An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

In this paper, an enriched radial point interpolation method (e-RPIM) is developed the for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newlydeveloped e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.

New stress and velocity fields for highly frictional granular materials

The idealised theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit that the angle of internal friction approaches $\pi/2$, and accordingly these materials may be referred to as being `highly frictional'. In this limit, the stress field for both two-dimensional and axially symmetric flows may be formulated in terms of a single nonlinear second order partial differential equation for the stress angle. To obtain an accompanying velocity field, a flow rule must be employed. Assuming the non-dilatant double-shearing flow rule, a further partial differential equation may be derived in each case, this time for the streamfunction. Using Lie symmetry methods, a complete set of group-invariant solutions is derived for both systems, and through this process new exact solutions are constructed. Only a limited number of exact solutions for gravity driven granular flows are known, so these results are potentially important in many practical applications. The problem of mass flow through a two-dimensional wedge hopper is examined as an illustration.

An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

In this paper, an enriched radial point interpolation method (e-RPIM) is developed the for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newlydeveloped e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.

Note on similarity solutions for viscous flow over an impermeable and non-linearly (quadratic) stretching sheet

Similarity solutions for flow over an impermeable, non-linearly (quadratic) stretching sheet were studied recently by Raptis and Perdikis (Int. J. Non-linear Mech. 41 (2006) 527–529) using a stream function of the form ψ=αxf(η)+βx2g(η). A fundamental error in their problem formulation is pointed out. On correction, it is shown that similarity solutions do not exist for this choice of ψ

A hybrid approach for resolving the electromagnetic fields inside a waveguide loaded with a lossy medium

In this work a novel hybrid approach is presented that uses a combination of both time domain and frequency domain solution strategies to predict the power distribution within a lossy medium loaded within a waveguide. The problem of determining the electromagnetic fields evolving within the waveguide and the lossy medium is decoupled into two components, one for computing the fields in the waveguide including a coarse representation of the medium (the exterior problem) and one for a detailed resolution of the lossy medium (the interior problem). A previously documented cell-centred Maxwell’s equations numerical solver can be used to resolve the exterior problem accurately in the time domain. Thereafter the discrete Fourier transform can be applied to the computed field data around the interface of the medium to estimate the frequency domain boundary condition in-formation that is needed for closure of the interior problem. Since only the electric fields are required to compute the power distribution generated within the lossy medium, the interior problem can be resolved efficiently using the Helmholtz equation. A consistent cell-centred finite-volume method is then used to discretise this equation on a fine mesh and the underlying large, sparse, complex matrix system is solved for the required electric field using the iterative Krylov subspace based GMRES iterative solver. It will be shown that the hybrid solution methodology works well when a single frequency is considered in the evaluation of the Helmholtz equation in a single mode waveguide. A restriction of the scheme is that the material needs to be sufficiently lossy, so that any penetrating waves in the material are absorbed.

Exponentiated gradient algorithms for conditional random fields and max-margin Markov Networks

Log-linear and maximum-margin models are two commonly-used methods in supervised machine learning, and are frequently used in structured prediction problems. Efficient learning of parameters in these models is therefore an important problem, and becomes a key factor when learning from very large data sets. This paper describes exponentiated gradient (EG) algorithms for training such models, where EG updates are applied to the convex dual of either the log-linear or max-margin objective function; the dual in both the log-linear and max-margin cases corresponds to minimizing a convex function with simplex constraints. We study both batch and online variants of the algorithm, and provide rates of convergence for both cases. In the max-margin case, O(1/ε) EG updates are required to reach a given accuracy ε in the dual; in contrast, for log-linear models only O(log(1/ε)) updates are required. For both the max-margin and log-linear cases, our bounds suggest that the online EG algorithm requires a factor of n less computation to reach a desired accuracy than the batch EG algorithm, where n is the number of training examples. Our experiments confirm that the online algorithms are much faster than the batch algorithms in practice. We describe how the EG updates factor in a convenient way for structured prediction problems, allowing the algorithms to be efficiently applied to problems such as sequence learning or natural language parsing. We perform extensive evaluation of the algorithms, comparing them to L-BFGS and stochastic gradient descent for log-linear models, and to SVM-Struct for max-margin models. The algorithms are applied to a multi-class problem as well as to a more complex large-scale parsing task. In all these settings, the EG algorithms presented here outperform the other methods.

Exponentiated gradient algorithms for large-margin structured classification

We consider the problem of structured classification, where the task is to predict a label y from an input x, and y has meaningful internal structure. Our framework includes supervised training of Markov random fields and weighted context-free grammars as special cases. We describe an algorithm that solves the large-margin optimization problem defined in [12], using an exponential-family (Gibbs distribution) representation of structured objects. The algorithm is efficient—even in cases where the number of labels y is exponential in size—provided that certain expectations under Gibbs distributions can be calculated efficiently. The method for structured labels relies on a more general result, specifically the application of exponentiated gradient updates [7, 8] to quadratic programs.

Propagation of low power low divergence Gaussian fields in unbiased self-defocusing photorefractive media and their interactions

Many optical networks are limited in speed and processing capability due to the necessity for the optical signal to be converted to an electrical signal and back again. In addition, electronically manipulated interconnects in an otherwise optical network lead to overly complicated systems. Optical spatial solitons are optical beams that propagate without spatial divergence. They are capable of phase dependent interactions, and have therefore been extensively researched as suitable all optical interconnects for over 20 years. However, they require additional external components, initially high voltage power sources were required, several years later, high power background illumination had replaced the high voltage. However, these additional components have always remained as the greatest hurdle in realising the applications of the interactions of spatial optical solitons as all optical interconnects. Recently however, self-focusing was observed in an otherwise self-defocusing photorefractive crystal. This observation raises the possibility of the formation of soliton-like fields in unbiased self-defocusing media, without the need for an applied electrical field or background illumination. This thesis will present an examination of the possibility of the formation of soliton-like low divergence fields in unbiased self-defocusing photorefractive media. The optimal incident beam and photorefractive media parameters for the formation of these fields will be presented, together with an analytical and numerical study of the effect of these parameters. In addition, preliminary examination of the interactions of two of these fields will be presented. In order to complete an analytical examination of the field propagating through the photorefractive medium, the spatial profile of the beam after propagation through the medium was determined. For a low power solution, it was found that an incident Gaussian field maintains its Gaussian profile as it propagates. This allowed the beam at all times to be described by an individual complex beam parameter, while also allowing simple analytical solutions to the appropriate wave equation. An analytical model was developed to describe the effect of the photorefractive medium on the Gaussian beam. Using this model, expressions for the required intensity dependent change in both the real and imaginary components of the refractive index were found. Numerical investigation showed that under certain conditions, a low powered Gaussian field could propagate in self-defocusing photorefractive media with divergence of approximately 0.1 % per metre. An investigation into the parameters of a Ce:BaTiO3 crystal showed that the intensity dependent absorption is wavelength dependent, and can in fact transition to intensity dependent transparency. Thus, with careful wavelength selection, the required intensity dependent change in both the real and imaginary components of the refractive index for the formation of a low divergence Gaussian field are physically realisable. A theoretical model incorporating the dependence of the change in real and imaginary components of the refractive index on propagation distance was developed. Analytical and numerical results from this model are congruent with the results from the previous model, showing low divergence fields with divergence less than 0.003 % over the propagation length of the photorefractive medium. In addition, this approach also confirmed the previously mentioned self-focusing effect of the self-defocusing media, and provided an analogy to a negative index GRIN lens with an intensity dependent focal length. Experimental results supported the findings of the numerical analysis. Two low divergence fields were found to possess the ability to interact in a Ce:BaTiO3 crystal in a soliton-like fashion. The strength of these interactions was found to be dependent on the degree of divergence of the individual beams. This research found that low-divergence fields are possible in unbiased self-defocusing photorefractive media, and that soliton-like interactions between two of these fields are possible. However, in order for these types of fields to be used in future all optical interconnects, the manipulation of these interactions, together with the ability for these fields to guide a second beam at a different wavelength, must be investigated.

Face recognition across pose on video using eigen light-fields

We propose an approach to employ eigen light-fields for face recognition across pose on video. Faces of a subject are collected from video frames and combined based on the pose to obtain a set of probe light-fields. These probe data are then projected to the principal subspace of the eigen light-fields within which the classification takes place. We modify the original light-field projection and found that it is more robust in the proposed system. Evaluation on VidTIMIT dataset has demonstrated that the eigen light-fields method is able to take advantage of multiple observations contained in the video.

Chaos or complex systems? Identifying factors influencing the success of international and NESB graduate research students in Engineering and Information Technology Fields

The paper explores the results an on-going research project to identify factors influencing the success of international and non-English speaking background (NESB) gradúate students in the fields of Engineering and IT at three Australian universities: the Queensland University of Technology (QUT), the University of Western Australia (UWA), and Curtin University (CU). While the larger study explores the influence of factors from both sides of the supervision equation (e.g., students and supervisors), this paper focusses primarily on the results of an online survey involving 227 international and/or NESB graduate students in the areas of Engineering and IT at the three universities. The study reveals cross-cultural differences in perceptions of student and supervisor roles, as well as differences in the understanding of the requirements of graduate study within the Australian Higher Education context. We argue that in order to assist international and NESB research students to overcome such culturally embedded challenges, it is important to develop a model which recognizes the complex interactions of factors from both sides of the supervision relationship, in order to understand this cohort‟s unique pedagogical needs and develop intercultural sensitivity within postgraduate research supervision.

A novel quadratic Edge-based Smoothed Conforming Point Interpolation Method (ES-CPIM) for elasticity problems

his paper formulates an edge-based smoothed conforming point interpolation method (ES-CPIM) for solid mechanics using the triangular background cells. In the ES-CPIM, a technique for obtaining conforming PIM shape functions (CPIM) is used to create a continuous and piecewise quadratic displacement field over the whole problem domain. The smoothed strain field is then obtained through smoothing operation over each smoothing domain associated with edges of the triangular background cells. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. Numerical studies have demonstrated that the ES-CPIM possesses the following good properties: (1) ES-CPIM creates conforming quadratic PIM shape functions, and can always pass the standard patch test; (2) ES-CPIM produces a quadratic displacement field without introducing any additional degrees of freedom; (3) The results of ES-CPIM are generally of very high accuracy.