A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

Facile synthesis of Lithium Niobate squares by a combustion route

A combustion synthesis of lithium niobate (LN) squares from activated niobium oxide (Nb2 O5.nH2O) and Li2CO3 was studied to understand all the chemical reactions involved, and the nucleation and square-growth mechanisms. It was found that first the lithium ions react with the fuel (urea), then niobium ions of Nb2 O5.nH2O begin a continuous reaction with the fuel to form metal-organic complexes. LN nuclei are formed by the solid-state reaction of Li- and Nb-organic complexes at 430 degrees celcius. Lithium niobate squares are obtained in the crystallization stasge at 700 degrees celcius, which go on the grow into larger squares at 850 degrees celcius because of the agglomeration effect.

Least-squares congealing for large numbers of images

In this paper we pursue the task of aligning an ensemble of images in an unsupervised manner. This task has been commonly referred to as “congealing” in literature. A form of congealing, using a least-squares criteria, has been recently demonstrated to have desirable properties over conventional congealing. Least-squares congealing can be viewed as an extension of the Lucas & Kanade (LK)image alignment algorithm. It is well understood that the alignment performance for the LK algorithm, when aligning a single image with another, is theoretically and empirically equivalent for additive and compositional warps. In this paper we: (i) demonstrate that this equivalence does not hold for the extended case of congealing, (ii) characterize the inherent drawbacks associated with least-squares congealing when dealing with large numbers of images, and (iii) propose a novel method for circumventing these limitations through the application of an inverse-compositional strategy that maintains the attractive properties of the original method while being able to handle very large numbers of images.

A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations

A vertex-centred finite volume method (FVM) for the Cahn-Hilliard (CH) and recently proposed Cahn-Hilliard-reaction (CHR) equations is presented. Information at control volume faces is computed using a high-order least-squares approach based on Taylor series approximations. This least-squares problem explicitly includes the variational boundary condition (VBC) that ensures that the discrete equations satisfy all of the boundary conditions. We use this approach to solve the CH and CHR equations in one and two dimensions and show that our scheme satisfies the VBC to at least second order. For the CH equation we show evidence of conservative, gradient stable solutions, however for the CHR equation, strict gradient-stability is more challenging to achieve.

Orthogonality defect and reduced search-space size for solving integer least-squares problems

In the context of ambiguity resolution (AR) of Global Navigation Satellite Systems (GNSS), decorrelation among entries of an ambiguity vector, integer ambiguity search and ambiguity validations are three standard procedures for solving integer least-squares problems. This paper contributes to AR issues from three aspects. Firstly, the orthogonality defect is introduced as a new measure of the performance of ambiguity decorrelation methods, and compared with the decorrelation number and with the condition number which are currently used as the judging criterion to measure the correlation of ambiguity variance-covariance matrix. Numerically, the orthogonality defect demonstrates slightly better performance as a measure of the correlation between decorrelation impact and computational efficiency than the condition number measure. Secondly, the paper examines the relationship of the decorrelation number, the condition number, the orthogonality defect and the size of the ambiguity search space with the ambiguity search candidates and search nodes. The size of the ambiguity search space can be properly estimated if the ambiguity matrix is decorrelated well, which is shown to be a significant parameter in the ambiguity search progress. Thirdly, a new ambiguity resolution scheme is proposed to improve ambiguity search efficiency through the control of the size of the ambiguity search space. The new AR scheme combines the LAMBDA search and validation procedures together, which results in a much smaller size of the search space and higher computational efficiency while retaining the same AR validation outcomes. In fact, the new scheme can deal with the case there are only one candidate, while the existing search methods require at least two candidates. If there are more than one candidate, the new scheme turns to the usual ratio-test procedure. Experimental results indicate that this combined method can indeed improve ambiguity search efficiency for both the single constellation and dual constellations respectively, showing the potential for processing high dimension integer parameters in multi-GNSS environment.

The magic of numbers and the amazing disappearing act : the politics of counting youth homelessness

No-one wants to see young people who are no longer able to stay at home with their parents living in situations that are neither stable nor safe. Most Australians also appreciate that youth homelessness is typically a result of factors beyond the control of young people like poverty, lack of affordable housing, parental divorce or separation, family conflict and violence, sexual abuse, or mental health problems.1 Since the Burdekin Report of 1989 first put the issue on the national agenda, youth homelessness has been a point of some political sensitivity as the numbers of young homeless stayed stubbornly high through the 1990s and into the 2000s.

Uncertainty analysis of pollutant build-up modelling based on a Bayesian Weighted Least Squares approach

Reliable pollutant build-up prediction plays a critical role in the accuracy of urban stormwater quality modelling outcomes. However, water quality data collection is resource demanding compared to streamflow data monitoring, where a greater quantity of data is generally available. Consequently, available water quality data sets span only relatively short time scales unlike water quantity data. Therefore, the ability to take due consideration of the variability associated with pollutant processes and natural phenomena is constrained. This in turn gives rise to uncertainty in the modelling outcomes as research has shown that pollutant loadings on catchment surfaces and rainfall within an area can vary considerably over space and time scales. Therefore, the assessment of model uncertainty is an essential element of informed decision making in urban stormwater management. This paper presents the application of a range of regression approaches such as ordinary least squares regression, weighted least squares Regression and Bayesian Weighted Least Squares Regression for the estimation of uncertainty associated with pollutant build-up prediction using limited data sets. The study outcomes confirmed that the use of ordinary least squares regression with fixed model inputs and limited observational data may not provide realistic estimates. The stochastic nature of the dependent and independent variables need to be taken into consideration in pollutant build-up prediction. It was found that the use of the Bayesian approach along with the Monte Carlo simulation technique provides a powerful tool, which attempts to make the best use of the available knowledge in the prediction and thereby presents a practical solution to counteract the limitations which are otherwise imposed on water quality modelling.

Sensuous geography : the role of sensuous experience and their contemporary implications in public squares, a Lefebvrian approach

This paper explores the sensuous relationship amongst people and the physical elements located in public squares. The research focuses on the study of sensuous geography and its social implications in contemporary city context. Case studies were drawn from various Western countries. A Lefebvrian approach was utilized to analyse the research findings. The study has generated a preliminary sensuous geography checklist for public squares that can predict the degree of popularity and experiential qualities of public squares. However, limits existed in the paper as sensory experiences are conditioned by individual, socio-cultural and climatic influences. The study suggests further integrated approach is needed in this field of study. The research findings indicated that better knowledge of sensuous geography is important in the design and planning disciplines.