Computational strategies for surface fitting using thin plate spline finite element methods

Thin plate spline finite element methods are used to fit a surface to an irregularly scattered dataset [S. Roberts, M. Hegland, and I. Altas. Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions. SIAM, 1:208--234, 2003]. The computational bottleneck for this algorithm is the solution of large, ill-conditioned systems of linear equations at each step of a generalised cross validation algorithm. Preconditioning techniques are investigated to accelerate the convergence of the solution of these systems using Krylov subspace methods. The preconditioners under consideration are block diagonal, block triangular and constraint preconditioners [M. Benzi, G. H. Golub, and J. Liesen. Numerical solution of saddle point problems. Acta Numer., 14:1--137, 2005]. The effectiveness of each of these preconditioners is examined on a sample dataset taken from a known surface. From our numerical investigation, constraint preconditioners appear to provide improved convergence for this surface fitting problem compared to block preconditioners.

Biodiesel production from non-edible beauty leaf (Calophyllum Inophyllum) oil : process optimization using response surface methodology (RSM)

In recent years, the beauty leaf plant (Calophyllum Inophyllum) is being considered as a potential 2nd generation biodiesel source due to high seed oil content, high fruit production rate, simple cultivation and ability to grow in a wide range of climate conditions. However, however, due to the high free fatty acid (FFA) content in this oil, the potential of this biodiesel feedstock is still unrealized, and little research has been undertaken on it. In this study, transesterification of beauty leaf oil to produce biodiesel has been investigated. A two-step biodiesel conversion method consisting of acid catalysed pre-esterification and alkali catalysed transesterification has been utilized. The three main factors that drive the biodiesel (fatty acid methyl ester (FAME)) conversion from vegetable oil (triglycerides) were studied using response surface methodology (RSM) based on a Box-Behnken experimental design. The factors considered in this study were catalyst concentration, methanol to oil molar ratio and reaction temperature. Linear and full quadratic regression models were developed to predict FFA and FAME concentration and to optimize the reaction conditions. The significance of these factors and their interaction in both stages was determined using analysis of variance (ANOVA). The reaction conditions for the largest reduction in FFA concentration for acid catalysed pre-esterification was 30:1 methanol to oil molar ratio, 10% (w/w) sulfuric acid catalyst loading and 75 °C reaction temperature. In the alkali catalysed transesterification process 7.5:1 methanol to oil molar ratio, 1% (w/w) sodium methoxide catalyst loading and 55 °C reaction temperature were found to result in the highest FAME conversion. The good agreement between model outputs and experimental results demonstrated that this methodology may be useful for industrial process optimization for biodiesel production from beauty leaf oil and possibly other industrial processes as well.

Building macroscale models from microscale probabilistic models : a general probabilistic approach for nonlinear diffusion and multispecies phenomena

A discrete agent-based model on a periodic lattice of arbitrary dimension is considered. Agents move to nearest-neighbor sites by a motility mechanism accounting for general interactions, which may include volume exclusion. The partial differential equation describing the average occupancy of the agent population is derived systematically. A diffusion equation arises for all types of interactions and is nonlinear except for the simplest interactions. In addition, multiple species of interacting subpopulations give rise to an advection-diffusion equation for each subpopulation. This work extends and generalizes previous specific results, providing a construction method for determining the transport coefficients in terms of a single conditional transition probability, which depends on the occupancy of sites in an influence region. These coefficients characterize the diffusion of agents in a crowded environment in biological and physical processes.

Surface reconstruction of wheat leaf morphology from three-dimensional scanned data

Realistic virtual models of leaf surfaces are important for a number of applications in the plant sciences, such as modelling agrichemical spray droplet movement and spreading on the surface. In this context, the virtual surfaces are required to be sufficiently smooth to facilitate the use of the mathematical equations that govern the motion of the droplet. While an effective approach is to apply discrete smoothing D2-spline algorithms to reconstruct the leaf surfaces from three-dimensional scanned data, difficulties arise when dealing with wheat leaves that tend to twist and bend. To overcome this topological difficulty, we develop a parameterisation technique that rotates and translates the original data, allowing the surface to be fitted using the discrete smoothing D2-spline methods in the new parameter space. Our algorithm uses finite element methods to represent the surface as a linear combination of compactly supported shape functions. Numerical results confirm that the parameterisation, along with the use of discrete smoothing D2-spline techniques, produces realistic virtual representations of wheat leaves.

Enterprise resource planning or enterprise resource plotting? Technological, organisational and inter-organisational aspects of enterprise resource planning package adoption and diffusion

Those in organisations tend to adopt new technologies as a way to improve their functions, reduce cost and attain best practices. Thus, technology promoters (or vendors) work along those lines in order to convince adopters to invest in those technologies and develop their own organisations profit in return. The possible resultant ‘conflicts of interest’ makes the study of reasons behind IT diffusion and adoption an interesting subject. In this paper we look at IT diffusion and adoption in terms of technology (system features), organisational aspects (firm level characteristics) and inter-organisational aspects (market dynamics) in order to see who might be the real beneficiaries of technology adoption. We use ERP packages as an example of an innovation that has been widely diffused and adopted for the last 10 years. We believe that our findings can be useful to those adopting ERP packages as it gives them a wider view of the situation.

Controlling the surface roughness of epitaxial SiC on silicon

The surface of cubic silicon carbide (3C-SiC) hetero-epitaxial films grown on the (111) surface of silicon is a promising template for the subsequent epitaxial growth of III-V semiconductor layers and graphene. We investigate growth and post-growth approaches for controlling the surface roughness of epitaxial SiC to produce an optimal template. We first explore 3C-SiC growth on various degrees of offcut Si(111) substrates, although we observe that the SiC roughness tends to worsen as the degree of offcut increases. Hence we focus on post-growth approaches available on full wafers, comparing chemical mechanical polishing (CMP) and a novel plasma smoothening process. The CMP leads to a dramatic improvement, bringing the SiC surface roughness down to sub-nanometer level, though removing about 200 nm of the SiC layer. On the other hand, our proposed HCl plasma process appears very effective in smoothening selectively the sharpest surface topography, leading up to 30% improvement in SiC roughness with only about 50 nm thickness loss. We propose a simple physical model explaining the action of the plasma smoothening.