Cognitive load and mental rotation : structuring orthographic projection for learning and problem solving

Cognitive load theory was used to generate a series of three experiments to investigate the effects of various worked example formats on learning orthographic projection. Experiments 1 and 2 investigated the benefits of presenting problems, conventional worked examples incorporating the final 2-D and 3-D representations only, and modified worked examples with several intermediate stages of rotation between the 2-D and 3-D representations. Modified worked examples proved superior to conventional worked examples without intermediate stages while conventional worked examples were, in turn, superior to problems. Experiment 3 investigated the consequences of varying the number and location of intermediate stages in the rotation trajectory and found three stages to be superior to one. A single intermediate stage was superior when nearer the 2-D than the 3-D end of the trajectory. It was concluded that (a) orthographic projection is learned best using worked examples with several intermediate stages and that (b) a linear relation between angle of rotation and problem difficulty did not hold for orthographic projection material. Cognitive load theory could be used to suggest the ideal location of the intermediate stages.

What is the apparent angle of a Kelvin ship wave pattern?

While the half-angle which encloses a Kelvin ship wave pattern is commonly accepted to be 19.47 degrees, recent observations and calculations for sufficiently fast-moving ships suggest that the apparent wake angle decreases with ship speed. One explanation for this decrease in angle relies on the assumption that a ship cannot generate wavelengths much greater than its hull length. An alternative interpretation is that the wave pattern that is observed in practice is defined by the location of the highest peaks; for wakes created by sufficiently fast-moving objects, these highest peaks no longer lie on the outermost divergent waves, resulting in a smaller apparent angle. In this paper, we focus on the problems of free surface flow past a single submerged point source and past a submerged source doublet. In the linear version of these problems, we measure the apparent wake angle formed by the highest peaks, and observe the following three regimes: a small Froude number pattern, in which the divergent waves are not visible; standard wave patterns for which the maximum peaks occur on the outermost divergent waves; and a third regime in which the highest peaks form a V-shape with an angle much less than the Kelvin angle. For nonlinear flows, we demonstrate that nonlinearity has the effect of increasing the apparent wake angle so that some highly nonlinear solutions have apparent wake angles that are greater than Kelvin's angle. For large Froude numbers, the effect on apparent wake angle can be more dramatic, with the possibility of strong nonlinearity shifting the wave pattern from the third regime to the second. We expect our nonlinear results will translate to other more complicated flow configurations, such as flow due to a steadily moving closed body such as a submarine.

Is there evidence to support the use of the angle of peak torque as a marker of hamstring injury and re-injury risk?

Hamstring strain injuries are the predominant injury in many sports, costing athletes and clubs a significant financial and performance burden. Therefore the ability to identify and intervene with individuals who are considered at a high risk of injury is important. One measure which has grown in popularity as an outcome variable following hamstring intervention/prevention studies and rehabilitation is the angle of peak knee flexor torque. This current opinion article will firstly introduce the measure and the processes behind it. Secondly, this article will summarise how the angle of peak knee flexor torque has been suggested to measure hamstring strain injury risk. Finally various limitations will be presented and outlined as to how they may influence the measure. These include the lack of muscle specificity, the common concentric contraction mode of assessment, reliability of the measure, various neural contributions (such as rate of force development and neuromuscular inhibition) as well as the lack of prospective data showing any predictive value in the measure.

Self-calibration of wireless cameras with restricted degrees of freedom

This paper presents an approach for the automatic calibration of low-cost cameras which are assumed to be restricted in their freedom of movement to either pan or tilt movements. Camera parameters, including focal length, principal point, lens distortion parameter and the angle and axis of rotation, can be recovered from a minimum set of two images of the camera, provided that the axis of rotation between the two images goes through the camera’s optical center and is parallel to either the vertical (panning) or horizontal (tilting) axis of the image. Previous methods for auto-calibration of cameras based on pure rotations fail to work in these two degenerate cases. In addition, our approach includes a modified RANdom SAmple Consensus (RANSAC) algorithm, as well as improved integration of the radial distortion coefficient in the computation of inter-image homographies. We show that these modifications are able to increase the overall efficiency, reliability and accuracy of the homography computation and calibration procedure using both synthetic and real image sequences

An examination of learning design in elite springboard diving

The overarching aim of this programme of work was to evaluate the effectiveness of the existing learning environment within the Australian Institute of Sport (AIS) elite springboard diving programme. Unique to the current research programme, is the application of ideas from an established theory of motor learning, specifically ecological dynamics, to an applied high performance training environment. In this research programme springboard diving is examined as a complex system, where individual, task, and environmental constraints are continually interacting to shape performance. As a consequence, this thesis presents some necessary and unique insights into representative learning design and movement adaptations in a sample of elite athletes. The questions examined in this programme of work relate to how best to structure practice, which is central to developing an effective learning environment in a high performance setting. Specifically, the series of studies reported in the chapters of this doctoral thesis: (i) provide evidence for the importance of designing representative practice tasks in training; (ii) establish that completed and baulked (prematurely terminated) take-offs are not different enough to justify the abortion of a planned dive; and (iii), confirm that elite athletes performing complex skills are able to adapt their movement patterns to achieve consistent performance outcomes from variable dive take-off conditions. Chapters One and Two of the thesis provide an overview of the theoretical ideas framing the programme of work, and include a review of literature pertinent to the research aims and subsequent empirical chapters. Chapter Three examined the representativeness of take-off tasks completed in the two AIS diving training facilities routinely used in springboard diving. Results highlighted differences in the preparatory phase of reverse dive take-offs completed by elite divers during normal training tasks in the dry-land and aquatic training environments. The most noticeable differences in dive take-off between environments began during the hurdle (step, jump, height and flight) where the diver generates the necessary momentum to complete the dive. Consequently, greater step lengths, jump heights and flight times, resulted in greater board depression prior to take-off in the aquatic environment where the dives required greater amounts of rotation. The differences observed between the preparatory phases of reverse dive take-offs completed in the dry-land and aquatic training environments are arguably a consequence of the constraints of the training environment. Specifically, differences in the environmental information available to the athletes, and the need to alter the landing (feet first vs. wrist first landing) from the take-off, resulted in a decoupling of important perception and action information and a decomposition of the dive take-off task. In attempting to only practise high quality dives, many athletes have followed a traditional motor learning approach (Schmidt, 1975) and tried to eliminate take-off variations during training. Chapter Four examined whether observable differences existed between the movement kinematics of elite divers in the preparation phases of baulked (prematurely terminated) and completed take-offs that might justify this approach to training. Qualitative and quantitative analyses of variability within conditions revealed greater consistency and less variability when dives were completed, and greater variability amongst baulked take-offs for all participants. Based on these findings, it is probable that athletes choose to abort a planned take-off when they detect small variations from the movement patterns (e.g., step lengths, jump height, springboard depression) of highly practiced comfortable dives. However, with no major differences in coordination patterns (topology of the angle-angle plots), and the potential for negative performance outcomes in competition, there appears to be no training advantage in baulking on unsatisfactory take-offs during training, except when a threat of injury is perceived by the athlete. Instead, it was considered that enhancing the athletes' movement adaptability would be a more functional motor learning strategy. In Chapter Five, a twelve-week training programme was conducted to determine whether a sample of elite divers were able to adapt their movement patterns and complete dives successfully, regardless of the perceived quality of their preparatory movements on the springboard. The data indeed suggested that elite divers were able to adapt their movements during the preparatory phase of the take-off and complete good quality dives under more varied take-off conditions; displaying greater consistency and stability in the key performance outcome (dive entry). These findings are in line with previous research findings from other sports (e.g., shooting, triple jump and basketball) and demonstrate how functional or compensatory movement variability can afford greater flexibility in task execution. By previously only practising dives with good quality take-offs, it can be argued that divers only developed strong couplings between information and movement under very specific performance circumstances. As a result, this sample was sometimes characterised by poor performance in competition when the athletes experienced a suboptimal take-off. Throughout this training programme, where divers were encouraged to minimise baulking and attempt to complete every dive, they demonstrated that it was possible to strengthen the information and movement coupling in a variety of performance circumstances, widening of the basin of performance solutions and providing alternative couplings to solve a performance problem even when the take-off was not ideal. The results of this programme of research provide theoretical and experimental implications for understanding representative learning design and movement pattern variability in applied sports science research. Theoretically, this PhD programme contributes empirical evidence to demonstrate the importance of representative design in the training environments of high performance sports programmes. Specifically, this thesis advocates for the design of learning environments that effectively capture and enhance functional and flexible movement responses representative of performance contexts. Further, data from this thesis showed that elite athletes performing complex tasks were able to adapt their movements in the preparatory phase and complete good quality dives under more varied take-off conditions. This finding signals some significant practical implications for athletes, coaches and sports scientists. As such, it is recommended that care should be taken by coaches when designing practice tasks since the clear implication is that athletes need to practice adapting movement patterns during ongoing regulation of multi-articular coordination tasks. For example, volleyball servers can adapt to small variations in the ball toss phase, long jumpers can visually regulate gait as they prepare for the take-off, and springboard divers need to continue to practice adapting their take-off from the hurdle step. In summary, the studies of this programme of work have confirmed that the task constraints of training environments in elite sport performance programmes need to provide a faithful simulation of a competitive performance environment in order that performance outcomes may be stabilised with practice. Further, it is apparent that training environments can be enhanced by ensuring the representative design of task constraints, which have high action fidelity with the performance context. Ultimately, this study recommends that the traditional coaching adage 'perfect practice makes perfect", be reconsidered; instead advocating that practice should be, as Bernstein (1967) suggested, "repetition without repetition".

Energy-based nonlinear control of ship roll gyro-stabiliser with precession angle constraints

In this paper, we consider a passivity-based approach for the design of a control law of multiple ship-roll gyro-stabiliser units. We extend previous work on control of ship roll gyro-stabilisation by considering the problem within a nonlinear framework. In particular, we derive an energy-based model using the port-Hamiltonian theory and then design an active precession controller using passivity-based control interconnection and damping assignment. The design considers the possibility of having multiple gyro-stabiliser units, and the desired potential energy of the system (in closed loop) is chosen to behave like a barrier function, which allows us to enforce constraints on the precession angle of the gyros.

Short-term changes in axial length during simulations of typical far, intermediate and near tasks

Purpose: To investigate the changes in axial length with the combined effect of accommodation and angle of gaze (convergence and downward gaze) over 5 minutes in groups of myopes and emmetropes. Methods: A total of 31 subjects (nine emmetropes, 10 low myopes, and 12 moderate to high myopes) aged from 18 to 31 years were recruited. To measure ocular biometrics in inferonasal gaze with accommodation, an optical biometer (Lenstar LS900) was inclined on a tilt and height adjustable stage, with the subject’s chinrest mounted on a rotary stage to induce various levels of convergence by rotation of the subject’s head in primary or downward gaze. Initially, the subjects performed a distance viewing task in primary gaze for 10 minutes to provide a ‘wash-out’ period for prior visual tasks, and then the subject’s axial length and ocular biometrics were measured in nine different combinations of gaze/accommodation over 5 minutes. These nine sessions for all gaze measurements (i.e. three levels of accommodation 9 three levels of convergence) were completed across 3 days of testing (one accommodation condition on each day).The nine combinations of gaze/accommodation were based on those required to view the centre, right and left edges of a distant TV at 6 m in primary gaze, an intermediate task (i.e. computer at 50 cm in 10° downward gaze) and a near task (i.e. reading A4 page at 20 cm in 20° downward gaze). Subjects were wearing a custom built three-axes head tracker throughout the experiment that monitored subjects’ relative head movements (roll, pitch and yaw) during measurements. Results: A significant increase in axial length occurred with the combined effect of accommodation, convergence and downward gaze (repeated measures ANOVA, p < 0.001), with the greatest axial elongation during the near task in downward gaze with convergence (i.e. downward 20°/inward 33°, with 5 D accommodation) (mean change 33 ± 13 lm, after 5 minutes task) followed by the intermediate task (i.e. downward 10°/inward 25°, with 2 D accommodation) (mean change 14 ± 11 lm, after 5 minutes task).Changes in axial length for the distance task (i.e. primary gaze/9° convergence, with 0.16 D accommodation) were not statistically significant (mean change 4 ± 8 lm, after 5 minutes task, p > 0.05). Moderate to high myopes had a greater change in the axial length (mean change 40 ± 11 lm after 5 minutes of near task) than that of emmetropes (mean change 29 ± 15 lm after 5 minutes of near task) and low myopes (mean change 29 ± 16 lm after 5 minutes of near task) associated with time (p = 0.02) and accommodation by time (p = 0.03). Conclusions: The combination of accommodation, convergence and downward angle has a significant short term effect on axial length over time. The near task in downward gaze with convergence caused a greater change in axial length than the intermediate and distant visual tasks. The greater axial elongation measured in the infero-nasal direction with accommodation is most likely associated with a combination of biomechanical factors such as, extraocular muscle forces and ciliary muscle contraction.

Effect of position on precision within the recording field of a markerless motion capture system

Introduction Markerless motion capture systems are relatively new devices that can significantly speed up capturing full body motion. A precision of the assessment of the finger’s position with this type of equipment was evaluated at 17.30 ± 9.56 mm when compare to an active marker system [1]. The Microsoft Kinect was proposed to standardized and enhanced clinical evaluation of patients with hemiplegic cerebral palsy [2]. Markerless motion capture systems have the potential to be used in a clinical setting for movement analysis, as well as for large cohort research. However, the precision of such system needs to be characterized. Global objectives • To assess the precision within the recording field of the markerless motion capture system Openstage 2 (Organic Motion, NY). • To compare the markerless motion capture system with an optoelectric motion capture system with active markers. Specific objectives • To assess the noise of a static body at 13 different location within the recording field of the markerless motion capture system. • To assess the smallest oscillation detected by the markerless motion capture system. • To assess the difference between both systems regarding the body joint angle measurement. Methods Equipment • OpenStage® 2 (Organic Motion, NY) o Markerless motion capture system o 16 video cameras (acquisition rate : 60Hz) o Recording zone : 4m * 5m * 2.4m (depth * width * height) o Provide position and angle of 23 different body segments • VisualeyezTM VZ4000 (PhoeniX Technologies Incorporated, BC) o Optoelectric motion capture system with active markers o 4 trackers system (total of 12 cameras) o Accuracy : 0.5~0.7mm Protocol & Analysis • Static noise: o Motion recording of an humanoid mannequin was done in 13 different locations o RMSE was calculated for each segment in each location • Smallest oscillation detected: o Small oscillations were induced to the humanoid mannequin and motion was recorded until it stopped. o Correlation between the displacement of the head recorded by both systems was measured. A corresponding magnitude was also measured. • Body joints angle: o Body motion was recorded simultaneously with both systems (left side only). o 6 participants (3 females; 32.7 ± 9.4 years old) • Tasks: Walk, Squat, Shoulder flexion & abduction, Elbow flexion, Wrist extension, Pronation / supination (not in results), Head flexion & rotation (not in results), Leg rotation (not in results), Trunk rotation (not in results) o Several body joint angles were measured with both systems. o RMSE was calculated between signals of both systems. Results Conclusion Results show that the Organic Motion markerless system has the potential to be used for assessment of clinical motor symptoms or motor performances However, the following points should be considered: • Precision of the Openstage system varied within the recording field. • Precision is not constant between limb segments. • The error seems to be higher close to the range of motion extremities.

Some surface profiles of a strip after plane-strain indentation by rigid bodies with serrated surfaces

This paper is concerned with the surface profiles of a strip after rigid bodies with serrated (saw-teeth) surfaces indent the strip and are subsequently removed. Plane-strain conditions are assumed. This has application in roughness transfer of final metal forming process. The effects of the semi-angle of the teeth, the depth of indentation and the friction on the contact surface on the profile are considered.

Sensitivity of proximal femoral stiffness and areal bone mineral density to changes in bone geometry and density

Areal bone mineral density (aBMD) is the most common surrogate measurement for assessing the bone strength of the proximal femur associated with osteoporosis. Additional factors, however, contribute to the overall strength of the proximal femur, primarily the anatomical geometry. Finite element analysis (FEA) is an effective and widely used computerbased simulation technique for modeling mechanical loading of various engineering structures, providing predictions of displacement and induced stress distribution due to the applied load. FEA is therefore inherently dependent upon both density and anatomical geometry. FEA may be performed on both three-dimensional and two-dimensional models of the proximal femur derived from radiographic images, from which the mechanical stiffness may be redicted. It is examined whether the outcome measures of two-dimensional FEA, two-dimensional, finite element analysis of X-ray images (FEXI), and three-dimensional FEA computed stiffness of the proximal femur were more sensitive than aBMD to changes in trabecular bone density and femur geometry. It is assumed that if an outcome measure follows known trends with changes in density and geometric parameters, then an increased sensitivity will be indicative of an improved prediction of bone strength. All three outcome measures increased non-linearly with trabecular bone density, increased linearly with cortical shell thickness and neck width, decreased linearly with neck length, and were relatively insensitive to neck-shaft angle. For femoral head radius, aBMD was relatively insensitive, with two-dimensional FEXI and threedimensional FEA demonstrating a non-linear increase and decrease in sensitivity, respectively. For neck anteversion, aBMD decreased non-linearly, whereas both two-dimensional FEXI and three dimensional FEA demonstrated a parabolic-type relationship, with maximum stiffness achieved at an angle of approximately 15o. Multi-parameter analysis showed that all three outcome measures demonstrated their highest sensitivity to a change in cortical thickness. When changes in all input parameters were considered simultaneously, three and twodimensional FEA had statistically equal sensitivities (0.41±0.20 and 0.42±0.16 respectively, p = ns) that were significantly higher than the sensitivity of aBMD (0.24±0.07; p = 0.014 and 0.002 for three-dimensional and two-dimensional FEA respectively). This simulation study suggests that since mechanical integrity and FEA are inherently dependent upon anatomical geometry, FEXI stiffness, being derived from conventional two-dimensional radiographic images, may provide an improvement in the prediction of bone strength of the proximal femur than currently provided by aBMD.

Theoretical and numerical investigation of plasmon nanofocusing in metallic tapered rods and grooves

Effective focusing of electromagnetic (EM) energy to nanoscale regions is one of the major challenges in nano-photonics and plasmonics. The strong localization of the optical energy into regions much smaller than allowed by the diffraction limit, also called nanofocusing, offers promising applications in nano-sensor technology, nanofabrication, near-field optics or spectroscopy. One of the most promising solutions to the problem of efficient nanofocusing is related to surface plasmon propagation in metallic structures. Metallic tapered rods, commonly used as probes in near field microscopy and spectroscopy, are of a particular interest. They can provide very strong EM field enhancement at the tip due to surface plasmons (SP’s) propagating towards the tip of the tapered metal rod. A large number of studies have been devoted to the manufacturing process of tapered rods or tapered fibers coated by a metal film. On the other hand, structures such as metallic V-grooves or metal wedges can also provide strong electric field enhancements but manufacturing of these structures is still a challenge. It has been shown, however, that the attainable electric field enhancement at the apex in the V-groove is higher than at the tip of a metal tapered rod when the dissipation level in the metal is strong. Metallic V-grooves also have very promising characteristics as plasmonic waveguides. This thesis will present a thorough theoretical and numerical investigation of nanofocusing during plasmon propagation along a metal tapered rod and into a metallic V-groove. Optimal structural parameters including optimal taper angle, taper length and shape of the taper are determined in order to achieve maximum field enhancement factors at the tip of the nanofocusing structure. An analytical investigation of plasmon nanofocusing by metal tapered rods is carried out by means of the geometric optics approximation (GOA), which is also called adiabatic nanofocusing. However, GOA is applicable only for analysing tapered structures with small taper angles and without considering a terminating tip structure in order to neglect reflections. Rigorous numerical methods are employed for analysing non-adiabatic nanofocusing, by tapered rod and V-grooves with larger taper angles and with a rounded tip. These structures cannot be studied by analytical methods due to the presence of reflected waves from the taper section, the tip and also from (artificial) computational boundaries. A new method is introduced to combine the advantages of GOA and rigorous numerical methods in order to reduce significantly the use of computational resources and yet achieve accurate results for the analysis of large tapered structures, within reasonable calculation time. Detailed comparison between GOA and rigorous numerical methods will be carried out in order to find the critical taper angle of the tapered structures at which GOA is still applicable. It will be demonstrated that optimal taper angles, at which maximum field enhancements occur, coincide with the critical angles, at which GOA is still applicable. It will be shown that the applicability of GOA can be substantially expanded to include structures which could be analysed previously by numerical methods only. The influence of the rounded tip, the taper angle and the role of dissipation onto the plasmon field distribution along the tapered rod and near the tip will be analysed analytically and numerically in detail. It will be demonstrated that electric field enhancement factors of up to ~ 2500 within nanoscale regions are predicted. These are sufficient, for instance, to detect single molecules using surface enhanced Raman spectroscopy (SERS) with the tip of a tapered rod, an approach also known as tip enhanced Raman spectroscopy or TERS. The results obtained in this project will be important for applications for which strong local field enhancement factors are crucial for the performance of devices such as near field microscopes or spectroscopy. The optimal design of nanofocusing structures, at which the delivery of electromagnetic energy to the nanometer region is most efficient, will lead to new applications in near field sensors, near field measuring technology, or generation of nanometer sized energy sources. This includes: applications in tip enhanced Raman spectroscopy (TERS); manipulation of nanoparticles and molecules; efficient coupling of optical energy into and out of plasmonic circuits; second harmonic generation in non-linear optics; or delivery of energy to quantum dots, for instance, for quantum computations.

Power sharing and stability enhancement of an autonomous microgrid with inertial and non-inertial DGs with DSTATCOM

This paper proposes a method of enhancing system stability with a distribution static compensator (DSTATCOM) in an autonomous microgrid with multiple distributed generators (DG). It is assumed that there are both inertial and non-inertial DGs connected to the microgrid. The inertial DG can be a synchronous machine of smaller rating while inertia less DGs (solar) are assumed as DC sources. The inertia less DGs are connected through Voltage Source Converter (VSC) to the microgrid. The VSCs are controlled by either state feedback or current feedback mode to achieve desired voltage-current or power outputs respectively. The power sharing among the DGs is achieved by drooping voltage angle. Once the reference for the output voltage magnitude and angle is calculated from the droop, state feedback controllers are used to track the reference. The angle reference for the synchronous machine is compared with the output voltage angle of the machine and the error is fed to a PI controller. The controller output is used to set the power reference of the synchronous machine. The rate of change in the angle in a synchronous machine is restricted by the machine inertia and to mimic this nature, the rate of change in the VSCs angles are restricted by a derivative feedback in the droop control. The connected distribution static compensator (DSTATCOM) provides ride through capability during power imbalance in the microgrid, especially when the stored energy of the inertial DG is not sufficient to maintain stability. The inclusion of the DSATCOM in such cases ensures the system stability. The efficacies of the controllers are established through extensive simulation studies using PSCAD.

Development of a computer simulation tool for application in adolescent spinal deformity surgery

Scoliosis is a three-dimensional spinal deformity which requires surgical correction in progressive cases. In order to optimize correction and avoid complications following scoliosis surgery, patient-specific finite element models (FEM) are being developed and validated by our group. In this paper, the modeling methodology is described and two clinically relevant load cases are simulated for a single patient. Firstly, a pre-operative patient flexibility assessment, the fulcrum bending radiograph, is simulated to assess the model's ability to represent spine flexibility. Secondly, intra-operative forces during single rod anterior correction are simulated. Clinically, the patient had an initial Cobb angle of 44 degrees, which reduced to 26 degrees during fulcrum bending. Surgically, the coronal deformity corrected to 14 degrees. The simulated initial Cobb angle was 40 degrees, which reduced to 23 degrees following the fulcrum bending load case. The simulated surgical procedure corrected the coronal deformity to 14 degrees. The computed results for the patient-specific FEM are within the accepted clinical Cobb measuring error of 5 degrees, suggested that this modeling methodology is capable of capturing the biomechanical behaviour of a scoliotic human spine during anterior corrective surgery.

Droop control of converter interfaced micro sources in rural distributed generation

This paper proposes new droop control methods for load sharing in a rural area with distributed generation. Highly resistive lines, typical of rural low voltage networks, always create a big challenge for conventional droop control. To overcome the conflict between higher feedback gain for better power sharing and system stability in angle droop, two control methods have been proposed. The first method considers no communication among the distributed generators (DGs) and regulates the converter output voltage and angle ensuring proper sharing of load in a system having strong coupling between real and reactive power due to high line resistance. The second method, based on a smattering of communication, modifies the reference output volt-age angle of the DGs depending on the active and reactive power flow in the lines connected to point of common coupling (PCC). It is shown that with the second proposed control method, an economical and minimum communication system can achieve significant improvement in load sharing. The difference in error margin between proposed control schemes and a more costly high bandwidth communication system is small and the later may not be justified considering the increase in cost. The proposed control shows stable operation of the system for a range of operating conditions while ensuring satisfactory load sharing.