Finite volume methods for simulating anomalous transport

In this thesis a new approach for solving a certain class of anomalous diffusion equations was developed. The theory and algorithms arising from this work will pave the way for more efficient and more accurate solutions of these equations, with applications to science, health and industry. The method of finite volumes was applied to discretise the spatial derivatives, and this was shown to outperform existing methods in several key respects. The stability and convergence of the new method were rigorously established.

Assessment and application of clustering techniques to atmospheric particle number size distribution for the purpose of source apportionment

Long-term measurements of particle number size distribution (PNSD) produce a very large number of observations and their analysis requires an efficient approach in order to produce results in the least possible time and with maximum accuracy. Clustering techniques are a family of sophisticated methods which have been recently employed to analyse PNSD data, however, very little information is available comparing the performance of different clustering techniques on PNSD data. This study aims to apply several clustering techniques (i.e. K-means, PAM, CLARA and SOM) to PNSD data, in order to identify and apply the optimum technique to PNSD data measured at 25 sites across Brisbane, Australia. A new method, based on the Generalised Additive Model (GAM) with a basis of penalised B-splines, was proposed to parameterise the PNSD data and the temporal weight of each cluster was also estimated using the GAM. In addition, each cluster was associated with its possible source based on the results of this parameterisation, together with the characteristics of each cluster. The performances of four clustering techniques were compared using the Dunn index and Silhouette width validation values and the K-means technique was found to have the highest performance, with five clusters being the optimum. Therefore, five clusters were found within the data using the K-means technique. The diurnal occurrence of each cluster was used together with other air quality parameters, temporal trends and the physical properties of each cluster, in order to attribute each cluster to its source and origin. The five clusters were attributed to three major sources and origins, including regional background particles, photochemically induced nucleated particles and vehicle generated particles. Overall, clustering was found to be an effective technique for attributing each particle size spectra to its source and the GAM was suitable to parameterise the PNSD data. These two techniques can help researchers immensely in analysing PNSD data for characterisation and source apportionment purposes.

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.

Novel non-linear elastic structural analysis with generalised transverse element loads using a refined finite element

In the finite element modelling of structural frames, external loads such as wind loads, dead loads and imposed loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. In addition, it is especially important for an element subjected to the first- and second-order elastic behaviour, to which the steel structure is critically prone to; in particular the thin-walled steel structures, when the stocky element section may be generally critical to the inelastic behaviour. In this sense, the accurate first- and second-order elastic displacement solutions of element load effect along an element is vitally crucial, but cannot be simulated using neither numerical nodal nor consistent load methods alone, as long as no equilibrium condition is enforced in the finite element formulation, which can inevitably impair the structural safety of the steel structure particularly. It can be therefore regarded as a unique element load method to account for the element load nonlinearly. If accurate displacement solution is targeted for simulating the first- and second-order elastic behaviour on an element on the basis of sophisticated non-linear element stiffness formulation, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, the present paper proposes a numerical technique to include the transverse element loading in the non-linear stiffness formulation without numerous prescribed stiffness matrices, and which is able to predict structural responses involving the effect of first-order element loads as well as the second-order coupling effect between the transverse load and axial force in the element. This paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the non-linear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the non-linear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at mid-span in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at mid-span. Therefore, it can be foreseen that the load-deflection behaviour may not be as accurate as those at mid-span, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal response (system analysis) to both nodal and element response (sophisticated element formulation). For the conventional finite element method, such as the cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within an element, and as a result, it hinders the engineering applications. The results of the paper are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple frames.

Numerical investigation of case hardening of plant tissue during dying and its influence on the cellular level shrinkage

Dried plant food materials are one of the major contributors to the global food industry. Widening the fundamental understanding on different mechanisms of food material alterations during drying assists the development of novel dried food products and processing techniques. In this regard, case hardening is an important phenomenon, commonly observed during the drying processes of plant food materials, which significantly influences the product quality and process performance. In this work, a recent meshfree-based numerical model of the authors is further improved and used to simulate the influence of case hardening on shrinkage characteristics of plant tissues during drying. In order to model fluid and wall mechanisms in each cell, Smoothed Particle Hydrodynamics (SPH) and the Discrete Element Method (DEM) are used. The model is fundamentally more capable of simulating large deformation of multiphase materials, when compared with conventional grid-based modelling techniques such as Finite Element Methods (FEM) or Finite Difference Methods (FDM). Case hardening is implemented by maintaining distinct moisture levels in the different cell layers of a given tissue. In order to compare and investigate different factors influencing tissue deformations under case hardening, four different plant tissue varieties (apple, potato, carrot and grape) are studied. The simulation results indicate that the inner cells of any given tissue undergo limited shrinkage and cell wall wrinkling compared to the case hardened outer cell layers of the tissues. When comparing unique deformation characteristics of the different tissues, irrespective of the normalised moisture content, the cell size, cell fluid turgor pressure and cell wall characteristics influence the tissue response to case hardening.

Numerical simulation of railway track supporting system using finite-infinite and thin layer elements under impulsive loads

The present study deals with two dimensional, numerical simulation of railway track supporting system subjected to dynamic excitation force. Under plane strain condition, the coupled finite-infinite elements to represent the near and far field stress distribution and thin layer interface element was employed to model the interfacial behavior between sleepers and ballast. To account for the relative debonding, slipping and crushing that could take place in the contact area between the sleepers and ballast, modified Mohr-Coulomb criterion was adopted. Furthermore an attempt has been made to consider the elasto-plastic material non-linearity of the railway track supporting media by employing different constitutive models to represent steel, concrete and supporting materials. Based on the proposed physical and constitutive modeling a code has been developed for dynamic loads. The applicability of the developed F.E code has been demonstrated by analyzing a real railway supporting structure.

Specificity and context in post-exercise recovery: It is not a one-size-fits-all approach

The concept of specificity of exercise prescription and training is a longstanding and widely accepted foundation of the exercise sciences. Simply, the principle holds that training adaptations are achieved relative to the stimulus applied. That is, the manipulation of training variables (e.g. intensity or loading, mode, volume and frequency) directly influences the acute training stimulus, and so the long-term adaptive response (Young et al., 2001; Bird et al., 2005). Translating this concept to practice then recommends that exercise be prescribed specific to the desired outcomes, and the more closely this is achieved, the greater the performance gain is likely to be. However, the cardiovascular and metabolic adaptations traditionally associated with long, slow distance training types, similarly achieved using high-intensity training methods (for a review see Gibala et al., 2012), highlights understanding of underlying physiology as paramount for effective training program design. Various other factors including illness, sleep and psychology also impact on the training stimulus (Halson, 2014) and must be managed collectively with appropriate post-exercise recovery to continue performance improvements and reduce overtraining and injury risks (Kenttä and Hassmén, 1998).

Wake angle for surface gravity waves on a finite depth fluid

Linear water wave theory suggests that wave patterns caused by a steadily moving disturbance are contained within a wedge whose half-angle depends on the depth-based Froude number $F_H$. For the problem of flow past an axisymmetric pressure distribution in a finite-depth channel, we report on the apparent angle of the wake, which is the angle of maximum peaks. For moderately deep channels, the dependence of the apparent wake angle on the Froude number is very different to the wedge angle, and varies smoothly as $F_H$ passes through the critical value $F_H=1$. For shallow water, the two angles tend to follow each other more closely, which leads to very large apparent wake angles for certain regimes.

A laboratory assessment of the choice of vessel size under individual transferable quota regimes

This paper examines the effect of individual transferable quota regimes on technology choice, such as choice of vessel size, by using the laboratory experiment method. We find that even if vessel sizes change over time, the quota price can converge to the fundamental value conditioned on the vessels chosen. We also find that subjects choose their vessel type to maximise their profits based on the quota trading prices in the previous period. This result implies that the efficiency of quota markets in the beginning period is important because any inefficiency in quota markets may affect vessel sizes in ensuing periods. Moreover, we find that the initial allocations may significantly influence vessel sizes through two channels: first, a higher initial allocation to a subject increases the likelihood that the subject invests in a large-sized vessel; second, the quota price may be higher and more unstable under unequal allocation than under equal allocation; thus, whether the allocation is equal influences subjects' choice of vessel type. © 2014 Australian Agricultural and Resource Economics Society Inc.

Size-resolved particle distribution and gaseous concentrations by real-world road tunnel measurement

Measurements of aerosol particle number size distributions (15-700 nm), CO and NOx were performed in a bus tunnel, Australia. Daily mean particle size distributions of mixed diesel/CNG (Compressed Natural Gas) buses traffic flow were determined in 4 consecutive measurement days. EFs (Emission Factors) of Particle size distribution of diesel buses and CNG buses were obtained by MLR (Multiple Linear Regression) methods, particle distributions of diesel buses and CNG buses were observed as single accumulation mode and nuclei-mode separately. Particle size distributions of mixed traffic flow were decomposed by two log-normal fitting curves for each 30 minutes interval mean scans, all the mix fleet PSD emission can be well fitted by the summation of two log-normal distribution curves, and these were composed of nuclei mode curve and accumulation curve, which were affirmed as the CNG buses and diesel buses PN emission curves respectively. Finally, particle size distributions of diesel buses and CNG buses were quantified by statistical whisker-box charts. For log-normal particle size distribution of diesel buses, accumulation mode diameters were 74.5～87.5nm, geometric standard deviations were 1.89～1.98. As to log-normal particle size distribution of CNG buses, nuclei-mode diameters were 21～24 nm, geometric standard deviations were 1.27～1.31.

Field size consistency of nominally matched linacs

Given that there is increasing recognition of the effect that submillimetre changes in collimator position can have on radiotherapy beam dosimetry, this study aimed to evaluate the potential variability in small field collimation that may exist between otherwise matched linacs. Field sizes and field output factors were measured using radiochromic film and an electron diode, for jaw- and MLC-collimated fields produced by eight dosimetrically matched Varian iX linacs (Varian Medical Systems, Palo Alto, USA). This study used nominal sizes from 0.6×0.6 to 10×10 cm215 , for jaw-collimated fields,and from 1×1 to 10×10 cm216 , for MLC-collimated fields, delivered from a zero (head up, beam directed vertically downward) gantry angle. Differences between the field sizes measured for the eight linacs exceeded the uncertainty of the film measurements and the repositioning uncertainty of the jaws and MLCs on one linac. The dimensions of fields defined by MLC leaves were more consistent between linacs, while also differing more from their nominal values than fields defined by orthogonal jaws. The field output factors measured for the different linacs generally increased with increasing measured field size for the nominal 0.6×0.6 and 1×1 cm2 fields, and became consistent between linacs for nominal field sizes of 2×2 cm2 25 and larger. The inclusion in radiotherapy treatment planning system beam data of small field output factors acquired in fields collimated by jaws (rather than the more-reproducible MLCs), associated with either the nominal or the measured field sizes, should be viewed with caution. The size and reproducibility of the fields (especially the small fields) used to acquire treatment planning data should be investigated thoroughly as part of the linac or planning system commissioning process. Further investigation of these issues, using different linac models, collimation systems and beam orientations, is recommended.

Effect of carrier size on the dispersion of salmeterol xinafoate from interactive mixtures

The objective of this study was to determine the influence of lactose carrier size on drug dispersion of salmeterol xinafoate (SX) from interactive mixtures. SX dispersion was measured by using the fine particle fractions determined by a twin stage impinger attached to a Rotahaler1. The particle size of the lactose carrier in the SX interactive mixtures was varied using a range of commercial inhalation-grade lactoses. In addition, differing size fractions of individual lactose samples were achieved by dry sieving. The dispersion ofSXappeared to increase as the particle size of the lactose carrier decreased for the mixtures prepared from different particle size commercial samples of lactose and from different sieve fractions of the same lactose. Fine particles of lactose (<5 mm) associated with the lactose carrier were removed from the carrier surface by a wet decantation process to produce lactose samples with low but similar concentrations of fine lactose particles. The fine particle fractions of SX in mixtures prepared with the decanted lactose decreased significantly (analysis of variance, p<0.001) and the degree of dispersion became independent of the volume mean diameter of the carriers (analysis of variance, p<0.05). The dispersion behavior is therefore associated with the presence of fine adhered particles associated with the carriers and the inherent size of the carrier itself has little influence on dispersion.

Automatic image scaling for place recognition in changing environments

Robustness to variations in environmental conditions and camera viewpoint is essential for long-term place recognition, navigation and SLAM. Existing systems typically solve either of these problems, but invariance to both remains a challenge. This paper presents a training-free approach to lateral viewpoint- and condition-invariant, vision-based place recognition. Our successive frame patch-tracking technique infers average scene depth along traverses and automatically rescales views of the same place at different depths to increase their similarity. We combine our system with the condition-invariant SMART algorithm and demonstrate place recognition between day and night, across entire 4-lane-plus-median-strip roads, where current algorithms fail.

Two-dimensional bow and stern flows in a finite-depth fluid with constant vorticity

This thesis is concerned with two-dimensional free surface flows past semi-infinite surface-piercing bodies in a fluid of finite-depth. Throughout the study, it is assumed that the fluid in question is incompressible, and that the effects of viscosity and surface tension are negligible. The problems considered are physically important, since they can be used to model the flow of water near the bow or stern of a wide, blunt ship. Alternatively, the solutions can be interpreted as describing the flow into, or out of, a horizontal slot. In the past, all research conducted on this topic has been dedicated to the situation where the flow is irrotational. The results from such studies are extended here, by allowing the fluid to have constant vorticity throughout the flow domain. In addition, new results for irrotational flow are also presented. When studying the flow of a fluid past a surface-piercing body, it is important to stipulate in advance the nature of the free surface as it intersects the body. Three different possibilities are considered in this thesis. In the first of these possibilities, it is assumed that the free surface rises up and meets the body at a stagnation point. For this configuration, the nonlinear problem is solved numerically with the use of a boundary integral method in the physical plane. Here the semi-infinite body is assumed to be rectangular in shape, with a rounded corner. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterised by a train of waves upstream. In the limit that the height of the body above the horizontal bottom vanishes, the flow approaches that due to a submerged line sink in a $90^\circ$ corner. This limiting problem is also examined as a special case. The second configuration considered in this thesis involves the free surface attaching smoothly to the front face of the rectangular shaped body. For this configuration, nonlinear solutions are computed using a similar numerical scheme to that used in the stagnant attachment case. It is found that these solution exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a corner is also considered. Finally, the flow of a fluid emerging from beneath a semi-infinite flat plate is examined. Here the free surface is assumed to detach from the trailing edge of the plate horizontally. A linear problem is formulated under the assumption that the elevation of the plate is close to the undisturbed free surface level. This problem is solved exactly using the Wiener-Hopf technique, and subcritical solutions are found which are characterised by a train of sinusoidal waves in the far field. The nonlinear problem is also considered. Exact relations between certain parameters for supercritical flow are derived using conservation of mass and momentum arguments, and these are confirmed numerically. Nonlinear subcritical solutions are computed, and the results are compared to those predicted by the linear theory.