow stress model, into a finite element analysis …


Active Stability Monitoring And Stability Control Of Dc Microgrids Using Incremental Continuous Injection, Rohail Hassan Aug 2021

Active Stability Monitoring And Stability Control Of Dc Microgrids Using Incremental Continuous Injection, Rohail Hassan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Electrified transportation and integration of renewable energy in the electric power grid requires the use of power electronic converters for integrating different forms of power; from ac to dc, dc to ac, dc to dc, etc. Recent trend towards electrifying automobiles, aircraft and ships, and increasing penetration of renewable energy has increased the required power levels and number of the power electronics converters connected together in a dc microgrid system. Stable operation of these interfacing converters for all operating conditions has been a topic of renewed interest in the last couple of decades. Traditionally, dc microgrids have been designed conservatively …


Study On Universal Characteristics Of Insect Population Ecological Network, Guilan Luo, Hongjun Hao, Wang Xiao, Zhang Mei Jul 2021

Study On Universal Characteristics Of Insect Population Ecological Network, Guilan Luo, Hongjun Hao, Wang Xiao, Zhang Mei

Journal of System Simulation

Abstract: In order to evaluate the current state of insect ecological development in Erhai wetland, complex network theory is used to construct a topological structure model of insect ecological network with insect populations as network nodes and correlations as edges. By analyzing the characteristic parameters of the model, it is concluded that the insect ecological network conforms to the characteristics of small world and scale-free network, and the node degree distribution obeys the power law distribution. The method of destroying the topology is used to simulate the dynamic evolution of the network ecology. The study shows that the disappearance of …


Lyapunov Function-Based Stabilizing Control Scheme For Wireless Power Transfer Systems With Lcc Compensation Network, Abu Shahir Md Khalid Hasan Jul 2021

Lyapunov Function-Based Stabilizing Control Scheme For Wireless Power Transfer Systems With Lcc Compensation Network, Abu Shahir Md Khalid Hasan

LSU Master's Theses

A stabilizing control scheme based on a Lyapunov function is proposed for wireless power transfer (or WPT) systems. A state-space model of the WPT system is developed and the Lyapunov function is formulated based on an energy equation of the system involving state variables. The internal resistance of a battery varies during charge and discharge. Therefore, if a WPT system is used to charge a battery, its output load will vary. Furthermore, the coupling coefficient between the transmitter (primary) and receiver (secondary) coils decreases when they are misaligned. Comparative case studies are conducted to verify the efficacy of the proposed …


Role Of Lithium Doping In P2-Na0.67Ni0.33Mn0.67O2 For Sodium-Ion Batteries, Yingying Xie, Eric Gabriel, Haoyu Zhu, Julie Pipkin, Malia Dustin, Hui Xiong Jun 2021

Role Of Lithium Doping In P2-Na0.67Ni0.33Mn0.67O2 For Sodium-Ion Batteries, Yingying Xie, Eric Gabriel, Haoyu Zhu, Julie Pipkin, Malia Dustin, Hui Xiong

Materials Science and Engineering Faculty Publications and Presentations

P2-structured Na0.67Ni0.33Mn0.67O2 (PNNMO) is a promising Na-ion battery cathode material, but its rapid capacity decay during cycling remains a hurdle. Li doping in layered transition-metal oxide (TMO) cathode materials is known to enhance their electrochemical properties. Nevertheless, the influence of Li at different locations in the structure has not been investigated. Here, the crystallographic role and electrochemical impact of lithium on different sites in PNNMO is investigated in LixNa0.67–yNi0.33Mn0.67O2+δ (0.00 ≤ x ≤ 0.2, y = 0, 0.1). Lithium occupancy on prismatic Na …


On Stability And Similarity Of Network Embeddings, Apurva Shriniwas Mulay May 2021

On Stability And Similarity Of Network Embeddings, Apurva Shriniwas Mulay

Theses - ALL

Machine Learning on graphs has become an active research area due to the prevailing graph-structured data in the real world. Many real-world applications can be modeled with graphs. Modern application domains include web-scale social networks [26], recommender systems, knowledge graphs, and biological or protein networks. However, there are various challenges. First, the graphs generated from such applications are often large. Moreover, in some scenarios, the complete graph is not available, e.g., for privacy reasons. Thus, it becomes impractical to perform network analysis or compute various graph measures. Hence, graph sampling becomes an important task.Sampling is often the first step to …


On Stability And Similarity Of Network Embeddings, Apurva Shriniwas Mulay May 2021

On Stability And Similarity Of Network Embeddings, Apurva Shriniwas Mulay

Theses - ALL

Machine Learning on graphs has become an active research area due to the prevailing graph-structured data in the real world. Many real-world applications can be modeled with graphs. Modern application domains include web-scale social networks [26], recommender systems, knowledge graphs, and biological or protein networks. However, there are various challenges. First, the graphs generated from such applications are often large. Moreover, in some scenarios, the complete graph is not available, e.g., for privacy reasons. Thus, it becomes impractical to perform network analysis or compute various graph measures. Hence, graph sampling becomes an important task.Sampling is often the first step to …


Stability Of Low Crested And Submerged Breakwaters: A Reanalysis And Model Development, Christopher P. Burgess Apr 2021

Stability Of Low Crested And Submerged Breakwaters: A Reanalysis And Model Development, Christopher P. Burgess

Civil & Environmental Engineering Theses & Dissertations

Low-crested and submerged structures (LCS) play an integral part in the stabilization of shorelines for recreational purposes, yet there are a plethora of empirical models and gaps in the understanding of their stability and damage progression. The objectives were: i) to evaluate the present formulae, ii) explore variable importance, iii) formulate a stability model, iv) extend the current datasets and v) explore a new model for LCS. The literature points to an increasing understanding of the initiation of damage of LCS and recent exploration of the shear stress-induced erosion (van Rijn, 2019). Assessment of two existing models (Kramer, 2006 and …


Controller Modeling And Stability Analysis Of Multiple Input Single Output Dc-Dc Converter, Astha Adhikari Mar 2021

Controller Modeling And Stability Analysis Of Multiple Input Single Output Dc-Dc Converter, Astha Adhikari

Master's Theses

This thesis entails the stability analysis of the Multiple Input Single Output (MISO) DC-DC converter developed for the DC House Project at Cal Poly. A frequency domain control system model of the MISO converter was designed and constructed using MATLAB Simulink. Transfer functions were derived and modeled for each stage of the converter to best fit the converter circuit system used in the original MISO circuit. Stability metrics such as overshoot, undershoot, rise time, phase margin and gain margin were measured to evaluate and analyze the stability of the converter. These metrics were measured with the original model including the …


In Vitro Analyses Of The Contributions Of The Hip Capsule To Joint Biomechanics, Emma Donnelly Jan 2021

In Vitro Analyses Of The Contributions Of The Hip Capsule To Joint Biomechanics, Emma Donnelly

Electronic Thesis and Dissertation Repository

Optimal management of the hip capsule during arthroscopic surgery has not been established. The impact of incisions made to the capsule during minimally invasive procedures on joint biomechanics, and whether repair provides any benefit, continue to be debated. The effectiveness of capsular repair to restore native kinematics may be insufficient. Therefore, a better understanding of joint behavior during various capsule conditions is needed. A new robotic system was used to analyze the effect of progressive capsulotomy incision and repairs on the behavior of a normal hip within range of motion (ROM) limits with respect to the intact joint. Complete repairs …


Feasibility Study To Measure The Impact Of A Specialized Core Exercise On Metabolic Efficiency And Stability During Walking For Above Knee Amputees, Shaye M. Tiell, Sabrina R. Segretario, Serena M. Myers, Emily G. Tully Jan 2021

Feasibility Study To Measure The Impact Of A Specialized Core Exercise On Metabolic Efficiency And Stability During Walking For Above Knee Amputees, Shaye M. Tiell, Sabrina R. Segretario, Serena M. Myers, Emily G. Tully

Williams Honors College, Honors Research Projects

The objective of this study is to determine the feasibility of improving the gait of above-knee (AK) amputees by performing daily core exercises aimed to provide an efficient and stable walking pattern. The goal of the exercise is to strengthen core muscles and form temporary neural connections in the brain aimed at improving metabolic efficiency and stability. We will be implementing the Wright Balance Core 360 Exercise Technique for completion by our subjects. Motion capture technology will be utilized in conjunction with a metabolic oxygen consumption analyzer to collect stability and metabolic efficiency data while amputees walk on a treadmill. …


Enhanced Oil Recovery By Hydrophilic Silica Nanofluid: Experimental Evaluation Of The Impact Of Parameters And Mechanisms On Recovery Potential, Tariq A. Chandio, Muhammad A. Manan, Khalil R. Memon, Ghulam Abbas, Ghazanfer R. Abbasi Jan 2021

Enhanced Oil Recovery By Hydrophilic Silica Nanofluid: Experimental Evaluation Of The Impact Of Parameters And Mechanisms On Recovery Potential, Tariq A. Chandio, Muhammad A. Manan, Khalil R. Memon, Ghulam Abbas, Ghazanfer R. Abbasi

Research outputs 2014 to 2021

Nanofluids as an EOR technique are reported to enhance oil recoveries. Among all the nanomaterial silica with promising lab results, economic and environmental acceptability are an ideal material for future applications. Despite the potential to enhance recoveries, understanding the two-fold impact of parameters such as concentration, salinity, stability, injection rate, and irreproducibility of results has arisen ambiguities that have delayed field applications. This integrated study is conducted to ascertain two-fold impacts of concentration and salinity on recovery and stability and evaluates corresponding changes in the recovery mechanism with variance in the parameters. Initially, silica nanofluids’ recovery potential was evaluated by …


Impacts Of Using Tubular Sections In Open Web Steel Joists, Hollis (Cas) L. Caswell V Jan 2021

Impacts Of Using Tubular Sections In Open Web Steel Joists, Hollis (Cas) L. Caswell V

Honors Theses

Open web steel joists are lightweight structural trusses used in place of I-beams to support long-span floors and roofs of open space buildings. Their slender geometry makes them highly efficient in resisting flexure, but susceptible to out-of-plane buckling in a failure mode known as lateral-torsional buckling. This failure can be avoided by running lateral bracing between joists called bridging or potentially by using tubular sections to build up the joists rather than angle sections.

It is possible that a joist design using tubular cross-sections could require less bridging and prevent the need to use erection bridging for initial joist construction. …


Aerodynamic Characterization Of Bio-Mimicked Pleated Dragonfly Aerofoil, Md Akhtar Khan, Chinmaya Padhy Jan 2021

Aerodynamic Characterization Of Bio-Mimicked Pleated Dragonfly Aerofoil, Md Akhtar Khan, Chinmaya Padhy

International Journal of Aviation, Aeronautics, and Aerospace

The work inspired by the dragonfly wing corrugation positioned at the front wing's radius section lying at 40% of the total wingspan of forewing from the root section. During gliding flight, dragonfly wings presumed to be an ultra-light aerofoil due to its well-defined cross-sectional corrugation. The aerodynamic simulation carried out to understand the aerodynamic performance of a bio-mimetic dragonfly corrugated airfoil at low Reynolds number range of 75000-150000 to explore the potential advantages of pleated airfoils at a varying angle of attack from 0° to 12°. CFD analysis accomplished by using ANSYS Fluent to understand the aerodynamic performance of the …


The Stability Of Nanobubbles And Its Application In Contaminated Sediment Treatment, Shaini Dilsha Aluthgun Hewage Dec 2020

The Stability Of Nanobubbles And Its Application In Contaminated Sediment Treatment, Shaini Dilsha Aluthgun Hewage

Dissertations

This dissertation consists of two sections. First, nanobubbles' stability and behavior are studied using experimental and theoretical approaches. Second, nanobubbles application combined with ultrasound to remediate contaminated sediments is discussed.

The stability study consists of four sections. (i). Laboratory investigation to determine bubble size distributions and zeta potentials for different gases, pH levels, temperatures, and salt conditions. (ii). A theoretical study based on the diffused double layer theory to explain nanobubbles' behavior in different NaCl concentrations. (iii). Nanobubbles' stability in electrolyte solutions under different ion valencies using deionized water, NaCl, Na2SO4, Na3PO4, …


Vibration Behavior In Modulated Tool Path (Mtp) Turning, Ryan William Copenhaver Dec 2020

Vibration Behavior In Modulated Tool Path (Mtp) Turning, Ryan William Copenhaver

Doctoral Dissertations

This project studies the process dynamics and surface finish effects of modulated tool path (MTP) turning. In MTP turning, a small amplitude (typically less than 0.5 mm), low frequency oscillation (typically less than 10 Hz) is superimposed on the feed motion by the machine controller to intentionally segment the traditionally long, continuous chips. The basic science to be examined is the vibration behavior of this special case of interrupted cutting, which is not turning because the chip formation is intentionally discontinuous and is not milling because the time-dependent chip geometry is defined by the oscillatory feed motion, not the trochoidal …


Theoretical Studies Of Spinning Line Parameters Of Ring Spinning Machines, Nurilla Dadaxanov Oct 2020

Theoretical Studies Of Spinning Line Parameters Of Ring Spinning Machines, Nurilla Dadaxanov

Acta of Turin Polytechnic University in Tashkent

The article studies the angle of discharge of exhaust devices and obtaining of analytical dependencies for calculating the angle of flow around the sliver of the exhaust cylinder on the spinning line of ring spinning machines.


Research Of The Influence Of Technological Factors On The State Of The Sides Of Deep Quarries, D.R. Mahmudov, V.R. Kadirov, Sh.V. Karimov, Y.R. Hamraev Sep 2020

Research Of The Influence Of Technological Factors On The State Of The Sides Of Deep Quarries, D.R. Mahmudov, V.R. Kadirov, Sh.V. Karimov, Y.R. Hamraev

Technical science and innovation

The article considers the influencing technological factors of mining operations on the state of the quarry sides. In technological processes, the stability of the sides of rock and semi-rock rocks and the value of the angle of inclination of the sides is most affected by drilling and blasting operations. It is determined that effective technological schemes in the zone of residual deformations should be carried out taking into account the geological structure of the contour array. Changing the opening scheme is associated with the development system and mining mode. To ensure the safety of the sides of deep quarries, several …


Design And Numerical Analyses Of High-Fill Slope Strengthened By Frame With Prestressed Anchor-Plates, Yan-Peng Zhu, Jun Tao, Xiao-Hui Yang, Jun-Guo Peng, Qiang Wu Sep 2020

Design And Numerical Analyses Of High-Fill Slope Strengthened By Frame With Prestressed Anchor-Plates, Yan-Peng Zhu, Jun Tao, Xiao-Hui Yang, Jun-Guo Peng, Qiang Wu

Rock and Soil Mechanics

Plenty of high-fill slopes need to be strengthened in engineering projects in the mountainous area of the northwestern district of China with complex geological conditions. To provide sufficient anchoring force to fill slopes and to ensure their stabilities, we put forward a new structure of safety, stability, economy and convenience, named frame with prestressed anchor-plates, which suits for reinforcing the slopes with large fill, and whose reinforcement effect is great. Based on the limit equilibrium theory, we proposed the formula for pull-out resistance and the checking calculation method for the stability. Finite element analysis software PLAXIS 3D was applied to …


Joint Dynamics Simulation Analysis And Optimization In Carrying Manipulator Of Sound-Absorbing Board Packing Device, Yanjun Xiao, Feng Hua, Wang Zhao, Yonggeng Wang Aug 2020

Joint Dynamics Simulation Analysis And Optimization In Carrying Manipulator Of Sound-Absorbing Board Packing Device, Yanjun Xiao, Feng Hua, Wang Zhao, Yonggeng Wang

Journal of System Simulation

Abstract: As an important part of the sound-absorbing board packing device, the efficiency and operational stability of carrying manipulator play a decisive role on packing. When the natural frequency of carrying manipulator is close to the excitation frequency of motor, the carrying manipulator will shake violently. In response to above problems, we put joint dynamic simulation analysis of ADAMS and ANSYS Workbench on the carrying manipulator which is in use. We got the important components’ stress situation with the acceleration time of 0.1 s and the low-order natural frequency of the traverse key displacement in return. And on this basis …


Research On Bifurcation Of A Class Of Cortical Eeg Model With Time Delay, Chunsheng Li, Zhang Xue Jul 2020

Research On Bifurcation Of A Class Of Cortical Eeg Model With Time Delay, Chunsheng Li, Zhang Xue

Journal of System Simulation

Abstract: The bifurcation characters of a cortical-model with bidirectional time delays were studied, proposed by Robinson, et al. before. Considering transmitting delay between excitatory and inhibitory populations, the stability, bifurcation characters and bifurcation region were achieved. The relationship of cortical potential spectrum density and transmit delay was analyzed when white noise was introduced. Result shows that time delay between different population acts as an important role of model’s dynamic characters and stability, and numerical simulation verifies the theoretical analysis. This research shows the importance of transmit delay in cortical-model, and provides theoretical illustration for further research of epileptic …


Multiple Salinity Equilibria And Resilience Of Persian/Arabian Gulf Basin Salinity To Brine Discharge, Hamed D. Ibrahim, Pengfei Xue, Elfatih A.B. Eltahir Jul 2020

Multiple Salinity Equilibria And Resilience Of Persian/Arabian Gulf Basin Salinity To Brine Discharge, Hamed D. Ibrahim, Pengfei Xue, Elfatih A.B. Eltahir

Michigan Tech Publications

The Persian/Arabian Gulf is the most important region for seawater desalination. Surrounding countries produce about 50% of global desalinated seawater. If Gulf salinity significantly rises because of desalination effluent (brine), marine ecosystems and the water supply for many population centers will be threatened. In order to quantify current and future impacts of seawater desalination on Gulf salinity and avoid costly environmental problems, it is vital to first examine the present Gulf salinity state and its response to salinity perturbation (i.e., determine its stability). Here, using a coupled Gulf-Atmosphere numerical climate model, we test the hypothesis that the Gulf has a …


Simulation Research Of Maglev Train During Uphill And Downhill Process, Songqi Li, Kunlun Zhang, Guoqing Liu, Chen Yin Jul 2020

Simulation Research Of Maglev Train During Uphill And Downhill Process, Songqi Li, Kunlun Zhang, Guoqing Liu, Chen Yin

Journal of System Simulation

Abstract: In the low speed EMS maglev test line experiments in Zhuzhou, it was found that vehicles are prone to hit the tracks, when the maglev train travels uphill or downhill through the tracks with slopes. This seriously affected the safety and comfort of the vehicle. In order to study the problem, a single low speed EMS maglev train carriages-track model with four degrees of freedom was built. It simulated and analyzed dynamic behaviors of the vehicle going uphill on different track curves, under different vehicle -track parameters. The simulation results show that the vehicle parameters, vehicle speed, and the …


Incorporating Stability In Deployable Origami-Based Engineering Applications, David Wayne Andrews Jul 2020

Incorporating Stability In Deployable Origami-Based Engineering Applications, David Wayne Andrews

Theses and Dissertations

For origami-based designs to be functional, they need to be stable. Typically, stability is achieved through the introduction of exterior supports or members. This work focuses on incorporating stability into deployable origami-based engineering applications, including the development of deployable stiffeners or hard stops and generating concepts for stable origami-based systems in specific applications. Two types of deployable stiffeners are developed. Models for transcrease hard stops are presented, which can be directly implemented into origami-patterns to block motion at a specified angle. Thickness Utilizing Deployable Hard Stops (ThUDS), adapted from the transcrease hard stop models, can be implemented into thick materials …


Stability Studies For A Membrane Electrode Assembly Type Co2 Electro-Reduction Electrolytic Cell, Qing Mao, Bing-Yu Li, Wei-Yun Jing, Jian Zhao, Song Liu, Yan-Qiang Huang, Zhao-Long Du Jun 2020

Stability Studies For A Membrane Electrode Assembly Type Co2 Electro-Reduction Electrolytic Cell, Qing Mao, Bing-Yu Li, Wei-Yun Jing, Jian Zhao, Song Liu, Yan-Qiang Huang, Zhao-Long Du

Journal of Electrochemistry

Electro-catalytic reduction is an efficient way to achieve resourcable transformation of CO2, which is one of the important techniques to solve the global environmental problems originated from excessive CO2 emission. In this study, a membrane electrode assembly(MEA) type CO2 electro-reduction electrolytic cell was constucted, which enables CO2 feeding and real-time KHCO3 aqueous updating on both sides of the cathode gas diffusion electrode (GDE). By means of the electrolytic cell, effects of KHCO3 concentration and updating inside the liquid electrolytic chamber on CO2 electro-reduction activity, production distribution and stability were investigated. The experimental …


Derivation And Exploration Of Analytical Aircraft Stability Analysis, Roderick Landreth Jun 2020

Derivation And Exploration Of Analytical Aircraft Stability Analysis, Roderick Landreth

Honors Theses

A comprehensive measure of the in-flight stability of an aircraft is essential, though it can take a large amount of resources to do accurately and usefully. Small companies and colleges often don't have the resources to attain accurate experimental or analytical data to describe stable flight before potential failure. This composition investigates methods of completing a static and dynamic stability analysis for an aircraft feasible for a college, small business or hobbyist to complete, with the goal to eliminate the 'barrier of entry' concerning a lack of information and resources. A sample analytical calculation for static stability of Union College's …


Stability Of Electrically Conducting Fluid Flow In Channel Under Magnetic Field, Dong Shuai, Lishuai Liu, Xuemin Ye Jun 2020

Stability Of Electrically Conducting Fluid Flow In Channel Under Magnetic Field, Dong Shuai, Lishuai Liu, Xuemin Ye

Journal of System Simulation

Abstract: The stability of conducting fluid flow in a channel under a vertical magnetic field was simulated by non-normal modal stability analysis. The perfect conductivity assumption of the channel wall was employed in the model, and its effect on the stability problem was considered. The results show that when the Hartmann number Ha is larger than 9, the two opposite Hartmann boundary layers are essentially independent of each other; however, when the Hartmann number Ha is smaller than 9, there are still residual interactions between the two opposite Hartmann boundary layers, which has influences on the stability of the flow. …