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Orthogonality, Lommel integrals and cross product zeros of linear combinations of Bessel functions
(2015)
The cylindrical Bessel differential equation and the spherical Bessel differential equation in the interval R\(\leq\)r\(\leq\)\(\gamma\)R with Neumann boundary conditions are considered. The eigenfunctions are linear combinations of the Bessel function \(\Phi\)\(_{n,ν}\)(r) = Y'\(_{ν}\) (\(\lambda\)\(_{n,ν}\))J\(_{ν}\)(\(\lambda\)\(_{n,ν}\) r/R) - J'\(_{ν}\)(\(\lambda\)\(_{n,ν}\))Y\(_{ν}\)(\(\lambda\)\(_{n,ν}\)r/R) or linear combinations of the spherical Bessel functions \(\psi\)\(_{m,ν}\)(r) = y'\(_{ν}\)(\(\lambda\)\(_{m,ν}\))j\(_{ν}\)(\(\lambda\)\(_{m,ν}\)r/R) - j'\(_{ν}\)(\(\lambda\)\(_{m,ν}\))y\(_{ν}\)(\(\lambda\)\(_{m,ν}\)r/R). The orthogonality relations with analytical expressions for the normalization constant are given. Explicit expressions for the Lommel integrals in terms of Lommel functions are derived. The cross product zeros Y'\(_{ν}\)\(\lambda\)\(_{n,ν}\))J'\(_{ν}\)(\(\gamma\)\(\lambda\)\(_{n,ν}\))- J'\(_{ν}\)(\(\lambda\)\(_{n,ν}\))Y'\(_{ν}\)(\(\gamma\)\(\lambda\)\(_{n,ν}\)) = 0 and y'\(_{ν}\)(\(\lambda\)\(_{m,ν}\))j'\(_{ν}\)(\(\gamma\)\(\lambda\)\(_{m,ν}\)) - j'\(_{ν}\)(\(\lambda\)\(_{m,ν}\))y'\(_{ν}\)(\(\gamma\)\(\lambda\)\(_{m,ν}\)) = 0 are considered in the complex plane for real as well as complex values of the index ν and approximations for the exceptional zero \(\lambda\)\(_{1,ν}\) are obtained. A numerical scheme based on the discretization of the twodimensional and three-dimensional Laplace operator with Neumann boundary conditions is presented. Explicit representations of the radial part of the Laplace operator in form of a tridiagonal matrix allow the simple computation of the cross product zeros.
Purpose
Non-invasive end-points for interventional trials and tailored treatment regimes in chronic obstructive pulmonary disease (COPD) for monitoring regionally different manifestations of lung disease instead of global assessment of lung function with spirometry would be valuable. Proton nuclear magnetic resonance imaging (1H-MRI) allows for a radiation-free assessment of regional structure and function. The aim of this study was to evaluate the short-term reproducibility of a comprehensive morpho-functional lungMRI protocol in COPD.
Materials and Methods
20 prospectively enrolled COPD patients (GOLD I-IV) underwent 1H-MRI of the lung at 1.5T on two consecutive days, including sequences for morphology, 4D contrast-enhanced perfusion, and respiratory mechanics. Image quality and COPD-related morphological and functional changes were evaluated in consensus by three chest radiologists using a dedicated MRI-based visual scoring system. Test-retest reliability was calculated per each individual lung lobe for the extent of large airway (bronchiectasis, wall thickening, mucus plugging) and small airway abnormalities (tree in bud, peripheral bronchiectasis, mucus plugging), consolidations, nodules, parenchymal defects and perfusion defects. The presence of tracheal narrowing, dystelectasis, pleural effusion, pulmonary trunk ectasia, right ventricular enlargement and, finally, motion patterns of diaphragma and chest wall were addressed.
Results
Median global scores [10(Q1:8.00; Q3:16.00) vs. 11(Q1:6.00; Q3:15.00)] as well as category subscores were similar between both timepoints, and kappa statistics indicated "almost perfect" global agreement (\(\kappa\)= 0.86, 95%CI = 0.81-0.91). Most subscores showed at least "substantial" agreement of MRI1 and MRI2 (\(\kappa\)= 0.64-1.00), whereas the agreement for the diagnosis of dystelectasis/effusion (\(\kappa\)= 0.42, 95%CI = 0.00-0.93) was "moderate" and of tracheal abnormalities (\(\kappa\)= 0.21, 95%CI = 0.00-0.75) "fair". Most MRI acquisitions showed at least diagnostic quality at MRI1 (276 of 278) and MRI2 (259 of 264).
Conclusion
Morpho-functional 1H-MRI can be obtained with reproducible image quality and high short-term test-retest reliability for COPD-related morphological and functional changes of the lung. This underlines its potential value for the monitoring of regional lung characteristics in COPD trials.
Efficient and fast on-demand single photon sources have been sought after as critical components of quantum information science. We report an efficient and tunable single photon source based on an InAs quantum dot (QD) embedded in a photonic crystal cavity coupled with a highly curved \(\mu\)-fibre. Exploiting evanescent coupling between the \(\mu\)-fibre and the cavity, a high collection efficiency of 23% and Purcell-enhanced spontaneous emissions are observed. In our scheme, the spectral position of a resonance can be tuned by as much as 1.5 nm by adjusting the contact position of the \(\mu\)-fibre, which increases the spectral coupling probability between the QD and the cavity mode. Taking advantage of the high photon count rate and the tunability, the collection efficiencies and the decay rates are systematically investigated as a function of the QD-cavity detuning.
The charge carrier lifetime is an important parameter in solar cells as it defines, together with the mobility, the diffusion length of the charge carriers, thus directly determining the optimal active layer thickness of a device. Herein, we report on charge carrier lifetime values in bromine doped planar methylammonium lead iodide (MAPbI\(_3\)) solar cells determined by transient photovoltage. The corresponding charge carrier density has been derived from charge carrier extraction. We found increased lifetime values in solar cells incorporating bromine compared to pure MAPbI\(_3\) by a factor of ~2.75 at an illumination intensity corresponding to 1 sun. In the bromine containing solar cells we additionally observe an anomalously high value of extracted charge, which we deduce to originate from mobile ions.
We report a giant thermal shift of 2.1 MHz/K related to the excited-state zero-field splitting in the silicon vacancy centers in 4H silicon carbide. It is obtained from the indirect observation of the optically detected magnetic resonance in the excited state using the ground state as an ancilla. Alternatively, relative variations of the zero-field splitting for small temperature differences can be detected without application of radiofrequency fields, by simply monitoring the photoluminescence intensity in the vicinity of the level anticrossing. This effect results in an all-optical thermometry technique with temperature sensitivity of 100 mK/Hz\(^{1/2}\) for a detection volume of approximately 10\(^{−6}\) mm\(^3\). In contrast, the zero-field splitting in the ground state does not reveal detectable temperature shift. Using these properties, an integrated magnetic field and temperature sensor can be implemented on the same center.
We uncover the fine structure of a silicon vacancy in isotopically purified silicon carbide (4H-\(^{28}\)SiC) and reveal not yet considered terms in the spin Hamiltonian, originated from the trigonal pyramidal symmetry of this spin-3/2 color center. These terms give rise to additional spin transitions, which would be otherwise forbidden, and lead to a level anticrossing in an external magnetic field. We observe a sharp variation of the photoluminescence intensity in the vicinity of this level anticrossing, which can be used for a purely all-optical sensing of the magnetic field. We achieve dc magnetic field sensitivity better than 100 nT/√Hz within a volume of 3×10\(^{−7}\)mm\(^3\) at room temperature and demonstrate that this contactless method is robust at high temperatures up to at least 500 K. As our approach does not require application of radio-frequency fields, it is scalable to much larger volumes. For an optimized light-trapping waveguide of 3 mm\(^3\), the projection noise limit is below 100 fT/√Hz.
Analysis of Triplet Exciton Loss Pathways in PTB7:PC\(_{71}\)BM Bulk Heterojunction Solar Cells
(2016)
A strategy for increasing the conversion efficiency of organic photovoltaics has been to increase the VOC by tuning the energy levels of donor and acceptor components. However, this opens up a new loss pathway from an interfacial charge transfer state to a triplet exciton (TE) state called electron back transfer (EBT), which is detrimental to device performance. To test this hypothesis, we study triplet formation in the high performing PTB7:PC\(_{71}\)BM blend system and determine the impact of the morphology-optimizing additive 1,8-diiodoctane (DIO). Using photoluminescence and spin-sensitive optically detected magnetic resonance (ODMR) measurements at low temperature, we find that TEs form on PC\(_{71}\)BM via intersystem crossing from singlet excitons and on PTB7 via EBT mechanism. For DIO blends with smaller fullerene domains, an increased density of PTB7 TEs is observed. The EBT process is found to be significant only at very low temperature. At 300 K, no triplets are detected via ODMR, and electrically detected magnetic resonance on optimized solar cells indicates that TEs are only present on the fullerenes. We conclude that in PTB7:PC\(_{71}\)BM devices, TE formation via EBT is impacted by fullerene domain size at low temperature, but at room temperature, EBT does not represent a dominant loss pathway.
The second-order correlation function g\(^2\)(\(\tau\) = 0), input-output curves and pulse duration of the emission from a microcavity exciton-polariton system subsequent to picosecond-pulsed excitation are measured for different temperatures. At low temperatures a two-threshold behaviour emerges, which has been attributed to the onset of polariton lasing and conventional lasing at the first and the second threshold, respectively. We observe that polariton lasing is stable up to temperatures comparable with the exciton binding energy. At higher temperatures a single threshold displays the direct transition from thermal emission to photon lasing.
The photoluminescence of annealed Cd\(_x\)Zn\(_{1-x}\)Se quantum dots (QDs) under the influence of an external magnetic field has been studied in this paper. Post-growth annealing was performed for different annealing times. Above a critical annealing time, the QD luminescence shows a pronounced red-shift of the Zeeman split magnetic subcomponents. This observation is in contrast to the blue-shift caused by the diamagnetic behavior that is usually observed in non-magnetic QDs. We attribute our finding to the paramagnetism caused by the mixing of heavy and light hole states. Hence, post-growth thermal annealing treatment might be employed to render undoped epitaxial QDs intrinsically magnetic in a controlled manner. Two theoretical models were developed: a few-particle model to account for excitonic complex effects and a multiband calculation that describes the valence band hybridization. Contrasting the two models allowed us to unambiguously elucidate the nature of such an effect.
Graphene's peculiar electronic band structure makes it of interest for new electronic and spintronic approaches. However, potential applications suffer from quantization effects when the spatial extension reaches the nanoscale. We show by photoelectron spectroscopy on nanoscaled model systems (disc-shaped, planar polyacenes) that the two-dimensional band structure is transformed into discrete states which follow the momentum dependence of the graphene Bloch states. Based on a simple model of quantum wells, we show how the band structure of graphene emerges from localized states, and we compare this result with ab initio calculations which describe the orbital structure.
This Letter presents a search at the LHC for s-channel single top-quark production in proton–proton collisions at a centre-of-mass energy of 8 TeV. The analyzed data set was recorded by the ATLAS detector and corresponds to an integrated luminosity of 20.3 fb\(^{−1}\). Selected events contain one charged lepton, large missing transverse momentum and exactly two b-tagged jets. A multivariate event classifier based on boosted decision trees is developed to discriminate s-channel single top-quark events from the main background contributions. The signal extraction is based on a binned maximum-likelihood fit of the output classifier distribution. The analysis leads to an upper limit on the s-channel single top-quark production cross-section of 14.6 pb at the 95% confidence level. The fit gives a cross-section of σs=5.0±4.3 pb, consistent with the Standard Model expectation.
Measurements of the centrality and rapidity dependence of inclusive jet production in \(\sqrt{^SNN}\)=5.02 TeV proton–lead (p+Pb) collisions and the jet cross-section in \(\sqrt{s}\)=2.76 TeV proton–proton collisions are presented. These quantities are measured in datasets corresponding to an integrated luminosity of 27.8 nb\(^{−1}\) and 4.0 pb\(^{−1}\), respectively, recorded with the ATLAS detector at the Large Hadron Collider in 2013. The p+Pb collision centrality was characterised using the total transverse energy measured in the pseudorapidity interval −4.9<η<−3.2 in the direction of the lead beam. Results are presented for the double-differential per-collision yields as a function of jet rapidity and transverse momentum (\(p_T\)) for minimum-bias and centrality-selected p+Pb collisions, and are compared to the jet rate from the geometric expectation. The total jet yield in minimum-bias events is slightly enhanced above the expectation in a \(p_T\)-dependent manner but is consistent with the expectation within uncertainties. The ratios of jet spectra from different centrality selections show a strong modification of jet production at all \(p_T\) at forward rapidities and for large \(p_T\) at mid-rapidity, which manifests as a suppression of the jet yield in central events and an enhancement in peripheral events. These effects imply that the factorisation between hard and soft processes is violated at an unexpected level in proton–nucleus collisions. Furthermore, the modifications at forward rapidities are found to be a function of the total jet energy only, implying that the violations may have a simple dependence on the hard parton–parton kinematics.
The spatial uniformity of GaSb- and InAs substrate-based structures containing type II quantum wells was probed by means of large-scale photoluminescence (PL) mapping realized utilizing a Fourier transform infrared spectrometer. The active region was designed and grown in a form of a W-shaped structure with InAs and GaInSb layers for confinement of electrons and holes, respectively. The PL spectra were recorded over the entire 2-in. wafers, and the parameters extracted from each spectrum, such as PL peak energy position, its linewidth and integrated intensity, were collected in a form of two-dimensional spatial maps. Throughout the analysis of these maps, the wafers' homogeneity and precision of the growth procedure were investigated. A very small variation of PL peak energy over the wafer indicates InAs quantum well width fluctuation of only a fraction of a monolayer and hence extraordinary thickness accuracy, a conclusion further supported by high uniformity of both the emission intensity and PL linewidth.
Practical quantum communication between remote quantum memories rely on single photons at telecom wavelengths. Although spin-photon entanglement has been demonstrated in atomic and solid-state qubit systems, the produced single photons at short wavelengths and with polarization encoding are not suitable for long-distance communication, because they suffer from high propagation loss and depolarization in optical fibres. Establishing entanglement between remote quantum nodes would further require the photons generated from separate nodes to be indistinguishable. Here, we report the observation of correlations between a quantum-dot spin and a telecom single photon across a 2-km fibre channel based on time-bin encoding and background-free frequency downconversion. The downconverted photon at telecom wavelengths exhibits two-photon interference with another photon from an independent source, achieving a mean wavepacket overlap of greater than 0.89 despite their original wavelength mismatch (900 and 911 nm). The quantum-networking operations that we demonstrate will enable practical communication between solid-state spin qubits across long distances.
Microstructural Analysis of Peripheral Lung Tissue through CPMG Inter-Echo Time R2 Dispersion
(2015)
Since changes in lung microstructure are important indicators for (early stage) lung pathology, there is a need for quantifiable information of diagnostically challenging cases in a clinical setting, e.g. to evaluate early emphysematous changes in peripheral lung tissue. Considering alveoli as spherical air-spaces surrounded by a thin film of lung tissue allows deriving an expression for Carr-Purcell-Meiboom-Gill transverse relaxation rates R-2 with a dependence on inter-echo time, local air-tissue volume fraction, diffusion coefficient and alveolar diameter, within a weak field approximation. The model relaxation rate exhibits the same hyperbolic tangent dependency as seen in the Luz-Meiboom model and limiting cases agree with Brooks et al. and Jensen et al. In addition, the model is tested against experimental data for passively deflated rat lungs: the resulting mean alveolar radius of RA = 31.46 \(\pm\) 13.15 \(\mu\)m is very close to the literature value (similar to 34 \(\mu\)m). Also, modeled radii obtained from relaxometer measurements of ageing hydrogel foam (that mimics peripheral lung tissue) are in good agreement with those obtained from mu CT images of the same foam (mean relative error: 0.06 \(\pm\) 0.01). The model's ability to determine the alveolar radius and/or air volume fraction will be useful in quantifying peripheral lung microstructure.
Search for the \(X_b\) and other hidden-beauty states in the \(π^+π^−ϒ\)(1S) channel at ATLAS
(2014)
This Letter presents a search for a hidden-beauty counterpart of the X(3872) in the mass ranges of 10.05–10.31 GeV and 10.40–11.00 GeV, in the channel X\(_b\)→π\(^+\)π\(^−\)ϒ(1S)(→μ\(^+\)μ\(^−\)), using 16.2 fb\(^{−1}\) of s=8 TeV \(pp\) collision data collected by the ATLAS detector at the LHC. No evidence for new narrow states is found, and upper limits are set on the product of the X\(_b\) cross section and branching fraction, relative to those of the ϒ(2S), at the 95% confidence level using the CLSCLS approach. These limits range from 0.8% to 4.0%, depending on mass. For masses above 10.1 GeV, the expected upper limits from this analysis are the most restrictive to date. Searches for production of the ϒ(1\(^3\)D\(_J\)), ϒ(10860), and ϒ(11020) states also reveal no significant signals.
A search for new charged massive gauge bosons, called W′W′, is performed with the ATLAS detector at the LHC, in proton–proton collisions at a centre-of-mass energy of \(\sqrt {s}\)=8 TeV, using a dataset corresponding to an integrated luminosity of 20.3 fb\(^{−1}\). This analysis searches for W′W′ bosons in the \(W′→t\overline{b}\) decay channel in final states with electrons or muons, using a multivariate method based on boosted decision trees. The search covers masses between 0.5 and 3.0 TeV, for right-handed or left-handed W′W′ bosons. No significant deviation from the Standard Model expectation is observed and limits are set on the \(W′→t\overline{b}\) cross-section times branching ratio and on the W′W′-boson effective couplings as a function of the W′W′-boson mass using the CL\(_s\) procedure. For a left-handed (right-handed) W′W′ boson, masses below 1.70 (1.92) TeV are excluded at 95% confidence level.
Detailed measurements of the electron performance of the ATLAS detector at the LHC are reported, using decays of the Z, W and J/ψ particles. Data collected in 2010 at s√=7 TeV are used, corresponding to an integrated luminosity of almost 40 pb\(^{−1}\). The inter-alignment of the inner detector and the electromagnetic calorimeter, the determination of the electron energy scale and resolution, and the performance in terms of response uniformity and linearity are discussed. The electron identification, reconstruction and trigger efficiencies, as well as the charge misidentification probability, are also presented.
A search for the Standard Model Higgs boson in the H→WW(⋆)→ℓνℓνH→WW(⋆)→ℓνℓν (ℓ=e,μℓ=e,μ) decay mode is presented. The search is performed using proton–proton collision data corresponding to an integrated luminosity of 4.7 fb\(^{−1}\) at a centre-of-mass energy of 7 TeV collected during 2011 with the ATLAS detector at the Large Hadron Collider. No significant excess of events over the expected background is observed. An upper bound is placed on the Higgs boson production cross section as a function of its mass. A Standard Model Higgs boson with mass in the range between 133 GeV and 261 GeV is excluded at 95% confidence level, while the expected exclusion range is from 127 GeV to 233 GeV.
In Vivo Imaging of Stepwise Vessel Occlusion in Cerebral Photothrombosis of Mice by \(^{19}\)F MRI
(2011)
Background
\(^{19}\)F magnetic resonance imaging (MRI) was recently introduced as a promising technique for in vivo cell tracking. In the present study we compared \(^{19}\)F MRI with iron-enhanced MRI in mice with photothrombosis (PT) at 7 Tesla. PT represents a model of focal cerebral ischemia exhibiting acute vessel occlusion and delayed neuroinflammation.
Methods/Principal Findings
Perfluorocarbons (PFC) or superparamagnetic iron oxide particles (SPIO) were injected intravenously at different time points after photothrombotic infarction. While administration of PFC directly after PT induction led to a strong \(^{19}\)F signal throughout the entire lesion, two hours delayed application resulted in a rim-like \(^{19}\)F signal at the outer edge of the lesion. These findings closely resembled the distribution of signal loss on T2-weighted MRI seen after SPIO injection reflecting intravascular accumulation of iron particles trapped in vessel thrombi as confirmed histologically. By sequential administration of two chemically shifted PFC compounds 0 and 2 hours after illumination the different spatial distribution of the \(^{19}\)F markers (infarct core/rim) could be visualized in the same animal. When PFC were applied at day 6 the fluorine marker was only detected after long acquisition times ex vivo. SPIO-enhanced MRI showed slight signal loss in vivo which was much more prominent ex vivo indicative for neuroinflammation at this late lesion stage.
Conclusion
Our study shows that vessel occlusion can be followed in vivo by \(^{19}\)F and SPIO-enhanced high-field MRI while in vivo imaging of neuroinflammation remains challenging. The timing of contrast agent application was the major determinant of the underlying processes depicted by both imaging techniques. Importantly, sequential application of different PFC compounds allowed depiction of ongoing vessel occlusion from the core to the margin of the ischemic lesions in a single MRI measurement.