Velocity Graphs Research Articles

Brownian motion in a magneto Thermo-diffusion fluid flow over a semi-circular stretching surface

The current study explores the mass and heat transport analysis of a Casson liquid stream past a curved surface. The current model considers the effect of magnetic strength brought on by the strength of the applied uniform magnetic field. The significance of thermophoresis and Brownian motion are also taken into account using the Buongiorno nano-liquid model. The study of liquid flow over stretching sheets frequently addresses practical issues that have garnered significant attention from researchers due to their importance in various domains, including microfluidics, fibreglass production, manufacturing, transportation, metal extrusion, thermal insulation, glass production, paper manufacturing, and acoustic blasting. The governing partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) using the similarity variables. These equations are numerically solved using the finite difference method (FDM). The concentration, temperature, and velocity graphs were produced by varying the different physical parameters. The upsurge in the magnetic parameter reduces the velocity profile. As the magnetic parameter increases, thermal and concentration profiles upsurge. The decrease in velocity profile can be seen as the Casson parameter rises. The intensification in values of thermophoretic parameter enhances the thermal and concentration profiles. The concentration and thermal profiles reduce as the curvature parameter upsurges.

Automobile response to road safety barriers upon collision

During a collision between an automobile and a road safety barrier, the vehicle will go through many behavior transition phases. This research will focus on determining the behavior of two car models including a sedan car and a pickup truck in collision with two safety road barriers using numerical simulation. This paper will also present images, total force graphs, and velocity graphs throughout the process to evaluate the vehicle's behavior at different impact speeds and angles. It is recognized that at similar impact speeds, collision angles, and barrier types, the pickup truck suffers more damage than the sedan. In addition, the pickup truck colliding with a concrete barrier exhibits the highest force, while the sedan colliding with a W-Beam barrier records the lowest force among the four collision types. Regarding the road safety barrier, the concrete barrier has a shorter force increase/decrease duration than the W-Beam barrier.

Thermal conductivity impact on MHD convective heat transfer over moving wedge with surface heat flux and high magnetic Prandtl number

The present evaluation focused on heat transfer and magnetic flux along the moving non-conducting wedge shape with thermal conductivity and surface heat flux effects. A suitable and well-known similarity transformation for integration is used for the coupled non-linear partial differential equations with stream formulations. The Keller Box technique is utilized to integrate the final non-similar equations numerically. The discretized algebraic equations are displayed graphically and numerically using the MATLAB software. The physical characteristics like temperature, magnetic field, velocity profiles, skin friction, heat transfer and magnetic intensity are investigated with various factors. The influence of relevant characteristics like thermal conductivity ξ, Prandtl number Pr, wedge parameter β, variable viscosity ε, and Biot number Bi is interpreted graphically and numerically. It is noted that velocity graph effects are declined at lower value of Biot number and enhanced value is obtained at the higher value of Biot number. The fluid temperature with highest thermal slip effects is displayed with minimum value of thermal conductivity but minimum value is obtained at large value of thermal conductivity. The maximum heat flux value is obtained at large value of moving parameter.

Numerical Investigation of Nucleotides’ Interaction Considering Changes Caused by Liquid Influences

This work is devoted to the interaction of nucleotides. The goal of this study is to learn or try to learn how the interaction between nucleotides with exposure to a liquid takes place. Will the interacting forces of the nucleotides be sufficient to approach the incision? A numerical imitation of the interaction is conducted using the discrete element method and a Gears predictor–corrector as part of the integrated scheme. In this work, the results reflect the dynamics of nucleotides: velocity, displacement, and force graphs are presented with and without the effect of the liquid. During changes caused by the influence of a liquid, the nucleotide interaction transforms and passes three stages: a full stop, one similar to viscous damping, and one similar to non-dissipative behaviors. The main contribution of this work is a better understanding of the behavior of infinitely small objects that would be difficult to observe in vivo. The changing influence of a liquid can transform into certain effects. As a result, a model is provided, which can be based on the results of well-known physical experiments (DNA unzipping) for modeling nucleotide interactions.

Unveiling thermal and hemodynamic effects of aneurysm on abdominal aorta using power law model and finite element analysis

The objective of this study is to find causes of aortic diseases and investigating the ways for better treatment. The governing system of equations has been demonstrated to account for characteristics of blood. The governing system of equation has been solved using the finite element method with appropriate boundary conditions. We analyzed into the relationship between flow characteristics via the aneurysmal abdominal aorta and the aneurysm height, aneurysm length, and non-Newtonian behavior. It investigates how thermal and hemodynamics effects change across the abdominal aortic aneurysm. The velocity, pressure, and temperature surface plots of the results are displayed. There have also been graphic displays of line graphs of axial velocity, radial velocity, axial pressure, radial pressure, axial temperature and radial temperature across the aneurysm. The blood flow simulations obtained results show that increasing blood temperature, pressure and intake velocity all contribute to an increase in viscosity. The results indicate that while the temperature varies little to not at all, the blood flow pressure decrease and velocity significantly vary.

Flow analysis of MHD ternary hybrid nanofluid over a permeable wedge with variable surface temperature and slip effect

A comparative flow analysis of a water based- ternary hybrid nanofluid has been studied in this article over a moving permeable wedge in the presence of variable wedge surface temperature. The model has been developed keeping in mind magnetic, velocity slip, buoyancy, and suction effects. The primary nanoparticle was Nimonic 80A, Fe 3 O 4 being the secondary nanoparticle and Graphene Oxide ( GO ) ternary nanoparticle. The velocity, temperature, heat transfer rate, and shear drag profiles for various parametric values of the magnetic parameter ( M ), velocity ratio parameter ( R ) , velocity slip parameter ( h ) , buoyancy parameter ( γ ) and suction parameter ( S ) was investigated. MATLAB bvp4c code was utilized for obtaining the numerical results by solving the nondimensional differential equations obtained using similarity transformations. All the results and graphs were formulated after a positive outcome of our results with that available in existing literature. An increase in the velocity slip parameter ( h ) and velocity ratio parameter ( R ) resulted in an increase in velocity profiles and local Nusselt number graphs while a reverse trend was observed for temperature and skin friction profiles. Also, the velocity graphs faced an increase by 0.09% with an increment in M = 0.4 to M = 0.8 . The present study finds its extensive applications in medical industries, water heaters, and forging of hot exhaust valve heads.

Comparative examine of fluid pressure within microchannel through integrated cantilevers for microfluidic applications

This paper aims to explore the concept of a microfluidic pressure sensing mechanism across a microchannel, integrated with different structures of microcantilevers. Various structures of microcantilevers are integrated into a microchannel where laminar fluid flows and the microcantilever senses the fluid velocity and pressure. The different structures of the microcantilever include rectangular, T-shaped, and Pi-shaped designs, which are placed at the centre of the microchannel. The 2D microchannel has a length of 4000 μm and a height of 840 μm, while the microcantilever is positioned at a distance of 2000 μm from the inlet of the microchannel. The analysis of the fluid sensor is observed by plotting graphs of velocity, pressure, displacement of the microcantilever, Reynolds number, and friction factor with respect to the time domain. An inlet velocity of 8.33 µm/s is applied at the microchannel, and the fluidic sensor shows a significant change in the fluid characteristics, comparing them across all types of microcantilevers. The simulation results show that the T-microcantilever has a maximum displacement of 4.97 µm compared to other microcantilevers, with a maximum pressure of 1.58 Pa for the Pi-cantilever. The integrated device is suitable for healthcare applications, measuring fluid pressure in syringes, where the T-microcantilever proves to be more compatible than the other two microcantilevers (R-cantilever and Pi-cantilever). The design and simulation of the microfluidic pressure sensing process are conducted using the FEM tool COMSOL Multiphysics.

MHD Stagnation Point Radiative Flow of Hybrid Casson Nanofluid across a Stretching Surface

This paper aims to investigate the hybrid stagnancy point in casson nanofluid on a transient elongation plane in accordance with impact of thermal heat. Resistive heating effect also considered in this study. Nano particles of assumed Cu and Al are utilized. Hence derived partial differential equations are broken down into nonlinear differential equations using suitable Transformations. Then succeeding results are worked out by employing Bvp4c Method. The obtained values for the analysis are indicated by indicating velocity and temperature graphs for distinct constants like radiation constant (Rd), Casson constant (β), magnetic variable (M), Prandtl constant (Pr), unsteady parameter (s). As well, the confined parameter, coefficient of skin friction is analysed. For continuing estimates of Casson parameter speed of liquid flow will be lessen. On intensifying Prandtl number of liquid shrink gradually. It is observed that for rapidly rised values of both Nano molecules velocity of the liquid lessens whereas reverse tendency is identified for temperature profile. Utilisation of hybrid nanoflows has a benifit of heat convertion improvement. The outcomes of current investigation are liquid is better within the congruence with comparision of subsist work.

Analyzing Physics Experiment using Sensor Smartphone in Traveling Carnival

Smartphone integration for high school students has significant potential in physics learning. This research aims to analyze smartphone sensor data in the context of physics experiments carried out at traveling carnivals. This research uses experimental methods to compare smartphone sensor data collected via the Phyphox application with video analysis data obtained using Tracker software. The research results show the effectiveness of smartphone sensors in several carnival games, including simple leg swings, bicycle spins, kora-kora vehicles, and merry-go-rounds. Smartphone sensors can show graphs of simple harmonic motion, angular velocity, and centripetal acceleration on the game vehicle. However, limitations arise in the case of Ferris wheels and mini Ferris wheels, where smartphone sensors show reduced effectiveness caused by the instability of passenger seats during the ride. This research suggests avenues for further exploration by computing physical quantity values derived from smartphone sensor data, offering insights into potential improvements and applications in dynamic environments such as theme parks.

Use of interactive mathematical simulations in Fundamentals of Biochemistry, a LibreText online educational resource, to promote understanding of dynamic reactions.

Biology is perhaps the most complex of the sciences, given the incredible variety of chemical species that are interconnected in spatial and temporal pathways that are daunting to understand. Their interconnections lead to emergent properties such as memory, consciousness, and recognition of self and non-self. To understand how these interconnected reactions lead to cellular life characterized by activation, inhibition, regulation, homeostasis, and adaptation, computational analyses and simulations are essential, a fact recognized by the biological communities. At the same time, students struggle to understand and apply binding and kinetic analyses for the simplest reactions such as the irreversible first-order conversion of a single reactant to a product. This likely results from cognitive difficulties in combining structural, chemical, mathematical, and textual descriptions of binding and catalytic reactions. To help students better understand dynamic reactions and their analyses, we have introduced two kinds of interactive graphs and simulations into the online educational resource, Fundamentals of Biochemistry, a LibreText biochemistry book. One is available for simple binding and kinetic reactions. The other displays progress curves (concentrations vs. time) for simple reactions and complex metabolic and signal transduction pathways. Users can move sliders to change dissociation and kinetic constants as well as initial concentrations and see instantaneous changes in the graphs. They can also export data into a spreadsheet for further processing, such as producing derivative Lineweaver-Burk and traditional Michaelis-Menten graphs of initial velocity (v0) versus substrate concentration.

CFD Analysis for Valve-Holding Camber Permanent Inhaler Spacer (AerospaAcer) with Different Valves

During the COVID-19 pandemic, data statistics showed that patients with respiratory problems become infected. One of the therapy techniques for the respiratory condition was the use of a metered-dose inhaler and spacer. The objective of this paper is to determine the flow parameters of three types of valves which is duckbill valve, cross slit valve and umbrella valve in inhaler spacer to compare fluid flow between valve Previous researchers chose the duckbill valve to control fluid flow in inhaler spacer. The flow characteristics are unaffected by the materials used in the new disposable inhaler spacers, such as paper and polylactic acid (PLA). Several design valves reduced the skewness below 0.94 by suppressing the fillet and chamfer. ANSYS Workbench Fluent 19.2 is used to calculate flow parameters such as turbulence kinetic energy (TKE), turbulence eddy dissipation (TED), velocity, particle velocity magnitude, streamline, and vector velocity. The setup input data is based on the previous researcher's specified parameters such as viscosity model, drug characteristics (salbutamol and propellant), discrete phase model (DPM) equal to 80, boundary condition model, and SIMPLE technique. For the three types of valves, the nozzle injection used a 0.50-millimetre dimension. The simulation work is cross-checked against the results of prior simulations. Within each iteration, the transient flow employed a time step size of 0.01 for 200 steps. The results show that computational analysis can distinguish between models of varying complexity. The TED, TKE, and velocity graphs showed the approximate value between the model geometries. Overall, the study was successful in achieving the desired velocity magnitude in terms of visual and graph representations of the various valve.

Comparing the Velocity Spectrum Caused by the Presence of Circular Urban Subway Tunnels With Free‐Field Conditions

For structures in the near field, the velocity spectrum is significant. The aim of this study is to examine, taking into account the soil–structure interaction (SSI), how metropolitan subway tunnels with a circular cross section in alluvial soils affect the ground surface velocity spectrum. The frequency of the soil–tunnel systems was altered by varying the parameters of the soil and the geometrical features of the tunnel, such as the radius, the lining’s thickness, and the depth of burial. The maximum velocity was determined at several sites on the ground surface as well as the tunnel crown. Based on the soil–tunnel system’s period, the spectrum velocity graph was produced by averaging and squaring the standard deviation of the highest velocity for every frequency. Ansys finite element software and Plaxis2D were used in this study. The findings demonstrate that the tunnel’s presence reduces spectral velocity (SV) relative to free‐field (FF) circumstances during the examined period at the position that corresponds to the ground‐based image of the tunnel crown. The tunnel’s existence lowers the ground‐level velocity range by 14.5 percent. By moving away from the image of the tunnel crown on the ground surface, the presence of the tunnel amplifies the SV at more points by 5.5% at long periods. In addition, the tunnel crown velocity spectrum was developed. The findings indicate that the velocity spectrum diagram’s envelope for the tunnel crown is a nonlinear function of the soil–tunnel system’s period.

LAND CONSERVATION FOR REHABILITATION OF CRITICAL WATERSHEDS: CASE IN WAY CENGKAAN, WAY BESAI SUB-WATERSHEDS, LAMPUNG, INDONESIA

Land and water conservation are the keys to success in controlling the rate of sedimentation. The sediment runoff rate represents the catchment area that increases erosion. This study was conducted to analyze the sedimentation rate in the upstream part of the Way Cengkaan, Way Campang tributary rivers located in Pekon Karang Agung, Way Tenong District, West Lampung Regency. It was carried out from January to December 2020. The research equipment included: a current meter, a stopwatch, a rollmeter, a rainfall recorder, an automatic water level recorder (AWLR), a peiscal, sediment bottles, scales, ovens, and cups. While the materials used are sediment samples, discharge measurement results, and water level. The calculation of flow was carried out at two observation points, upstream and downstream of the Cengkaan River before entering the Way Campang River. Calculation of flow rate using the velocity-area methods using the current meter and the float method. During the observation period from January to July 2020, the sediment velocity increased in line with the trend of the sediment velocity map. The sediment velocity curve for upstream stations is steeper than for downstream stations. The sediment volume decreased relatively in December 2020, and the slope of the sediment velocity graph at the downstream observation point is larger than that at the upstream observation point. This finding reflected that in the one-year observation period from January to December 2020, the evaluation resulted from a decreasing trend of sedimentation in the Way Cengkaan River. Based on these conditions, the implementation of a land conservation program carried out in collaboration between farmer groups and beneficiary stakeholders has a positive impact and effectively contributes to improving the quality of the watershed by reducing the sedimentation rate.

Influence of complete slip conditions on peristaltic transport of third-grade fluid with suction and injection

This study is important for the fields of pharmaceutical nano-drug suspension, biomedical engineering, pressure surges and food processing systems. The slip condition is necessary for polishing internal cavities and artificial heart valves in a variety of manufactured objects, micro- or nano-channels, and applications. Low Reynolds number (Re[Formula: see text] and long wavelength ([Formula: see text]) considerations are used in the formulation of the mathematical model at low non-Newtonian parameter values, nonlinear boundary conditions and the governing nonlinear equation are analytically solved using the perturbation method. The graphs of frictional force, pressure rise, velocity, pressure gradient, and streamline graphs are done using Wolfram MATHEMATICA software. In this paper, we compared the results of the total slip condition with those of the first-order slip condition and the absence of any slip effects. It has been noticed that increasing the suction and injection parameters leads to a decrease the pressure rate with complete slip effects, partial slip effects and no slip effects. We show that an increase in the third grade fluid parameter [Formula: see text] increases the magnitude of axial velocity. From a physical perspective, it shows the shear thinning characteristic, which causes a decrease in viscosity and an increase in fluid velocity. Frictional force behaves differently when compared to pressure rate. In other words, the pressure gradient acts as an obstacle to the peristalsis-driven flow. The objective of the study is to find the impact of the peristaltic flow phenomena and the impact of peristaltic on third-grade non-Newtonian fluid where the suction and injection are prevailing which is similar to the thing in biomechanical devices, like blood vessels, etc. there is a change of oxygen and carbon dioxide from the tissue layer to the fluid within the blood vessel.

Optimization of Non-Newtonian Flow through a Coat-Hanger Die Using the Adjoint Method

The use of coat-hanger dies is prevalent in the plastic film and sheet extrusion industry. The product quality and the power of the extrusion machine depend on the uniformities of the fluid velocity at the exit and the pressure drop. Die manufacturers face the challenge of producing coat-hanger dies that can extrude materials uniformly and with a minimal pressure drop. Previous studies have analyzed the die outlet’s flow homogeneity and pressure drop using various numerical simulations. However, the combination of the scheme programming language together with the Adjoint Method of Optimization has yet to be attempted. The adjoint optimization method has been demonstrated to be beneficial in addressing issues related to shape optimization problems and it may also be beneficial in optimizing the design of dies used in polymer melt extrusion. In this study, the proposed innovations involve incorporating both the Scheme programming language and Adjoint solver to examine and optimize the coat hanger’s flow homogeneity and pressure drop. Before optimization, the outlet velocity was almost 10 times higher at the die center than at the edges but after optimization, it became more uniform. The proposed optimized coat-hanger die geometry results in more uniform melt flow as demonstrated by the velocity contour plot and the outlet velocity graph in the die slit area, reducing the deviation value from 0.097 to 0.015. Additionally, the mass flux variance across the die outlet decreased by 71.6% from 0.015069 kg m−2 s−1 to 0.004281 kg m−2 s−1. Therefore, using this method reduces the amount of time wasted on trial and error or other optimization techniques that may be limited by design constraints.

Analysis of Forchheimer Effect for Double Diffusive Convection With Dusty Fluids and MHD

An attempt has been made to analyze the effect of second order resistance for a steady, dusty fluid considering magnetohydrodynamic (MHD) and also the characteristics of fluid like permeability, porosity, solutal diffusivity and thermal conductivity being varied. Here the basic equations are coupled, non-linear Partial Differential Equations (PDEs), which are changed by similarity transformations to higher order Ordinary Differential Equations (ODE). After being transformed the higher order ODE that where obtained are resolved numerically. Shooting technique is employed here and the values are tabulated for various pertinent parameter variations. The effects of the inertia, concentration and interaction, mixed convection, magnetic and many other parameters are discussed and plotted graphs for velocity, concentration and temperature. The magnetic force enhances velocity. It was found that the present study correlates with the existence results.

Effect of roof design on wind load of buildings through numerical simulation

When the wind blows against a building, the resulting force acting on the building at a particular elevation is called the wind load. Measuring and minimizing the wind load is crucial to ensure the safety of buildings. Therefore, the objective of this study is to investigate the effect of a buildings roof design on the wind load by evaluating and comparing the wind pressure differences p that different building models experience by leveraging Computational Fluid Dynamics (CFD) simulations. The 3D CAD (Computer-Aided Design) software SolidWorks was used to construct building models of identical dimensions with the exception of roofs harboring different shapes and angles. By exerting a wind velocity through flow simulation, flow trajectories and cut plot graphs of wind velocity and pressure surrounding the building models are generated. Wind pressure differences p for each situation were calculated and compared based on the CFD results. Wind tunnel experimentation with building models will also executed to test the computed data and prove its reliability and applicability. The data shows that, among all tested roof designs, the barrel-vaulted roof exhibits the minimum pressure difference (of 171.15 Pa) between the windward and the leeward surface and experiences the least wind load and resists strong wind most effectively. It reduces up to roughly 15% of wind load compared to the worst case tested. For symmetric triangular gable roof designs, the greater base angle leads to greater wind load. Overall, this study provides the theoretical basis and scientific evidence for the building designs of the next generation.

Experimental investigation of detonation decay in rough narrow channels

The conditions for detonation propagation in narrow channels are of great interest for ensuring explosion safety in industrial facilities using hydrogen. The roughness of the channel walls can lead to either flame acceleration or to the detonation decay. In this work the propagation of detonation of hydrogen–air mixtures in smooth and rough narrow channels was experimentally studied. The experimental setup consisted of a 3000 mm long driver section and a 1200 mm long diagnostic section with a 7×7mm cross-section. One or two walls of the diagnostic channel were covered with sandpaper which had a grain size of 500–600μm and 80–100μm. Lean, stoichiometric and rich mixtures were used for hydrogen with air. Based on the flame velocity graphs and shock wave pressure in the diagnostic section, several flame propagation regimes were recorded, depending on the fuel concentration and channel roughness. Non-linear effect of the roughness on the detonation propagation was observed. When two pieces of sandpaper were placed on the opposite sides of the narrow channel, a drop in flame velocity to the sound speed of the combustion products was registered for hydrogen mixtures with air. However, covering one wall with small grain sandpaper could lead to expanding of the detonation limits compared to the smooth channel.

Determination of long-term deformation behaviours with InSAR data at a dump site of an open-pit coal mine in Turkey

Dump sites with broken overburden layers in surface mines have the risk of instability due to their loose bulk structures. In this study, deformations at a dump site of the Kangal/Kalburçayırı open-pit coal mine and their long-term behaviours were revealed with InSAR data for a total period of 4.5 years. Firstly, 9-periods involving different time ranges were created considering the presence of LiCSAR products. Then, the deformation velocities of each period were calculated by LiCSBAS software using LiCSAR products. The area where high deformations were concentrated from the LiCSBAS result products was determined and divided into 4 zones for more detailed evaluations. At the final stage, the period-deformation velocity graphs were drawn separately for each zone with the data obtained using two different approaches from the deformation velocities of all periods, and long-term deformation behaviours were determined. More reliable future behaviour projections could be made considering the current increasing or decreasing trend of deformation behaviours. It was revealed that vertical deformations at the dump site had an increasing trend in the first periods and a decreasing trend in the later periods. Maximum vertical deformation velocities ranging between −111.4 mm/year and −178.0 mm/year in the first 4 months reached the highest values (ranging from −141.9 mm/year to −261.8 mm/year) at the end of two years and decreased to values ranging from −33.0 mm/year to −44.3 mm/year in the later periods. It was found that horizontal deformation velocities ranged between +0.5 mm/year and +55.4 mm/year in the east–west direction and between −7.0 mm/year and −56.8 mm/year in the west-east direction, were approximately 5 times lower than vertical velocities and did not have a constantly increasing or decreasing trend in any direction. It was observed that deformations exhibited a behaviour resulting from the structural property of the dump bulk material. The results of the evaluations showed that the risk of instability gradually decreased at the dump site. The methodology of this study can enable the determination of similar areas that may pose a threat in a short time, the prioritization of risky areas, the planning of more detailed studies, and taking the necessary measures in a timely manner.

Could Physics Teachers Also Have Misconceptions on Basic Kinematics?

The role of a physics teacher in learning is to facilitate student activities to construct correct conceptual understanding as that of a scientist. As the primary source of knowledge for students, a physics teacher is required to have the right concept, but this demand is not necessarily fully fulfilled. This study aims to determine the profile of physics teachers’ understanding of concepts on kinematics material detected by a four-tier misconception test. Participants in this study were 20 high school physics teachers in Surabaya. Based on the results of data analysis, it was found that the dominant misconceptions included: (1) Two objects that make the same displacement at the same time interval will have the same velocity, regardless of the type of movement of the two objects (2) Objects that move vertically straight up or down will always have the acceleration of motion equal to the acceleration of gravity which is directed downwards. (3) As long as the object’s position is at positive coordinates, it means the object is moving in the forward direction. (4) The graph of velocity against time, which has a positive gradient, means that the object always moves forward (5) In parabolic motion, the length of time an object is in the air only depends on the length of its path, the longest path will require the longest time. (6) In parabolic motion, the final speed of an object when it lands on the ground depends not only on its initial speed but also on its elevation angle. The findings of several misconceptions above show that even a physics teacher cannot escape misconceptions. Therefore, it is crucial for a teacher to be able to remedy the misconceptions he suffers so that these misconceptions are not transmitted to the students he teaches. This finding is the first step for researchers to detect misconceptions, followed by the application of certain learning methods to remedy misconceptions in future research.