Draft tube discharge fluctuation during self-sustained pressure surge: fluorescent particle image velocimetry in two-phase flow

Hydraulic machines play an increasingly important role in providing a secondary energy reserve for the integration of renewable energy sources in the existing power grid. This requires a significant extension of their usual operating range, involving the presence of cavitating flow regimes in the draft tube. At overload conditions, the self-sustained oscillation of a large cavity at the runner outlet, called vortex rope, generates violent periodic pressure pulsations. In an effort to better understand the nature of this unstable behavior and its interaction with the surrounding hydraulic and mechanical system, the flow leaving the runner is investigated by means of particle image velocimetry. The measurements are performed in the draft tube cone of a reduced scale model of a Francis turbine. A cost-effective method for the in-house production of fluorescent seeding material is developed and described, based on off-the-shelf polyamide particles and Rhodamine B dye. Velocity profiles are obtained at three streamwise positions in the draft tube cone, and the corresponding discharge variation in presence of the vortex rope is calculated. The results suggest that 5-10% of the discharge in the draft tube cone is passing inside the vortex rop

The gender profile of the South African actuarial profession

The aim of this paper is to contextualise the gender status of the South African actuarial profession, both historically and relative to elsewhere in the world, as well as to establish the current level of representation of women in the profession. The authors have investigated the extent to which women are represented in different age groups and at various stages of the qualification process. They find that 85% of Fellow members of the Actuarial Society in 2010 are male but that women represent at least 30% of student members and younger cohorts. Given that people enter the profession primarily from undergraduate degrees in actuarial science, the authors have analysed the relative performance of female students enrolling for an Actuarial Science degree at the University of Cape Town. They find that the proportion of entrants who are female has increased over time but that persistency rates for female students are lower than for male students. They identify the need for further research to establish the underlying reasons for the gender differentials in entrants to university programmes and persistency, and conclude that universities, actuarial employers and the profession have a role to play in improving the perception of the profession and the experiences of women in the classroom and workplace

On the emergence of Lorentzian signature and scalar gravity

In recent years, a growing momentum has been gained by the emergent gravity framework. Within the latter, the very concepts of geometry and gravitational interaction are not seen as elementary aspects of Nature but rather as collective phenomena associated to the dynamics of more fundamental objects. In this paper we want to further explore this possibility by proposing a model of emergent Lorentzian signature and scalar gravity. Assuming that the dynamics of the fundamental objects can give rise in first place to a Riemannian manifold and a set of scalar fields we show how time (in the sense of hyperbolic equations) can emerge as a property of perturbations dynamics around some specific class of solutions of the field equations. Moreover, we show that these perturbations can give rise to a spin-0 gravity via a suitable redefinition of the fields that identifies the relevant degrees of freedom. In particular, we find that our model gives rise to Nordstrom gravity. Since this theory is invariant under general coordinate transformations, this also shows how diffeomorphism invariance (albeit of a weaker form than the one of general relativity) can emerge from much simpler systems.Comment: 10 pages, revtex4. Replaced with the published versio

Riemann solvers and undercompressive shocks of convex FPU chains

We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space-time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We allow the flux to have a turning point, and observe a third type of elementary wave (conservative shocks) in the atomistic simulations. These waves are heteroclinic travelling waves and correspond to non-classical, undercompressive shocks of the p-system. We analyse such shocks for fluxes with one or more turning points. Depending on the convexity properties of the flux we propose FPU-Riemann solvers. Our numerical simulations confirm that Lax-shocks are replaced by so called dispersive shocks. For convex-concave flux we provide numerical evidence that convex FPU chains follow the p-system in generating conservative shocks that are supersonic. For concave-convex flux, however, the conservative shocks of the p-system are subsonic and do not appear in FPU-Riemann solutions

Quantum Histories and Quantum Gravity

This paper reviews the histories approach to quantum mechanics. This discussion is then applied to theories of quantum gravity. It is argued that some of the quantum histories must approximate (in a suitable sense) to classical histories, if the correct classical regime is to be recovered. This observation has significance for the formulation of new theories (such as quantum gravity theories) as it puts a constraint on the kinematics, if the quantum/classical correspondence principle is to be preserved. Consequences for quantum gravity, particularly for Lorentz symmetry and the idea of "emergent geometry", are discussed.Comment: 35 pages (29 pages main body), two figure

Parameterized Inapproximability of Target Set Selection and Generalizations

In this paper, we consider the Target Set Selection problem: given a graph and a threshold value $thr(v)$ for any vertex $v$ of the graph, find a minimum size vertex-subset to "activate" s.t. all the vertices of the graph are activated at the end of the propagation process. A vertex $v$ is activated during the propagation process if at least $thr(v)$ of its neighbors are activated. This problem models several practical issues like faults in distributed networks or word-to-mouth recommendations in social networks. We show that for any functions $f$ and $\rho$ this problem cannot be approximated within a factor of $\rho(k)$ in $f(k) \cdot n^{O(1)}$ time, unless FPT = W[P], even for restricted thresholds (namely constant and majority thresholds). We also study the cardinality constraint maximization and minimization versions of the problem for which we prove similar hardness results

Modelling the unfolding pathway of biomolecules: theoretical approach and experimental prospect

We analyse the unfolding pathway of biomolecules comprising several independent modules in pulling experiments. In a recently proposed model, a critical velocity $v_{c}$ has been predicted, such that for pulling speeds $v>v_{c}$ it is the module at the pulled end that opens first, whereas for $v<v_{c}$ it is the weakest. Here, we introduce a variant of the model that is closer to the experimental setup, and discuss the robustness of the emergence of the critical velocity and of its dependence on the model parameters. We also propose a possible experiment to test the theoretical predictions of the model, which seems feasible with state-of-art molecular engineering techniques.Comment: Accepted contribution for the Springer Book "Coupled Mathematical Models for Physical and Biological Nanoscale Systems and Their Applications" (proceedings of the BIRS CMM16 Workshop held in Banff, Canada, August 2016), 16 pages, 6 figure