Plasmons as sensors

“Plasmon” is a synonym for collective oscillations of the conduction electrons in a metal nanoparticle (excited by an incoming light wave), which cause strong optical responses like efficient light scattering. The scattering cross-section with respect to the light wavelength depends not only on material, size and shape of the nanoparticle, but also on the refractive index of the embedding medium. For this reason, plasmonic nanoparticles are interesting candidates for sensing applications. Here, two novel setups for rapid spectral investigations of single nanoparticles and different sensing experiments are presented.rnrnPrecisely, the novel setups are based on an optical microscope operated in darkfield modus. For the fast single particle spectroscopy (fastSPS) setup, the entrance pinhole of a coupled spectrometer is replaced by a liquid crystal device (LCD) acting as spatially addressable electronic shutter. This improvement allows the automatic and continuous investigation of several particles in parallel for the first time. The second novel setup (RotPOL) usesrna rotating wedge-shaped polarizer and encodes the full polarization information of each particle within one image, which reveals the symmetry of the particles and their plasmon modes. Both setups are used to observe nanoparticle growth in situ on a single-particle level to extract quantitative data on nanoparticle growth.rnrnUsing the fastSPS setup, I investigate the membrane coating of gold nanorods in aqueous solution and show unequivocally the subsequent detection of protein binding to the membrane. This binding process leads to a spectral shift of the particles resonance due to the higher refractive index of the protein compared to water. Hence, the nanosized addressable sensor platform allows for local analysis of protein interactions with biological membranes as a function of the lateral composition of phase separated membranes.rnrnThe sensitivity on changes in the environmental refractive index depends on the particles’ aspect ratio. On the basis of simulations and experiments, I could present the existence of an optimal aspect ratio range between 3 and 4 for gold nanorods for sensing applications. A further sensitivity increase can only be reached by chemical modifications of the gold nanorods. This can be achieved by synthesizing an additional porous gold cage around the nanorods, resulting in a plasmon sensitivity raise of up to 50 % for those “nanorattles” compared to gold nanorods with the same resonance wavelength. Another possibility isrnto coat the gold nanorods with a thin silver shell. This reduces the single particle’s resonance spectral linewidth about 30 %, which enlarges the resolution of the observable shift. rnrnThis silver coating evokes the interesting effect of reducing the ensemble plasmon linewidth by changing the relation connecting particle shape and plasmon resonance wavelength. This change, I term plasmonic focusing, leads to less variation of resonance wavelengths for the same particle size distribution, which I show experimentally and theoretically.rnrnIn a system of two coupled nanoparticles, the plasmon modes of the transversal and longitudinal axis depend on the refractive index of the environmental solution, but only the latter one is influenced by the interparticle distance. I show that monitoring both modes provides a self-calibrating system, where interparticle distance variations and changes of the environmental refractive index can be determined with high precision.

Measurements of ttbar Differential Cross Section at the ATLAS Experiment in pp Collisions at sqrt(s)=7TeV and sqrt(s)=8TeV

This PhD thesis presents two measurements of differential production cross section of top and anti-top pairs tt ̅ decaying in a lepton+jets final state. The normalize cross section is measured as a function of the top transverse momentum and the tt ̅ mass, transverse momentum and rapidity using the full 2011 proton-proton (pp) ATLAS data taking at a center of mass energy of √s=7 TeV and corresponding to an integrated luminosity of L=4.6 〖fb〗^(-1). The cross section is also measured at the particle level as a function of the hadronic top transverse momentum for highly energetic events using the full 2012 data taking at √s=8 TeV and with L=20 〖fb〗^(-1). The measured spectra are fully corrected for detector efficiency and resolution effects and are compared to several theoretical predictions showing a quite good agreement, depending on different spectra.

Rheology of arrested colloids : a parameter study using novel experimental methods

The steadily increasing diversity of colloidal systems demands for new theoretical approaches and a cautious experimental characterization. Here we present a combined rheological and microscopical study of colloids in their arrested state whereas we did not aim for a generalized treatise but rather focused on a few model colloids, liquid crystal based colloidal suspensions and sedimented colloidal films. We laid special emphasis on the understanding of the mutual influence of dominant interaction mechanisms, structural characteristics and the particle properties on the mechanical behavior of the colloid. The application of novel combinations of experimental techniques played an important role in these studies. Beside of piezo-rheometry we employed nanoindentation experiments and associated standardized analysis procedures. These rheometric methods were complemented by real space images using confocal microscopy. The flexibility of the home-made setup allowed for a combination of both techniques and thereby for a simultaneous rheological and three-dimensional structural analysis on a single particle level. Though, the limits of confocal microscopy are not reached by now. We show how hollow and optically anisotropic particles can be utilized to quantify contact forces and rotational motions for individual particles. In future such data can contribute to a better understanding of particle reorganization processes, such as the liquidation of colloidal gels and glasses under shear.

Wet and dry model granulates under mechanical load : a confocal microscopy study

Granular matter, also known as bulk solids, consists of discrete particles with sizes between micrometers and meters. They are present in many industrial applications as well as daily life, like in food processing, pharmaceutics or in the oil and mining industry. When handling granular matter the bulk solids are stored, mixed, conveyed or filtered. These techniques are based on observations in macroscopic experiments, i.e. rheological examinations of the bulk properties. Despite the amply investigations of bulk mechanics, the relation between single particle motion and macroscopic behavior is still not well understood. For exploring the microscopic properties on a single particle level, 3D imaging techniques are required.rnThe objective of this work was the investigation of single particle motions in a bulk system in 3D under an external mechanical load, i.e. compression and shear. During the mechanical load the structural and dynamical properties of these systems were examined with confocal microscopy. Therefor new granular model systems in the wet and dry state were designed and prepared. As the particles are solid bodies, their motion is described by six degrees of freedom. To explore their entire motion with all degrees of freedom, a technique to visualize the rotation of spherical micrometer sized particles in 3D was developed. rnOne of the foci during this dissertation was a model system for dry cohesive granular matter. In such systems the particle motion during a compression of the granular matter was investigated. In general the rotation of single particles was the more sensitive parameter compared to the translation. In regions with large structural changes the rotation had an earlier onset than the translation. In granular systems under shear, shear dilatation and shear zone formation were observed. Globally the granular sediments showed a shear behavior, which was known already from classical shear experiments, for example with Jenike cells. Locally the shear zone formation was enhanced, when near the applied load a pre-diluted region existed. In regions with constant volume fraction a mixing between the different particle layers occurred. In particular an exchange of particles between the current flowing region and the non-flowing region was observed. rnThe second focus was on model systems for wet granular matter, where an additional binding liquid is added to the particle suspension. To examine the 3D structure of the binding liquid on the micrometer scale independently from the particles, a second illumination and detection beam path was implemented. In shear and compression experiments of wet clusters and bulk systems completely different dynamics compared to dry cohesive models systems occured. In a Pickering emulsion-like system large structural changes predominantly occurred in the local environment of binding liquid droplets. These large local structural changes were due to an energy interplay between the energy stored in the binding droplet during its deformation and the binding energy of particles at the droplet interface. rnConfocal microscopy in combination with nanoindentation gave new insights into the single particle motions and dynamics of granular systems under a mechanical load. These novel experimental results can help to improve the understanding of the relationship between bulk properties of granular matter, such as volume fraction or yield stress and the dynamics on a single particle level.rnrn

Plasmon-enhanced dynamic light scattering of gold nanorods in bulk and near a wall

Transportprozesse von anisotropen metallischen Nanopartikeln wie zum Beispiel Gold-Nanostäbchen in komplexen Flüssigkeiten und/oder begrenzten Geometrien spielen eine bedeutende Rolle in einer Vielzahl von biomedizinischen und industriellen Anwendungen. Ein Weg zu einem tiefen, grundlegenden Verständnis von Transportmechanismen ist die Verwendung zweier leistungsstarker Methoden - dynamischer Lichtstreuung (DLS) und resonanzverstärkter Lichtstreuung (REDLS) in der Nähe einer Grenzfläche. In dieser Arbeit wurden nanomolare Suspensionen von Gold-Nanostäbchen, stabilisiert mit Cetyltrimethylammoniumbromid (CTAB), mit DLS sowie in der Nähe einer Grenzfläche mit REDLS untersucht. Mit DLS wurde eine wellenlängenabhängige Verstärkung der anisotropen Streuung beobachtet, welche sich durch die Anregung von longitudinaler Oberflächenplasmonenresonanz ergibt. Die hohe Streuintensität nahe der longitudinalen Oberflächenplasmonenresonanzfrequenz für Stäbchen, welche parallel zum anregenden optischen Feld liegen, erlaubte die Auflösung der translationalen Anisotropie in einem isotropen Medium. Diese wellenlängenabhängige anisotrope Lichtstreuung ermöglicht neue Anwendungen wie etwa die Untersuchung der Dynamik einzelner Partikel in komplexen Umgebungen mittels depolarisierter dynamischer Lichtstreuung. In der Nähe einer Grenzfläche wurde eine starke Verlangsamung der translationalen Diffusion beobachtet. Hingegen zeigte sich für die Rotation zwar eine ausgeprägte aber weniger starke Verlangsamung. Um den möglichen Einfluss von Ladung auf der festen Grenzfläche zu untersuchen, wurde das Metall mit elektrisch neutralem Polymethylmethacrylat (PMMA) beschichtet. In einem weiteren Ansatz wurde das CTAB in der Gold-Nanostäbchen Lösung durch das kovalent gebundene 16-Mercaptohexadecyltrimethylammoniumbromid (MTAB) ersetzt. Daraus ergab sich eine deutlich geringere Verlangsamung.

Studio e sviluppo di un metodo di detezione della camera atriale in ecografia intracardiaca

Il lavoro di tesi si è svolto in collaborazione con il laboratorio di elettrofisiologia, Unità Operativa di Cardiologia, Dipartimento Cardiovascolare, dell’ospedale “S. Maria delle Croci” di Ravenna, Azienda Unità Sanitaria Locale della Romagna, ed ha come obiettivo lo sviluppo di un metodo per l’individuazione dell’atrio sinistro in sequenze di immagini ecografiche intracardiache acquisite durante procedure di ablazione cardiaca transcatetere per il trattamento della fibrillazione atriale. La localizzazione della parete posteriore dell'atrio sinistro in immagini ecocardiografiche intracardiache risulta fondamentale qualora si voglia monitorare la posizione dell'esofago rispetto alla parete stessa per ridurre il rischio di formazione della fistola atrio esofagea. Le immagini derivanti da ecografia intracardiaca sono state acquisite durante la procedura di ablazione cardiaca ed esportate direttamente dall’ecografo in formato Audio Video Interleave (AVI). L’estrazione dei singoli frames è stata eseguita implementando un apposito programma in Matlab, ottenendo così il set di dati su cui implementare il metodo di individuazione della parete atriale. A causa dell’eccessivo rumore presente in alcuni set di dati all’interno della camera atriale, sono stati sviluppati due differenti metodi per il tracciamento automatico del contorno della parete dell’atrio sinistro. Il primo, utilizzato per le immagini più “pulite”, si basa sull’utilizzo del modello Chan-Vese, un metodo di segmentazione level-set region-based, mentre il secondo, efficace in presenza di rumore, sfrutta il metodo di clustering K-means. Entrambi i metodi prevedono l’individuazione automatica dell’atrio, senza che il clinico fornisca informazioni in merito alla posizione dello stesso, e l’utilizzo di operatori morfologici per l’eliminazione di regioni spurie. I risultati così ottenuti sono stati valutati qualitativamente, sovrapponendo il contorno individuato all'immagine ecografica e valutando la bontà del tracciamento. Inoltre per due set di dati, segmentati con i due diversi metodi, è stata eseguita una valutazione quantitativa confrontatoli con il risultato del tracciamento manuale eseguito dal clinico.

L'informazione di fase per la segmentazione volumetrica di dati ecocardiografici

L’imaging ad ultrasuoni è una tecnica di indagine utilizzata comunemente per molte applicazioni diagnostiche e terapeutiche. La tecnica ha numerosi vantaggi: non è invasiva, fornisce immagini in tempo reale e l’equipaggiamento necessario è facilmente trasportabile. Le immagini ottenute con questa tecnica hanno tuttavia basso rapporto segnale rumore a causa del basso contrasto e del rumore caratteristico delle immagini ad ultrasuoni, detto speckle noise. Una corretta segmentazione delle strutture anatomiche nelle immagini ad ultrasuoni è di fondamentale importanza in molte applicazioni mediche . Nella pratica clinica l’identificazione delle strutture anatomiche è in molti casi ancora ottenuta tramite tracciamento manuale dei contorni. Questo processo richiede molto tempo e produce risultati scarsamente riproducibili e legati all’esperienza del clinico che effettua l’operazione. In ambito cardiaco l’indagine ecocardiografica è alla base dello studio della morfologia e della funzione del miocardio. I sistemi ecocardiografici in grado di acquisire in tempo reale un dato volumetrico, da pochi anni disponibili per le applicazioni cliniche, hanno dimostrato la loro superiorità rispetto all’ecocardiografia bidimensionale e vengono considerati dalla comunità medica e scientifica, la tecnica di acquisizione che nel futuro prossimo sostituirà la risonanza magnetica cardiaca. Al fine di sfruttare appieno l’informazione volumetrica contenuta in questi dati, negli ultimi anni sono stati sviluppati numerosi metodi di segmentazione automatici o semiautomatici tesi alla valutazione della volumetria del ventricolo sinistro. La presente tesi descrive il progetto, lo sviluppo e la validazione di un metodo di segmentazione ventricolare quasi automatico 3D, ottenuto integrando la teoria dei modelli level-set e la teoria del segnale monogenico. Questo approccio permette di superare i limiti dovuti alla scarsa qualità delle immagini grazie alla sostituzione dell’informazione di intensità con l’informazione di fase, che contiene tutta l’informazione strutturale del segnale.

Intracellular imaging of nanoparticles: is it an elemental mistake to believe what you see?

In order to understand how nanoparticles (NPs <100 nm) interact with cellular systems, potentially causing adverse effects, it is important to be able to detect and localize them within cells. Due to the small size of NPs, transmission electron microscopy (TEM) is an appropriate technique to use for visualizing NPs inside cells, since light microscopy fails to resolve them at a single particle level. However, the presence of other cellular and non-cellular nano-sized structures in TEM cell samples, which may resemble NPs in size, morphology and electron density, can obstruct the precise intracellular identification of NPs. Therefore, elemental analysis is recommended to confirm the presence of NPs inside the cell. The present study highlights the necessity to perform elemental analysis, specifically energy filtering TEM, to confirm intracellular NP localization using the example of quantum dots (QDs). Recently, QDs have gained increased attention due to their fluorescent characteristics, and possible applications for biomedical imaging have been suggested. Nevertheless, potential adverse effects cannot be excluded and some studies point to a correlation between intracellular particle localization and toxic effects. J774.A1 murine macrophage-like cells were exposed to NH2 polyethylene (PEG) QDs and elemental co-localization analysis of two elements present in the QDs (sulfur and cadmium) was performed on putative intracellular QDs with electron spectroscopic imaging (ESI). Both elements were shown on a single particle level and QDs were confirmed to be located inside intracellular vesicles. Nevertheless, ESI analysis showed that not all nano-sized structures, initially identified as QDs, were confirmed. This observation emphasizes the necessity to perform elemental analysis when investigating intracellular NP localization using TEM.

Automated cement segmentation in vertebroplasty

Vertebroplasty is a minimally invasive procedure with many benefits; however, the procedure is not without risks and potential complications, of which leakage of the cement out of the vertebral body and into the surrounding tissues is one of the most serious. Cement can leak into the spinal canal, venous system, soft tissues, lungs and intradiscal space, causing serious neurological complications, tissue necrosis or pulmonary embolism. We present a method for automatic segmentation and tracking of bone cement during vertebroplasty procedures, as a first step towards developing a warning system to avoid cement leakage outside the vertebral body. We show that by using active contours based on level sets the shape of the injected cement can be accurately detected. The model has been improved for segmentation as proposed in our previous work by including a term that restricts the level set function to the vertebral body. The method has been applied to a set of real intra-operative X-ray images and the results show that the algorithm can successfully detect different shapes with blurred and not well-defined boundaries, where the classical active contours segmentation is not applicable. The method has been positively evaluated by physicians.

THE HOLOGRAPHIC DETECTOR FOR CLOUDS FROM TRL 5 TO TRL 8

Clouds are one of the most influential elements of weather on the earth system, yet they are also one of the least understood. Understanding their composition and behavior at small scales is critical to understanding and predicting larger scale feedbacks. Currently, the best method to study clouds on the microscale is through airborne in situ measurements using optical instruments capable of resolving clouds on the individual particle level. However, current instruments are unable to sufficiently resolve the scales important to cloud evolution and behavior. The Holodec is a new generation of optical cloud instrument which uses digital inline holography to overcome many of the limitations of conventional instruments. However, its performance and reliability was limited due to several deficiencies in its original design. These deficiencies were addressed and corrected to advance the instrument from the prototype stage to an operational instrument. In addition, the processing software used to reconstruct and analyze digitally recorded holograms was improved upon to increase robustness and ease of use.

Measurement of kT splitting scales in W→lv events at sqrt(s)=7 TeV with the ATLAS detector

A measurement of splitting scales, as defined by the kT clustering algorithm, is presented for final states containing a W boson produced in proton-proton collisions at a centre-of-mass energy of 7 TeV. The measurement is based on the full 2010 data sample corresponding to an integrated luminosity of 36 pb(-1) which was collected using the ATLAS detector at the CERN Large Hadron Collider. Cluster splitting scales are measured in events containing W bosons decaying to electrons or muons. The measurement comprises the four hardest splitting scales in a k(T) cluster sequence of the hadronic activity accompanying the W boson, and ratios of these splitting scales. Backgrounds such as multi-jet and top-quark-pair production are subtracted and the results are corrected for detector effects. Predictions from various Monte Carlo event generators at particle level are compared to the data. Overall, reasonable agreement is found with all generators, but larger deviations between the predictions and the data are evident in the soft regions of the splitting scales.

Measurement of differential production cross-sections for a ℤ boson in association with b-jets in 7 TeV proton-proton collisions with the ATLAS detector

Measurements of differential production cross-sections of a Z boson in association with b-jets in pp collisions at √s = 7TeV are reported. The data analysed correspond to an integrated luminosity of 4.6 fb−1 recorded with the ATLAS detector at the Large Hadron Collider. Particle-level cross-sections are determined for events with a Z boson decaying into an electron or muon pair, and containing b-jets. For events with at least one b-jet, the cross-section is presented as a function of the Z boson transverse momentum and rapidity, together with the inclusive b-jet cross-section as a function of b-jet transverse momentum, rapidity and angular separations between the b-jet and the Z boson. For events with at least two b-jets, the cross-section is determined as a function of the invariant mass and angular separation of the two highest transverse momentum b-jets, and as a function of the Z boson transverse momentum and rapidity. Results are compared to leading-order and next-to-leading-order perturbative QCD calculations.

Measurement of dijet cross sections in pp collisions at 7 TeV centre-of-mass energy using the ATLAS detector

Double-differential dijet cross-sections measured in pp collisions at the LHC with a 7TeV centre-of-mass energy are presented as functions of dijet mass and half the rapidity separation of the two highest-pT jets. These measurements are obtained using data corresponding to an integrated luminosity of 4.5 fb−1, recorded by the ATLAS detector in 2011. The data are corrected for detector effects so that cross-sections are presented at the particle level. Cross-sections are measured up to 5TeV dijet mass using jets reconstructed with the anti-kt algorithm for values of the jet radius parameter of 0.4 and 0.6. The cross-sections are compared with next-to-leading-order perturbative QCD calculations by NLOJet++ corrected to account for non-perturbative effects. Comparisons with POWHEG predictions, using a next-to-leading-order matrix element calculation interfaced to a partonshower Monte Carlo simulation, are also shown. Electroweak effects are accounted for in both cases. The quantitative comparison of data and theoretical predictions obtained using various parameterizations of the parton distribution functions is performed using a frequentist method. In general, good agreement with data is observed for the NLOJet++ theoretical predictions when using the CT10, NNPDF2.1 and MSTW 2008 PDF sets. Disagreement is observed when using the ABM11 and HERAPDF1.5 PDF sets for some ranges of dijet mass and half the rapidity separation. An example setting a lower limit on the compositeness scale for a model of contact interactions is presented, showing that the unfolded results can be used to constrain contributions to dijet production beyond that predicted by the Standard Model.

Seaweed - epiphyte - mesograzer communities were tested for their responses to elevated seawater temperature and [CO2] in benthic mesocosms experiments across four consecutive seasons of one year in Kiel, Germany

Rising seawater temperature and CO2 concentrations (ocean acidification) represent two of the most influential factors impacting marine ecosystems in the face of global climate change. In ecological climate change research full-factorial experiments across seasons in multi-species, cross-trophic level set-ups are essential as they allow making realistic estimations about direct and indirect effects and the relative importance of both major environmental stressors on ecosystems. In benthic mesocosm experiments we tested the responses of coastal Baltic Sea Fucus vesiculosus communities to elevated seawater temperature and CO2 concentrations across four seasons of one year. While increasing [CO2] levels only had minor effects, warming had strong and persistent effects on grazers which affected the Fucus community differently depending on season. In late summer a temperature-driven collapse of grazers caused a cascading effect from the consumers to the foundation species resulting in overgrowth of Fucus thalli by epiphytes. In fall/ winter, outside the growing season of epiphytes, intensified grazing under warming resulted in a significant reduction of Fucus biomass. Thus, we confirm the prediction that future increasing water temperatures influence marine food-web processes by altering top-down control, but we also show that specific consequences for food-web structure depend on season. Since Fucus vesiculosus is the dominant habitat-forming brown algal system in the Baltic Sea, its potential decline under global warming implicates the loss of key functions and services such as provision of nutrient storage, substrate, food, shelter and nursery grounds for a diverse community of marine invertebrates and fish in Baltic Sea coastal waters.

Uso de DES y RANS no estacionario para la simulación del flujo alrededor de una carena Wigley - Use of Unsteady RANS and DES to simulate flows around a Wigley Hull)

Computer Fluid Dynamics tools have already become a valuable instrument for Naval Architects during the ship design process, thanks to their accuracy and the available computer power. Unfortunately, the development of RANSE codes, generally used when viscous effects play a major role in the flow, has not reached a mature stage, being the accuracy of the turbulence models and the free surface representation the most important sources of uncertainty. Another level of uncertainty is added when the simulations are carried out for unsteady flows, as those generally studied in seakeeping and maneuvering analysis and URANS equations solvers are used. Present work shows the applicability and the benefits derived from the use of new approaches for the turbulence modeling (Detached Eddy Simulation) and the free surface representation (Level Set) on the URANS equations solver CFDSHIP-Iowa. Compared to URANS, DES is expected to predict much broader frequency contents and behave better in flows where boundary layer separation plays a major role. Level Set methods are able to capture very complex free surface geometries, including breaking and overturning waves. The performance of these improvements is tested in set of fairly complex flows, generated by a Wigley hull at pure drift motion, with drift angle ranging from 10 to 60 degrees and at several Froude numbers to study the impact of its variation. Quantitative verification and validation are performed with the obtained results to guarantee their accuracy. The results show the capability of the CFDSHIP-Iowa code to carry out time-accurate simulations of complex flows of extreme unsteady ship maneuvers. The Level Set method is able to capture very complex geometries of the free surface and the use of DES in unsteady simulations highly improves the results obtained. Vortical structures and instabilities as a function of the drift angle and Fr are qualitatively identified. Overall analysis of the flow pattern shows a strong correlation between the vortical structures and free surface wave pattern. Karman-like vortex shedding is identified and the scaled St agrees well with the universal St value. Tip vortices are identified and the associated helical instabilities are analyzed. St using the hull length decreases with the increase of the distance along the vortex core (x), which is similar to results from other simulations. However, St scaled using distance along the vortex cores shows strong oscillations compared to almost constants for those previous simulations. The difference may be caused by the effect of the free-surface, grid resolution, and interaction between the tip vortex and other vortical structures, which needs further investigations. This study is exploratory in the sense that finer grids are desirable and experimental data is lacking for large α, especially for the local flow. More recently, high performance computational capability of CFDSHIP-Iowa V4 has been improved such that large scale computations are possible. DES for DTMB 5415 with bilge keels at α = 20º were conducted using three grids with 10M, 48M and 250M points. DES analysis for flows around KVLCC2 at α = 30º is analyzed using a 13M grid and compared with the results of DES on the 1.6M grid by. Both studies are consistent with what was concluded on grid resolution herein since dominant frequencies for shear-layer, Karman-like, horse-shoe and helical instabilities only show marginal variation on grid refinement. The penalties of using coarse grids are smaller frequency amplitude and less resolved TKE. Therefore finer grids should be used to improve V&V for resolving most of the active turbulent scales for all different Fr and α, which hopefully can be compared with additional EFD data for large α when it becomes available.