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.

Pressure, oxygen tension and temperature in the periosteal callus during bone healing - An in vivo study in sheep

Adequate blood supply and sufficient mechanical stability are necessary for timely fracture healing. Damage to vessels impairs blood supply; hindering the transport of oxygen which is an essential metabolite for cells involved in repair. The degree of mechanical stability determines the mechanical conditions in the healing tissues. The mechanical conditions can influence tissue differentiation and may also inhibit revascularization. Knowledge of the actual conditions in a healing fracture in vivo is extremely limited. This study aimed to quantify the pressure, oxygen tension and temperature in the external callus during the early phase of bone healing. Six Merino-mix sheep underwent a tibial osteotomy. The tibia was stabilized with a standard mono-lateral external fixator. A multi-parameter catheter was placed adjacent to the osteotomy gap on the medial aspect of the tibia. Measurements of oxygen tension and temperature were performed for ten days post-op. Measurements of pressure were performed during gait on days three and seven. The ground reaction force and the interfragmentary movements were measured simultaneously. The maximum pressure during gait increased (p=0.028) from three (41.3 [29.2-44.1] mm Hg) to seven days (71.8 [61.8-84.8] mm Hg). During the same interval, there was no change (p=0.92) in the peak ground reaction force or in the interfragmentary movement (compression: p=0.59 and axial rotation: p=0.11). Oxygen tension in the haematoma (74.1 mm Hg [68.6-78.5]) was initially high post-op and decreased steadily over the first five days. The temperature increased over the first four days before reaching a plateau at approximately 38.5 degrees C on day four. This study is the first to report pressure, oxygen tension and temperature in the early callus tissues. The magnitude of pressure increased even though weight bearing and IFM remained unchanged. Oxygen tensions were initially high in the haematoma and fell gradually with a low oxygen environment first established after four to five days. This study illustrates that in bone healing the local environment for cells may not be considered constant with regard to oxygen tension, pressure and temperature.

High-pressure Raman spectroscopic and other structural studies of hydrotalcites containing intercalated dicarboxylic acid anions

The results of pressure-tuning Raman spectroscopic, X-ray powder diffraction and solid-state 13C-NMR studies of selected dicarboxylate anions intercalated in a Mg-Al layered double hydroxide (talcite) lattice are reported. The pressure dependences of the vibrational modes are linear for pressures up to 4.6 GPa indicating that no phase transitions occur. The interlayer spacings show that the oxalate, malonate and succinate dianions are oriented perpendicular to the layers, but the glutarate and adipate are tilted. The solid-state 13C-NMR spectra of these materials show full chemical shift anisotropy and, therefore, the anions are not mobile at room temperature.

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.

Alone against the crowd: Individual differences in referees' ability to cope under pressure

This paper contributes to the recent debate about the role of referees in the home advantage phenomenon. Specifically, it aims to provide a convincing answer to the newly posed question of the existence of individual differences among referees in terms of the home advantage (Boyko, Boyko, & Boyko, 2007; Johnston, 2008). Using multilevel modelling on a large and representative dataset we find that (1) the home advantage effect differs significantly among referees, and (2) this relationship is moderated by the size of the crowd. These new results suggest that a part of the home advantage is due to the effect of the crowd on the referees, and that some referees are more prone to be influenced by the crowd than others. This provides strong evidence to indicate that referees are a significant contributing factor to the home advantage. The implications of these findings are discussed both in terms of the relevant social psychological research, and with respect to the selection, assessment, and training of referees.