A note on mixed boundary value problems involving triple trigonometrical series

This study was motivated by the two-dimensional hydrodynamic slamming problem of a steep wave hitting a vertical wall. The fundamental problem considers dual impact on the wall at the lower and upper regions resembling the impact of a wave at the time of its breaking. The solution method results into a mixed-boundary value problem that involves a triplet of trigonometrical series which, to the author’s best knowledge, has not been investigated in the past. The formulation of the mixed-boundary value problem is generic and could be used in different fields as well

Race, Australian Colonialism and Technologies of Mobility in Kalgoorlie

This article argues that the legal texts that record the death of Indigenous boy Elijah Doughty in a reserve in Kalgoorlie-Boulder in 2016 highlights the intersections of technologies of mobility within the Australian colonial project. Elijah died when the small motorcycle he was riding was run over by a large utility vehicle driven by the non-Indigenous assailant, ‘WSM’. This occurred within a wider social media centred context of racist anxieties and hate speech directed towards Indigenous children being in public and mobile around Kalgoorlie-Boulder. Elijah’s death and the subsequent legal reactions, to Indigenous protests, to the endurance of social media racist hate speech directed to Kalgoorlie-Boulder’s Indigenous children, to determining the location of the trial and who can speak at the trial, to the concern and pity expressed towards ‘WSM’, shows how technologies of mobility, reinstate and bolster colonial mobilities and their destructive effects on Indigenous people

Periodic solutions of coupled Boussinesq equations and Ostrovsky-type models free from zero-mass contradiction

Coupled Boussinesq equations describe long weakly-nonlinear longitudinal strain waves in a bi-layer with a soft bonding between the layers (e.g. a soft adhesive). From the mathematical viewpoint, a particularly difficult case appears when the linear long-wave speeds in the layers are significantly different (high-contrast case). The traditional derivation of the uni-directional models leads to four uncoupled Ostrovsky equations, for the right- and left-propagating waves in each layer. However, the models impose a ``zero-mass constraint'' i.e. the initial conditions should necessarily have zero mean, restricting the applicability of that description. Here, we bypass the contradiction in this high-contrast case by constructing the solution for the deviation from the evolving mean value, using asymptotic multiple-scale expansions involving two pairs of fast characteristic variables and two slow-time variables. By construction, the Ostrovsky equations emerging within the scope of this derivation are solved for initial conditions with zero mean while initial conditions for the original system may have non-zero mean values. Asymptotic validity of the solution is carefully examined numerically. We apply the models to the description of counter-propagating waves generated by solitary wave initial conditions, or co-propagating waves generated by cnoidal wave initial conditions, as well as the resulting wave interactions, and contrast with the behaviour of the waves in bi-layers when the linear long-wave speeds in the layers are close (low-contrast case). One local (classical) and two non-local (generalised) conservation laws of the coupled Boussinesq equations for strains are derived, and these are used to control the accuracy of the numerical simulations.Comment: 25 pages, 11 figures; previously this version appeared as arXiv:2210.14107 which was submitted as a new work by acciden

Consumer attitudes towards production diseases in intensive production systems

Many members of the public and important stakeholders operating at the upper end of the food chain, may be unfamiliar with how food is produced, including within modern animal production systems. The intensification of production is becoming increasingly common in modern farming. However, intensive systems are particularly susceptible to production diseases, with potentially negative consequences for farm animal welfare (FAW). Previous research has demonstrated that the public are concerned about FAW, yet there has been little research into attitudes towards production diseases, and their approval of interventions to reduce these. This research explores the public’s attitudes towards, and preferences for, FAW interventions in five European countries (Finland, Germany, Poland, Spain and the UK). An online survey was conducted for broilers (n = 789), layers (n = 790) and pigs (n = 751). Data were analysed by means of Kruskal-Wallis ANOVA, exploratory factor analysis and structural equation modelling. The results suggest that the public have concerns regarding intensive production systems, in relation to FAW, naturalness and the use of antibiotics. The most preferred interventions were the most “proactive” interventions, namely improved housing and hygiene measures. The least preferred interventions were medicine-based, which raised humane animal care and food safety concerns amongst respondents. The results highlighted the influence of the identified concerns, perceived risks and benefits on attitudes and subsequent behavioural intention, and the importance of supply chain stakeholders addressing these concerns in the subsequent communications with the public

Periodic solutions of coupled Boussinesq equations and Ostrovsky-type models free from zero-mass contradiction

Coupled Boussinesq equations are used to describe long weakly-nonlinear longitudinal strain waves in a bi-layer with a soft bonding between the layers (e.g. a soft adhesive). From the mathematical viewpoint, a particularly difficult case appears when the linear long-wave speeds in the layers are significantly different (high-contrast case). The traditional derivation of the uni-directional models leads to four uncoupled Ostrovsky equations, for the right-and left-propagating waves in each layer. However, the models impose a "zero-mass constraint" i.e. the initial conditions should necessarily have zero mean, restricting the applicability of that description. Here, we bypass the contradiction in this high-contrast case by constructing the solution for the deviation from the evolving mean value, using asymptotic multiple-scale expansions involving two pairs of fast characteristic variables and two slow-time variables. By construction, the Ostro-vsky equations emerging within the scope of this derivation are solved for initial conditions with zero mean while initial conditions for the original system may have non-zero mean values. Asymptotic validity of the solution is carefully examined numerically. We apply the models to the description of counter-propagating waves generated by solitary wave initial conditions, or co-propagating waves generated by cnoidal wave initial conditions, as well as the resulting wave interactions, and contrast with the behaviour of the waves in bi-layers when the linear long-wave speeds in the layers are close (low-contrast case). One local (classical) and two non-local (generalised) conservation laws of the coupled Boussinesq equations for strains are derived and used to control the accuracy of the numerical simulations. A weakly-nonlinear solution to the coupled Boussinesq equations on a finite interval with periodic boundary conditions is constructed, resolving the zero-mass contradiction. The solution is shown to be asymptotically valid by comparison to direct numerical simulations of the original coupled Boussinesq equations, with the additional control of derived generalised conservation laws. Examples include counter-propagating radiating solitary waves and Ostrovsky-type wave packets when the period of the solution is large compared to the size of a localised initial condition, while decreasing the period of the solution for the localised perturbations and using non-localised initial conditions leads to more complicated scenarios. We observe that, in many cases, the waves appear to interact in a nearly-elastic manner, similarly to that of solitary waves, with small phase shift and amplitude changes compared to the case with no interaction, while in other cases strong interactions lead to formation of new wave structures

Remote Cationic Curing

A procedure is described for the polymerisation of cationically polymeriseable resins, using solid- state onium and organometallic salt photoinitiators bearing complex anions of group V elements. The initiator is irradiated in the solid state by UV light and the gas(es) produced are allowed to diffuse into the resin film which is adjacent to but not in contact with the initiator, within a closed cell. Epoxide and vinyl ether monomers were successfully cured in this manner. The progress of polymerisation is followed by FTIR spectroscopy. The reaction is thought to be initiated via a Lewis Acid catalyst, but propagated via Brønsted species following interaction of the former with trace water in the film. The effects of water on the polymerisation of epoxides were studied. Atmospheric moisture (humidity) was found to have a detrimental effect on the polymerisation while bulk water was tolerated at levels up to 5% w/w. These results are discussed in detail in the context of industry findings. The presence of HF (hydrogen fluoride) in the gaseous photodecomposition products was determined by gas phase FTIR. and confirmed by ion chromatography. The rate of evolution of gaseous products upon irradiation of the initiator(s) is quantified in real time by dissolution in water and conductometric measurement using a fluoride ion specific electrode. A large proportion of the detected fluoride ion yield is attributed to the presence in the gaseous photo-products of XF5, the pentafluoride of the group V element. This is subsequently hydrolysed to yield multi-molar equivalents of fluoride ion per initiator molecule irradiated. Hybrid systems are described which permit the selective and step-wise polymerisation of acrylate resins (by the conventional process) and epoxide resins by the above method

Three-dimensional steep wave impact on a vertical plate with an open rectangular section

The present study treats the three-dimensional hydrodynamic slamming problem on a vertical plate subjected to the impact of a steep wave moving towards the plate with a constant velocity. The problem is complicated significantly by assuming that there is a rectangular opening on the plate which allows a discharge of the liquid. The analysis is conducted analytically assuming linear potential theory. The examined configuration determines two boundary value problems with mixed conditions which fully are taken into account. The mathematical process assimilates the plate with a degenerate elliptical cylinder allowing the employment of elliptical harmonics that ensure the satisfaction of the free-surface boundary condition of the front face of the steep wave, away from the plate. This assumption leads to an additional boundary value problem with mixed conditions in the vertical direction. The associated problem involves triple trigonometrical series and it is solved through a transformation into integral equations. To tackle the boundary value problem in the vertical direction a perturbation technique is employed. Extensive numerical calculations are presented as regards the variation of the velocity potential on the plate at the instant of the impact which reveals the influence of the opening. The theory is extended to the computation of the total impulse exerted on the plate using pressure-impulse theory

The costs of poultry production diseases: what do we actually know?

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The exometabolome of microbial communities inhabiting bare ice surfaces on the southern Greenland Ice Sheet

Microbial blooms colonize the Greenland Ice Sheet bare ice surface during the ablation season and significantly reduce its albedo. On the ice surface, microbes are exposed to high levels of irradiance, freeze–thaw cycles, and low nutrient concentrations. It is well known that microorganisms secrete metabolites to maintain homeostasis, communicate with other microorganisms, and defend themselves. Yet, the exometabolome of supraglacial microbial blooms, dominated by the pigmented glacier ice algae Ancylonema alaskanum and Ancylonema nordenskiöldii, remains thus far unstudied. Here, we use a high-resolution mass spectrometry-based untargeted metabolomics workflow to identify metabolites in the exometabolome of microbial blooms on the surface of the southern tip of the Greenland Ice Sheet. Samples were collected every 6 h across two diurnal cycles at 5 replicate sampling sites with high similarity in community composition, in terms of orders and phyla present. Time of sampling explained 46% (permutational multivariate analysis of variance [PERMANOVA], pseudo-F = 3.7771, p = 0.001) and 27% (PERMANOVA, pseudo-F = 1.8705, p = 0.001) of variance in the exometabolome across the two diurnal cycles. Annotated metabolites included riboflavin, lumichrome, tryptophan, and azelaic acid, all of which have demonstrated roles in microbe–microbe interactions in other ecosystems and should be tested for potential roles in the development of microbial blooms on bare ice surfaces