Interpolation for Function Spaces Related to Mixed Boundary Value Problems

Interpolation theorems are proved for Sobolev spaces of functions on nonsmooth domains with vanishing trace on a part of the boundary.     

Optimal control in NMR spectroscopy: Numerical implementation in SIMPSON

We present the implementation of optimal control into the open source simulation package SIMPSON for development and optimization of nuclear magnetic resonance experiments for a wide range of applications, including liquid- and solid-state NMR, magnetic resonance imaging, quantum computation, and combinations between NMR and other spectroscopies. Optimal control enables efficient optimization of NMR experiments in terms of amplitudes, phases, offsets etc. for hundreds-to-thousands of pulses to fully exploit the experimentally available high degree of freedom in pulse sequences to combat variations/limitations in experimental or spin system parameters or design experiments with specific properties typically not covered as easily by standard design procedures. This facilitates straightforward optimization of experiments under consideration of rf and static field inhomogeneities, limitations in available or desired rf field strengths (e.g., for reduction of sample heating), spread in resonance offsets or coupling parameters, variations in spin systems etc. to meet the actual experimental conditions as close as possible. The paper provides a brief account on the relevant theory and in particular the computational interface relevant for optimization of state-to-state transfer (on the density operator level) and the effective Hamiltonian on the level of propagators along with several representative examples within liquid- and solid-state NMR spectroscopy.     

A comparison of NCO and NCA transfer methods for biological solid-state NMR spectroscopy

Three different techniques (adiabatic passage Hartman-Hahn cross-polarization, optimal control designed pulses, and EXPORT) are compared for transferring (15)N magnetization to (13)C in solid-state NMR experiments under magic-angle-spinning conditions. We demonstrate that, in comparison to adiabatic passage Hartman-Hahn cross-polarization, optimal control transfer pulses achieve similar or better transfer efficiencies for uniformly-(13)C,(15)N labeled samples and are generally superior for samples with non-uniform labeling schemes (such as 1,3- and 2-(13)C glycerol labeling). In addition, the optimal control pulses typically use substantially lower average RF field strengths and are more robust with respect to experimental variation and RF inhomogeneity. Consequently, they are better suited for demanding samples.     

Solubility and Crystallization in the System MgCl2–MgSO4–H2O at 50 and 75°C

The system MgCl₂–MgSO₄–H₂O has been investigated experimentally and modeled thermodynamically according to the Pitzer method at 50 and 75°C. It was found that, even when seemingly all requirements for reaching the stable thermodynamic equilibrium are fulfilled, the crystallization of higher hydrates as metastable phases is possible, and cannot be avoided in each crystallization field of a stable lower hydrate of magnesium sulfate. Crystallization of MgSO₄ · x H₂O (x = 1, 4, 6) and MgCl₂ · 6 H₂O at 50°C and of MgSO₄ · H₂O and MgCl₂ · 6 H₂O at 75°C as stable phases has been observed. Three metastable crystallization fields of MgSO₄ · x H₂O (x = 4, 6, 7) have been detected at 50°C and two of MgSO₄ · x H₂O (x = 4, 6) at 75°C. The results obtained and the contradictions existing in the literature with respect to the solubility and the crystallizing solid phases are discussed in terms of the crystal structures.     

On Kato’s Method for Navier–Stokes Equations

We investigate Kato’s method for parabolic equations with a quadratic non-linearity in an abstract form. We extract several properties known from linear systems theory which turn out to be the essential ingredients for the method. We give necessary and sufficient conditions for these conditions and provide new and more general proofs, based on real interpolation. In application to the Navier–Stokes equations, our approach unifies several results known in the literature, partly with different proofs. Moreover, we establish new existence and uniqueness results for rough initial data on arbitrary domains in \mathbbR³{\mathbb{R}}^{3} and irregular domains in \mathbbRⁿ{\mathbb{R}}^{n}.