Flow in a slowly-tapering channel with oscillating walls

The flow of a fluid in a channel with walls inclined at an angle to each other is investigated at arbitrary Reynolds number. The flow is driven by an oscillatory motion of the wall incorporating a time-periodic displacement perpendicular to the channel centreline. The gap between the walls varies linearly with distance along the channel and is a prescribed periodic function of time. An approximate solution is constructed assuming that the angle of inclination of the walls is small. At leading order the flow corresponds to that in a channel with parallel, vertically oscillating walls examined by Hall and Papageorgiou \cite{HP}. A careful study of the governing partial differential system for the first order approximation controlling the tapering flow due to the wall inclination is conducted. It is found that as the Reynolds number is increased from zero the tapering flow loses symmetry and undergoes exponential growth in time. The loss of symmetry occurs at a lower Reynolds number than the symmetry-breaking for the parallel-wall flow. A window of asymmetric, time-periodic solutions is found at higher Reynolds number, and these are reached via a quasiperiodic transient from a given set of initial conditions. Beyond this window stability is again lost to exponentially growing solutions as the Reynolds number is increased

Patterns in rational base number systems

Number systems with a rational number $a/b > 1$ as base have gained interest in recent years. In particular, relations to Mahler's 3/2-problem as well as the Josephus problem have been established. In the present paper we show that the patterns of digits in the representations of positive integers in such a number system are uniformly distributed. We study the sum-of-digits function of number systems with rational base $a/b$ and use representations w.r.t. this base to construct normal numbers in base $a$ in the spirit of Champernowne. The main challenge in our proofs comes from the fact that the language of the representations of integers in these number systems is not context-free. The intricacy of this language makes it impossible to prove our results along classical lines. In particular, we use self-affine tiles that are defined in certain subrings of the ad\'ele ring $\mathbb{A}_\mathbb{Q}$ and Fourier analysis in $\mathbb{A}_\mathbb{Q}$. With help of these tools we are able to reformulate our results as estimation problems for character sums

Classification of non-indigenous species based on their impacts: Considerations for application in marine management

Assessment of the ecological and economic/societal impacts of the introduction of non-indigenous species (NIS) is one of the primary focus areas of bioinvasion science in terrestrial and aquatic environments, and is considered essential to management. A classification system of NIS, based on the magnitude of their environmental impacts, was recently proposed to assist management. Here, we consider the potential application of this classification scheme to the marine environment, and offer a complementary framework focussing on value sets in order to explicitly address marine management concerns. Since existing data on marine NIS impacts are scarce and successful marine removals are rare, we propose that management of marine NIS adopt a precautionary approach, which not only would emphasise preventing new incursions through pre-border and at-border controls but also should influence the categorisation of impacts. The study of marine invasion impacts requires urgent attention and significant investment, since we lack the luxury of waiting for the knowledge base to be acquired before the window of opportunity closes for feasible management

The role of C-reactive protein (CRP) as a prognostic marker in COVID-19

Funding declaration This study received no specific funding. The study was partially supported through the NIHR Maudsley Biomedical Research Centre at the South London and Maudsley NHS Foundation Trust in partnership with King's College London (BC)Peer reviewedPostprin

Hole concentration and phonon renormalization in Ca-doped YBa_2Cu_3O_y (6.76 < y < 7.00)

In order to access the overdoped regime of the YBa_2Cu_3O_y phase diagram, 2% Ca is substituted for Y in YBa_2Cu_3O_y (y = 7.00,6.93,6.88,6.76). Raman scattering studies have been carried out on these four single crystals. Measurements of the superconductivity-induced renormalization in frequency (Delta \omega) and linewidth (\Delta 2\gamma) of the 340 cm^{-1} B_{1g} phonon demonstrate that the magnitude of the renormalization is directly related to the hole concentration (p), and not simply the oxygen content. The changes in \Delta \omega with p imply that the superconducting gap (\Delta_{max}) decreases monotonically with increasing hole concentration in the overdoped regime, and \Delta \omega falls to zero in the underdoped regime. The linewidth renormalization \Delta 2\gamma is negative in the underdoped regime, crossing over at optimal doping to a positive value in the overdoped state.Comment: 18 pages; 5 figures; submitted to Phys. Rev. B Oct. 24, 2002 (BX8292

Diversity and patterns of marine non‐native species in the archipelagos of Macaronesia

Aims The present study is the first attempt to grasp the scale and richness of marine biological invasions in Macaronesia. We pioneered a comprehensive non-native species (NNS), inventory in the region to determine their diversity patterns and native distribution origins. NNS were defined here as the result of both introductions and range expansions. We also used statistical modelling to examine relationships among NNS richness, anthropogenic activities, demographic and geographical variables across Macaronesia. Location Macaronesia. Methods A comprehensive literature search was conducted for marine NNS records in Macaronesia, registering the first record's location and year from 1884 to 2020. We used univariate and multivariate analyses to evaluate differences and similarities in community composition. By applying a Generalized Linear Model (GLM), we tested hypotheses regarding NNS richness as a function of anthropogenic activities, demographic and geographical variables. Results A total of 144 marine non-native species (NNS) were recorded for the whole of Macaronesia. The highest NNS richness was registered in the Canary Islands (76 NNS), followed by the Azores (66 NNS), Madeira (59 NNS) and finally Cabo Verde (18 NNS). Some differences amongst archipelagos were observed, such as the high number of non-native macroalgae in the Azores, fishes in the Canary Islands and tunicates in Cabo Verde. Overall, macroalgae, tunicates and bryozoans were the predominant taxonomic groups in the Macaronesian archipelagos. Madeira and Canary Islands were the archipelagos with more similarity in marine NNS, and Cabo Verde the most divergent. Finally, GLM suggested that non-native richness patterns across Macaronesia were dependent on the considered archipelago and strongly affected by (1) minimum distance to the mainland, (2) the total number of ports and marinas and (3) total marinas area (km2). Conclusions The model results and NNS listing in the present study will likely raise the awareness and response regarding marine NNS in the whole Macaronesia region, serving as a baseline for future research as well as implementing and enforcing regulations related to the introduction of marine NNS in oceanic islands

Nosocomial COVID-19 infection : examining the risk of mortality. The COPE-Nosocomial Study (COVID in Older PEople)

In the United Kingdom, authority to conduct the study was granted by the Health Research Authority (20/HRA/1898), and in Italy by the Ethics Committee of Policlinico Hospital Modena (Reference 369/2020/OSS/AOUMO). Cardiff University was the study sponsor.Peer reviewedPostprin

The Similarity Hypothesis in General Relativity

Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories will naturally evolve to a self-similar form. We will find there is good evidence for this in the context of both spatially homogenous and inhomogeneous cosmological models, although in some cases the self-similar model is only an intermediate attractor. There are also a wide variety of situations, including critical pheneomena, in which spherically symmetric models tend towards self-similarity. However, this does not happen in all cases and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra

I will not go, I cannot go: cultural and social limitations of disaster preparedness in Asia, Africa, and Oceania

While much work has been invested in addressing the economic and technical basis of disaster preparedness, less effort has been directed towards understanding the cultural and social obstacles to and opportunities for disaster risk reduction. This paper presents local insights from five different national settings into the cultural and social contexts of disaster preparedness. In most cases, an early warning system was in place, but it failed to alert people to diverse environmental shocks. The research findings show that despite geographical and typological differences in these locations, the limitations of the systems were fairly similar. In Kenya, people received warnings, but from contradictory systems, whereas in the Philippines and on the island of Saipan, people did not understand the messages or take them seriously. In Bangladesh and Nepal, however, a deeper cultural and religious reasoning serves to explain disasters, and how to prevent them or find safety when they strike