Cartographic experiment for Latin America

The author has identified the following significant results. The two experiments clearly demonstrate the practical application of the Skylab photography to update existing maps at an optimum scale of 1:100,000. The photography can even be used, by employing first order photogrammetric instruments, for updating the cultural features in 1:50,000 scale mapping. The S190A imagery has also shown itself to be most economical in preparing new photomap products over previously unmapped areas, such as Concepcion, Paraguay. These maps indicate that Skylab quality imagery is invaluable to the Latin American cartographers in their efforts to provide the mapping products required to develop their countries. In Latin America, where over 5,000 people are employed in map production and where the Latin American governments are expending over $20 million in this effort, the use of such systems to maintain existing mapping and publish new mapping over previously unmapped areas, is of great economic value and could release the conventional Latin American mapping resources to be utilized to produce large scale 1:25,000 and 1:1,000 scale mapping that is needed for specific development projects

A coarse-grid projection method for accelerating incompressible flow computations

We present a coarse-grid projection (CGP) method for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. The CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. After solving the Poisson equation on a coarsened grid, an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid. A particular version of the method is applied here to the vorticity-stream function, primitive variable, and vorticity-velocity formulations of incompressible Navier-Stokes equations. We compute several benchmark flow problems on two-dimensional Cartesian and non-Cartesian grids, as well as a three-dimensional flow problem. The method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field, which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid. A linear acceleration rate is obtained for all the cases we consider due to the linear-cost elliptic Poisson solver used, with reduction factors in computational time between 2 and 42. The computational savings are larger when a suboptimal Poisson solver is used. We also find that the computational savings increase with increasing distortion ratio on non-Cartesian grids, making the CGP method a useful tool for accelerating generalized curvilinear incompressible flow solvers

An Efficient Coarse Grid Projection Method for Quasigeostrophic Models of Large-Scale Ocean Circulation

This paper puts forth a coarse grid projection (CGP) multiscale method to accelerate computations of quasigeostrophic (QG) models for large scale ocean circulation. These models require solving an elliptic sub-problem at each time step, which takes the bulk of the computational time. The method we propose here is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for solving the elliptic sub-problem and potential vorticity equations in the QG flow solvers. After solving the elliptic sub-problem on a coarsened grid, an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid. The potential vorticity field is then updated on the fine grid with savings in computational time due to the reduced number of grid points for the elliptic solver. The method is applied to both single layer barotropic and two-layer stratified QG ocean models for mid-latitude oceanic basins in the beta plane, which are standard prototypes of more realistic ocean dynamics. The method is found to accelerate these computations while retaining the same level of accuracy in the fine-resolution field. A linear acceleration rate is obtained for all the cases we consider due to the efficient linear-cost fast Fourier transform based elliptic solver used. We expect the speed-up of the CGP method to increase dramatically for versions of the method that use other, suboptimal, elliptic solvers, which are generally quadratic cost. It is also demonstrated that numerical oscillations due to lower grid resolutions, in which the Munk scales are not resolved adequately, are effectively eliminated with CGP method.Comment: International Journal for Multiscale Computational Engineering, 2013. arXiv admin note: substantial text overlap with arXiv:1212.0140, arXiv:1212.0922, arXiv:1104.273

An improved model for reduced-order physiological fluid flows

An improved one-dimensional mathematical model based on Pulsed Flow Equations (PFE) is derived by integrating the axial component of the momentum equation over the transient Womersley velocity profile, providing a dynamic momentum equation whose coefficients are smoothly varying functions of the spatial variable. The resulting momentum equation along with the continuity equation and pressure-area relation form our reduced-order model for physiological fluid flows in one dimension, and are aimed at providing accurate and fast-to-compute global models for physiological systems represented as networks of quasi one-dimensional fluid flows. The consequent nonlinear coupled system of equations is solved by the Lax-Wendroff scheme and is then applied to an open model arterial network of the human vascular system containing the largest fifty-five arteries. The proposed model with functional coefficients is compared with current classical one-dimensional theories which assume steady state Hagen-Poiseuille velocity profiles, either parabolic or plug-like, throughout the whole arterial tree. The effects of the nonlinear term in the momentum equation and different strategies for bifurcation points in the network, as well as the various lumped parameter outflow boundary conditions for distal terminal points are also analyzed. The results show that the proposed model can be used as an efficient tool for investigating the dynamics of reduced-order models of flows in physiological systems and would, in particular, be a good candidate for the one-dimensional, system-level component of geometric multiscale models of physiological systems

The Development of the Numeracy Apprehension Scale for Children Aged 4-7 Years: Qualitative Exploration of Associated Factors and Quantitative Testing

Previous psychological literature has shown mathematics anxiety in older populations to have an association with many factors, including an adverse effect on task performance. However, the origins of mathematics anxiety have, until recently, received limited attention. It is now accepted that this anxiety is rooted within the early educational years, but research has not explored the associated factors in the first formal years of schooling. Based on previous focus groups with children aged 4-7 years, ‘numeracy apprehension’ is suggested in this body of work, as the foundation phase of negative emotions and experiences, in which mathematics anxiety can develop. Building on this research, the first piece of research utilized 2 interviews and 5 focus groups to obtain insight from parents (n=7), teachers (n=9) and mathematics experts (n=2), to explore how children experience numeracy and their observations of children’s attitudes and responses. Thematic and content analysis uncovered a range of factors that characterised children’s numeracy experiences. These included: stigma and peer comparisons; the difficulty of numeracy and persistent failure; a low sense of ability; feelings of inadequacy; peer evaluation; transference of teacher anxieties; the right or wrong nature of numeracy; parental influences; dependence on peers; avoidance and children being aware of a hierarchy based on numeracy performance. Key themes reflected the focus group findings of children aged 4-7 years. This contributed to an item pool for study 2, to produce a first iteration of the Numeracy Apprehension Scale (NAS) that described day-to-day numeracy lesson situations. This 44-item measure was implemented with 307 children aged 4-7 years, across 4 schools in the U.K. Exploratory factor analysis led to a 26-item iteration of the NAS, with a 2-factor structure of Prospective Numeracy Task Apprehension and On-line Number Apprehension, which related to, for example, observation and evaluation anxiety, worry and teacher anxiety. The results suggested that mathematics anxiety may stem from the initial development of numeracy apprehension and is based on consistent negative experiences throughout an educational career. The 26-item iteration of the NAS was further validated in study 3 with 163 children aged 4-7 years, across 2 schools in the U.K. The construct validity of the scale was tested by comparing scale scores against numeracy performance on a numeracy task to determine whether a relationship between scale and numeracy task scores was evident. Exploratory factor analysis was again conducted and resulted in the current 19-item iteration of the NAS that related to a single factor of On-line Number Apprehension. This related to the experience of an entire numeracy lesson, from first walking in to completing a task and was associated with, for example, explaining an answer to the teacher, making mistakes and getting work wrong. A significant negative correlation was observed between the NAS and numeracy performance scores, suggesting that apprehensive children demonstrate a performance deficit early in education and that the NAS has the potential to be a reliable assessment of children’s numeracy apprehension. This empirical reinforces that the early years of education are the origins of mathematics anxiety, in the form of numeracy apprehension