Search results for "Mathematik"
showing 9 items of 59 documents
Near-IR to Near-IR Upconversion Luminescence in Molecular Chromium Ytterbium Salts
2020
Abstract Upconversion photoluminescence in hetero‐oligonuclear metal complex architectures featuring organic ligands is an interesting but still rarely observed phenomenon, despite its great potential from a basic research and application perspective. In this context, a new photonic material consisting of molecular chromium(III) and ytterbium(III) complex ions was developed that exhibits excitation‐power density‐dependent cooperative sensitization of the chromium‐centered 2E/2T1 phosphorescence at approximately 775 nm after excitation of the ytterbium band 2F7/2→2F5/2 at approximately 980 nm in the solid state at ambient temperature. The upconversion process is insensitive to atmospheric ox…
Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation
2020
We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comp., 69:481-500, 2000] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computa…
Chiroptical inversion of a planar chiral redox-switchable rotaxane.
2019
Reversible redox-switching of a planar chiral [2]rotaxane with a tetrathiafulvalene-bearing crown ether macrocycle generates a complete sign reversal of the main band in the ECD spectrum, as shown by experiment and rationalised by DFT calculations.
Fracture Shape and Orientation Contributions to P-Wave Velocity and Anisotropy of Alpine Fault Mylonites
2021
P-wave anisotropy is significant in the mylonitic Alpine Fault shear zone. Mineral- and texture-induced anisotropy are dominant in these rocks but further complicated by the presence of fractures. Electron back-scattered diffraction and synchrotron X-ray microtomography (micro-CT) data are acquired on exhumed schist, protomylonite, mylonite and ultramylonite samples to quantify mineral phases, crystal preferred orientations, microfractures and porosity. The samples are composed of quartz, plagioclase, mica and accessory garnet, and contain 3-5% porosity. Based on the micro-CT data, the representative pore shape has an aspect ratio of 5:2:1. Two numerical models are compared to calculate the…
Surprising solvent-induced structural rearrangements in large [N⋯I+⋯N] halogen-bonded supramolecular capsules
2018
Coordinative halogen bonds have recently gained interest for the assembly of supramolecular capsules. Ion mobility-mass spectrometry and theoretical calculations now reveal the well-defined gas-phase structures of dimeric and hexameric [N...I+...N] halogen-bonded capsules with counterions located inside their cavities as guests. The solution reactivity of the large hexameric capsule shows the intriguing solvent-dependent equilibrium between the hexamer and an unprecedented pentameric [N...I+...N] halogen-bonded capsule, when the solvent is changed from chloroform to dichloromethane. The intrinsic flexibility of the cavitands enables this novel structure to adopt a pseudo-trigonal bipyramida…
Fundamental bounds on qubit reset
2020
Qubit reset is a basic prerequisite for operating quantum devices, requiring the export of entropy. The fastest and most accurate way to reset a qubit is obtained by coupling the qubit to an ancilla on demand. Here, we derive fundamental bounds on qubit reset in terms of maximum fidelity and minimum time, assuming control over the qubit and no control over the ancilla. Using the Cartan decomposition of the Lie algebra of qubit plus two-level ancilla, we identify the types of interaction and controls for which the qubit can be purified. For these configurations, we show that a time-optimal protocol consists of purity exchange between qubit and ancilla brought into resonance, where the maximu…
Functional a posteriori error estimates for boundary element methods
2019
Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary element method (BEM). One key feature is that the derived error estimates are independent of the BEM discretization and provide guaranteed lower and upper bounds for the unknown error. In particular, our analysis covers Galerkin BEM and the collocation method, what makes the approach of particular interest for scientific computations and engineering applications. Numerical experiments for the Laplace problem confirm the theoretical results.
Polyester microplastic fibers in soil increase nitrogen loss via leaching and decrease plant biomass production and N uptake
2022
Abstract Microplastic contamination, like other global change factors, can induce effects on ecosystem functions and processes, affecting various soil biophysical properties. However, effects of such contaminants on nutrient cycles in agroecosystems are still poorly understood. We here performed two pot experiments to investigate the effect of polyester microplastic fibers (PMFs) on soil physical properties, nitrogen cycle, and plant performance in a maize-based agroecosystem. Moreover, we followed the N loss via leaching in soil contaminated or not with PMFs by simulating heavy rainfall events that mimic a future scenario of climate change. Our results show that soil contaminated with PMFs…
Estimates of the modeling error generated by homogenization of an elliptic boundary value problem
2016
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