Detection of Voigt Spectral Line Profiles of Hydrogen Radio Recombination Lines toward Sagittarius B2(N)

We report the detection of Voigt spectral line profiles of radio recombination lines (RRLs) toward Sagittarius B2(N) with the 100 m Green Bank Telescope (GBT). At radio wavelengths, astronomical spectra are highly populated with RRLs, which serve as ideal probes of the physical conditions in molecular cloud complexes. An analysis of the Hn alpha lines presented herein shows that RRLs of higher principal quantum number (n > 90) are generally divergent from their expected Gaussian profiles and, moreover, are well described by their respective Voigt profiles. This is in agreement with the theory that spectral lines experience pressure broadening as a result of electron collisions at lower radio frequencies. Given the inherent technical difficulties regarding the detection and profiling of true RRL wing spans and shapes, it is crucial that the observing instrumentation produce flat baselines as well as high-sensitivity, high-resolution data. The GBT has demonstrated its capabilities regarding all of these aspects, and we believe that future observations of RRL emission via the GBT will be crucial toward advancing our knowledge of the larger-scale extended structures of ionized gas in the interstellar medium (ISM).

Xheal: A localized self-healing algorithm using expanders

We consider the problem of self-healing in reconfigurable networks e.g., peer-to-peer and wireless mesh networks. For such networks under repeated attack by an omniscient adversary, we propose a fully distributed algorithm, Xheal, that maintains good expansion and spectral properties of the network, while keeping the network connected. Moreover, Xheal does this while allowing only low stretch and degree increase per node. The algorithm heals global properties like expansion and stretch while only doing local changes and using only local information. We also provide bounds on the second smallest eigenvalue of the Laplacian which captures key properties such as mixing time, conductance, congestion in routing etc. Xheal has low amortized latency and bandwidth requirements. Our work improves over the self-healing algorithms Forgiving tree [PODC 2008] andForgiving graph [PODC 2009] in that we are able to give guarantees on degree and stretch, while at the same time preserving the expansion and spectral properties of the network.

How does Oyster work? The simple interpretation of Oyster mathematics

Oyster® is a surface-piercing flap-type device designed to harvest wave energy in the nearshore environment. Established mathematical theories of wave energy conversion, such as 3D point-absorber and 2D terminator theory, are inadequate to accurately describe the behaviour of Oyster, historically resulting in distorted conclusions regarding the potential of such a concept to harness the power of ocean waves. Accurately reproducing the dynamics of Oyster requires the introduction of a new reference mathematical model, the “flap-type absorber”. A flap-type absorber is a large thin device which extracts energy by pitching about a horizontal axis parallel to the ocean bottom. This paper unravels the mathematics of Oyster as a flap-type absorber. The main goals of this work are to provide a simple–yet accurate–physical interpretation of the laws governing the mechanism of wave power absorption by Oyster and to emphasise why some other, more established, mathematical theories cannot be expected to accurately describe its behaviour.

Spectral isometries into commutative Banach algebras

We determine the structure of spectral isometries between unital Banach algebras under the hypothesis that the codomain is commutative.

Kelvin-Helmholtz instability in solar chromospheric jets: theory and observation

Using data obtained by the high-resolution CRisp Imaging SpectroPolarimeter instrument on the Swedish 1 m Solar Telescope, we investigate the dynamics and stability of quiet-Sun chromospheric jets observed at the disk center. Small-scale features, such as rapid redshifted and blueshifted excursions, appearing as high-peed jets in the wings of the Hα line, are characterized by short lifetimes and rapid fading without any descending behavior. To study the theoretical aspects of their stability without considering their formation mechanism, we model chromospheric jets as twisted magnetic flux tubes moving along their axis, and use the ideal linear incompressible magnetohydrodynamic approximation to derive the governing dispersion equation. Analytical solutions of the dispersion equation indicate that this type of jet is unstable to Kelvin–Helmholtz instability (KHI), with a very short (few seconds) instability growth time at high upflow speeds. The generated vortices and unresolved turbulent flows associated with the KHI could be observed as a broadening of chromospheric spectral lines. Analysis of the Hα line profiles shows that the detected structures have enhanced line widths with respect to the background. We also investigate the stability of a larger-scale Hα jet that was ejected along the line of sight. Vortex-like features, rapidly developing around the jet’s boundary, are considered as evidence of the KHI. The analysis of the energy equation in the partially ionized plasma shows that ion–neutral collisions may lead to fast heating of the KH vortices over timescales comparable to the lifetime of chromospheric jets.