A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if an s-stage SRK contains Stratonovich integrals up to order p then the strong order of the SRK cannot exceed min{(p + 1)/2, (s - 1)/2), p greater than or equal to 2, s greater than or equal to 3 or 1 if p = 1.

Higher-order spectral analysis of nonlinear ocean surface gravity waves

Higher-order spectral analysis is used to detect the presence of secondary and tertiary forced waves associated with the nonlinearity of energetic swell observed in 8- and 13-m water depths. Higher-order spectral analysis techniques are first described and then applied to the field data, followed by a summary of the results.

Accurate series solutions for gravity-driven Stokes waves

In the past, high order series expansion techniques have been used to study the nonlinear equations that govern the form of periodic Stokes waves moving steadily on the surface of an inviscid fluid. In the present study, two such series solutions are recomputed using exact arithmetic, eliminating any loss of accuracy due to accumulation of round-off error, allowing a much greater number of terms to be found with confidence. It is shown that higher order behaviour of series generated by the solution casts doubt over arguments that rely on estimating the series’ radius of convergence. Further, the exact nature of the series is used to shed light on the unusual nature of convergence of higher order Pade approximants near the highest wave. Finally, it is concluded that, provided exact values are used in the series, these Pade approximants prove very effective in successfully predicting three turning points in both the dispersion relation and the total energy.

The flammability of metallic materials in normal and reduced gravity

Metallic materials exposed to oxygen-enriched atmospheres – as commonly used in the medical, aerospace, aviation and numerous chemical processing industries – represent a significant fire hazard which must be addressed during design, maintenance and operation. Hence, accurate knowledge of metallic materials flammability is required. Reduced gravity (i.e. space-based) operations present additional unique concerns, where the absence of gravity must also be taken into account. The flammability of metallic materials has historically been quantified using three standardised test methods developed by NASA, ASTM and ISO. These tests typically involve the forceful (promoted) ignition of a test sample (typically a 3.2 mm diameter cylindrical rod) in pressurised oxygen. A test sample is defined as flammable when it undergoes burning that is independent of the ignition process utilised. In the standardised tests, this is indicated by the propagation of burning further than a defined amount, or „burn criterion.. The burn criterion in use at the onset of this project was arbitrarily selected, and did not accurately reflect the length a sample must burn in order to be burning independent of the ignition event and, in some cases, required complete consumption of the test sample for a metallic material to be considered flammable. It has been demonstrated that a) a metallic material.s propensity to support burning is altered by any increase in test sample temperature greater than ~250-300 oC and b) promoted ignition causes an increase in temperature of the test sample in the region closest to the igniter, a region referred to as the Heat Affected Zone (HAZ). If a test sample continues to burn past the HAZ (where the HAZ is defined as the region of the test sample above the igniter that undergoes an increase in temperature of greater than or equal to 250 oC by the end of the ignition event), it is burning independent of the igniter, and should be considered flammable. The extent of the HAZ, therefore, can be used to justify the selection of the burn criterion. A two dimensional mathematical model was developed in order to predict the extent of the HAZ created in a standard test sample by a typical igniter. The model was validated against previous theoretical and experimental work performed in collaboration with NASA, and then used to predict the extent of the HAZ for different metallic materials in several configurations. The extent of HAZ predicted varied significantly, ranging from ~2-27 mm depending on the test sample thermal properties and test conditions (i.e. pressure). The magnitude of the HAZ was found to increase with increasing thermal diffusivity, and decreasing pressure (due to slower ignition times). Based upon the findings of this work, a new burn criterion requiring 30 mm of the test sample to be consumed (from the top of the ignition promoter) was recommended and validated. This new burn criterion was subsequently included in the latest revision of the ASTM G124 and NASA 6001B international test standards that are used to evaluate metallic material flammability in oxygen. These revisions also have the added benefit of enabling the conduct of reduced gravity metallic material flammability testing in strict accordance with the ASTM G124 standard, allowing measurement and comparison of the relative flammability (i.e. Lowest Burn Pressure (LBP), Highest No-Burn Pressure (HNBP) and average Regression Rate of the Melting Interface(RRMI)) of metallic materials in normal and reduced gravity, as well as determination of the applicability of normal gravity test results to reduced gravity use environments. This is important, as currently most space-based applications will typically use normal gravity information in order to qualify systems and/or components for reduced gravity use. This is shown here to be non-conservative for metallic materials which are more flammable in reduced gravity. The flammability of two metallic materials, Inconel® 718 and 316 stainless steel (both commonly used to manufacture components for oxygen service in both terrestrial and space-based systems) was evaluated in normal and reduced gravity using the new ASTM G124-10 test standard. This allowed direct comparison of the flammability of the two metallic materials in normal gravity and reduced gravity respectively. The results of this work clearly show, for the first time, that metallic materials are more flammable in reduced gravity than in normal gravity when testing is conducted as described in the ASTM G124-10 test standard. This was shown to be the case in terms of both higher regression rates (i.e. faster consumption of the test sample – fuel), and burning at lower pressures in reduced gravity. Specifically, it was found that the LBP for 3.2 mm diameter Inconel® 718 and 316 stainless steel test samples decreased by 50% from 3.45 MPa (500 psia) in normal gravity to 1.72 MPa (250 psia) in reduced gravity for the Inconel® 718, and 25% from 3.45 MPa (500 psia) in normal gravity to 2.76 MPa (400 psia) in reduced gravity for the 316 stainless steel. The average RRMI increased by factors of 2.2 (27.2 mm/s in 2.24 MPa (325 psia) oxygen in reduced gravity compared to 12.8 mm/s in 4.48 MPa (650 psia) oxygen in normal gravity) for the Inconel® 718 and 1.6 (15.0 mm/s in 2.76 MPa (400 psia) oxygen in reduced gravity compared to 9.5 mm/s in 5.17 MPa (750 psia) oxygen in normal gravity) for the 316 stainless steel. Reasons for the increased flammability of metallic materials in reduced gravity compared to normal gravity are discussed, based upon the observations made during reduced gravity testing and previous work. Finally, the implications (for fire safety and engineering applications) of these results are presented and discussed, in particular, examining methods for mitigating the risk of a fire in reduced gravity.

Flow regime transition criteria for two-phase flow at reduced gravity conditions

Flow regime transition criteria are of practical importance for two-phase flow analyses at reduced gravity conditions. Here, flow regime transition criteria which take the friction pressure loss effect into account were studied in detail. Criteria at reduced gravity conditions were developed by extending an existing model with various experimental datasets taken at microgravity conditions showed satisfactory agreement. Sample computations of the model were performed at various gravity conditions, such as 0.196, 1.62, 3.71, and 9.81 m/s2 corresponding to micro-gravity and lunar, Martian and Earth surface gravity, respectively. It was found that the effect of gravity on bubbly-slug and slug-annular (churn) transitions in a two-phase flow system was more pronounced at low liquid flow conditions, whereas the gravity effect could be ignored at high mixture volumetric flux conditions. While for the annular flow transitions due to flow reversal and onset of dropset entrainment, higher superficial gas velocity was obtained at higher gravity level.

Trends in policies, programs and practices in the Australasian First Year Experience literature 2000-2010. The First Year in Higher Education Research Series on Evidence-based Practice. Number 1

This publication is the first in a series of scholarly reports on research-based practice related to the First Year Experience in Higher Education. This report synthesises evidence about practice-based initiatives and pragmatic approaches in Aotearoa (New Zealand) and Australia that aim to enhance the experience of commencing students in the higher education sector. Trends in policies, programs and practices ... examines the first year experience literature from 2000-2010. It acknowledges the uniqueness of the Australasian socio-political context and its influence on the interests and output of researchers. The review surveyed almost 400 empirical reports and conceptual discussions produced over the decade that dealt with the stakeholders, institutions and the higher education sector in Australasia. The literature is examined through two theoretical constructs or “lenses”: first, a set of first year curriculum design principles and second, the generational approach to describing the maturation of initiatives. These outcomes and suggested directions for further research provide the challenges and the opportunities for FYE adherents, both scholars and practitioners, to grapple with in the next decade.

Synthesis and characterisation of titanium sol-gels in varied gravity environments

Sol-gel synthesis in varied gravity is only a relatively new topic in the literature and further investigation is required to explore its full potential as a method to synthesise novel materials. Although trialled for systems such as silica, the specific application of varied gravity synthesis to other sol-gel systems such as titanium has not previously been undertaken. Current literature methods for the synthesis of sol-gel material in reduced gravity could not be applied to titanium sol-gel processing, thus a new strategy had to be developed in this study. To successfully conduct experiments in varied gravity a refined titanium sol-gel chemical precursor had to be developed which allowed the single solution precursor to remain un-reactive at temperatures up to 50oC and only begin to react when exposed to a pressure decrease from a vacuum. Due to the new nature of this precursor, a thorough characterisation of the reaction precursors was subsequently undertaken with the use of techniques such as Nuclear Magnetic Resonance, Infra-red and UV-Vis spectroscopy in order to achieve sufficient understanding of precursor chemistry and kinetic stability. This understanding was then used to propose gelation reaction mechanisms under varied gravity conditions. Two unique reactor systems were designed and built with the specific purpose to allow the effects of varied gravity (high, normal, reduced) during synthesis of titanium sol-gels to be studied. The first system was a centrifuge capable of providing high gravity environments of up to 70 g’s for extended periods, whilst applying a 100 mbar vacuum and a temperature of 40-50oC to the reaction chambers. The second system to be used in the QUT Microgravity Drop Tower Facility was also required to provide the same thermal and vacuum conditions used in the centrifuge, but had to operate autonomously during free fall. Through the use of post synthesis characterisation techniques such as Raman Spectroscopy, X-Ray diffraction (XRD) and N2 adsorption, it was found that increased gravity levels during synthesis, had the greatest effect on the final products. Samples produced in reduced and normal gravity appeared to form amorphous gels containing very small particles with moderate surface areas. Whereas crystalline anatase (TiO2), was found to form in samples synthesised above 5 g with significant increases in crystallinity, particle size and surface area observed when samples were produced at gravity levels up to 70 g. It is proposed that for samples produced in higher gravity, an increased concentration gradient of water is forms at the bottom of the reacting film due to forced convection. The particles formed in higher gravity diffuse downward towards this excess of water, which favours the condensation reaction of remaining sol gel precursors with the particles promoting increased particle growth. Due to the removal of downward convection in reduced gravity, particle growth due to condensation reaction processes are physically hindered hydrolysis reactions favoured instead. Another significant finding from this work was that anatase could be produced at relatively low temperatures of 40-50oC instead of the conventional method of calcination above 450oC solely through sol-gel synthesis at higher gravity levels. It is hoped that the outcomes of this research will lead to an increased understanding of the effects of gravity on chemical synthesis of titanium sol-gel, potentially leading to the development of improved products suitable for diverse applications such as semiconductor or catalyst materials as well as significantly reducing production and energy costs through manufacturing these materials at significantly lower temperatures.

Application of kaolin amorphous derivative as a nitrogen carrier

Sandy soils have low nutrient holding capacity and high water conductivity. Consequently, nutrients applied as highly soluble chemical fertilisers are prone to leaching, particularly in heavily irrigated environments such as horticultural soils and golf courses. Amorphous derivatives of kaolin with high cation exchange capacity may be loaded with desired nutrients and applied as controlledrelease fertilisers. Kaolin is an abundant mineral, which can be converted to a meso-porous amorphous derivative (KAD) using facile chemical processes. KAD is currently being used to sequester ammonium from digester effluent in sewage treatment plants in a commercial environment. This material is also known in Australia by the trade name MesoLite. The ammonium-saturated form of KAD may be applied to soils as a nitrogen fertiliser. Up to 7% N can be loaded onto KAD by contacting it with high-ammonia concentration wastewater from sewerage treatment plants. This poster paper demonstrates plant uptake of nitrogen from KAD and compares its efficiency as a fertiliser with NH4SO4. Rye grass was grown in 1kg pots in a glass-house. Nitrogen was applied at a range of rates using NH4SO4 and two KAD materials carrying 7% and 3% nitrogen, respectively. All other nutrients were applied in adequate amounts. All treatments were replicated three times. Plants were harvested after four weeks. Dry mass and N concentrations were determined by standard methods. At all N application rates, ammonium-loaded KAD produced significantly higher plant mass than for NH4SO4. The lower fertiliser effectiveness of NH4SO4 is attributed to possible loss of some N through volatilisation. Of the two KAD types, the material with lower CEC value supported slightly higher plant yields. The KAD materials did not show any adverse effect on availability of trace elements, as evidenced by lack of deficiency symptoms and plant analyses. Clearly, nitrogen loaded on to KAD in the form of ammonium is likely to be protected from leaching, but is still available to plants. These data suggest that KAD-based fertilisers may be suitable substitutes for water soluble N, K and other cation fertilisers for leaching soils.

Segmental torso masses and joint torques produced by gravity in the adolescent scoliotic spine

Introduction Calculating segmental torso masses in Adolescent Idiopathic Scoliosis (AIS) patients allows the gravitational loading on the scoliotic spine during relaxed standing to be estimated. Methods Low dose CT data was used to calculate vertebral level-by-level torso masses and spinal joint torques for 20 female AIS patients (mean age 15.0 ± 2.7 years, mean Cobb angle 53 ± 7.1°). ImageJ software (v1.45 NIH USA) was used to threshold the T1 to L5 CT images and calculate the segmental torso volume and mass for each vertebral level. Masses for the head, neck and arms were taken from published data.1 Intervertebral joint torques in the coronal and sagittal planes at each vertebral level were found from the position of the centroid of the segment masses relative to the joint centres (assumed to be at the centre of the intervertebral disc). The joint torque at each level was found by summing torque contributions for all segments above that joint. Results Segmental torso mass increased from 0.6kg at T1 to 1.5kg at L5. The coronal plane joint torques due to gravity were 5-7Nm at the apex of the curve; sagittal torques were 3-5.4Nm. Conclusion CT scans were in the supine position and curve magnitudes are known to be smaller than those in standing.2 Hence, this study has shown that gravity produces joint torques potentially of higher than 7Nm in the coronal plane and 5Nm in the sagittal plane during relaxed standing in scoliosis patients. The magnitude of these torques may help to explain the mechanics of AIS progression and the mechanics of bracing. This new data on torso segmental mass in AIS patients will assist biomechanical models of scoliosis.

Synthesis and characterization of titanium sol–gels in varied gravity

Two unique test systems were designed and built to allow the effects of varied gravity (high, normal, reduced) during synthesis of titanium sol–gels to be studied. A centrifuge capable of providing high gravity environments of up to 70 g for extended periods while applying a 100 mbar vacuum and a temperature of 40–50 °C to the reaction chambers was developed. The second system was used in the QUT Microgravity Drop Tower Facility also provided the same thermal and vacuum conditions used in the centrifuge, but was required to operate autonomously during free fall. Through the use of post synthesis instrumental characterization, it was found that increased gravity levels during synthesis, had the greatest effect on the final products. Samples produced in reduced and normal gravity appeared to form amorphous gels containing very small particles with moderate surface areas. Whereas crystalline anatase (TiO2), was found to form in samples synthesized above 5 g with significant increases in crystallinity, particle size and surface area observed when samples were produced at gravity levels up to 70 g. It is proposed that for samples produced in higher gravity, an increased concentration gradient of water is forms at the bottom of the reacting film due to forced convection. The particles formed in higher gravity diffuse downward toward this excess of water, which favors the condensation reaction of remaining sol–gel precursors with the particles promoting increased particle growth. Due to the removal of downward convection in reduced gravity, particle growth due to condensation reaction processes are physically hindered hydrolysis reactions favored instead. Another significant finding from this work was that anatase could be produced at relatively low temperatures of 40–50 °C instead of the conventional method of calcination above 450 °C solely through sol–gel synthesis at higher gravity levels.

Segmental torso masses and joint torques produced by gravity in the adolescent scoliotic spine

Introduction Calculating segmental torso masses in Adolescent Idiopathic Scoliosis (AIS) patients allows the gravitational loading on the scoliotic spine during relaxed standing to be estimated. Methods Low dose CT data was used to calculate vertebral level-by-level torso masses and spinal joint torques for 20 female AIS patients (mean age 15.0 ± 2.7 years, mean Cobb angle 53 ± 7.1°). ImageJ software (v1.45 NIH USA) was used to threshold the T1 to L5 CT images and calculate the segmental torso volume and mass for each vertebral level. Masses for the head, neck and arms were taken from published data. Intervertebral joint torques in the coronal and sagittal planes at each vertebral level were found from the position of the centroid of the segment masses relative to the joint centres (assumed to be at the centre of the intervertebral disc. The joint torque at each level was found by summing torque contributions for all segments above that joint. Results Segmental torso mass increased from 0.6kg at T1 to 1.5kg at L5. The coronal plane joint torques due to gravity were 5-7Nm at the apex of the curve; sagittal torques were 3-5.4Nm. Conclusion CT scans were in the supine position and curve magnitudes are known to be smaller than those in standing. Hence, this study has shown that gravity produces joint torques potentially of higher than 7Nm in the coronal plane and 5Nm in the sagittal plane during relaxed standing in scoliosis patients. The magnitude of these torques may help to explain the mechanics of AIS progression and the mechanics of bracing. This new data on torso segmental mass in AIS patients will assist biomechanical models of scoliosis.

Gravity-induced coronal plane joint moments in adolescent idiopathic scoliosis

Background Adolescent Idiopathic Scoliosis is the most common type of spinal deformity, and whilst the risk of progression appears to be biomechanically mediated (larger deformities are more likely to progress), the detailed biomechanical mechanisms driving progression are not well understood. Gravitational forces in the upright position are the primary sustained loads experienced by the spine. In scoliosis they are asymmetrical, generating moments about the spinal joints which may promote asymmetrical growth and deformity progression. Using 3D imaging modalities to estimate segmental torso masses allows the gravitational loading on the scoliotic spine to be determined. The resulting distribution of joint moments aids understanding of the mechanics of scoliosis progression. Methods Existing low-dose CT scans were used to estimate torso segment masses and joint moments for 20 female scoliosis patients. Intervertebral joint moments at each vertebral level were found by summing the moments of each of the torso segment masses above the required joint. Results The patients’ mean age was 15.3 years (SD 2.3; range 11.9 – 22.3 years); mean thoracic major Cobb angle 52° (SD 5.9°; range 42°-63°) and mean weight 57.5 kg (SD 11.5 kg; range 41 – 84.7 kg). Joint moments of up to 7 Nm were estimated at the apical level. No significant correlation was found between the patients’ major Cobb angles and apical joint moments. Conclusions Patients with larger Cobb angles do not necessarily have higher joint moments, and curve shape is an important determinant of joint moment distribution. These findings may help to explain the variations in progression between individual patients. This study suggests that substantial corrective forces are required of either internal instrumentation or orthoses to effectively counter the gravity-induced moments acting to deform the spinal joints of idiopathic scoliosis patients.