Asymptotics of Block Toeplitz Determinants and the Classical Dimer Model

We compute the asymptotics of a block Toeplitz determinant which arises in the classical dimer model for the triangular lattice when considering the monomer-monomer correlation function. The model depends on a parameter interpolating between the square lattice (t = 0) and the triangular lattice (t = 1), and we obtain the asymptotics for 0 < t ≤ 1. For 0 < t < 1 we apply the Szegö Limit Theorem for block Toeplitz determinants. The main difficulty is to evaluate the constant term in the asymptotics, which is generally given only in a rather abstract form.     

NIFTy 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters

NIFTy , “Numerical Information Field Theory,” is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high‐dimensional real‐world problems. This paper introduces NIFTy  3, a major upgrade to the original NIFTy  framework. NIFTy  3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy  3 is able to handle non‐scalar fields, such as vector or tensor fields. The functionality and performance of the software package is demonstrated with example code, which implements a mock inference inspired by a real‐world algorithm from the realm of information field theory. NIFTy  3 is open‐source software available under the GNU General Public License v3 (GPL‐3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/tree/NIFTy_3 .     

Formation of Sim and SimCn clusters by C60 sputtering of Si

The secondary ion mass spectrum of silicon sputtered by high energy C₆₀⁺ ions in sputter equilibrium is found to be dominated by Si clusters and we report the relative yields of Si_m⁺ (1 ≤ m ≤ 15) and various Si_mC_n⁺ clusters (1 ≤ m ≤ 11 for n = 1; 1 ≤ m ≤ 6 for n = 2; 1 ≤ m ≤ 4 for n = 3). The yields of Si_m⁺ clusters up to Si₇⁺ are significant (between 0.1 and 0.6 of the Si⁺ yield) with even numbered clusters Si₄⁺ and Si₆⁺ having the highest probability of formation. The abundances of cluster ions between Si₈⁺ and Si₁₁⁺ are still significant (>1% relative to Si⁺) but drop by a factor of ∼100 between Si₁₁⁺ and Si₁₃⁺. The probability of formation of clusters Si₁₃⁺-Si₁₅⁺ is approximately constant at ∼5 × 10⁻⁴ relative to Si⁺ and rising a little for Si₁₅⁺, but clusters beyond Si₁₅ are not detected (Si_m≥16⁺/Si⁺ < 1 × 10⁻⁴). The probability of formation of Si_m⁺ and Si_mC_n⁺ clusters depends only very weakly on the C₆₀⁺ primary ion energy between 13.5 keV and 37.5 keV. The behaviour of Si_m⁺ and Si_mC_n⁺ cluster ions was also investigated for impacts onto a fresh Si surface to study the effects that saturation of the surface with C₆₀⁺ in reaching sputter equilibrium may have had on the measured abundances. By comparison, there are very minor amounts of pure Si_m⁺ clusters produced during C₆₀⁺ sputtering of silica (SiO₂) and various silicate minerals. The abundances for clusters heavier than Si₂⁺ are very small compared to the case where Si is the target.The data reported here suggest that Si_m⁺ and Si_mC_n⁺ cluster abundances may be consistent in a qualitative way with theoretical modelling by others which predicts each carbon atom to bind with 3-4 Si atoms in the sample. This experimental data may now be used to improve theoretical modelling.     

The importance of cochlear processing for the formation of auditory brainstem and frequency following responses

A model for the generation of auditory brainstem responses (ABR) and frequency following responses (FFRs) is presented. The model is based on the concept introduced by Goldstein and Kiang [J. Acoust. Soc. Am. 30, 107-114 (1958)] that evoked potentials recorded at remote electrodes can theoretically be given by convolution of an elementary unit waveform (unitary response) with the instantaneous discharge rate function for the corresponding unit. In the present study, the nonlinear computational auditory-nerve model recently developed by Heinz et al. [ARLO 2(3), 91-96 (2001)] was used to calculate the instantaneous discharge rate ri(t) for fibers i in the frequency range from 0.1 and 10 kHz. The summed activity across frequency was convolved with a unitary response which is assumed to reflect contributions from different cell populations within the auditory brainstem, recorded at a given pair of electrodes on the scalp. Predicted potential patterns are compared with experimental data for a number of stimulus and level conditions. Clicks, chirps as defined in Dau et al. [J. Acoust. Soc. Am. 107, 1530-1540 (2000)], long-duration stimuli comprising the chirp, as well as tones and slowly varying tonal sweeps were considered. The results demonstrate the importance of considering the effects of the basilar-membrane traveling wave and auditory-nerve processing for the formation of ABR and FFR. Specifically, the results support the hypothesis that the FFR to low-frequency tones represents synchronized activity mainly stemming from mid- and high-frequency units at more basal sites, and not from units tuned to frequencies around the signal frequency.     

Imaging by sensitized oxygenations of photochromic anthracene films: examination of effects that improve performance and reversibility

The aliphatic anthracene compound 1 and the oligomeric anthracene 2 were synthesized. Thin films of 1 and 2 mixed with the sensitizers tetraphenylporphyrin (TPP) and methylene blue (MB) were irradiated with visible light in air. Upon formation of singlet oxygen, the anthracene units were converted quantitatively to the corresponding endoperoxides. Heating of the irradiated samples afforded the parent anthracenes with high yields. Here, we demonstrate that the kinetics and reversibility of this reaction strongly depend on the microenvironment of the anthracene groups in the two compounds. The photooxidation of thin films of 1 is accompanied by interesting changes in the morphology of the film and allows the first application of 1 as a nondestructive negative-tone photoresist for lithography and as an oxidizing ink. The morphology of 2 remained unchanged after photooxidation as a result of the stabilizing oligomer backbone. This stabilizing effect significantly improves the photochromic performance of 2. The reversibility of the photooxidation is very high (>90 %) for oligomeric films of 2 after several cycles of irradiation and heating. Decomposition of the anthracene and a loss of the activity of the sensitizer diminish slightly the performance of the monomeric species.     

Remote substituent effects on the photooxygenation of 9,10-diarylanthracenes: strong evidence for polar intermediates

Two different reaction pathways in the photooxygenation of 9,10-diarylanthracenes are identified, with strong evidence for polar (forward, singlet oxygen addition) and radical (backward, thermolysis) intermediates.     

What is the role of acid–acid interactions in asymmetric phosphoric acid organocatalysis? A detailed mechanistic study using interlocked and non-interlocked catalysts

Organocatalysis has revolutionized asymmetric synthesis. However, the supramolecular interactions of organocatalysts in solution are often neglected, although the formation of catalyst aggregates can have a strong impact on the catalytic reaction. For phosphoric acid based organocatalysts, we have now established that catalyst–catalyst interactions can be suppressed by using macrocyclic catalysts, which react predominantly in a monomeric fashion, while they can be favored by integration into a bifunctional catenane, which reacts mainly as phosphoric acid dimers. For acyclic phosphoric acids, we found a strongly concentration dependent behavior, involving both monomeric and dimeric catalytic pathways. Based on a detailed experimental analysis, DFT-calculations and direct NMR-based observation of the catalyst aggregates, we could demonstrate that intermolecular acid–acid interactions have a drastic influence on the reaction rate and stereoselectivity of asymmetric transfer-hydrogenation catalyzed by chiral phosphoric acids.

Supramolecular acid–acid interactions lead to competing monomeric and dimeric pathways in phosphoric acid catalysis – so that stereoselectivities depend on catalyst concentration.