Relaxed Bell inequalities and Kochen-Specker theorems

The combination of various physically plausible properties, such as no signaling, determinism, and experimental free will, is known to be incompatible with quantum correlations. Hence, these properties must be individually or jointly relaxed in any model of such correlations. The necessary degrees of relaxation are quantified here, via natural distance and information-theoretic measures. This allows quantitative comparisons between different models in terms of the resources, such as the number of bits, of randomness, communication, and/or correlation, that they require. For example, measurement dependence is a relatively strong resource for modeling singlet state correlations, with only 1/15 of one bit of correlation required between measurement settings and the underlying variable. It is shown how various 'relaxed' Bell inequalities may be obtained, which precisely specify the complementary degrees of relaxation required to model any given violation of a standard Bell inequality. The robustness of a class of Kochen-Specker theorems, to relaxation of measurement independence, is also investigated. It is shown that a theorem of Mermin remains valid unless measurement independence is relaxed by 1/3. The Conway-Kochen 'free will' theorem and a result of Hardy are less robust, failing if measurement independence is relaxed by only 6.5% and 4.5%, respectively. An appendix shows the existence of an outcome independent model is equivalent to the existence of a deterministic model.Comment: 19 pages (including 3 appendices); v3: minor clarifications, to appear in PR

Robust design optimisation of gas turbine compression systems

Engineering design commonly assumes nominal values for uncertain parameters to simplify the design process: the design of a gas turbine, or one of its modules, is generally approached with some specific operating conditions in mind (its design point). Unfortunately, engine components never exactly meet their specifications and do not operate at just one condition, but over a range of power settings. This simplification can then lead to a product that exhibits performance significantly worse than nominal in real-world conditions. This problem is exacerbated in the presence of heavily optimised designs, which tend to lie in extreme regions of the design space.15 In gas turbine design, safe and satisfactory off-design operation must be guaranteed and is generally evaluated before moving to the next phase of the design process. This approach, while guaranteeing that some minimum requirements are met, introduces a further loop in the design process and does not ensure the final design will be optimal with respect to this new requirement. The introduction of some robustness considerations into the design process can reduce the level of fragmentation and iteration typical of gas turbine engine design and produce further (and more robust) improvements relative to the traditional method. In this study, two approaches for dealing with off-design performance analysis are presented, integrated into an automatic optimisation system and applied to the preliminary design of a core compression system from a three-spool modern turbofan engine. Designs that are more robust than those found if only design-point performance is considered are successfully identified

Multi-Objective Optimisation of Aero-Engine Compressors

The design of a new aero-engine compressor is a complex task: design objectives are almost always conflicting, the design space is large, nonlinear and highly constrained, and the effects of some geometrical changes can be difficult to predict. Computational fluid dynamics (CFD) is now widely used in real-world applications and especially in the design of turbomachinery. However, the large design space and the time required for the numerical simulation of the whole turbomachine make the use of CFD in the early phases of the design process infeasible: preliminary design relies on a number of physical and empirical relations, still quite similar to those used in the early history of turbomachinery design. In this study, 87 independent parameters were used to define the geometry of a 7-stage compressor, the performance of which was evaluated using proprietary design codes for mean-line, multi-stage analysis. The effects on efficiency and surge margin of changing 44 design variables were analysed and their optimal values found by means of deterministic (gradient-based) and meta-heuristic (Tabu Search [TS]) optimisation methods. The results show clearly how the use of meta-heuristic optimisation tools can improve the preliminary design of turbomachinery, allowing a more thorough but still rapid exploration of the design space to identify the most promising regions that will then be verified and further analysed with higher fidelity tools. The results also reveal the impact of introducing various constraints into the design process, highlighting the effects of design decomposition

Not throwing out the baby with the bathwater: Bell's condition of local causality mathematically 'sharp and clean'

The starting point of the present paper is Bell's notion of local causality and his own sharpening of it so as to provide for mathematical formalisation. Starting with Norsen's (2007, 2009) analysis of this formalisation, it is subjected to a critique that reveals two crucial aspects that have so far not been properly taken into account. These are (i) the correct understanding of the notions of sufficiency, completeness and redundancy involved; and (ii) the fact that the apparatus settings and measurement outcomes have very different theoretical roles in the candidate theories under study. Both aspects are not adequately incorporated in the standard formalisation, and we will therefore do so. The upshot of our analysis is a more detailed, sharp and clean mathematical expression of the condition of local causality. A preliminary analysis of the repercussions of our proposal shows that it is able to locate exactly where and how the notions of locality and causality are involved in formalising Bell's condition of local causality.Comment: 14 pages. To be published in PSE volume "Explanation, Prediction, and Confirmation", edited by Dieks, et a

Bell's theorem as a signature of nonlocality: a classical counterexample

For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local probabilistic interaction in the measurement process can lead to a violation of the Bell inequalities. We first introduce two-particle phase-space distributions in classical mechanics constructed to be the analogs of quantum mechanical angular momentum eigenstates. These distributions are then employed in four schemes characterized by different types of detectors measuring the angular momenta. When the model includes an interaction between the detector and the measured particle leading to ensemble dependencies, the relevant Bell inequalities are violated if total angular momentum is required to be conserved. The violation is explained by identifying assumptions made in the derivation of Bell's theorem that are not fulfilled by the model. These assumptions will be argued to be too restrictive to see in the violation of the Bell inequalities a faithful signature of nonlocality.Comment: Extended manuscript. Significant change

Radio galaxies and their magnetic fields out to z <= 3

We present polarisation properties at $1.4\,$GHz of two separate extragalactic source populations: passive quiescent galaxies and luminous quasar-like galaxies. We use data from the {\it Wide-Field Infrared Survey Explorer} data to determine the host galaxy population of the polarised extragalactic radio sources. The quiescent galaxies have higher percentage polarisation, smaller radio linear size, and $1.4\,$GHz luminosity of $6\times10^{21}<L_{\rm 1.4}<7\times10^{25}\,$W Hz$^{-1}$, while the quasar-like galaxies have smaller percentage polarisation, larger radio linear size at radio wavelengths, and a $1.4\,$GHz luminosity of $9\times10^{23}<L_{\rm 1.4}<7\times10^{28}\,$W Hz$^{-1}$, suggesting that the environment of the quasar-like galaxies is responsible for the lower percentage polarisation. Our results confirm previous studies that found an inverse correlation between percentage polarisation and total flux density at $1.4\,$GHz. We suggest that the population change between the polarised extragalactic radio sources is the origin of this inverse correlation and suggest a cosmic evolution of the space density of quiescent galaxies. Finally, we find that the extragalactic contributions to the rotation measures (RMs) of the nearby passive galaxies and the distant quasar-like galaxies are different. After accounting for the RM contributions by cosmological large-scale structure and intervening Mg\,{II} absorbers we show that the distribution of intrinsic RMs of the distant quasar-like sources is at most four times as wide as the RM distribution of the nearby quiescent galaxies, if the distribution of intrinsic RMs of the WISE-Star sources itself is at least several rad m$^{-2}$ wide.Comment: 12 pages, 8 figures, accepted for publication into MNRA

Galaxies behind the Galactic plane: First results and perspectives from the VVV Survey

Vista Variables in The Via Lactea (VVV) is an ESO variability survey that is performing observations in near infrared bands (ZYJHKs) towards the Galactic bulge and part of the disk with the completeness limits at least 3 mag deeper than 2MASS. In the present work, we searched in the VVV survey data for background galaxies near the Galactic plane using ZYJHKs photometry that covers 1.636 square degrees. We identified 204 new galaxy candidates by analyzing colors, sizes, and visual inspection of multi-band (ZYJHKs) images. The galaxy candidates colors were also compared with the predicted ones by star counts models considering a more realistic extinction model at the same completeness limits observed by VVV. A comparison of the galaxy candidates with the expected one by Milennium simulations is also presented. Our results increase the number density of known galaxies behind the Milky Way by more than one order of magnitude. A catalog with galaxy properties including ellipticity, Petrosian radii and ZYJHKs magnitudes is provided, as well as comparisons of the results with other surveys of galaxies towards Galactic plane.Comment: 27 pages, 10 figures, 2 tables; in press at The Astronomical Journa