The first Dirac eigenvalues on manifolds with positive scalar curvature

We show that on every compact spin manifold admitting a Riemannian metric of positive scalar curvature Friedrich's eigenvalue estimate for the Dirac operator can be made sharp up to an arbitrarily small given error by choosing the metric suitably.

     

Resolving flame thickness using high-speed chemiluminescence imaging of OH* and CH* in spherically expanding methane–air flames

The coupling of CFD simulations with detailed chemical kinetics presents great progress in predicting the complex behavior of reacting flows, but also requires validated input parameters in the form of experimental data. The spatial profile of a combustion wave represents one such parameter, which can be directly measured using chemiluminescence imaging of a spherically expanding flame. In this work, emission signals from electronically excited methylidyne (CH*) and hydroxyl (OH*) radicals near 434 nm and 315 nm, respectively, from spherically expanding methane–air flames at 1 atm and 298 K were recorded for equivalence ratios of 0.8, 1.0, and 1.2. Spatial profiles of normalized intensity were compared to predicted profiles from AramcoMech2.0. The effect of image resolution was investigated by repeating experiments for three levels of image pixel density. An Abel inversion was employed to extract intensity profiles of CH* and OH* at flame radii up to 6.5 cm. Measured flame thickness increased as flames grew in size, but this behavior diminished as image resolution increased. A linear stretch correlation was used to extrapolate measured thicknesses to an unstretched thickness for each experimental condition. Radical-based flame thicknesses and corresponding spatial profiles were found to be highly dependent on image resolution, and at high resolution, measured flame thickness appeared to approach the kinetically predicted radical-based thicknesses. This paper lays the foundation for future, comprehensive measurements of spherical, laminar flames that can resolve the flame zone details to a level of precision not typically seen in the literature, providing benchmark data for both kinetics model validation and CFD model inputs. As a result, the measurements thus far indicate that the measured flame zone thickness based on electronically excited species is much closer to the length scale typically predicted by kinetics models than what has been seen in most experiments to date.     

MFI zeolite as adsorbent for selective recovery of hydrocarbons from ABE fermentation broths

1-Butanol and butyric acid are two interesting compounds that may be produced by acetone, butanol, and ethanol fermentation using e.g. Clostridium acetobutylicum. The main drawback, restricting the commercialization potential of this process, is the toxicity of butanol for the cell culture resulting in low concentrations of this compound in the broth. To make this process economically viable, an efficient recovery process has to be developed. In this work, a hydrophobic MFI type zeolite with high silica to alumina ratio was evaluated as adsorbent for the recovery of butanol and butyric acid from model solutions. Dual component adsorption experiments revealed that both butanol and butyric acid showed a high affinity for the hydrophobic MFI zeolite when adsorbed from aqueous model solutions. Multicomponent adsorption experiments using model solutions, mimicking real fermentation broths, revealed that the adsorbent was very selective to the target compounds. Further, the adsorption of butyric and acetic acid was found to be pH dependent with high adsorption below, and low adsorption above, the respective pKa values of the acids. Thermal desorption of butanol from MFI type zeolite was also studied and a suitable desorption temperature was identified.     

Parametrization of seesaw models and light sterile neutrinos

The recent recomputation of the neutrino fluxes from nuclear reactors relaxes the tension between the LSND and MiniBooNE anomalies and disappearance data when interpreted in terms of sterile neutrino oscillations. The simplest extension of the Standard Model with such fermion singlets is the addition of right-handed sterile neutrinos with small Majorana masses. Even when introducing three right-handed neutrinos, this scenario has less free parameters than the 3 + 2 scenarios studied in the literature. This begs the question whether the best fit regions obtained can be reproduced by this simplest extension of the Standard Model. In order to address this question, we devise an exact parametrization of Standard Model extensions with right-handed neutrinos. Apart from the usual 3×3 neutrino mixing matrix and the 3 masses of the lightest neutrinos, the extra degrees of freedom are encoded in another 3×3 unitary matrix and 3 additional mixing angles. The parametrization includes all the correlations among masses and mixings and is valid beyond the usual seesaw approximation. Through this parametrization we find that the best fit regions for the LSND and MiniBooNE anomalies in a 3 + 2 scenario can indeed be reproduced despite the smaller number of degrees of freedom.     

An automatic peak finding method for LC‐MS data using Gaussian second derivative filtering

A highly automated procedure for localising and characterising peaks in the chromatographic time domain of LC‐MS data has been developed. The work was initiated by an identified need to facilitate the detection and tracking of chromatographic peaks during method development for the analysis of impurities in pharmaceutical products. The algorithm is mainly based on a digital filter for which the settings are automatically adapted to the data set under study. The procedure was evaluated for synthetic data sets with various S/N levels, peak widths and baseline properties. It was found that even for the worst case tested with S/N=10 and a high variability in the baseline, 94% of the simulated analytical peaks could be detected without producing any false‐positive identifications. Furthermore, the number of correctly estimated peak heights and peak widths falling within a 10% error of the true values were 94 and 91%, respectively. For experimental data sets, peak height, and width estimations were more difficult, but the processed reconstructions showed an excellent agreement with the analytical signals of the raw data, and also a clearly improved visualisation in total ion‐ and base‐peak chromatograms.     

Triplet excitation energy transfer in porphyrin-based donor--bridge--acceptor systems with conjugated bridges of varying length: an experimental and DFT study

A series of donor--bridge--acceptor (D--B--A) systems with varying donor-acceptor distances have been studied with respect to their triplet energy transfer properties. The donor and acceptor moieties, zinc(II), and free-base porphyrin, respectively, were separated by 2-5 oligo-p-phenyleneethynylene units (OPE) giving rise to edge-to-edge separations ranging between 12.7 and 33.4 A. The study was performed in 2-MTHF at 150 K and it was established that triplet excitation energy transfer occurs with high efficiency in all of the studied D--B--A systems. The distance dependence was exponential with an attenuation factor, beta, equal to 0.45 +/- 0.015 A(-1). The experimental study was also supported by quantum mechanical DFT and TD-DFT calculations on a series of closely related model systems. A thorough analysis of the OPE-bridge conformational dynamics led to an equation that quantitatively models the distance dependence of the electronic coupling found in the experimental study.     

Option pricing for large agents

This paper considers arbitrage-free option pricing in the presence of large agents. These large agents have a significant market power, and their trading strategies influence the dynamics of the financial asset prices. First, a simple asset pricing model in the presence of large agents is presented. Then a nonlinear partial differential equation is found for the prices of European options in the model. The unit option price depends on the large agent's asset holdings. Finally, a game model is introduced for the interaction between different market players. In this game, the outstanding number of options, as well as the option price, is found as a Nash equilibrium.     

Optimal static-dynamic hedges for exotic options under convex risk measures

We study the problem of optimally hedging exotic derivatives positions using a combination of dynamic trading strategies in underlying stocks and static positions in vanilla options when the performance is quantified by a convex risk measure. We establish conditions for the existence of an optimal static position for general convex risk measures, and then analyze in detail the case of shortfall risk with a power loss function. Here we find conditions for uniqueness of the static hedge. We illustrate the computational challenge of computing the market-adjusted risk measure in a simple diffusion model for an option on a non-traded asset.     

Supercycled symmetry-based double-quantum dipolar recoupling of quadrupolar spins in MAS NMR: I. Theory

Using average Hamiltonian (AH) theory, we analyze recently introduced homonuclear dipolar recoupling pulse sequences for exciting central-transition double-quantum coherences (2QC) between half-integer spin quadrupolar nuclei undergoing magic-angle-spinning. Several previously observed differences among the recoupling schemes concerning their compensation to resonance offsets and radio-frequency (rf) inhomogeneity may qualitatively be rationalized by an AH analysis up to third perturbation order, despite its omission of first-order quadrupolar interactions. General aspects of the engineering of 2Q-recoupling pulse sequences applicable to half-integer spins are discussed, emphasizing the improvements offered from a diversity of supercycles providing enhanced suppression of undesirable AH cross-terms between resonance offsets and rf amplitude errors.     

Fast 29Si magic-angle-spinning NMR acquisitions by RAPT-CP 27Al --> 29Si polarization transfer

Using enhancement of the 27Al central-transition magnetization by applying RAPT prior to 27Al --> 29Si cross-polarization, we demonstrate fast acquisition of 29Si one-dimensional MAS and two-dimensional 27Al-29Si HETCOR spectra on a new sialon phase Ba2Al3Si9N13O5.