Accurate series solutions for gravity-driven Stokes waves

In the past, high order series expansion techniques have been used to study the nonlinear equations that govern the form of periodic Stokes waves moving steadily on the surface of an inviscid fluid. In the present study, two such series solutions are recomputed using exact arithmetic, eliminating any loss of accuracy due to accumulation of round-off error, allowing a much greater number of terms to be found with confidence. It is shown that higher order behaviour of series generated by the solution casts doubt over arguments that rely on estimating the series’ radius of convergence. Further, the exact nature of the series is used to shed light on the unusual nature of convergence of higher order Pade approximants near the highest wave. Finally, it is concluded that, provided exact values are used in the series, these Pade approximants prove very effective in successfully predicting three turning points in both the dispersion relation and the total energy.

Academic rigour in science assessment tasks

The critical problem of student disengagement and underachievement in the middle years of schooling (Years 4 . 9) has focussed attention on the quality of educational programs in schools, in Australia and elsewhere. The loss of enthusiasm for science in the middle years is particularly problematic given the growing demand for science professionals. Reshaping middle years programs has included an emphasis on integrating Information and Communication Technologies (ICTs) and improving assessment practices to engage students in higher cognitive processes and enhance academic rigour. Understanding the nature of academic rigour and how to embed it in students. science assessment tasks that incorporate the use of ICTs could enable teachers to optimise the quality of the learning environment. However, academic rigour is not clearly described or defined in the literature and there is little empirical evidence upon which researchers and teachers could draw to enhance understandings. This study used a collective case study design to explore teachers' understandings of academic rigour within science assessment tasks. The research design is based on a conceptual framework that is underpinned by socio-cultural theory. Three methods were used to collect data from six middle years teachers and their students. These methods were a survey, focus group discussion with teachers and a group of students and individual semi-structured interviews with teachers. Findings of the case study revealed six criteria of academic rigour, namely, higher order thinking, alignment, building on prior knowledge, scaffolding, knowledge construction and creativity. Results showed that the middle years teachers held rich understandings of academic rigour that led to effective utilisation of ICTs in science assessment tasks. Findings also indicated that teachers could further enhance their understandings of academic rigour in some aspects of each of the criteria. In particular, this study found that academic rigour could have been further optimised by: promoting more thoughtful discourse and interaction to foster higher order thinking; increasing alignment between curriculum, pedagogy, and assessment, and students. prior knowledge; placing greater emphasis on identifying, activating and building on prior knowledge; better differentiating the level of scaffolding provided and applying it more judiciously; fostering creativity throughout tasks; enhancing teachers‟ content knowledge and pedagogical content knowledge, and providing more in-depth coverage of fewer topics to support knowledge construction. Key contributions of this study are a definition and a model which clarify the nature of academic rigour.

Influence of spherical intraocular lens implantation and conventional laser in situ keratomileusis on peripheral ocular aberrations

Aim: To measure the influence of spherical intraocular lens implantation and conventional myopic laser in situ keratomileusis on peripheral ocular aberrations. Setting: Visual & Ophthalmic Optics Laboratory, School of Optometry & Institute of Health and Biomedical Innovation, Queensland University of Technology, Brisbane, Australia. Methods: Peripheral aberrations were measured using a modified commercial Hartmann-Shack aberrometer across 42° x 32° of the central visual field in 6 subjects after spherical intraocular lens (IOL) implantation and in 6 subjects after conventional laser in situ keratomileusis (LASIK) for myopia. The results were compared with those of age matched emmetropic and myopic control groups. Results: The IOL group showed a greater rate of quadratic change of spherical equivalent refraction across the visual field, higher spherical aberration, and greater rates of change of higher-order root-mean-square aberrations and total root-mean-square aberrations across the visual field than its emmetropic control group. However, coma trends were similar for the two groups. The LASIK group had a greater rate of quadratic change of spherical equivalent refraction across the visual field, higher spherical aberration, the opposite trend in coma across the field, and greater higher-order root-mean-square aberrations and total root-mean-square aberrations than its myopic control group. Conclusion: Spherical IOL implantation and conventional myopia LASIK increase ocular peripheral aberrations. They cause considerable increase in spherical aberration across the visual field. LASIK reverses the sign of the rate of change in coma across the field relative to that of the other groups. Keywords: refractive surgery, LASIK, IOL implantation, aberrations, peripheral aberrations

Exponential asymptotics with multiple stokes lines

When asymptotic series methods are applied in order to solve problems that arise in applied mathematics in the limit that some parameter becomes small, they are unable to demonstrate behaviour that occurs on a scale that is exponentially small compared to the algebraic terms of the asymptotic series. There are many examples of physical systems where behaviour on this scale has important effects and, as such, a range of techniques known as exponential asymptotic techniques were developed that may be used to examinine behaviour on this exponentially small scale. Many problems in applied mathematics may be represented by behaviour within the complex plane, which may subsequently be examined using asymptotic methods. These problems frequently demonstrate behaviour known as Stokes phenomenon, which involves the rapid switches of behaviour on an exponentially small scale in the neighbourhood of some curve known as a Stokes line. Exponential asymptotic techniques have been applied in order to obtain an expression for this exponentially small switching behaviour in the solutions to orginary and partial differential equations. The problem of potential flow over a submerged obstacle has been previously considered in this manner by Chapman & Vanden-Broeck (2006). By representing the problem in the complex plane and applying an exponential asymptotic technique, they were able to detect the switching, and subsequent behaviour, of exponentially small waves on the free surface of the flow in the limit of small Froude number, specifically considering the case of flow over a step with one Stokes line present in the complex plane. We consider an extension of this work to flow configurations with multiple Stokes lines, such as flow over an inclined step, or flow over a bump or trench. The resultant expressions are analysed, and demonstrate interesting implications, such as the presence of exponentially sub-subdominant intermediate waves and the possibility of trapped surface waves for flow over a bump or trench. We then consider the effect of multiple Stokes lines in higher order equations, particu- larly investigating the behaviour of higher-order Stokes lines in the solutions to partial differential equations. These higher-order Stokes lines switch off the ordinary Stokes lines themselves, adding a layer of complexity to the overall Stokes structure of the solution. Specifically, we consider the different approaches taken by Howls et al. (2004) and Chap- man & Mortimer (2005) in applying exponential asymptotic techniques to determine the higher-order Stokes phenomenon behaviour in the solution to a particular partial differ- ential equation.

Combination of Kalman filter and least error square techniques in power system

An algorithm based on the concept of combining Kalman filter and Least Error Square (LES) techniques is proposed in this paper. The algorithm is intended to estimate signal attributes like amplitude, frequency and phase angle in the online mode. This technique can be used in protection relays, digital AVRs, DGs, DSTATCOMs, FACTS and other power electronics applications. The Kalman filter is modified to operate on a fictitious input signal and provides precise estimation results insensitive to noise and other disturbances. At the same time, the LES system has been arranged to operate in critical transient cases to compensate the delay and inaccuracy identified because of the response of the standard Kalman filter. Practical considerations such as the effect of noise, higher order harmonics, and computational issues of the algorithm are considered and tested in the paper. Several computer simulations and a laboratory test are presented to highlight the usefulness of the proposed method. Simulation results show that the proposed technique can simultaneously estimate the signal attributes, even if it is highly distorted due to the presence of non-linear loads and noise.

Peripheral ocular aberrations in mild and moderate keratoconus

Purpose: To investigate the influence of keratoconus on peripheral ocular aberrations. Methods: Aberrations of 7 mild and 5 moderate keratoconics were determined over a 42°horizontal x 32° vertical visual field with a modified COAS-HD aberrometer. Control data were obtained from an emmetropic group. Results: Most aberrations in keratoconics showed field dependence predominately along the vertical meridian. Mean spherical equivalent M, oblique astigmatism J45 and regular astigmatism J180 refraction components and total root mean square aberrations (excluding defocus) had high magnitudes in the inferior visual field. The rates of change of aberrations were higher in moderate than in mild keratoconics. Coma was the dominant peripheral higher-order aberration in both emmetropes and keratoconics; for the latter it had high magnitudes in the centre and periphery of the visual field. Conclusion: Greater rates of change of aberrations across the visual field occurred for the keratoconic groups than for the emmetropic control group. Moderate keratoconics had more rapid changes in, and higher magnitudes of aberrations across the visual field than mild keratoconics. The dominant higher-order aberration for the keratoconics across the visual field was vertical coma.

Lateral shearing interferometry, dynamic wavefront sensing, and high-speed videokeratoscopy for noninvasive assessment of tear film surface characteristics : a comparitive study

There are several noninvasive techniques for assessing the kinetics of tear film, but no comparative studies have been conducted to evaluate their efficacies. Our aim is to test and compare techniques based on high-speed videokeratoscopy (HSV), dynamic wavefront sensing (DWS), and lateral shearing interferometry (LSI). Algorithms are developed to estimate the tear film build-up time TBLD, and the average tear film surface quality in the stable phase of the interblink interval TFSQAv. Moderate but significant correlations are found between TBLD measured with LSI and DWS based on vertical coma (Pearson's r2=0.34, p<0.01) and higher order rms (r2=0.31, p<0.01), as well as between TFSQAv measured with LSI and HSV (r2=0.35, p<0.01), and between LSI and DWS based on the rms fit error (r2=0.40, p<0.01). No significant correlation is found between HSV and DWS. All three techniques estimate tear film build-up time to be below 2.5 sec, and they achieve a remarkably close median value of 0.7 sec. HSV appears to be the most precise method for measuring tear film surface quality. LSI appears to be the most sensitive method for analyzing tear film build-up.

Subjective blur limits for cylinder

Purpose: To compare subjective blur limits for cylinder and defocus. ---------- Method: Blur was induced with a deformable, adaptive-optics mirror when either the subjects’ own astigmatisms were corrected or when both astigmatisms and higher-order aberrations were corrected. Subjects were cyclopleged and had 5 mm artificial pupils. Black letter targets (0.1, 0.35 and 0.6 logMAR) were presented on white backgrounds. Results: For ten subjects, blur limits were approximately 50% greater for cylinder than for defocus (in diopters). While there were considerable effects of axis for individuals, overall this was not strong, with the 0° (or 180°) axis having about 20% greater limits than oblique axes. In a second experiment with text (equivalent in angle to N10 print at 40 cm distance), cylinder blur limits for 6 subjects were approximately 30% greater than those for defocus; this percentage was slightly smaller than for the three letters. Blur limits of the text were intermediate between those of 0.35 logMAR and 0.6 logMAR letters. Extensive blur limit measurements for one subject with single letters did not show expected interactions between target detail orientation and cylinder axis. ---------- Conclusion: Subjective blur limits for cylinder are 30%-50% greater than those for defocus, with the overall influence of cylinder axis being 20%.

Effect of optical aberrations on the color appearance of small defocused lights

We investigated influences of optics and surround area on color appearance of defocused, small narrow band photopic lights (1’ arc diameter, λmax 510 - 628 nm) centered within a black annulus and surrounded by a white field. Participants included seven normal trichromats with L- or M-cone biased ratios. We controlled chromatic aberration with elements of a Powell achromatizing lens and corrected higher-order aberrations with an adaptive-optics system. Longitudinal chromatic aberrations, but not monochromatic aberrations, are involved in changing appearance of small lights with defocus. Surround field structure is important because color changes were not observed when lights were presented on a uniform white surround.

“Diving into reading” : revisiting reciprocal teaching in the middle years

This paper reports on a project that was designed to support teachers to introduce reciprocal teaching and student-generated questioning in the middle years. It began as a solution to teachers expressing a concern that there was a lack of professional development related to the teaching of reading in the middle years.

Embracing diversity : empowering preservice teachers for teaching gifted and talented students

This study investigated preservice teachers’ perceptions for teaching and sustaining gifted and talented students while developing, modifying and implementing activities to cater for the diverse learner. Participants were surveyed at the end of a gifted and talented education program on their perceptions to differentiate the curriculum for meeting the needs of the student (n=22). SPSS data analysis with the five-part Likert scale indicated these preservice teachers agreed or strongly agreed they had developed skills in curriculum planning (91%) with well-designed activities (96%), and lesson preparation skills (96%). They also claimed they were enthusiastic for teaching (91%) and understanding of school practices and policies (96%). However, 46% agreed they had knowledge of syllabus documents with 50% claiming an ability to provide written feedback on student’s learning. Furthermore, nearly two-thirds suggested they had educational language from the syllabus and effective student management strategies. Preservice teachers require more direction on how to cater for diversity and begin creating sustainable societies by building knowledge from direct GAT experiences. Designing diagnostic surveys associated with university coursework can be used to determine further development for specific preservice teacher development in GAT education. Preservice teachers need to create opportunities for students to realise their potential by involving cognitive challenges through a differentiated curriculum. Differentiation requires modification of four primary areas of curriculum development (Maker, 1975) content (what we teach), process (how we teach), product (what we expect the students to do or show) and learning environment (where we teach/our class culture). Ashman and Elkins (2009) and Glasson (2008) emphasise the need for preservice teachers, teachers and other professionals to be able to identify what gifted and talented (GAT) students know and how they learn in relation to effective teaching. Glasson (2008) recommends that educators keep up to date with practices in pedagogy, support, monitoring and profiling of GAT students to create an environment conducive to achieving. Oral feedback is one method to communicate to learners about their progress but has advantages and disadvantages for some students. Oral feedback provides immediate information to the student on progress and performance (Ashman & Elkins, 2009). However, preservice teachers must have clear understandings of key concepts to assist the GAT student. Implementing teaching strategies to engage innovate and extend students is valuable to the preservice teacher in focusing on GAT student learning in the classroom (Killen, 2007). Practical teaching strategies (Harris & Hemming, 2008; Tomlinson et al., 1994) facilitate diverse ways for assisting GAT students to achieve learning outcomes. Such strategies include activities to enhance creativity, co-operative learning and problem-solving activities (Chessman, 2005; NSW Department of Education and Training, 2004; Taylor & Milton, 2006) for GAT students to develop a sense of identity, belonging and self esteem towards becoming an autonomous learner. Preservice teachers need to understand that GAT students learn in a different way and therefore should be assessed differently. Assessment can be through diverse options to demonstrate the student’s competence, demonstrate their understanding of the material in a way that highlights their natural abilities (Glasson, 2008; Mack, 2008). Preservice teachers often are unprepared to assess students understanding but this may be overcome with teacher education training promoting effective communication and collaboration in the classroom, including the provision of a variety of assessment strategies to improve teaching and learning (Callahan et al., 2003; Tomlinson et al., 1994). It is also critical that preservice teachers have enthusiasm for teaching to demonstrate inclusion, involvement and the excitement to communicate to GAT students in the learning process (Baum, 2002). Evaluating and reflecting on teaching practices must be part of a preservice teacher’s repertoire for GAT education. Evaluating teaching practices can assist to further enhance student learning (Mayer, 2008). Evaluation gauges the success or otherwise of specific activities and teaching in general (Mayer, 2008), and ensures that preservice teachers and teachers are well prepared and maintain their commitment to their students and the community. Long and Harris (1999) advocate that reflective practices assist teachers in creating improvements in educational practices. Reflective practices help preservice teachers and teachers to improve their ability to pursue improved learning outcomes and professional growth (Long & Harris, 1999). Context This study is set at a small regional campus of a large university in Queensland. As a way to address departmental policies and the need to prepare preservice teachers for engaging a diverse range of learners (see Queensland College of Teachers, Professional Standards for Teachers, 2006), preservice teachers at this campus completed four elective units within their Bachelor of Education (primary) degree. The electives include: 1. Middle years students and schools 2. Teaching strategies for engaging learners 3. Teaching students with learning difficulties, and 4. Middle-years curriculum, pedagogy and assessment. In the university-based component of this unit, preservice teachers engaged in learning about middle years students and schools, and gained knowledge of government policies pertaining to GAT students. Further explored within in this unit was the importance of: collaboration between teachers, parents/carers and school personnel in supporting middle years GAT students; incorporating challenging learning experiences that promoted higher order thinking and problem solving skills; real world learning experiences for students and; the alignment and design of curriculum, pedagogy and assessment that is relevant to the students development, interests and needs. The participants were third-year Bachelor of Education (primary) preservice teachers who were completing an elective unit as part of the middle years of schooling learning with a focus on GAT students. They were assigned one student from a local school. In the six subsequent ninety minute weekly lessons, the preservice teachers were responsible for designing learning activities that would engage and extend the GAT students. Furthermore, preservice teachers made decisions about suitable pedagogical approaches and designed the assessment task to align with the curriculum and the developmental needs of their middle years GAT student. This research aims to describe preservice teachers’ perceptions of their education for teaching gifted and talented students.

Measurement of affect during simulation-based training

Training designed to support and strengthen higher-order mental abilities now often involves immersion in Virtual Reality where dangerous real world scenarios can be safely replicated. However despite the growing popularity of advanced training simulations, methods for evaluating their use rely heavily on subjective measures or analysis of final outcomes. Without dynamic, objective performance measures the outcome of training in terms of impact on cognitive skills and ability to transfer newly acquired skills to the real world is unknown. The relationship between affective intensity and cognitive learning provides a potential new approach to ensure the processing of cognitions which occur prior to final outcomes, such as problem-solving and decision-making, are adequately evaluated. This paper describes the technical aspects of pilot work recently undertaken to develop a new measurement tool designed to objectively track individual affect levels during simulation-based training.

Teaching and learning mathematics with robotics in middle-years of schooling

Engaging and motivating students in mathematics lessons can be challenging. The traditional approach of chalk and talk can sometimes be problematic. The new generation of educational robotics has the potential to not only motivate students but also enable teachers to demonstrate concepts in mathematics by connecting concepts with the real world. Robotics hardware and the software are becoming increasing more user-friendly and as a consequence they can be blended in with classroom activities with greater ease. Using robotics in suitably designed activities promotes a constructivist learning environment and enables students to engage in higher order thinking through hands-on problem solving. Teamwork and collaborative learning are also enhanced through the use of this technology. This paper discusses a model for teaching concepts in mathematics in middle year classrooms. It will also highlight some of the benefits and challenges of using robotics in the learning environment.