A RBF meshless approach for modeling a fractal mobile/immobile transport model

A fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBFs) to discretize the space variable. In contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example which is presented to describe a fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating fractional differential equations, and it has good potential in the development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

An application of fractal image-set coding in facial recognition

Faces are complex patterns that often differ in only subtle ways. Face recognition algorithms have difficulty in coping with differences in lighting, cameras, pose, expression, etc. We propose a novel approach for facial recognition based on a new feature extraction method called fractal image-set encoding. This feature extraction method is a specialized fractal image coding technique that makes fractal codes more suitable for object and face recognition. A fractal code of a gray-scale image can be divided in two parts – geometrical parameters and luminance parameters. We show that fractal codes for an image are not unique and that we can change the set of fractal parameters without significant change in the quality of the reconstructed image. Fractal image-set coding keeps geometrical parameters the same for all images in the database. Differences between images are captured in the non-geometrical or luminance parameters – which are faster to compute. Results on a subset of the XM2VTS database are presented.

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

Fractal dimension of dried foods : a correlation between microstructure and porosity

The quality of dried food is affected by a number of factors including quality of raw material, initial microstructure, and drying conditions. The structure of the food materials goes through deformations due to the simultaneous effect of heat and mass transfer during the drying process. Shrinkage and changes in porosity, microstructure and appearance are some of the most remarkable features that directly influence overall product quality. Porosity and microstructure are the important material properties in relation to the quality attributes of dried foods. Fractal dimension (FD) is a quantitative approach of measuring surface, pore characteristics, and microstructural changes [1]. However, in the field of fractal analysis, there is a lack of research in developing relationship between porosity, shrinkage and microstructure of different solid food materials in different drying process and conditions [2-4]. Establishing a correlation between microstructure and porosity through fractal dimension during convective drying is the main objective of this work.

Task profiling : A task-Based approach to measuring the integration of ICT in the classroom

The measurement of ICT (information and communication technology) integration is emerging as an area of research interest with such systems as Education Queensland including it in their recently released list of research priorities. Studies to trial differing integration measurement instruments have taken place within Australia in the last few years, particularly Western Australia (Trinidad, Clarkson, & Newhouse, 2004; Trinidad, Newhouse & Clarkson, 2005), Tasmania (Fitzallen 2005) and Queensland (Finger, Proctor, & Watson, 2005). This paper will add to these investigations by describing an alternate and original methodological approach which was trialled in a small-scale pilot study conducted jointly by Queensland Catholic Education Commission (QCEC) and the Centre of Learning Innovation, Queensland University of Technology (QUT) in late 2005. The methodology described is based on tasks which, through a process of profiling, can be seen to be artefacts which embody the internal and external factors enabling and constraining ICT integration.