What is the value of an observable between pre- and postselection?

Hall's recent derivation of an exact uncertainty relation [Phys. Rev. A64, 052103 (2001)] is revisited. It is found that the Bayes estimator of an observable between pre- and postselection equals the real part of the weak value. The quadratic loss function equals the expectation of the squared imaginary part of the weak value.Comment: 5 pages, accepted in Phys. Lett.

Nonclassical Properties of Coherent States

It is demonstrated that a weak measurement of the squared quadrature observable may yield negative values for coherent states. This result cannot be reproduced by a classical theory where quadratures are stochastic $c$-numbers. The real part of the weak value is a conditional moment of the Margenau-Hill distribution. The nonclassicality of coherent states can be associated with negative values of the Margenau-Hill distribution. A more general type of weak measurement is considered, where the pointer can be in an arbitrary state, pure or mixed.Comment: 4 pages. Some arguments rewritten, reference added to quant-ph/0402050. Conclusion unchange

Expression of messenger molecules and receptors in rat and human sphenopalatine ganglion indicating therapeutic targets

Background: Migraine and Cluster Headache (CH) are two primary headaches with severe disease burden. The disease expression and the mechanisms involved are poorly known. In some attacks of migraine and in most attacks of CH, there is a release of vasoactive intestinal peptide (VIP) originating from parasympathetic cranial ganglia such as the sphenopalatine ganglion (SPG). Patients suffering from these diseases are often deprived of effective drugs. The aim of the study was to examine the localization of the botulinum toxin receptor element synaptic vesicle glycoprotein 2A (SV-2A) and the vesicular docking protein synaptosomal-associated protein 25 (SNAP25) in human and rat SPG. Additionally the expression of the neurotransmitters pituitary adenylate cyclase activating polypeptide (PACAP-38), nitric oxide synthase (nNOS), VIP and 5-hydroxttryptamine subtype receptors (5-HT1B,1D,1F) were examined. Methods: SPG from adult male rats and from humans, the later removed at autopsy, were prepared for immunohistochemistry using specific antibodies against neurotransmitters, 5-HT1B,1D,1F receptors, and botulinum toxin receptor elements. Results: We found that the selected neurotransmitters and 5-HT receptors were expressed in rat and human SPG. In addition, we found SV2-A and SNAP25 expression in both rat and human SPG. We report that all three 5-HT receptors studied occur in neurons and satellite glial cells (SGCs) of the SPG. 5-HT1B receptors were in addition found in the walls of intraganglionic blood vessels. Conclusions: Recent focus on the SPG has emphasized the role of parasympathetic mechanisms in the pathophysiology of mainly CH. The development of next generation’s drugs and treatment of cranial parasympathetic symptoms, mediated through the SPG, can be modulated by treatment with BoNT-A and 5-HT receptor agonists

Quantum Mechanics of Successive Measurements with Arbitrary Meter Coupling

We study successive measurements of two observables using von Neumann's measurement model. The two-pointer correlation for arbitrary coupling strength allows retrieving the initial system state. We recover Luders rule, the Wigner formula and the Kirkwood-Dirac distribution in the appropriate limits of the coupling strength

Investigation of erosion behavior of EB-PVD-TBCs and sacrificial coatings after CMAS infiltration

Aero-engines operating in sand laden environments often encounter severe problems with thermal barrier coatings (TBCs) due to erosion damage. Since the turbine entry temperatures are raising, the life-time of TBC coatings as well as its thermal conductivity are additionally influenced by molten sand (calcium-magnesium-alumino-silicate/ CMAS). Few attempts have been made in understanding the combined impact of both erosion and CMAS effects [1,2]. Wellman and Nicholls [1] have found that a fully CMAS infiltrated electron-beam physical vapor deposited (EB-PVD) TBC behaves like a continuum during erosion and slightly improves its erosion behavior under room temperature compared to pure TBC. Development of CMAS resistant coatings has been a hot topic for the last two decades and one of the proposed method is the application of sacrificial oxide layers such as Al2O3, MgO, Sc2O3 et al. [3], on top of the TBCs. These sacrificial layers chemically react with the CMAS and modify the melting temperature or the viscosity of CMAS and thus the infiltration of CMAS into the TBC is inhibited. Since both damage mechanisms (erosion and corrosion) occur parallel and competitively in a turbine, this study focuses on deeper understanding of the erosion behavior of CMAS-infiltrated 7wt.-% yttria stabilized zirconia (7YSZ) TBCs. 400 µm thick 7YSZ coatings with two different microstructures were produced by EB-PVD. Additionally, sacrificial Al2O3 coatings were also applied on the top of 7YSZ by means of suspension plasma spraying (SPS) and suspension high velocity oxy-fuel spraying (SHVOF) using water-based suspensions. CMAS infiltration experiments were carried out at 1250 °C using different CMAS compositions and different infiltration times. Erosion tests were realized at room temperature in an in-house erosion test rig and evaluated partly by confocal microscopy. Microstructural examinations as well as crack identification before and after testing were carried out using scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX). Infiltrated TBCs behaved as a continuum material during erosion exposure which lead mainly to surface spallation. Furthermore, the CMAS infiltration in the TBCs and partly the sintering effect at 1250 °C lead to a network of vertical cracks. These vertical cracks are weak areas where severe erosion occurs. The different TBC microstructures, infiltration times and CMAS compositions strongly influence the erosion behavior of the TBC. In case of alumina top coats the microstructure and especially the presence of porosity in the coating has strongly influenced the CMAS infiltration depth, the erosion behavior, and the stability of the entire coating system. [1] R.G. Wellman, J.R. Nicholls, Erosion, corrosion and erosion–corrosion of EB PVD thermal barrier coatings, Tribology International. 41 (2008) 657–662. doi:10.1016/j.triboint.2007.10.004. [2] S. Rezanka, D.E. Mack, G. Mauer, D. Sebold, O. Guillon, R. Vaßen, Investigation of the resistance of open-column-structured PS-PVD TBCs to erosive and high-temperature corrosive attack, Surface and Coatings Technology. 324 (2017) 222–235. doi:10.1016/j.surfcoat.2017.05.003. [3] A.K. Rai, R.S. Bhattacharya, D.E. Wolfe, T.J. Eden, CMAS-Resistant Thermal Barrier Coatings (TBC), International Journal of Applied Ceramic Technology. 7 (2010) 662–674. doi:10.1111/j.1744-7402.2009.02373.x

Investigation of CMAS resistance of SPS- and SHVOF-alumina topcoats on EB-PVD 7YSZ layers

Thermal barrier coatings (TBCs) undergo severe degradation by interaction with molten calcium-magnesium-aluminum-silicate (CMAS) minerals that are found mainly in volcanic ashes (VA) or desert sands. After the infiltration of the CMAS, chemical reactions, diffusion and phase transformation can lead to residual stress, cracks and spallation and thus significantly shorten the life-time of the components. As the state-of-the-art material 7 wt.-% Y2O3 stabilized ZrO2 (7YSZ) offers limited resistance to the CMAS attack, development of CMAS-resistant TBCs has undergone intense research during the last decades. One of the proposed approaches is the application of a sacrificial layer on top of the TBC which reacts with the molten CMAS/VA to crystalline phases and in this way inhibits further infiltration by sealing the gaps and pores. Al2O3 is one candidate for such a sacrificial layer which exhibits good CMAS resistance by formation of arresting phases. However, EB‑PVD Al2O3-topcoats suffer locally from cracks that arise from crystallization and sintering shrinkage, thereby providing only a discontinuous protection against CMAS infiltration due to their characteristic morphology. Even though the alumina is a candidate material, the coating density and the arrangement of porosity has been found to be a critical factor for restricting CMAS infiltration. In this work alumina coatings were sprayed on top of EB‑PVD 7YSZ TBCs using suspension plasma spraying (SPS) and suspension high velocity oxygen fuel spraying (SHVOF) starting from an aqueous suspension containing fine dispersed Al2O3 (d50 about 2.3 µm). The spray parameters were optimized in order to produce Al2O3 topcoats with homogeneous distributed porosity from very porous (porosity about 30 %) to denser (porosity about 10-15 %). These coatings were tested under CMAS attack by performing infiltration experiments at 1250 °C for different time intervals from 5 min to 10 hours. One Island volcanic ash from the Eyjafjallajökull volcano (IVA) and two types of synthetic CMAS compositions were tested in this study. The infiltration kinetics and reaction products were studied by SEM, energy-dispersive spectroscopy (EDS) and x-ray diffraction (XRD). It was observed that the microstructure and especially the presence of the porosity in the Al2O3 coatings strongly influenced the CMAS infiltration kinetics. Due to its high and non-uniform porosity, CMAS/VA melt infiltrated the 100 µm thick, very porous alumina SPS‑coating inhomogeneously and reached the subjacent 7YSZ layer already after one hour of annealing at 1250°C. Additionally, it was found that the infiltration kinetics varies also with the chemical composition of the CMAS/VA. Different crystalline phases such as anorthite, spinel or others were formed as reaction products of the SPS‑Alumina-TBC with the CMAS/VA-melt. The exact phases and its location depend on the used CMAS/VA composition. Furthermore, the annealing time has a major influence on the presence of the various phases. The infiltration kinetics of the SHVOF‑coatings was different due to a change in morphology. The current experiments clearly demonstrate that CMAS/VA mitigation depends on the interplay between morphology of the coating which dictates the driving force for infiltration, the reaction speed between alumina and the deposit, and the deposit chemistry

Microstructure Refinement of EB-PVD Gadolinium Zirconate Thermal Barrier Coatings to Improve Their CMAS Resistance

Rare-earth zirconates are proven to be very effective in restricting the CMAS attack against thermal barrier coatings (TBCs) by forming quick crystalline reaction products that seal the porosity against infiltration. The microstructural effects on the efficacy of Electron Beam-Physical Vapor Deposition gadolinium zirconate (EB-PVD GZO) against CMAS attack are explored in this study. Four distinct GZO microstructures were manufactured and the response of two selected GZO variants to different CMAS and volcanic ash melts was studied for annealing times between 10 min and 50 h at 1250°C. A significant variation in the microstructural characteristics was achieved by altering substrate temperature and rotation speed. A refined microstructure with smaller intercolumnar gaps and long feather arms lowered the CMAS infiltration by 56%-72%. Garnet phase, which formed as a continuous layer on top of apatite and fluorite, is identified as a beneficial reaction product that improves the CMAS resistance

Quantized algebras of functions on homogeneous spaces with Poisson stabilizers

Let G be a simply connected semisimple compact Lie group with standard Poisson structure, K a closed Poisson-Lie subgroup, 0<q<1. We study a quantization C(G_q/K_q) of the algebra of continuous functions on G/K. Using results of Soibelman and Dijkhuizen-Stokman we classify the irreducible representations of C(G_q/K_q) and obtain a composition series for C(G_q/K_q). We describe closures of the symplectic leaves of G/K refining the well-known description in the case of flag manifolds in terms of the Bruhat order. We then show that the same rules describe the topology on the spectrum of C(G_q/K_q). Next we show that the family of C*-algebras C(G_q/K_q), 0<q\le1, has a canonical structure of a continuous field of C*-algebras and provides a strict deformation quantization of the Poisson algebra \C[G/K]. Finally, extending a result of Nagy, we show that C(G_q/K_q) is canonically KK-equivalent to C(G/K).Comment: 23 pages; minor changes, typos correcte

Erosion behavior of CMAS/VA infiltrated EB-PVD Gd2Zr2O7 TBCs: Special emphasis on the effect of mechanical properties of the reaction products

Aero-engines operating in sand-laden (CMAS/CaO-MgO-Al2O3-SiO2) environments often encounter severe problems with thermal barrier coatings (TBCs) due to CMAS infiltration and erosion damage. This study focuses on a deeper understanding of the erosion behavior of CMAS-infiltrated EB-PVD Gd2Zr2O7 TBCs. The study includes isothermal infiltration of different CMAS and subsequent erosion tests at room temperature. In addition to the erosion behavior of the entire coating, the influence of different reaction products within the reaction layer on erosion failure was investigated by measuring the hardness and Young’s modulus of the individual phases using in-situ REM-Nanoindentation. It was found that a garnet layer above the reaction layer and spinel inclusions within a thick apatite/fluorite reaction layer, can improve the erosion resistance of this reaction layer by 30-40%. Furthermore, a correlation between the erosion behavior and the hardness vs. Young’s modulus relation, obtained from nanoindentation over the entire coating, was observed for a consistent microstructure

Azimuthal Anisotropy of Photon and Charged Particle Emission in Pb+Pb Collisions at 158 A GeV/c

The azimuthal distributions of photons and charged particles with respect to the event plane are investigated as a function of centrality in Pb + Pb collisions at 158 A GeV/c in the WA98 experiment at the CERN SPS. The anisotropy of the azimuthal distributions is characterized using a Fourier analysis. For both the photon and charged particle distributions the first two Fourier coefficients are observed to decrease with increasing centrality. The observed anisotropies of the photon distributions compare well with the expectations from the charged particle measurements for all centralities.Comment: 8 pages and 6 figures. The manuscript has undergone a major revision. The unwanted correlations were enhanced in the random subdivision method used in the earlier version. The present version uses the more established method of division into subevents separated in rapidity to minimise short range correlations. The observed results for charged particles are in agreement with results from the other experiments. The observed anisotropy in photons is explained using flow results of pions and the correlations arising due to the decay of the neutral pion