Nonlinear gas oscillations in pipes. Part 1. Theory

The problem of forced acoustic oscillations in a pipe is studied theoretically. The oscillations are produced by a moving piston in one end of the pipe, while a variety of boundary conditions ranging from a completely closed to a completely open mouth at the other end are considered. All these boundary conditions are modelled by two parameters: a length correction and a reflexion coefficient equivalent to the acoustic impedance. The linear theory predicts large amplitudes near resonance and nonlinear effects become crucially important. By expanding the equations of motion in a series in the Mach number, both the amplitude and wave form of the oscillation are predicted there. In both the open- and closed-end cases the need for shock waves in some range of parameters is found. The amplitude of the oscillation is different for the two cases, however, being proportional to the square root of the piston amplitude in the closed-end case and to the cube root for the open end

Aristotle on Enduring Evils While Staying Happy

In what ways and how far does virtue shield someone against suffering evils? In other words, how do non-moral evils affect the lives of virtuous people and to what extent can someone endure evils while staying happy? The central purpose of this chapter is to answer these questions by exploring what Aristotle has to say about the effects of evils in human well-being in general and his treatment of extreme misfortunes

On the linear stability of the inviscid Kármán vortex street

The classical point-vortex model for a Kármán vortex street is linearly stable only for an isolated case. This property has been shown numerically to hold for other, more complicated, models of the same flow. It is shown here that it is a consequence of the Hamiltonian structure of the model, related to the codimension of the set of matrices with a particular Jordan block structure in the space of Hamiltonian matrices, and that it can be expected to hold generically for any two-dimensional inviscid array of vortices that has back-to-fore symmetry, and that is 'close enough' to the point-vortex model

Warming and Ocean Acidification Effects in the Seaweed Community of West Spitsbergen

Global change-related warming and ocean acidification (OA) are major threats to the Svalbard coastal ecosystem. Rock bottom areas are mainly dominated by dense forests of a multi-species community of seaweeds. Different species are shown to respond to warming and OA in different ways and degrees, posing a potential shift in community structure as the new scenario develops. An increase in CO2 is shown to modify the carbon balance of two representative species in opposing ways. Growth rate of Desmarestia aculeata was negatively affected by CO2 enrichment, while Alaria esculenta was positively affected, as a result of a different reorganization of the cellular carbon budget in both species. D. aculeata showed increased respiration, enhanced accumulation of storage biomolecules and elevated release of dissolved organic carbon, whereas A. esculenta showed decreased respiration and lower accumulation of storage biomolecules. Moreover, incubation of 6 species from Kongsfjorden at different CO2 and temperature levels indicated that temperature affected mainly the photosynthetic performance as measured by PAM fluorescence, particularly the initial slope of ETR curves, the light saturation parameter (Ek), and Fv/Fm values, as well as the protein content, especially in the phaeophytes. On the other hand, CO2 affected mainly the internal accumulation of carbohydrates and lipids. The C:N balance was largely unaffected. The resulting growth rate was not altered by the treatments in three out of the six species studied. For example, Phycodris rubens showed a positive effect of increasing temperature, while Saccorhiza dermatodea was positively affected by CO2. Significant interactions between CO2 and temperature were found in 20 % of the analyses. Whether additive or synergistic, the co-occurrence of a higher temperature with other stressors such as elevated CO2 increases the probability of community changes by modifying the performance of these species. To test whether this kind of responses was characteristic of Arctic populations, Saccharina latissima from Kongsfjorden was compared to the population from Helgoland (Germany). Ecotypic variations were revealed by a significantly higher O2 production rate and an increase in Chl a, Rubisco, and D1 protein content in the Arctic population thalli, but a lower growth rate, in comparison to the Atlantic population. At 10 °C, the Arctic population had a higher content of total C, soluble carbohydrates, and lipids, whereas the N- and protein content was lower. Conclusively, the Arctic ecotype was more resilient to increased CO2 than the temperate one, and both ecotypes differed in their response pattern to temperature. Overall, Arctic ecotypes of seaweeds have shown an array of responses pointing to an altered community as the “atlantification” and acidification of the West Spitsbergen coastal system take place. Further research will focus on potential alteration of the nutrient regime due to increased discharge from land and its consequences on seaweeds metabolic performance.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Covering techniques and rational points on some genus 5 curves

We describe a method that allows, under some hypotheses, to compute all the rational points of some genus 5 curves defined over a number field. This method is used to solve some arithmetic problems that remained open.Comment: Contemporary Mathematics AMS, to appea