Scattering matrices and Weyl functions

For a scattering system {A, A₀} consisting of self-adjoint extensionsA and A₀ of a symmetric operator A with finite deficiency indices,the scattering matrix {S()} and a spectral shift function arecalculated in terms of the Weyl function associated with a boundarytriplet for A*, and a simple proof of the Krein–Birmanformula is given. The results are applied to singular Sturm–Liouvilleoperators with scalar and matrix potentials, to Dirac operatorsand to Schrödinger operators with point interactions.     

Rationalizing In Situ Active Repair in Hydrogen Evolution Photocatalysis via Non-Invasive Raman Spectroscopy

Currently, most photosensitizers and catalysts used in the field of artificial photosynthesis are still based on rare earth metals and should thus be utilized as efficiently and economically as possible. While repair of an inactivated catalyst is a potential mitigation strategy, this remains a challenge. State-of-the-art methods are crucial for characterizing reaction products during photocatalysis and repair, and are currently based on invasive analysis techniques limiting real-time access to the involved mechanisms. Herein, we use an innovative in situ technique for detecting both initially evolved hydrogen and after active repair via advanced non-invasive rotational Raman spectroscopy. This facilitates unprecedently accurate monitoring of gaseous reaction products and insight into the mechanism of active repair during light-driven catalysis enabling the identification of relevant mechanistic details along with innovative repair strategies.     

Time-dependent density-functional theory in the projector augmented-wave method

We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we found perfect agreement in the calculated photoabsorption spectra. We discuss the strengths and weaknesses of the two methods as well as their convergence properties. We demonstrate different applications of the methods by calculating excitation energies and excited state Born-Oppenheimer potential surfaces for a set of atoms and molecules with the linear-response method and by calculating nonlinear emission spectra using the time-propagation method.     

Rotation of methyl radicals in a solid argon matrix

Electron spin resonance (ESR) measurements were carried out to study the rotation of methyl radicals (CH3) in a solid argon matrix at 14-35 K temperatures. The radicals were produced by dissociating methane by plasma bursts generated either by a focused 193 nm laser radiation or a radio frequency discharge device during the gas condensation on the substrate. The ESR spectrum exhibits axial symmetry at the lowest temperature and is ascribed to ground state molecules with symmetric total nuclear spin function I=3/2. The hyperfine anisotropy (Aparallel)-Aperpendicular) was found to be -0.01 mT, whereas that of the g value was 2.5x10(-5). The anisotropy is observed for the first time in Ar and is manifested by the splitting of the low-field transition. Elevation of temperature leads reversibly to the appearance of excited state contribution having antisymmetric I=1/2. As a function of the sample temperature, the relative intensities of symmetric and antisymmetric spin states corresponding to ground and excited rotor states, respectively, proton hyperfine and electron g-tensor components, and spin-lattice relaxation rates were determined by a numerical fitting procedure. The experimental observations were interpreted in terms of a free rotation about the C3 axis and a thermal activation of the C2-type rotations above 15 K. The ground and excited rotational state energy levels were found to be separated by 11.2 cm-1 and to exhibit significantly different spin-lattice coupling. A crystal field model has been applied to evaluate the energy levels of the hindered rotor in the matrix, and crystal field parameter varepsilon4=-200 cm-1, corresponding to a 60 cm-1 effective potential barrier for rotation of the C3 axis, was obtained.     

Composition Operators and Vector-valued BMOA

Analytic composition operators are studied on X-valued versions of BMOA, the space of analytic functions on the unit disk that have bounded mean oscillation on the unit circle, where X is a complex Banach space. It is shown that if X is reflexive and C _φ is compact on BMOA, then C _φ is weakly compact on the X-valued space BMOA _C (X) defined in terms of Carleson measures. A related function-theoretic characterization is given of the compact composition operators on BMOA.     

Ultrasonically determined thickness of long cortical bones: two-dimensional simulations of in vitro experiments

Previously it has been demonstrated that cortical bone thickness can be estimated from ultrasonic guided-wave measurements, in an axial transmission configuration, together with an appropriate analytical model. This study considers the impact of bone thickness variation within the measurement region on the ultrasonically determined thickness (UTh). To this end, wave velocities and UTh were determined from experiments and from time-domain finite-difference simulations of wave propagation, both performed on a set of ten human radius specimens (29 measurement sites). A two-dimensional numerical bone model was developed with tunable material properties and individualized geometry based on x-ray computed-tomography reconstructions of human radius. Cortical thickness (CTh) was determined from the latter. UTh data for simulations were indeed in a excellent accordance (root-mean-square error was 0.26 mm; r2=0.94, p<0.001) with average CTh within the measurement region. These results indicate that despite variations in cortical thickness along the propagation path, the measured phase velocity can be satisfactorily modeled by a simple analytical model (the A(0) plate mode in this case). Most of the variability (up to 85% when sites were carefully matched) observed in the in vitro ultrasound data was explained through simulations by variability in the cortical thickness alone.     

Eigenvalues of Schrödinger operators and Dirichlet-to-Neumann maps

Eigenvalues and eigenspaces of selfadjoint Schrödinger operators on are expressed in terms of Dirichlet-to-Neumann maps corresponding to Schrödinger operators on the upper and lower half space. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Open Problem: Accumulation of Nonreal Eigenvalues of Indefinite Sturm–Liouville Operators

In this note we conjecture that the eigenvalues of singular indefinite Sturm–Liouville operators accumulate to the real axis whenever the eigenvalues of the corresponding definite Sturm–Liouville operator accumulate to the bottom of the essential spectrum from below.     

Resuspension of radionuclides into the atmosphere due to forest fires

Two major wild fire episodes occurred in north-western Russia in April/May and August 2008. The burning biomass and heating of the surface soil released several hazardous components into the atmosphere. During the spring smoke episode the ¹³⁷Cs activity concentration in the air in southern Finland increased by a factor of 10 compared to values just before the episode. Simultaneously there was an increase of a same order of magnitude in the concentrations of PM₁₀, trace metals (e.g. lead), polycyclic aromatic hydrocarbons (e.g. benzo[a]pyrene) and potassium. The ²¹⁰Po/²¹⁰Pb activity ratio increased from the usual 3–5% to even as high as 35% because Po is more volatile than Pb. The summer episode was less severe but still the mercury concentration in the air increased by a factor of two while ¹³⁷Cs activity concentration rose by a factor of eight. From the radiological point of view the exposure to the increased radionuclide concentration was insignificant compared to health hazards due to the increased concentration of aerosol particles and their chemical components.     

The Effect of Void Structure on the Permeability of Fibrous Networks

A Kozeny–Carman-based model of permeability for fibrous networks is proposed: the original model is extended by incorporating information about the local structure of the void space. Furthermore, it is demonstrated how in practice this added structural information can be retrieved from a three-dimensional digital image of a fibrous material. The proposed model is then validated for both foam- and water-deposited laboratory sheets of bleached kraft pulp (Scots pine) and chemi-thermo-mechanical pulp (CTMP, Norway spruce). The validation is carried out by comparing the model predictions against computationally determined permeability values. The related fluid-flow simulations are executed using the lattice-Boltzmann method together with high-resolution X-ray microtomography images. For both pulp materials, the sample sets had nearly equal porosities, but deviated substantially in their permeabilities. The proposed model was shown to improve prediction of permeability for the fibrous materials considered: the deviation between the predicted and computationally determined values was no more than 8%.