Power law distributions in pattern dynamics of attacker-defender dyads in the team sport of Rugby Union : phenomena in a region of self-organized criticality?

In the region of self-organized criticality (SOC) interdependency between multi-agent system components exists and slight changes in near-neighbor interactions can break the balance of equally poised options leading to transitions in system order. In this region, frequency of events of differing magnitudes exhibits a power law distribution. The aim of this paper was to investigate whether a power law distribution characterized attacker-defender interactions in team sports. For this purpose we observed attacker and defender in a dyadic sub-phase of rugby union near the try line. Videogrammetry was used to capture players’ motion over time as player locations were digitized. Power laws were calculated for the rate of change of players’ relative position. Data revealed that three emergent patterns from dyadic system interactions (i.e., try; unsuccessful tackle; effective tackle) displayed a power law distribution. Results suggested that pattern forming dynamics dyads in rugby union exhibited SOC. It was concluded that rugby union dyads evolve in SOC regions suggesting that players’ decisions and actions are governed by local interactions rules.

Contracting bubbles in Hele-Shaw cells with a power-law fluid

The problem of bubble contraction in a Hele-Shaw cell is studied for the case in which the surrounding fluid is of power-law type. A small perturbation of the radially symmetric problem is first considered, focussing on the behaviour just before the bubble vanishes, it being found that for shear-thinning fluids the radially symmetric solution is stable, while for shear-thickening fluids the aspect ratio of the bubble boundary increases. The borderline (Newtonian) case considered previously is neutrally stable, the bubble boundary becoming elliptic in shape with the eccentricity of the ellipse depending on the initial data. Further light is shed on the bubble contraction problem by considering a long thin Hele-Shaw cell: for early times the leading-order behaviour is one-dimensional in this limit; however, as the bubble contracts its evolution is ultimately determined by the solution of a Wiener-Hopf problem, the transition between the long-thin limit and the extinction limit in which the bubble vanishes being described by what is in effect a similarity solution of the second kind. This same solution describes the generic (slit-like) extinction behaviour for shear-thickening fluids, the interface profiles that generalise the ellipses that characterise the Newtonian case being constructed by the Wiener-Hopf calculation.

Analytical solutions of the multi-term modified power law wave equations in a finite domain

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi term time-space fractional models including fractional Laplacian.

Power-law viscous materials for analogue experiments: New data on the rheology of highly-filled silicone polymers

The selection of appropriate analogue materials is a central consideration in the design of realistic physical models. We investigate the rheology of highly-filled silicone polymers in order to find materials with a power-law strain-rate softening rheology suitable for modelling rock deformation by dislocation creep and report the rheological properties of the materials as functions of the filler content. The mixtures exhibit strain-rate softening behaviour but with increasing amounts of filler become strain-dependent. For the strain-independent viscous materials, flow laws are presented while for strain-dependent materials the relative importance of strain and strain rate softening/hardening is reported. If the stress or strain rate is above a threshold value some highly-filled silicone polymers may be considered linear visco-elastic (strain independent) and power-law strain-rate softening. The power-law exponent can be raised from 1 to ~3 by using mixtures of high-viscosity silicone and plasticine. However, the need for high shear strain rates to obtain the power-law rheology imposes some restrictions on the usage of such materials for geodynamic modelling. Two simple shear experiments are presented that use Newtonian and power-law strain-rate softening materials. The results demonstrate how materials with power-law rheology result in better strain localization in analogue experiments.

Non-Newtonian natural convection flow along an isothermal horizontal circular cylinder using modified power-law model

Laminar two-dimensional natural convection boundary-layer flow of non-Newtonian fluids along an isothermal horizontal circular cylinder has been studied using a modified power-law viscosity model. In this model, there are no unrealistic limits of zero or infinite viscosity. Therefore, the boundary-layer equations can be solved numerically by using marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning as well as shear thickening fluids in terms of the fluid velocity and temperature distributions, shear stresses and rate of heat transfer in terms of the local skin-friction and local Nusselt number respectively.

Steady natural convection of non-Newtonian power-law fluid in a trapezoidal enclosure

Numerically investigation of free convection heat transfer in a differentially heated trapezoidal cavity filled with non-Newtonian Power-law fluid has been performed in this study. The left inclined surface is uniformly heated whereas the right inclined surface is maintained as uniformly cooled. The top and bottom surfaces are kept adiabatic with initially quiescent fluid inside the enclosure. Finite volume based commercial software FLUENT 14.5 is used to solve the governing equations. Dependency of various flow parameters of fluid flow and heat transfer is analyzed including Rayleigh number, Ra ranging from 10^5 to 10^7, Prandtl number, Pr of 100 to 10,000 and power index, n of 0.6 to 1.4. Outcomes have been reported in terms of isotherms, streamline, and local Nusselt number for various Ra, Pr, n and inclined angles. Grid sensitivity analysis is performed and numerically obtained results have been compared with those results available in the literature and found good agreement.

Power law distributions in entrepreneurship : implications for theory and research

A long-held assumption in entrepreneurship research is that normal (i.e., Gaussian) distributions characterize variables of interest for both theory and practice. We challenge this assumption by examining more than 12,000 nascent, young, and hyper-growth firms. Results reveal that variables which play central roles in resource-, cognition-, action-, and environment-based entrepreneurship theories exhibit highly skewed power law distributions, where a few outliers account for a disproportionate amount of the distribution's total output. Our results call for the development of new theory to explain and predict the mechanisms that generate these distributions and the outliers therein. We offer a research agenda, including a description of non-traditional methodological approaches, to answer this call.

The constitutional power to make war: domestic legal issues raised by Australia's action in Iraq

The legal power to declare war has traditionally been a part of a prerogative to be exercised solely on advice that passed from the King to the Governor-General no later than 1942. In 2003, the Governor- General was not involved in the decision by the Prime Minister and Cabinet to commit Australian troops to the invasion of Iraq. The authors explore the alternative legal means by which Australia can go to war - means the government in fact used in 2003 - and the constitutional basis of those means. While the prerogative power can be regulated and/or devolved by legislation, and just possibly by practice, there does not seem to be a sound legal basis to assert that the power has been devolved to any other person. It appears that in 2003 the Defence Minister used his legal powers under the Defence Act 1903 (Cth) (as amended in 1975) to give instructions to the service head(s). A powerful argument could be made that the relevant sections of the Defence Act were not intended to be used for the decision to go to war, and that such instructions are for peacetime or in bello decisions. If so, the power to make war remains within the prerogative to be exercised on advice. Interviews with the then Governor-General indicate that Prime Minister Howard had planned to take the matter to the Federal Executive Council 'for noting', but did not do so after the Governor-General sought the views of the then Attorney-General about relevant issues of international law. The exchange raises many issues, but those of interest concern the kinds of questions the Governor-General could and should ask about proposed international action and whether they in any way mirror the assurances that are uncontroversially required for domestic action. In 2003, the Governor-General's scrutiny was the only independent scrutiny available because the legality of the decision to go to war was not a matter that could be determined in the High Court, and the federal government had taken action in March 2002 that effectively prevented the matter coming before the International Court of Justice

Quantification of the relationship between Fuser Roller Temperature and Laser Printer Emissions

Recently published studies not only demonstrated that laser printers are often significant sources of ultrafine particles, but they also shed light on particle formation mechanisms. While the role of fuser roller temperature as a factor affecting particle formation rate has been postulated, its impact has never been quantified. To address this gap in knowledge, this study measured emissions from 30 laser printers in chamber using a standardized printing sequence, as well as monitoring fuser roller temperature. Based on a simplified mass balance equation, the average emission rates of particle number, PM2.5 and O3 were calculated. The results showed that: almost all printers were found to be high particle number emitters (i.e. > 1.01×1010 particles/min); colour printing generated more PM2.5 than monochrome printing; and all printers generated significant amounts of O3. Particle number emissions varied significantly during printing and followed the cycle of fuser roller temperature variation, which points to temperature being the strongest factor controlling emissions. For two sub-groups of printers using the same technology (heating lamps), systematic positive correlations, in the form of a power law, were found between average particle number emission rate and average roller temperature. Other factors, such as fuser material and structure, are also thought to play a role, since no such correlation was found for the remaining two sub-groups of printers using heating lamps, or for the printers using heating strips. In addition, O3 and total PM2.5 were not found to be statistically correlated with fuser temperature.

Carbon dioxide emissions from diesel and compressed natural gas buses during acceleration

Motor vehicle emission factors are generally derived from driving tests mimicking steady state conditions or transient drive cycles. However, neither of these test conditions completely represents real world driving conditions. In particular, they fail to determine emissions generated during the accelerating phase – a condition in which urban buses spend much of their time. In this study we analyse and compare the results of time-dependant emission measurements conducted on diesel and compressed natural gas (CNG) buses during an urban driving cycle on a chassis dynamometer and we derive power-law expressions relating carbon dioxide (CO2) emission factors to the instantaneous speed while accelerating from rest. Emissions during acceleration are compared with that during steady speed operation. These results have important implications for emission modelling particularly under congested traffic conditions.

Large-Eddy Simulation of physiological pulsatile non-newtonian flow in a channel with double constriction

Physiological pulsatile flow in a 3D model of arterial double stenosis, using the modified Power-law blood viscosity model, is investigated by applying Large Eddy Simulation (LES) technique. The computational domain has been chosen is a simple channel with biological type stenoses. The physiological pulsation is generated at the inlet of the model using the first four harmonics of the Fourier series of the physiological pressure pulse. In LES, a top-hat spatial grid-filter is applied to the Navier-Stokes equations of motion to separate the large scale flows from the subgrid scale (SGS). The large scale flows are then resolved fully while the unresolved SGS motions are modelled using the localized dynamic model. The flow Reynolds numbers which are typical of those found in human large artery are chosen in the present work. Transitions to turbulent of the pulsatile non-Newtonian along with Newtonian flow in the post stenosis are examined through the mean velocity, wall shear stress, mean streamlines as well as turbulent kinetic energy and explained physically along with the relevant medical concerns.

Stochastic simulation of chemical reactions in spatially complex media

Discrete stochastic simulations, via techniques such as the Stochastic Simulation Algorithm (SSA) are a powerful tool for understanding the dynamics of chemical kinetics when there are low numbers of certain molecular species. However, an important constraint is the assumption of well-mixedness and homogeneity. In this paper, we show how to use Monte Carlo simulations to estimate an anomalous diffusion parameter that encapsulates the crowdedness of the spatial environment. We then use this parameter to replace the rate constants of bimolecular reactions by a time-dependent power law to produce an SSA valid in cases where anomalous diffusion occurs or the system is not well-mixed (ASSA). Simulations then show that ASSA can successfully predict the temporal dynamics of chemical kinetics in a spatially constrained environment.

Characteristics of airborne ultrafine and coarse particles during the Australian dust storm of 23 September 2009

Particle number concentrations and size distributions, visibility and particulate mass concentrations and weather parameters were monitored in Brisbane, Australia, on 23 September 2009, during the passage of a dust storm that originated 1400 km away in the dry continental interior. The dust concentration peaked at about mid-day when the hourly average PM2.5 and PM10 values reached 814 and 6460 µg m-3, respectively, with a sharp drop in atmospheric visibility. A linear regression analysis showed a good correlation between the coefficient of light scattering by particles (Bsp) and both PM10 and PM2.5. The particle number in the size range 0.5-20 µm exhibited a lognormal size distribution with modal and geometrical mean diameters of 1.6 and 1.9 µm, respectively. The modal mass was around 10 µm with less than 10% of the mass carried by particles smaller than 2.5 µm. The PM10 fraction accounted for about 68% of the total mass. By mid-day, as the dust began to increase sharply, the ultrafine particle number concentration fell from about 6x103 cm-3 to 3x103 cm-3 and then continued to decrease to less than 1x103 cm-3 by 14h, showing a power-law decrease with Bsp with an R2 value of 0.77 (p<0.01). Ultrafine particle size distributions also showed a significant decrease in number during the dust storm. This is the first scientific study of particle size distributions in an Australian dust storm.

Deformation behaviours of coarse-grained and nanocrystalline Mg-5wt% Al alloys

Magnesium alloys have been of growing interest to various engineering applications, such as the automobile, aerospace, communication and computer industries due to their low density, high specific strength, good machineability and availability as compared with other structural materials. However, most Mg alloys suffer from poor plasticity due to their Hexagonal Close Packed structure. Grain refinement has been proved to be an effective method to enhance the strength and alter the ductility of the materials. Several methods have been proposed to produce materials with nanocrystalline grain structures. So far, most of the research work on nanocrystalline materials has been carried out on Face-Centered Cubic and Body-Centered Cubic metals. However, there has been little investigation of nanocrystalline Mg alloys. In this study, bulk coarse-grained and nanocrystalline Mg alloys were fabricated by a mechanical alloying method. The mixed powder of Mg chips and Al powder was mechanically milled under argon atmosphere for different durations of 0 hours (MA0), 10 hours (MA10), 20 hours (MA20), 30 hours (MA30) and 40 hours (MA40), followed by compaction and sintering. Then the sintered billets were hot-extruded into metallic rods with a 7 mm diameter. The obtained Mg alloys have a nominal composition of Mg–5wt% Al, with grain sizes ranging from 13 μm down to 50 nm, depending on the milling durations. The microstructure characterization and evolution after deformation were carried out by means of Optical microscopy, X-Ray Diffraction, Scanning Electron Microscopy, Transmission Electron Microscopy, Scanning Probe Microscopy and Neutron Diffraction techniques. Nanoindentaion, compression and micro-compression tests on micro-pillars were used to study the size effects on the mechanical behaviour of the Mg alloys. Two kinds of size effects on the mechanical behaviours and deformation mechanisms were investigated: grain size effect and sample size effect. The nanoindentation tests were composed of constant strain rate, constant loading rate and indentation creep tests. The normally reported indentation size effect in single crystal and coarse-grained crystals was observed in both the coarse-grained and nanocrystalline Mg alloys. Since the indentation size effect is correlated to the Geometrically Necessary Dislocations under the indenter to accommodate the plastic deformation, the good agreement between the experimental results and the Indentation Size Effect model indicated that, in the current nanocrystalline MA20 and MA30, the dislocation plasticity was still the dominant deformation mechanism. Significant hardness enhancement with decreasing grain size, down to 58 nm, was found in the nanocrystalline Mg alloys. Further reduction of grain size would lead to a drop in the hardness values. The failure of grain refinement strengthening with the relatively high strain rate sensitivity of nanocrystalline Mg alloys suggested a change in the deformation mechanism. Indentation creep tests showed that the stress exponent was dependent on the loading rate during the loading section of the indentation, which was related to the dislocation structures before the creep starts. The influence of grain size on the mechanical behaviour and strength of extruded coarse-grained and nanocrystalline Mg alloys were investigated using uniaxial compression tests. The macroscopic response of the Mg alloys transited from strain hardening to strain softening behaviour, with grain size reduced from 13 ìm to 50 nm. The strain hardening was related to the twinning induced hardening and dislocation hardening effect, while the strain softening was attributed to the localized deformation in the nanocrystalline grains. The tension–compression yield asymmetry was noticed in the nanocrystalline region, demonstrating the twinning effect in the ultra-fine-grained and nanocrystalline region. The relationship k tensions < k compression failed in the nanocrystalline Mg alloys; this was attributed to the twofold effect of grain size on twinning. The nanocrystalline Mg alloys were found to exhibit increased strain rate sensitivity with decreasing grain size, with strain rate ranging from 0.0001/s to 0.01/s. Strain rate sensitivity of coarse-grained MA0 was increased by more than 10 times in MA40. The Hall-Petch relationship broke down at a critical grain size in the nanocrystalline region. The breakdown of the Hall-Petch relationship and the increased strain rate sensitivity were due to the localized dislocation activities (generalization and annihilation at grain boundaries) and the more significant contribution from grain boundary mediated mechanisms. In the micro-compression tests, the sample size effects on the mechanical behaviours were studied on MA0, MA20 and MA40 micro-pillars. In contrast to the bulk samples under compression, the stress-strain curves of MA0 and MA20 micro-pillars were characterized with a number of discrete strain burst events separated by nearly elastic strain segments. Unlike MA0 and MA20, the stress-strain curves of MA40 micro-pillars were smooth, without obvious strain bursts. The deformation mechanisms of the MA0 and MA20 micro-pillars under micro-compression tests were considered to be initially dominated by deformation twinning, followed by dislocation mechanisms. For MA40 pillars, the deformation mechanisms were believed to be localized dislocation activities and grain boundary related mechanisms. The strain hardening behaviours of the micro-pillars suggested that the grain boundaries in the nanocrystalline micro-pillars would reduce the source (nucleation sources for twins/dislocations) starvation hardening effect. The power law relationship of the yield strength on pillar dimensions in MA0, MA20 supported the fact that the twinning mechanism was correlated to the pre-existing defects, which can promote the nucleation of the twins. Then, we provided a latitudinal comparison of the results and conclusions derived from the different techniques used for testing the coarse-grained and nanocrystalline Mg alloy; this helps to better understand the deformation mechanisms of the Mg alloys as a whole. At the end, we summarized the thesis and highlighted the conclusions, contributions, innovations and outcomes of the research. Finally, it outlined recommendations for future work.