On a class of extremal solutions of a moment problem for rational matrix-valued functions in the nondegenerate case II

AbstractThe main theme of this paper is the discussion of a family of extremal solutions of a finite moment problem for rational matrix functions in the nondegenerate case. We will point out that each member of this family is extremal in several directions. Thereby, the investigations below continue the studies in Fritzsche et al. (in press) [1]. In doing so, an application of the theory of orthogonal rational matrix functions with respect to a nonnegative Hermitian matrix Borel measure on the unit circle is used to get some insights into the structure of the extremal solutions in question. In particular, we explain characterizations of these solutions in the whole solution set in terms of orthogonal rational matrix functions. We will also show that the associated Riesz–Herglotz transform of such a particular solution admits specific representations, where orthogonal rational matrix functions are involved

Real and imaginary edge states in stacked Floquet honeycomb lattices

We present a non-Hermitian Floquet model with topological edge states in real and imaginary band gaps. The model utilizes two stacked honeycomb lattices which can be related via four different types of non-Hermitian time-reversal symmetry. Implementing the correct time-reversal symmetry provides us with either two counterpropagating edge states in a real gap, or a single edge state in an imaginary gap. The counterpropagating edge states allow for either helical or chiral transport along the lattice perimeter. In stark contrast, we find that the edge state in the imaginary gap does not propagate. Instead, it remains spatially localized while its amplitude continuously increases. Our model is well-suited for realizing these edge states in photonic waveguide lattices

The Akademii Nauk ice core and solar activity

Ice cores are well established archives for paleo-environmental studies, but this requires a reliable ice core chronology. The concentration of cosmogenic radionuclides in ice cores reflects the solar activity in the past and can be used as dating tool for ice cores. Accelerator mass spectrometry (AMS) allows the determination of nuclides in high resolution. Here we present results of a 10Be study in an ice core from Akademii Nauk (Severnaya Zemlya, Russian Arctic). AMS analyses of more than 500 samples were carried out using the 6 MV accelerator facility of the Ion Beam Centre of the Helmholtz-Zentrum Dresden-Rossendorf. For the time period 400 to 2000 CE the temporal variations of 10Be reflect the centennial variations of solar activity known from similar studies of Greenlandic ice cores and from 14C production reconstructions. The 10Be peak of 775 CE, today understood as result of the strongest known solar particle storm, was found by high resolution core analysis. This peak is used as tie point (additionally to volcanic reference horizons) for the development of the depth-age relationship of the Akademii Nauk ice core. Indications of the so called “Carrington Event” of 1859 CE, 20 to 30 times weaker than 775 CE, could also be detected in the core

Structure and composition of Fe-OM co-precipitates that form in soil-derived solutions

Iron oxides represent a substantial fraction of secondary minerals and particularly affect the reactive properties of natural systems in which they formed, e.g. in soils and sediments. Yet, it is still obscure how transient conditions in the solution will affect the properties of in situ precipitated Fe oxides. Transient compositions, i.e. compositions that change with time, arise due to predominant non-equilibrium states in natural systems, e.g. between liquid and solid phases in soils. In this study, we characterize Fe-OM co-precipitates that formed in pH-neutral exfiltrates from anoxic topsoils under transient conditions. We applied soil column outflow experiments, in which Fe2+was discharged with the effluent from anoxic soil and subsequently oxidized in the effluent due to contact with air. Our study features three novel aspects being unconsidered so far: i) the transient composition of soil-derived solutions, ii) that pedogenic Fe oxides instead of Fe salts serve as major source for Fe2+ in soil solution and iii) the presence of exclusively soil-derived organic and inorganic compounds during precipitation. The experiments were carried out with two topsoil materials that differed in composition, texture and land use. Derived from Mössbauer spectroscopy, broad distributions in quadrupole splittings (0 - 2 mm s-1) and magnetic hyperfine fields (35 - 53 T) indicated the presence of low-crystalline ferrihydrite and even lower crystalline Fe phases in all Fe-OM co-precipitates. There was no unequivocal evidence for other Fe oxides, i.e. lepidocrocite and (nano)goethite. The Fe-OM co-precipitates contained inorganic (P, sulfate, silicate, Al, As) and organic compounds (proteins, polysaccharides), which were concurrently discharged from the soils. Their content in the Fe-OM co-precipitates was controlled by their respective concentration in the soil-derived solution. On a molar basis, OC and Fe were the main components in the Fe-OM co-precipitates (OC/Fe ratio = 0.5 - 2). The elemental composition of the Fe-OM co-precipitates was in accordance with the sequential precipitation of Fe(III)phosphates/arsenates prior to the formation of ferrihydrite. This explains decreasing Si contents in the Fe-OM co-precipitates with increasing availability of P. With respect to constant mean quadrupole splittings and slightly decreasing mean magnetic hyperfine fields, increasing contents of OC, P and Al in the Fe-OM co-precipitates did not further increase the structural disorder of the Fe polyhedra, while the crystallite interactions slightly decreased. Scanning electron microscopy and dynamic light scattering revealed the coincidental presence of variably sized aggregates and a considerable amount of Fe-OM co-precipitates, which remained dispersed in solution for months. Thus, variably composed Fe-OM co-precipitates with highly diverse aggregate sizes and comparably constant poor crystallinity can be expected after the oxidation of Fe2+ in transient, soil-derived solutions