An examination of isotherm generation : impact of bottle-point method upon potassium ion exchange with strong acid cation resin

This paper relates to the importance of impact of the chosen bottle-point method when conducting ion exchange equilibria experiments. As an illustration, potassium ion exchange with strong acid cation resin was investigated due to its relevance to the treatment of various industrial effluents and groundwater. The “constant mass” bottle-point method was shown to be problematic in that depending upon the resin mass used the equilibrium isotherm profiles were different. Indeed, application of common equilibrium isotherm models revealed that the optimal fit could be with either the Freundlich or Temkin equations, depending upon the conditions employed. It could be inferred that the resin surface was heterogeneous in character, but precise conclusions regarding the variation in the heat of sorption were not possible. Estimation of the maximum potassium loading was also inconsistent when employing the “constant mass” method. The “constant concentration” bottle-point method illustrated that the Freundlich model was a good representation of the exchange process. The isotherms recorded were relatively consistent when compared to the “constant mass” approach. Unification of all the equilibrium isotherm data acquired was achieved by use of the Langmuir Vageler expression. The maximum loading of potassium ions was predicted to be at least 116.5 g/kg resin.

Illuminative evaluation as a method applied to Australian Government policy borrowing and implementation in higher education

Any government deciding to invoke widespread change in its higher education sector through implementation of new policies impacts on every institution and all staff and students, often in both the time taken up and the heightened emotions caused. The central phenomenon that this study addresses is the process and consequences of policy changes in higher education in Australia. The aim of this article is to record the research design through the perspective (evaluation research), theoretical framework (program evaluation) and methods (content analysis, descriptive statistical analysis and bibliometric analysis) applied to the investigation of the 2003 federal government higher education reform package. This approach allows both the intended and unintended consequences arising from the policy implementation of three national initiatives focused on learning and teaching in higher education in Australia to surface. As a result, this program evaluation, also known in some disciplines as policy implementation analysis, will demonstrate the applicability of illuminative evaluation as a methodology and reinforce how program evaluation will assist and advise future government reform and policy implementation, and will serve as a legacy for future evaluative research.Any government deciding to invoke widespread change in its higher education sector through implementation of new policies impacts on every institution and all staff and students, often in both the time taken up and the heightened emotions caused. The central phenomenon that this study addresses is the process and consequences of policy changes in higher education in Australia. The aim of this article is to record the research design through the perspective (evaluation research), theoretical framework (program evaluation) and methods (content analysis, descriptive statistical analysis and bibliometric analysis) applied to the investigation of the 2003 federal government higher education reform package. This approach allows both the intended and unintended consequences arising from the policy implementation of three national initiatives focused on learning and teaching in higher education in Australia to surface. As a result, this program evaluation, also known in some disciplines as policy implementation analysis, will demonstrate the applicability of illuminative evaluation as a methodology and reinforce how program evaluation will assist and advise future government reform and policy implementation, and will serve as a legacy for future evaluative research.

A method to quantify a descriptor's illumination variance

This paper presents a new metric, which we call the lighting variance ratio, for quantifying descriptors in terms of their variance to illumination changes. In many applications it is desirable to have descriptors that are robust to changes in illumination, especially in outdoor environments. The lighting variance ratio is useful for comparing descriptors and determining if a descriptor is lighting invariant enough for a given environment. The metric is analysed across a number of datasets, cameras and descriptors. The results show that the upright SIFT descriptor is typically the most lighting invariant descriptor.

A method to evaluate the response of the coronary circulation of perfused rat heart to adenosine

Exogenous adenosine causes a monophasic dilation of the coronary vessels in paced, perfused rat heart preparations. Because levels of endogenous adenosine in paced hearts may mask the presence of high potency adenosine receptors, we have developed a method to measure coronary vascular responses in a potassium-arrested heart. Hearts from adult male, Wistar rats were perfused at a constant flow rate of 10 mL/min in the nonrecirculating, Langendorff mode, using Krebs-Henseleit buffer. After 30 min, coronary perfusion pressure was 44 +/- 1 mmHg (mean +/- SEM). Hearts were then perfused with a modified Krebs-Henseleit buffer containing 35 mM potassium. Coronary perfusion pressure increased by 84 +/- 3 mmHg. Adenosine-induced reductions in coronary perfusion pressure were expressed as a percentage of the maximal increase in pressure produced by modified Krebs-Henseleit buffer from the equilibration level. A concentration-response curve for adenosine (n = 6) was biphasic and best described by the presence of two adenosine receptors, with negative log EC50 values of 8.8 +/- 0.3 and 4.3 +/- 0.1, representing 29 +/- 3 and 71 +/- 3%, respectively, of the observed response. Interstitial adenosine sampled by microdialysis during potassium arrest was 25% of the concentration found in paced hearts. Endogenous adenosine in nonarrested hearts may obscure the biphasic response of the coronary vessels to adenosine.

A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation

This paper aims to develop a meshless approach based on the Point Interpolation Method (PIM) for numerical simulation of a space fractional diffusion equation. Two fully-discrete schemes for the one-dimensional space fractional diffusion equation are obtained by using the PIM and the strong-forms of the space diffusion equation. Numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach.

Analyzing the impact of learning inputs on near-to-far terrain traversability estimation

With the increasing need to adapt to new environments, data-driven approaches have been developed to estimate terrain traversability by learning the rover’s response on the terrain based on experience. Multiple learning inputs are often used to adequately describe the various aspects of terrain traversability. In a complex learning framework, it can be difficult to identify the relevance of each learning input to the resulting estimate. This paper addresses the suitability of each learning input by systematically analyzing the impact of each input on the estimate. Sensitivity Analysis (SA) methods provide a means to measure the contribution of each learning input to the estimate variability. Using a variance-based SA method, we characterize how the prediction changes as one or more of the input changes, and also quantify the prediction uncertainty as attributed from each of the inputs in the framework of dependent inputs. We propose an approach built on Analysis of Variance (ANOVA) decomposition to examine the prediction made in a near-to-far learning framework based on multi-task GP regression. We demonstrate the approach by analyzing the impact of driving speed and terrain geometry on the prediction of the rover’s attitude and chassis configuration in a Marsanalogue terrain using our prototype rover Mawson.

A semi-alternating direction method for a 2-D fractional FitzHugh–Nagumo monodomain model on an approximate irregular domain

A FitzHugh-Nagumo monodomain model has been used to describe the propagation of the electrical potential in heterogeneous cardiac tissue. In this paper, we consider a two-dimensional fractional FitzHugh-Nagumo monodomain model on an irregular domain. The model consists of a coupled Riesz space fractional nonlinear reaction-diffusion model and an ordinary differential equation, describing the ionic fluxes as a function of the membrane potential. Secondly, we use a decoupling technique and focus on solving the Riesz space fractional nonlinear reaction-diffusion model. A novel spatially second-order accurate semi-implicit alternating direction method (SIADM) for this model on an approximate irregular domain is proposed. Thirdly, stability and convergence of the SIADM are proved. Finally, some numerical examples are given to support our theoretical analysis and these numerical techniques are employed to simulate a two-dimensional fractional Fitzhugh-Nagumo model on both an approximate circular and an approximate irregular domain.

A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

Maximum principle and numerical method for the multi-term time–space Riesz–Caputo fractional differential equations

The maximum principle for the space and time–space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time–space Riesz–Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor–corrector method combining the L1 and L2 discrete schemes, we present a numerical method for the specified equation. Two examples are given to illustrate the obtained results.

Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

In this paper, we consider a two-sided space-fractional diffusion equation with variable coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new fractional finite volume method for the two-sided space-fractional diffusion equation and derive the implicit scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the implicit fractional finite volume method and conclude that the method is unconditionally stable and convergent. Finally, some numerical examples are given to show the effectiveness of the new numerical method, and the results are in excellent agreement with theoretical analysis.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

A method for optimal fit of patient-specific fracture fixation plates

Anatomically pre-contoured fracture fixation plates are a treatment option for bone fractures. A well-fitting plate can be used as a tool for anatomical reduction of the fractured bone. However, recent studies showed that some plates fit poorly for many patients due to considerable shape variations between bones of the same anatomical site. Therefore, the plates have to be manually fitted and deformed by surgeons to fit each patient optimally. The process is time-intensive and labor-intensive, and could lead to adverse clinical implications such as wound infection or plate failure. This paper proposes a new iterative method to simulate the patient-specific deformation of an optimally fitting plate for pre-operative planning purposes. We further demonstrate the validation of the method through a case study. The proposed method involves the integration of four commercially available software tools, Matlab, Rapidform2006, SolidWorks, and ANSYS, each performing specific tasks to obtain a plate shape that fits optimally for an individual tibia and is mechanically safe. A typical challenge when crossing multiple platforms is to ensure correct data transfer. We present an example of the implementation of the proposed method to demonstrate successful data transfer between the four platforms and the feasibility of the method.

An improved modal strain energy method for structural damage detection, 2D simulation

Structural damage detection using modal strain energy (MSE) is one of the most efficient and reliable structural health monitoring techniques. However, some of the existing MSE methods have been validated for special types of structures such as beams or steel truss bridges which demands improving the available methods. The purpose of this study is to improve an efficient modal strain energy method to detect and quantify the damage in complex structures at early stage of formation. In this paper, a modal strain energy method was mathematically developed and then numerically applied to a fixed-end beam and a three-story frame including single and multiple damage scenarios in absence and presence of up to five per cent noise. For each damage scenario, all mode shapes and natural frequencies of intact structures and the first five mode shapes of assumed damaged structures were obtained using STRAND7. The derived mode shapes of each intact and damaged structure at any damage scenario were then separately used in the improved formulation using MATLAB to detect the location and quantify the severity of damage as compared to those obtained from previous method. It was found that the improved method is more accurate, efficient and convergent than its predecessors. The outcomes of this study can be safely and inexpensively used for structural health monitoring to minimize the loss of lives and property by identifying the unforeseen structural damages.