Completeness of Inertial Modes of an Incompressible Non-Viscous Fluid in a Corotating Ellipsoid

Inertial modes are the eigenmodes of contained rotating fluids restored by the Coriolis force. When the fluid is incompressible, inviscid and contained in a rigid container, these modes satisfy Poincar\'e's equation that has the peculiarity of being hyperbolic with boundary conditions. Inertial modes are therefore solutions of an ill-posed boundary-value problem. In this paper we investigate the mathematical side of this problem. We first show that the Poincar\'e problem can be formulated in the Hilbert space of square-integrable functions, with no hypothesis on the continuity or the differentiability of velocity fields. We observe that with this formulation, the Poincar\'e operator is bounded and self-adjoint and as such, its spectrum is the union of the point spectrum (the set of eigenvalues) and the continuous spectrum only. When the fluid volume is an ellipsoid, we show that the inertial modes form a complete base of polynomial velocity fields for the square-integrable velocity fields defined over the ellipsoid and meeting the boundary conditions. If the ellipsoid is axisymmetric then the base can be identified with the set of Poincar\'e modes, first obtained by Bryan (1889), and completed with the geostrophic modes.Comment: 19 pages, 1 figure, to appear in Physical Review

Review of experimental research on supercritical and transcritical thermodynamic cycles designed for heat recovery application

Supercritical operation is considered a main technique to achieve higher cycle efficiency in various thermodynamic systems. The present paper is a review of experimental investigations on supercritical operation considering both heat-to-upgraded heat and heat-to-power systems. Experimental works are reported and subsequently analyzed. Main findings can be summarized as: steam Rankine cycles does not show much studies in the literature, transcritical organic Rankine cycles are intensely investigated and few plants are already online, carbon dioxide is considered as a promising fluid for closed Brayton and Rankine cycles but its unique properties call for a new thinking in designing cycle components. Transcritical heat pumps are extensively used in domestic and industrial applications, but supercritical heat pumps with a working fluid other than CO2 are scarce. To increase the adoption rate of supercritical thermodynamic systems further research is needed on the heat transfer behavior and the optimal design of compressors and expanders with special attention to the mechanical integrity

The effect of thrombolysis on short-term improvement depends on initial stroke severity

A large number of parameters have been identified as predictors of early outcome in patients with acute ischemic stroke. In the present work we analyzed a wide range of demographic, metabolic, physiological, clinical, laboratory and neuroimaging parameters in a large population of consecutive patients with acute ischemic stroke with the aim of identifying independent predictors of the early clinical course. We used prospectively collected data from the Acute Stroke Registry and Analysis of Lausanne. All consecutive patients with ischemic stroke admitted to our stroke unit and/or intensive care unit between 1 January 2003 and 12 December 2008 within 24h after last-well time were analyzed. Univariate and multivariate analyses were performed to identify significant associations with the National Institute of Health Stroke Scale (NIHSS) score at admission and 24h later. We also sought any interactions between the identified predictors. Of the 1,730 consecutive patients with acute ischemic stroke who were included in the analysis, 260 (15.0%) were thrombolyzed (mostly intravenously) within the recommended time window. In multivariate analysis, the NIHSS score at 24h after admission was associated with the NIHSS score at admission (β=1, p<0.001), initial glucose level (β=0.05, p<0.002) and thrombolytic intervention (β=−2.91, p<0.001). There was a significant interaction between thrombolysis and the NIHSS score at admission (p<0.001), indicating that the short-term effect of thrombolysis decreases with increasing initial stroke severity. Thrombolytic treatment, lower initial glucose level and lower initial stroke severity predict a favorable early clinical course. The short-term effect of thrombolysis appears mainly in minor and moderate strokes, and decreases with increasing initial stroke severit

When protoindustry collapsed fertility and the demographic regime in rural Eastern Belgium during the industrial revolution

'Die Geschichte der demographischen Transition wird oft als ein Gegensatz zwischen einem dynamischen städtisch-industriellen Sektor und einem statischen und Traditionen verhafteten Land dargestellt. Ländliche Gebiete werden als Bastionen der Stabilität gesehen, welche den transformierenden ökonomischen und kulturellen Kräften widerstanden, die von den städtischen Zentren ausgingen. Dieser Stereotyp ignoriert den Wandel, der innerhalb des ländlichen Bereichs sowohl in seiner Beziehung zur städtisch-industriellen Welt als auch in seiner eigenen internen Ökonomie erfolgte. Wenn wir ihr generatives Verhalten betrachten, sehen wir, dass die Bewohner des ostbelgischen Landes in einem großen Umfang in der Lage waren, mit ländlicher Desindustrialisierung, Bevölkerungsdruck und urbaner industrieller Entwicklung fertig zu werden. Es ist nicht angebracht, den späten Übergang zu niedriger ehelicher Fruchtbarkeit als ein Mangel an Anpassungsfähigkeit zu sehen, denn das Jahrhundert hindurch wurde genau das Gegenteil unter Beweis gestellt.' (Autorenreferat)'The story of the demographic transition is often told as a contrast between a dynamic urban-industrial sector and a static and traditional countryside. Rural areas are viewed as bastions of stability that resisted the transformative economic and cultural forces emanating from urban centers. This stereotype ignores the transformation occurring within the rural sector, in both its relationships with the urban-industrial world and its own internal economy. Looking at their demographic regime, especially the fertility pattern, we see that to a large extent, inhabitants of East Belgian countryside were able to cope with rural deindustrialization, population pressure and urban industrial development. It is not reasonable to see their late transition to low marital fertility as a lack of adaptive capacities, when they showed exactly the contrary throughout the century.' (author's abstract

Instrumented Collective Learning Situations (ICLS): the Gap between Theoretical Research and Observed Practices

According to socio-constructivism approach, collective situations are promoted to favor learning in classroom, at a distance or in a blended educational context. So, many Information and Communication Technologies (ICT) are provided to teachers but there are no clear studies about the way they are used and perceived. Our research is based on the hypothesis that practices of educational actors (instructional designers and tutors) are far away from theoretical results of research in education technologies. In this paper, we consider a precise kind of situation: Instrumented Collective Learning Situations (ICLS). By a survey on 13 fields in higher education in France, Switzerland and Canada, we present how ICLS are designed and how teachers used them. Conclusions give an indication on the gap between the way information technologies are prescribed and the way they are actually used and perceived by teachers