Computing derivative-based global sensitivity measures using polynomial chaos expansions

In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance decomposition methods leading to the well-known Sobol' indices are recognized as accurate techniques, at a rather high computational cost though. The use of polynomial chaos expansions (PCE) to compute Sobol' indices has allowed to alleviate the computational burden though. However, when dealing with large dimensional input vectors, it is good practice to first use screening methods in order to discard unimportant variables. The {\em derivative-based global sensitivity measures} (DGSM) have been developed recently in this respect. In this paper we show how polynomial chaos expansions may be used to compute analytically DGSMs as a mere post-processing. This requires the analytical derivation of derivatives of the orthonormal polynomials which enter PC expansions. The efficiency of the approach is illustrated on two well-known benchmark problems in sensitivity analysis

Micro heat exchanger by using MEMS impinging jets

A micro impinging-jet heat exchanger is presented here. Heat transfer is studied for single jet, slot arrays and jet arrays. In order to facilitate micro heat transfer measurements with these devices, a MEMS sensor chip, which has an 8 x 8 temperature-sensor array on one side, and an integrated heater on the other side has been designed and fabricated. This sensor chip allows 2-D surface temperature measurement with various jets impinging on it. It is found that micro impinging jets can be highly efficient when compared to existing macro impinging-jet microelectronics packages such as IBM 4381. For example, using a single nozzle jet (500-μm diameter driven by 5 psig pressure), the sensor chip (2 x 2 cm^2) temperature can be cooled down from 70 to 33°C. The cooling becomes more efficient when nozzle arrays (4x5 over 1 cm^2 area) are used under the same driving pressure. Interestingly, although higher driving pressure gives better cooling (lower surface temperature), the cooling efficiency, defined as h/0.5pv^2, is actually higher for lower driving pressure

A suspended microchannel with integrated temperature sensors for high-pressure flow studies

A freestanding microchannel, with integrated temperature sensors, has been developed for high-pressure flow studies. These microchannels are approximately 20μm x 2μm x 4400μm, and are suspended above 80 μm deep cavities, bulk micromachined using BrF3 dry etch. The calibration of the lightly boron-doped thermistor-type sensors shows that the resistance sensitivity of these integrated sensors is parabolic with respect to temperature and linear with respect to pressure. Volumetric flow rates of N2 in the microchannel were measured at inlet pressures up to 578 psig. The discrepancy between the data and theory results from the flow acceleration in a channel, the non-parabolic velocity profile, and the bulging of the channel. Bulging effects were evaluated by using incompressible water flow measurements, which also measures 1.045x10^-3N-s/m^2 for the viscosity of DI water. The temperature data from sensors on the channel shows the heating of the channel due to the friction generated by the high-pressure flow inside

Magnetic Fields Recorded by Chondrules Formed in Nebular Shocks

Recent laboratory efforts (Fu et al., 2014) have constrained the remanent magnetizations of chondrules and the magnetic field strengths at which the chondrules were exposed to as they cooled below their Curie points. An outstanding question is whether the inferred paleofields represent the background magnetic field of the solar nebula or were unique to the chondrule-forming environment. We investigate the amplification of the magnetic field above background values for two proposed chondrule formation mechanisms, large-scale nebular shocks and planetary bow shocks. Behind large-scale shocks, the magnetic field parallel to the shock front is amplified by factors $\sim 10-30$, regardless of the magnetic diffusivity. Therefore, chondrules melted in these shocks probably recorded an amplified magnetic field. Behind planetary bow shocks, the field amplification is sensitive to the magnetic diffusivity. We compute the gas properties behind a bow shock around a 3000 km-radius planetary embryo, with and without atmospheres, using hydrodynamics models. We calculate the ionization state of the hot, shocked gas, including thermionic emission from dust, and thermal ionization of gas-phase potassium atoms, and the magnetic diffusivity due to Ohmic dissipation and ambipolar diffusion. We find that the diffusivity is sufficiently large that magnetic fields have already relaxed to background values in the shock downstream where chondrules acquire magnetizations, and that these locations are sufficiently far from the planetary embryos that chondrules should not have recorded a significant putative dynamo field generated on these bodies. We conclude that, if melted in planetary bow shocks, chondrules probably recorded the background nebular field.Comment: 17 pages, 11 figures, accepted for publication in Ap

Evaluating deterrents of illegal behaviour in conservation: Carnivore killing in rural Taiwan

Rules restricting resource use are ubiquitous to conservation. Recent increases in poaching of iconic species such as African elephant and rhino have triggered high-profile interest in enforcement. Previous studies have used economic models to explore how the probability and severity of sanctions influence poacher-behaviour. Yet despite evidence that compliance can be substantial when the threat of state-imposed sanctions is low and profits high, few have explored other factors deterring rule-breaking. We use the randomised response technique (RRT) and direct questions to estimate the proportion of rural residents in north-western Taiwan illegally killing wildlife. We then model how potential sources of deterrence: perceived probabilities of detection and punishment, social norms and self-imposed guilt, relate to non-compliant behaviour (reported via RRT). The perceived likelihood of being punished and two types of social norms (injunctive and descriptive) predict behaviour and deter rule-breaking. Harnessing social norms that encourage compliance offers potential for reducing the persecution of threatened species