Radical Anions,Radical-Anion Salts,and Anionic Complexes of 2,1,3-Benzochalcogenadiazoles

By means of cyclic voltammetry (CV) and DFT calculations, it was found that the electron-acceptor ability of 2,1,3-benzochalcogenadiazoles 1 – 3 (chalcogen: S, Se, and Te, respectively) increases with increasing atomic number of the chalcogen. This trend is nontrivial, since it contradicts the electronegativity and atomic electron affinity of the chalcogens. In contrast to radical anions (RAs) [ 1 ]^.− and [ 2 ]^.−, RA [ 3 ]^.− was not detected by EPR spectroscopy under CV conditions. Chemical reduction of 1 – 3 was performed and new thermally stable RA salts [K(THF)]⁺[ 2 ]^.− ( 8 ) and [K(18-crown-6)]⁺[ 2 ]^.− ( 9 ) were isolated in addition to known salt [K(THF)]⁺[ 1 ]^.− ( 7 ). On contact with air, RAs [ 1 ]^.− and [ 2 ]^.− underwent fast decomposition in solution with the formation of anions [ECN]⁻, which were isolated in the form of salts [K(18-crown-6)]⁺[ECN]⁻ ( 10 , E=S; 11 , E=Se). In the case of 3 , RA [ 3 ]^.− was detected by EPR spectroscopy as the first representative of tellurium–nitrogen π-heterocyclic RAs but not isolated. Instead, salt [K(18-crown-6)]⁺₂[ 3 -Te₂]²⁻ ( 12 ) featuring a new anionic complex with coordinate Te−Te bond was obtained. On contact with air, salt 12 transformed into salt [K(18-crown-6)]⁺₂[ 3 -Te₄- 3 ]²⁻ ( 13 ) containing an anionic complex with two coordinate Te−Te bonds. The structures of 8 – 13 were confirmed by XRD, and the nature of the Te−Te coordinate bond in [ 3 -Te₂]²⁻ and [ 3 -Te₄- 3 ]²⁻ was studied by DFT calculations and QTAIM analysis.     

Raman Spectroscopic Signature of Ectoine Conformations in Bulk Solution and Crystalline State

Recent crystallographic results revealed conformational changes of zwitterionic ectoine upon hydration. By means of confocal Raman spectroscopy and density functional theory calculations, we present a detailed study of this transformation process as part of a Fermi resonance analysis. The corresponding findings highlight that all resonant couplings are lifted upon exposure to water vapor as a consequence of molecular binding processes. The importance of the involved molecular groups for water binding and conformational changes upon hydration is discussed. Our approach further shows that the underlying rapid process can be reversed by carbon dioxide saturated atmospheres. For the first time, we also confirm that the conformational state of ectoine in aqueous bulk solution coincides with crystalline ectoine in its dihydrate state, thereby highlighting the important role of a few bound water molecules.     

The Peierls instability in one-dimensional conductors with arbitrary bandfilling

Mean field calculations of the Peierls instability have been carried out for arbitrary bandfilling both in the case of free electrons as well as for the tightbinding approximation. New expressions for Δ(0) and T_p are derived which change the experimentally derived λ to a more reasonable value. Δ(0)/k_BT_p may differ significantly from the BCS value 1.76 in the tightbinding approximation.     

Simulation of the inherent turbulence and wake interaction inside an infinitely long row of wind turbines

The turbulence in the interior of a wind farm is simulated using large eddy simulation and the actuator line technique implemented in the Navier–Stokes equations. The simulations are carried out for an infinitely long row of turbines simulated by applying cyclic boundary conditions at the inlet and outlet. The simulations investigate the turbulence inherent to the wind turbines as no ambient turbulence or shear is added to this idealised case. The simulated data give insight into the performance of the wind turbines operating in the wake of others as well as details on key turbulent quantities. One of the key features of wakes behind wind turbines is the dynamic wake meandering, which is shown to be related to the wind turbine spacing and the vortex shedding from the turbine as a bluff body. The flow is analysed and reconstructed by applying proper orthogonal decomposition.     

L p -Estimates for the Navier–Stokes Equations for Steady Compressible Flow

We consider the Navier–Stokes equations for compressible isentropic flow in the steady three-dimensional case. The pressure and the kinetic energy are estimated uniformly in L^q with being the density. This is an improvement of known estimates in the case Mathematics Subject Classification (2000): 35Q30, 76N10     

Surfaces of prescribed mean curvature in a cone

We show existence of surfaces of prescribed mean curvature in central projection for such values of the mean curvature for which estimates for the corresponding Euler–Lagrange equations are generally not known. This is achieved by extending the variational problem to the space \({BV(\Omega)}\), where graphs in a cone must satisfy a side condition, and using variational methods. Moreover, we give an example of a solution in \({BV(\Omega)}\) which does not solve the Dirichlet problem for the Euler-Lagrange equation.     

Partial regularity for parabolic systems with non-standard growth

We study non-linear parabolic systems with non-standard p(z)-growth conditions and establish that the gradient of weak solutions is locally H?lder continuous with H?lder exponent b ? (0,1){\beta \in (0,1)} with respect to the parabolic metric on an open set of full Lebesgue measure, provided the exponent function p(z) itself is H?lder continuous with exponent β with respect to the parabolic metric.     

Fair optimization of fortnightly physician schedules with flexible shifts

This research addresses a shift scheduling problem in which physicians are assigned to demand periods. We develop a reduced set covering approach that requires shift templates to be generated for a single day and compare it to an implicit modeling technique where shift-building rules are implemented as constraints. Both techniques allow full flexibility in terms of different shift starting times and lengths as well as break placements. The objective is to minimize the paid out hours under the restrictions given by the labor agreement. Furthermore, we integrate physician preferences and fairness aspects into the scheduling model. Computational results show the efficiency of the reduced set covering formulation in comparison to the implicit modeling approach.