Mathematical modelling of curtain coating

We present a simple mathematical model for the fluid flow in the curtain coating process, exploiting the small aspect ratio, and examine the model in the large-Reynolds-number limit of industrial interest. We show that the fluid is in free fall except for a region close to the substrate, but find that the model can not describe the turning of the curtain onto the substrate. We find that the inclusion of a viscous bending moment close to the substrate allows the curtain to “turn the corner”

Bailouts in a common market: a strategic approach

Governments in the EU grant Rescue and Restructure Subsidies to bail out ailing firms. In an international asymmetric Cournot duopoly we study effects of such subsidies on market structure and welfare. We adopt a common market setting, where consumers from the two countries form one market. We show that the subsidy is positive also when it fails to prevent the exit. The reason is a strategic effect, which forces the more efficient firm to make additional cost-reducing effort. When the exit is prevented, allocative and productive efficiencies are lower and the only gaining player is the rescued firm

Mathematical Model of Easter Island Society Collapse

In this paper we consider a mathematical model for the evolution and collapse of the Easter Island society, starting from the fifth century until the last period of the society collapse (fifteen century). Based on historical reports, the available primary sources consisted almost exclusively on the trees. We describe the inhabitants and the resources as an isolated system and both considered as dynamic variables. A mathematical analysis about why the structure of the Easter Island community collapse is performed. In particular, we analyze the critical values of the fundamental parameters driving the interaction humans-environment and consequently leading to the collapse. The technological parameter, quantifying the exploitation of the resources, is calculated and applied to the case of other extinguished civilization (Cop\'an Maya) confirming, with a sufficiently precise estimation, the consistency of the adopted model.Comment: 9 pages, 1 figure, final version published on EuroPhysics Letter

Estimations of rip current rescues and drowning in the United States

Rip currents are the greatest hazard to swimmers on surf beaches, but due to a lack of consistent incident reporting in many countries, it is often difficult to quantify the number of rip-current-related rescues and drowning deaths occurring along surf beaches. This study examines this problem using rescue data reported to the United States Lifesaving Association (USLA) by surf beach rescuers from 1997 through 2016. These data were checked, corrected, and culled so that only data from surf beach rescue agencies that reported the primary cause of rescue were included. Results show that rip currents are the primary cause of 81.9&thinsp;% of rescues on surf beaches, with regional variation from 75.3&thinsp;% (East Coast) to 84.7&thinsp;% (West Coast). These values are significantly higher than those previously reported in the scientific literature (e.g., 36.5&thinsp;%, 53.7&thinsp;%). Using this value as a proxy when examining overall surf beach drowning fatalities, it is suggested that more than 100 fatal drownings per year occur due to rip currents in the United States. However, it is clear that the United States data would benefit by an increase in the number of lifeguard agencies which report surf-related rescues by primary cause.</p

Surveying rip current survivors: Preliminary insights into the experiences of being caught in rip currents

This paper begins a process of addressing a significant gap in knowledge about people's responses to being caught in rip currents. While rip currents are the primary hazard facing recreational ocean swimmers in Australia, debate exists about the best advice to give swimmers caught in rip currents. Such surf rescue advice - on what to do and how to respond when caught in a rip - relies on empirical evidence. However, at present, knowledge about swimmers reactions and responses to rip currents is limited. This gap is a considerable barrier to providing effective advice to beach goers and to understanding how this advice is utilised (or not) when actually caught in the rip current. This paper reports the findings of a pilot study that focussed on garnering a better understanding of swimmers' experiences when caught in rip currents. A large scale questionnaire survey instrument generated data about rip current survivors' demographics, knowledge of beach safety and their reactions and responses when caught in a rip current. A mix of online and paper surveys produced a total of 671 completed surveys. Respondents were predominantly an informed group in terms of rip current knowledge, beach experience and had a high self-rated swimming ability. Preliminary insights from the survey show that most respondents recalled a "swim across the rip/parallel to the beach" message when caught in the rip and most escaped unassisted by acting on this message. However, while nearly a quarter of respondents recalled a message of "not to panic", short answer responses revealed that the onset of panic inhibited some respondents from recalling or enacting any other type of beach safety message when caught in the rip current. Results also showed that despite the research sample being younger, competent and frequent ocean swimmers, they were more likely to swim at unpatrolled beaches and outside of the red and yellow safety flags. Moreover, they were still caught in a rip current and they panicked. The findings of this study have significant implications for a range of demographic groups of differing beach safety knowledge and swimming ability who may be caught in rip currents behave, we know very little about how beach goers may respond to being caught in them. © 2012 Author(s)