Fast computation of quadrupole and hexadecapole approximations in microlensing with a single point-source evaluation

The exoplanet detection rate from gravitational microlensing has grown significantly in recent years thanks to a great enhancement of resources and improved observational strategy. Current observatories include ground-based wide-field and/or robotic world-wide networks of telescopes, as well as space-based observatories such as satellites Spitzer or Kepler/K2. This results in a large quantity of data to be processed and analyzed, which is a challenge for modeling codes because of the complexity of the parameter space to be explored, and the intensive computations required to evaluate the models. In this work, I present a method that allows to compute the quadrupole and hexadecapole approximation of the finite-source magnification with more efficiency that previously available codes, with routines about x6 and x4 faster respectively. The quadrupole takes just about twice the time of a point-source evaluation, which advocates for generalizing its use to large portion of the light curves. The corresponding routines are available as open-source python codes.Comment: Published in MNRAS (7 pages, 2 figures, 1 table). Open source codes available on GitHub (cf. reference in the paper

Experimental and Numerical Investigation of Flow under Sluice Gates

The flow characteristics upstream and downstream of sluice gates are studied experimentally and numerically using Reynolds averaged Navier-Stokes two-dimensional simulations with a volume of fluid method. Special attention was brought to large opening and submergence, a frequent situation in distribution canals that is little seldom addressed in the literature. Experimental results obtained by ADV measurements provide mean velocity distributions and turbulence characteristics. The flow is shown to be mostly two-dimensional. Velocity fields were simulated using renormalization group k-epsilon and Reynolds stress model turbulence models, leading to an estimation of energy and momentum correction coefficients, head loss, and bed friction. The contraction coefficient is also shown to increase with gate opening at large submergence, which is consistent with the energy-momentum balance. This result can be used to derive accurate discharge equation

Experimental and numerical studies of the flow structure generated by a submerged sluice gate

Sluice gates are commonly used to control discharge and levels, and to monitor discharge. However discharge formulas perform poorly at large opening and large submergence. This study explores the flow structure under such gates in order to verify commonly used assumptions about contraction coefficient and energy losses. The study is based on experimental results acquired in a laboratory flume. The flow structure was determined experimentally by ADV and numerically with RANS simulations performed with Fluent TM for different configurations of submerged gates and different modelling assumptions. Attention is given to the contracted flow and to the recirculating zone upstream of the gate. The experimental results on velocity are consistent with RANS simulations as far as discharge coefficients, wall shear stress and flow structure are concerned. Contraction coefficients were compared with analytical calculations based on potential flow and momentum balance. It is verified that, as usually assumed, the viscosity effects have a limited influence on the flow structure. We show that contraction coefficients should not be considered as constant at large submergence and large opening, which is a reason of the poor performance of the discharge formulas in these regimes

Bayesian analysis of caustic-crossing microlensing events

Aims: Caustic-crossing binary-lens microlensing events are important anomalous events because they are capable of detecting an extrasolar planet companion orbiting the lens star. Fast and robust modelling methods are thus of prime interest in helping to decide whether a planet is detected by an event. Cassan (2008) introduced a new set of parameters to model binary-lens events, which are closely related to properties of the light curve. In this work, we explain how Bayesian priors can be added to this framework, and investigate on interesting options. Methods: We develop a mathematical formulation that allows us to compute analytically the priors on the new parameters, given some previous knowledge about other physical quantities. We explicitly compute the priors for a number of interesting cases, and show how this can be implemented in a fully Bayesian, Markov chain Monte Carlo algorithm. Results: Using Bayesian priors can accelerate microlens fitting codes by reducing the time spent considering physically implausible models, and helps us to discriminate between alternative models based on the physical plausibility of their parameters.Comment: Accepted in A&A - 7 pages, 4 figure

Calculation of Contraction Coefficient under Sluice Gates and Application to Discharge Measurement

The contraction coefficient under sluice gates on flat beds is studied for both free flow and submerged conditions based on the principle of momentum conservation, relying on an analytical determination of the pressure force exerted on the upstream face of the gate together with the energy equation. The contraction coefficient varies with the relative gate opening and the relative submergence, especially at large gate openings. The contraction coefficient may be similar in submerged flow and free flow at small openings but not at large openings, as shown by some experimental results. An application to discharge measurement is also presented

Should They Stay or Should They Go? African Cultural Goods in France’s Public Domain, Between Inalienability, Transfers, and Circulations

France’s colonialism over Subsharan Africa until the 1960s has had persistant psychological and material consequences. Amongst them is the lingering presence of a significant amount of African objects in French museum collections. In the last five years, Subsaharan African countries have reiterated their desire to receive parts of these collections. Through their “restitution requests,” they identify themselves as the objects’ legitimate owners and claim to have been robbed of their cultural property during colonialism. The exact conditions under which each Subsaharan artifact arrived on French grounds—whether through theft, donations, sales, or looting—remain unsettled. Even where thefts can be proven, they occurred at a time where colonialism was approved by international law. The French government’s recent favorable responses to African restitution requests might have concluded this debate had France’s national heritage not been protected by the five-century old inalienability principle, which prohibits the transfer of any property out of France’s public domain, including the Subsaharan objects in its public museum collections. This Note studies these legal difficulties and proposes a solution based on France’s international duty to promote African culture as a human right. Rather than amending the fundamental inalienability rule, this Note calls for the creation of a legislative commission that will study individual requests in the respect of French legislations, international conventions, national objectives, and world heritage

Comparison of four methods for quantification of biofilms in biphasic cultures

Three methods for determining the total biofilm amount in biphasic cultures have been compared: dry weight by filtration after solvent treatment, optical density with a biomass probe and protein content. The activity of the biofilm was estimated through mineral nitrogen consumption. Calculation of the coefficients of variation shows that these parameters could be used to characterise such a biofilm. The optical density by biomass probe was the most reliable one (repeatability <0.5%) to quantify total biofilm and a linear relation was verified against dry weight

Bond orbital description of the strain induced second order optical susceptibility in silicon

We develop a theoretical model, relying on the well established sp3 bond-orbital theory, to describe the strain-induced $\chi^{(2)}$ in tetrahedrally coordinated centrosymmetric covalent crystals, like silicon. With this approach we are able to describe every component of the $\chi^{(2)}$ tensor in terms of a linear combination of strain gradients and only two parameters $\alpha$ and $\beta$ which can be estimated theoretically. The resulting formula can be applied to the simulation of the strain distribution of a practical strained silicon device, providing an extraordinary tool for optimization of its optical nonlinear effects. By doing that, we were able not only to confirm the main valid claims known about $\chi^{(2)}$ in strained silicon, but also estimate the order of magnitude of the $\chi^{(2)}$ generated in that device

Commercial Applications of Microalgae

The first use of microalgae by humans dates back 2000 years to the Chinese, who used Nostoc to survive during famine. However, microalgal biotechnology only really began to develop in the middle of the last century. Nowadays, there are numerous commercial applications of microalgae. For example, (1) microalgae can be used to enhance the nutritional value of food and animal feed owing to their chemical composition, (2) they play a crucial role in aquaculture and (3) they can be incorporated into cosmetics. Moreover, they are cultivated as a source of highly valuable molecules. For example, polyunsaturated fatty acid oils are added to infant formulas and nutritional supplements and pigments are important as natural dyes. Stable isotope biochemicals help in structural determination and metabolic studies. Future research should focus on the improvement of production systems and the genetic modification of strains. Microalgal products would in that way become even more diversified and economically competitive

Interferometric visibility of single-lens models: the thin-arcs approximation

Long baseline interferometry of microlensing events can resolve the individual images of the source produced by the lens, which combined with the modelling of the microlensing light curve, leads to the exact lens mass and distance. Interferometric observations thus offer a unique opportunity to constrain the mass of exoplanets detected by microlensing, and to precisely measure the mass of distant isolated objects such as stars and brown dwarfs, and of stellar remnants such as white dwarfs, neutron stars, and stellar black holes. Having accurate models and reliable numerical methods is of particular importance as the number of targets is expected to increase significantly in the near future. In this work we discuss the different approaches to calculating the fringe complex visibility for the important case of a single lens. We propose a robust integration scheme to calculate the exact visibility, and introduce a novel approximation, which we call the `thin-arcs approximation', which can be applied over a wide range of lens--source separations. We find that this approximation runs six to ten times faster than the exact calculation, depending of the characteristics of the event and the required accuracy. This approximation provides accurate results for microlensing events of medium to high magnification observed around the peak (i.e. a large fraction of potential observational targets).Comment: Same as published versio