Solving Large-Scale Optimization Problems Related to Bell's Theorem

Impossibility of finding local realistic models for quantum correlations due to entanglement is an important fact in foundations of quantum physics, gaining now new applications in quantum information theory. We present an in-depth description of a method of testing the existence of such models, which involves two levels of optimization: a higher-level non-linear task and a lower-level linear programming (LP) task. The article compares the performances of the existing implementation of the method, where the LPs are solved with the simplex method, and our new implementation, where the LPs are solved with a matrix-free interior point method. We describe in detail how the latter can be applied to our problem, discuss the basic scenario and possible improvements and how they impact on overall performance. Significant performance advantage of the matrix-free interior point method over the simplex method is confirmed by extensive computational results. The new method is able to solve problems which are orders of magnitude larger. Consequently, the noise resistance of the non-classicality of correlations of several types of quantum states, which has never been computed before, can now be efficiently determined. An extensive set of data in the form of tables and graphics is presented and discussed. The article is intended for all audiences, no quantum-mechanical background is necessary.Comment: 19 pages, 7 tables, 1 figur

Linear Contraction Behavior of Low-Carbon, Low-Alloy Steels During and After Solidification Using Real-Time Measurements

A technique for measuring the linear contraction during and after solidification of low-alloy steel was developed and used for examination of two commercial low-carbon and low-alloy steel grades. The effects of several experimental parameters on the contraction were studied. The solidification contraction behavior was described using the concept of rigidity in a solidifying alloy, evolution of the solid fraction, and the microstructure development during solidification. A correlation between the linear contraction properties in the solidification range and the hot crack susceptibility was proposed and used for the estimation of hot cracking susceptibility for two studied alloys and verified with the real casting practice. The technique allows estimation of the contraction coefficient of commercial steels in a wide range of temperatures and could be helpful for computer simulation and process optimization during continuous casting. © 2013 The Minerals, Metals & Materials Society and ASM International

An update on the Hirsch conjecture

The Hirsch conjecture was posed in 1957 in a letter from Warren M. Hirsch to George Dantzig. It states that the graph of a d-dimensional polytope with n facets cannot have diameter greater than n - d. Despite being one of the most fundamental, basic and old problems in polytope theory, what we know is quite scarce. Most notably, no polynomial upper bound is known for the diameters that are conjectured to be linear. In contrast, very few polytopes are known where the bound $n-d$ is attained. This paper collects known results and remarks both on the positive and on the negative side of the conjecture. Some proofs are included, but only those that we hope are accessible to a general mathematical audience without introducing too many technicalities.Comment: 28 pages, 6 figures. Many proofs have been taken out from version 2 and put into the appendix arXiv:0912.423

Solidification of Al alloys under electromagnetic pulses and characterization of the 3D microstructures under synchrotron x-ray tomography

A novel programmable electromagnetic pulse device was developed and used to study the solidification of Al-15 pct Cu and Al-35 pct Cu alloys. The pulsed magnetic fluxes and Lorentz forces generated inside the solidifying melts were simulated using finite element methods, and their effects on the solidification microstructures were characterized using electron microscopy and synchrotron X-ray tomography. Using a discharging voltage of 120 V, a pulsed magnetic field with the peak Lorentz force of ~1.6 N was generated inside the solidifying Al-Cu melts which were showed sufficiently enough to disrupt the growth of the primary Al dendrites and the Al2Cu intermetallic phases. The microstructures exhibit a strong correlation to the characteristics of the applied pulse, forming a periodical pattern that resonates the frequency of the applied electromagnetic field

Effect of a nurse-coordinated prevention programme on cardiovascular risk after an acute coronary syndrome: main results of the RESPONSE randomised trial

Objective To quantify the impact of a practical, hospital-based nurse-coordinated prevention programme on cardiovascular risk, integrated into the routine clinical care of patients discharged after an acute coronary syndrome, as compared with usual care only. Design RESPONSE (Randomised Evaluation of Secondary Prevention by Outpatient Nurse SpEcialists) was a randomised clinical trial. Setting Multicentre trial in secondary and tertiary healthcare settings. Participants 754 patients admitted for acute coronary syndrome. Intervention A nurse-coordinated prevention programme, consisting of four outpatient nurse clinic visits, focusing on healthy lifestyles, biometric risk factors and medication adherence, in addition to usual care. Main outcome measures The main outcome was 10-year cardiovascular mortality risk as estimated by Systematic Coronary Risk Evaluation at 12 months follow-up. Secondary outcomes included Framingham Coronary Risk Score at 12 months, in addition to changes in individual risk factors. Risk factor control was classified as ‘poor’ if 0 to 3 factors were on target, ‘fair’ if 4 to 6 factors were on target, and ‘good’ if 7 to 9 were on target. Results The mean Systematic Coronary Risk Evaluation at 12 months was 4.4 per cent (SD 4.5) in the intervention group and 5.4 per cent (SD 6.2) in the control group (p=0.021), representing a 17.4% relative risk reduction. At 12 months, risk factor control classified as ‘good’ was achieved in 35% of patients in the intervention group compared with 25% in the control group (p=0.003). Attendance to the nurse-coordinated prevention programme was 92%. In the intervention group, 86 rehospitalisations were observed against 132 in the control group (relative risk reduction 34.8%, p=0.023). Conclusions The nurse-coordinated hospital-based prevention programme in addition to usual care is a practical, yet effective method for reduction of cardiovascular risk in patients with coronary disease. Our data suggest that the counselling component of the programme may lead to a reduction in hospital readmissions

The Influence of the effect of solute on the thermodynamic driving force on grain refinement of Al alloys

Grain refinement is known to be strongly affected by the solute in cast alloys. Addition of some solute can reduce grain size considerably while others have a limited effect. This is usually attributed to the constitutional supercooling which is quantified by the growth restriction factor, Q. However, one factor that has not been considered is whether different solutes have differing effects on the thermodynamic driving force for solidification. This paper reveals that addition of solute reduces the driving force for solidification for a given undercooling, and that for a particular Q value, it is reduced more substantially when adding eutectic-forming solutes than peritectic-forming elements. Therefore, compared with the eutectic-forming solutes, addition of peritectic-forming solutes into Al alloys not only possesses a higher initial nucleation rate resulted from the larger thermodynamic driving force for solidification, but also promotes nucleation within the constitutionally supercooled zone during growth. As subsequent nucleation can occur at smaller constitutional supercoolings for peritectic-forming elements, a smaller grain size is thus produced. The very small constitutional supercooling required to trigger subsequent nucleation in alloys containing Ti is considered as a major contributor to its extraordinary grain refining efficiency in cast Al alloys even without the deliberate addition of inoculants.The Australian Research Council (ARC DP10955737)

An epitaxial model for heterogeneous nucleation on potent substrates

© The Minerals, Metals & Materials Society and ASM International 2012In this article, we present an epitaxial model for heterogeneous nucleation on potent substrates. It is proposed that heterogeneous nucleation of the solid phase (S) on a potent substrate (N) occurs by epitaxial growth of a pseudomorphic solid (PS) layer on the substrate surface under a critical undercooling (ΔT ). The PS layer with a coherent PS/N interface mimics the atomic arrangement of the substrate, giving rise to a linear increase of misfit strain energy with layer thickness. At a critical thickness (h ), elastic strain energy reaches a critical level, at which point, misfit dislocations are created to release the elastic strain energy in the PS layer. This converts the strained PS layer to a strainless solid (S), and changes the initial coherent PS/N interface into a semicoherent S/N interface. Beyond this critical thickness, further growth will be strainless, and solidification enters the growth stage. It is shown analytically that the lattice misfit (f) between the solid and the substrate has a strong influence on both h and ΔT ; h decreases; and ΔT increases with increasing lattice misfit. This epitaxial nucleation model will be used to explain qualitatively the generally accepted experimental findings on grain refinement in the literature and to analyze the general approaches to effective grain refinement.EPSRC Centre for Innovative Manufacturing in Liquid Metal Engineerin

Simulation of Channel Segregation During Directional Solidification of In—75 wt pct Ga. Qualitative Comparison with In Situ Observations

International audienceFreckles are common defects in industrial casting. They result from thermosolutal convection due to buoyancy forces generated from density variations in the liquid. The present paper proposes a numerical analysis for the formation of channel segregation using the three-dimensional (3D) cellular automaton (CA)—finite element (FE) model. The model integrates kinetics laws for the nucleation and growth of a microstructure with the solution of the conservation equations for the casting, while introducing an intermediate modeling scale for a direct representation of the envelope of the dendritic grains. Directional solidification of a cuboid cell is studied. Its geometry, the alloy chosen as well as the process parameters are inspired from experimental observations recently reported in the literature. Snapshots of the convective pattern, the solute distribution, and the morphology of the growth front are qualitatively compared. Similitudes are found when considering the coupled 3D CAFE simulations. Limitations of the model to reach direct simulation of the experiments are discussed