Local Central Limit Theorem for Multi-group Curie–Weiss Models

We study a multi-group version of the mean-field Ising model, also called Curie–Weiss model. It is known that, in the high-temperature regime of this model, a central limit theorem holds for the vector of suitably scaled group magnetisations, that is, for the sum of spins belonging to each group. In this article, we prove a local central limit theorem for the group magnetisations in the high-temperature regime.

High-Temperature Ignition Kinetics of Gas Turbine Lubricating Oils

Lubricant ignition is a highly undesirable event in any mechanical system, and surprisingly minimal work has been conducted to investigate the auto-ignition properties of gas turbine lubricants. To this end, using a recently established spray injection scheme in a shock tube, two gas turbine lubricants (Mobil DTE 732 and Lubricant A from Cooper et al. 2020) were subjected to high-temperature, post-reflected-shock conditions, and OH* chemiluminescence was monitored at the sidewall location of the shock tube to measure ignition delay time (τign). A combination of an extended shock-tube driver and driver-gas tailoring were utilized to observe ignition between 1183 K and 1385 K at near-atmospheric pressures. A clear, two-stage-ignition process was observed for all tests with Mobil DTE 732, and both first and second stage τign are compared. Second stage ignition was found to be more indicative of lubricant ignition and was used to compare τign values with lubricant A. Both lubricants exhibit three ignition regimes: a high-temperature, Arrhenius-like regime (> 1275 K); an intermediate, negative-temperature-coefficient-like regime (1230–1275 K); and a low-temperature ignition regime (< 1230 K). Similar τign behavior in the high-temperature regime was seen for both lubricants, and a regression analysis using τign data from both lubricants in this region produced the Arrhenius expression τign(μs) = 4.4 × 10−14exp(96.7(kcal/mol)/RT). While lubricant A was found to be less reactive in the intermediate-temperature regime, Mobil DTE 732 was less reactive in the low-temperature regime. As the low-temperature regime is more relevant to gas turbine conditions, Mobil DTE 732 is considered more desirable for system implementation. Chemical kinetic modeling was also performed using n-hexadecane models (a lubricant surrogate suggested in the literature). The current models are unable to reproduce the three regimes observed and predict activation energies much lower than those observed in the high-temperature regime, suggesting n-hexadecane is a poor surrogate for lubricant ignition. Additionally, experiments were conducted with Jet-A for temperatures between 1145 and 1419 K around 1 atm. Good agreement is seen with both literature data and model predictions, anchoring the experiment with previously established τign measurement methods and calculations. A linear regression analysis of the Jet-A data produced the Arrhenius expression: τign(μs) = 6.39 × 10−5exp(41.4(kcal/mol)/RT).

Glyphosate Resistance in Sonchus oleraceus and Alternative Herbicide Options for Its Control in Southeast Australia

Sonchus oleraceus is becoming a hard-to-control weed in Australian cropping systems, especially in glyphosate-tolerant cotton and during summer fallows. Several biotypes of this weed have developed resistance to glyphosate as a result of common management practices under conservation agriculture systems in the country. A series of pot experiments were conducted to evaluate the effect of temperature on glyphosate efficacy and performance of several post-emergence and pre-emergence herbicides on a glyphosate-resistant (GR) and a glyphosate-susceptible (GS) biotype of S. oleraceus. At low temperatures (19–24 °C), no plants of the GS biotype survived glyphosate application at 570 g/ha; however, in the high-temperature regime (28–30 °C), 83% of the plants survived this rate of glyphosate. Similarly, for the GR biotype, up to 58% of the plants survived at 2280 g/ha of glyphosate when applied during the high-temperature regime and no plants survived this rate during the low-temperature regime. A number of post-emergence herbicides were found to be effective for S. oleraceus control. However, herbicide application delayed to the six-leaf stage compared with the four-leaf stage reduced control, especially for bromoxynil and saflufenacil herbicides. Glufosinate and paraquat were the most effective herbicides for S. oleraceus control, resulting in no seedling survival for both biotypes. Isoxaflutole, pendimethalin or s-metolachlor efficacy was not reduced by the presence of crop residue, suggesting that these herbicides could be used to control S. oleraceus in conservation agriculture systems. The results of this study suggest that growers will need to reduce over-reliance on glyphosate for weed control in summer fallows and use alternative post-emergence herbicides.