Scaling analysis of natural convection boundary layers : Application to attic space

The natural convection thermal boundary layer adjacent to an inclined flat plate and inclined walls of an attic space subject to instantaneous and ramp heating and cooling is investigated. A scaling analysis has been performed to describe the flow behaviour and heat transfer. Major scales quantifying the flow velocity, flow development time, heat transfer and the thermal and viscous boundary layer thicknesses at different stages of the flow development are established. Scaling relations of heating-up and cooling-down times and heat transfer rates have also been reported for the case of attic space. The scaling relations have been verified by numerical simulations over a wide range of parameters. Further, a periodic temperature boundary condition is also considered to show the flow features in the attic space over diurnal cycles.

Breaching the standardised assessment boundary : assessment for learning as a field of exchange

The introduction of the Australian curriculum, the use of standardised testing (e.g. NAPLAN) and the My School website are couched in a context of accountability. This circumstance has stimulated and in some cases renewed a range of boundaries in Australian Education. The consequences that arise from standardised testing have accentuated the boundaries produced by social reproduction in education which has led to an increase in the numbers of students disengaging from mainstream education and applying for enrolment at the Edmund Rice Education Australia Flexible Learning Centre Network (EREAFLCN). Boundaries are created for many young people who are denied access to credentials and certification as a result of being excluded from or in some way disengaging from standardised education and testing. Young people who participate at the EREAFLCN arrive with a variety of forms of cultural capital that are not valued in current education and employment fields. This is not to say that these young people’s different forms of cultural capital have no value, but rather that such funds of knowledge, repertoires and cultural capital are not valued by the majority of powerful agents in educational and employment fields. How then can the qualitative value of traditionally unorthodox - yet often intricate, ingenious, and astute - versions of cultural capital evident in the habitus of many young people be made to count, be recognised, be valuated? Can a process of educational assessment be a field of capital exchange and a space which breaches boundaries through a valuating process? This paper reports on the development of an innovative approach to assessment in an alternative education institution designed for the re-engagement of ‘at risk’ youth who have left formal schooling. A case study approach has been used to document the engagement of six young people, with an educational approach described as assessment for learning as a field of exchange across two sites in the EREAFLCN. In order to capture the broad range of students’ cultural and social capital, an electronic portfolio system (EPS) is under trial. The model draws on categories from sociological models of capital and reconceptualises the eportfolio as a sociocultural zone of learning and development. Results from the trial show a general tendency towards engagement with the EPS and potential for the attainment of socially valued cultural capital in the form of school credentials. In this way restrictive boundaries can be breached and a more equitable outcome achieved for many young Australians.

Scaling for the Prandtl number of the natural convection boundary layer of an inclined flat plate under uniform surface heat flux

An improved scaling analysis and direct numerical simulations are performed for the unsteady natural convection boundary layer adjacent to a downward facing inclined plate with uniform heat flux. The development of the thermal or viscous boundary layers may be classified into three distinct stages: a start-up stage, a transitional stage and a steady stage, which can be clearly identified in the analytical as well as the numerical results. Previous scaling shows that the existing scaling laws of the boundary layer thickness, velocity and steady state time scale for the natural convection flow on a heated plate of uniform heat flux provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings perform very well with Rayleigh number and aspect ratio dependency. In this study, a modified Prandtl number scaling is developed using a triple layer integral approach for Pr > 1. It is seen that in comparison to the direct numerical simulations, the modified scaling performs considerably better than the previous scaling.

Next generation low-cost motion capture systems can provide comparable spatial accuracy to high-end systems

The objective quantification of three-dimensional kinematics during different functional and occupational tasks is now more in demand than ever. The introduction of new generation of low-cost passive motion capture systems from a number of manufacturers has made this technology accessible for teaching, clinical practice and in small/medium industry. Despite the attractive nature of these systems, their accuracy remains unproved in independent tests. We assessed static linear accuracy, dynamic linear accuracy and compared gait kinematics from a Vicon MX20 system to a Natural Point OptiTrack system. In all experiments data were sampled simultaneously. We identified both systems perform excellently in linear accuracy tests with absolute errors not exceeding 1%. In gait data there was again strong agreement between the two systems in sagittal and coronal plane kinematics. Transverse plane kinematics differed by up to 3 at the knee and hip, which we attributed to the impact of soft tissue artifact accelerations on the data. We suggest that low-cost systems are comparably accurate to their high-end competitors and offer a platform with accuracy acceptable in research for laboratories with a limited budget.

A radiological method to determine the accuracy of motion capture marker placement on palpable anatomical landmarks through a shoe

The accuracy of marker placement on palpable surface anatomical landmarks is an important consideration in biomechanics. Although marker placement reliability has been studied in some depth, it remains unclear whether or not the markers are accurately positioned over the intended landmark in order to define the static position and orientation of the segment. A novel method using commonly available X-ray imaging was developed to identify the accuracy of markers placed on the shoe surface by palpating landmarks through the shoe. An anterior–posterior and lateral–medial X-ray was taken on 24 participants with a newly developed marker set applied to both the skin and shoe. The vector magnitude of both skin- and shoe-mounted markers from the anatomical landmark was calculated, as well as the mean marker offset between skin- and shoe-mounted markers. The accuracy of placing markers on the shoe relative to the skin-mounted markers, accounting for shoe thickness, was less than 5mm for all markers studied. Further, when using the developed guidelines provided in this study, the method was deemed reliable (Intra-rater ICCs¼0.50–0.92). In conclusion, the method proposed here can reliably assess marker placement accuracy on the shoe surface relative to chosen anatomical landmarks beneath the skin.

A comparison of two commercially available motion capture systems for gait analysis : high end vs low-cost

In 1999 Richards compared the accuracy of commercially available motion capture systems commonly used in biomechanics. Richards identified that in static tests the optical motion capture systems generally produced RMS errors of less than 1.0 mm. During dynamic tests, the RMS error increased to up to 4.2 mm in some systems. In the last 12 years motion capture systems have continued to evolve and now include high-resolution CCD or CMOS image sensors, wireless communication, and high full frame sampling frequencies. In addition to hardware advances, there have also been a number of advances in software, which includes improved calibration and tracking algorithms, real time data streaming, and the introduction of the c3d standard. These advances have allowed the system manufactures to maintain a high retail price in the name of advancement. In areas such as gait analysis and ergonomics many of the advanced features such as high resolution image sensors and high sampling frequencies are not required due to the nature of the task often investigated. Recently Natural Point introduced low cost cameras, which on face value appear to be suitable as at very least a high quality teaching tool in biomechanics and possibly even a research tool when coupled with the correct calibration and tracking software. The aim of the study was therefore to compare both the linear accuracy and quality of angular kinematics from a typical high end motion capture system and a low cost system during a simple task.

Reducing Actuator Switchings for Motion Control of Autonomous Underwater Vehicles

A priority when designing control strategies for autonomous underwater vehicles is to emphasize their cost of implementation on a real vehicle. Indeed, due to the vehicles' design and the actuation modes usually under consideration for underwater plateforms the number of actuator switchings must be kept to a small value to insure feasibility and precision. This is the main objective of the algorithm presented in this paper. The theory is illustrated on two examples, one is a fully actuated underwater vehicle capable of motion in six-degrees-of freedom and one is minimally actuated with control motions in the vertical plane only.

A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1].

Prandtl number scaling of the unsteady natural convection boundary layer adjacent to a vertical flat plate for Pr > 1 subject to ramp surface heat flux

It is found in the literature that the existing scaling results for the boundary layer thickness, velocity and steady state time for the natural convection flow over an evenly heated plate provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings provide a good prediction of two other governing parameters’ dependency, the Rayleigh number and the aspect ratio. Therefore, an improved scaling analysis using a triple-layer integral approach and direct numerical simulations have been performed for the natural convection boundary layer along a semi-infinite flat plate with uniform surface heat flux. This heat flux is a ramp function of time, where the temperature gradient on the surface increases with time up to some specific time and then remains constant. The growth of the boundary layer strongly depends on the ramp time. If the ramp time is sufficiently long, the boundary layer reaches a quasi steady mode before the growth of the temperature gradient is completed. In this mode, the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the ramp time is sufficiently short, the boundary layer develops differently, but after the wall temperature gradient growth is completed, the boundary layer develops as though the startup had been instantaneous.

Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

Reducing actuator switchings for motion control of autonomous underwater vehicles

A priority when designing control strategies for autonomous underwater vehicles is to emphasize their cost of implementation on a real vehicle and at the same time to minimize a prescribed criterion such as time, energy, payload or combination of those. Indeed, the major issue is that due to the vehicles' design and the actuation modes usually under consideration for underwater platforms the number of actuator switchings must be kept to a small value to ensure feasibility and precision. This constraint is typically not verified by optimal trajectories which might not even be piecewise constants. Our goal is to provide a feasible trajectory that minimizes the number of switchings while maintaining some qualities of the desired trajectory, such as optimality with respect to a given criterion. The one-sided Lipschitz constant is used to derive theoretical estimates. The theory is illustrated on two examples, one is a fully actuated underwater vehicle capable of motion in six degrees-of-freedom and one is minimally actuated with control motions constrained to the vertical plane.