The mystery of ten wooden blocks: Hjelmslev’s geometry of reality

Mathematische Semesterberichte - I shall argue that a collection of wood models at the University of Copenhagen was made by Johannes Hjelmslev as an aid in his elementary...     

In-situ mechanical characterization of wurtzite InAs nanowires

High aspect ratio vertical InAs nanowires were mechanically characterized in a scanning electron microscope equipped with two micromanipulators. One, equipped with a calibrated atomic force microscope probe, was used for in-situ static bending of single nanowires along the 〈11–20〉 crystallographic direction. The other one was equipped with a tungsten tip for dynamic resonance excitation of the same nanowires. This setup enabled a direct comparison between the two techniques. The crystal structure was analyzed using transmission electron microscopy, and for InAs nanowires with a hexagonal wutzite crystal structure, the bending modulus value was found to BM=43.5 GPa. This value is significantly lower than previously reported for both cubic zinc blende InAs bulk crystals and InAs nanowires. Besides, due to their high resonance quality factor (Q>1200), the wurtzite InAs nanowires are shown to be a promising candidate for sub-femtogram mass detectors.     

Group cohomology and control of p-fusion

We show that if an inclusion of finite groups H≤G of index prime to p induces a homeomorphism of mod p cohomology varieties, or equivalently an F-isomorphism in mod p cohomology, then H controls p-fusion in G, if p is odd. This generalizes classical results of Quillen who proved this when H is a Sylow p-subgroup, and furthermore implies a hitherto difficult result of Mislin about cohomology isomorphisms. For p=2 we give analogous results, at the cost of replacing mod p cohomology with higher chromatic cohomology theories. The results are consequences of a general algebraic theorem we prove, that says that isomorphisms between p-fusion systems over the same finite p-group are detected on elementary abelian p-groups if p odd and abelian 2-groups of exponent at most 4 if p=2.     

Adsorption of ammonia on multilayer iron phthalocyanine

The adsorption of ammonia on multilayers of well-ordered, flat-lying iron phthalocyanine (FePc) molecules on a Au(111) support was investigated by x-ray photoelectron spectroscopy. We find that the electron-donating ammonia molecules coordinate to the metal centers of iron phthlalocyanine. The coordination of ammonia induces changes of the electronic structure of the iron phthalocyanine layer, which, in particular, lead to a modification of the FePc valence electron spin.     

Metallomics in drug development: characterization of a liposomal cisplatin drug formulation in human plasma by CE–ICP–MS

A capillary electrophoresis inductively coupled plasma mass spectrometry method for separation of free cisplatin from liposome-encapsulated cisplatin and protein-bound cisplatin was developed. A liposomal formulation of cisplatin based on PEGylated liposomes was used as model drug formulation. The effect of human plasma matrix on the analysis of liposome-encapsulated cisplatin and intact cisplatin was studied. The presence of 1 % of dextran and 4 mM of sodium dodecyl sulfate in HEPES buffer was demonstrated to be effective in improving the separation of liposomes and cisplatin bound to proteins in plasma. A detection limit of 41 ng/mL of platinum and a precision of 2.1 % (for 10 μg/mL of cisplatin standard) were obtained. Simultaneous measurements of phosphorous and platinum allows the simultaneous monitoring of the liposomes, liposome-encapsulated cisplatin, free cisplatin and cisplatin bound to plasma constituents in plasma samples. It was demonstrated that this approach is suitable for studies of the stability of liposome formulations as leakage of active drug from the liposomes and subsequent binding to biomolecules in plasma can be monitored. This methodology has not been reported before and will improve characterization of liposomal drugs during drug development and in studies on kinetics.

On Semi-Classical States of Quantum Gravity and Noncommutative Geometry

We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated as a spectral triple over holonomy loops. The semi-classical limit of the spectral triple gives the Dirac Hamiltonian in 3+1 dimensions. Also, time-independent lapse and shift fields emerge from the semi-classical states. Our analysis shows that the model might contain fermionic matter degrees of freedom.     

A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids

A new family of cell-centered finite-volume schemes is presented for solving the general full-tensor pressure equation of subsurface flow in porous media on arbitary unstructured triangulations. The new schemes are flux continuous and have full pressure support (FPS) over each subcell with continuous pressure imposed across each control-volume sub-interface, in contrast to earlier formulations. The earlier methods are point-wise continuous in pressure and flux with triangle-pressure-support (TPS) which leads to a more limited quadrature range. An M-matrix analysis identifies bounding limits for the schemes to posses a local discrete maximum principle. Conditions for the schemes to be positive definite are also derived.A range of computational examples are presented for unstructured triangular grids, including highly irregular grids, and the new FPS schemes are compared against the earlier pointwise continuous TPS formulations. The earlier pointwise TPS methods can induce strong spurious oscillations for problems involving strong full-tensor anisotropy where the M-matrix conditions are violated, and can lead to decoupled solutions in such cases. Unstructured cell-centered decoupling is investigated. In contrast to TPS, the new FPS formulation leads to well resolved solutions that are essentially free of spurious oscillations.A substantial degree of improved convergence behavior, for both pressure and velocity, is also observed in all convergence tests. This is particularly important for problems involving high anisotropy ratios. Also the new formulation proves to be highly beneficial for an upscaling example, where enhancement of convergence is highly significant for certain quadrature points, clearly demonstrating further advantages of the new formulation.     

Impact of the liquid phase shape on the structure of III-V nanowires

The III-V nanowire structure (zinc blende or wurtzite) grown by the vapor-liquid-solid process is shown to be highly dependent on the parameters which shape the droplet at the top of the nanowire. Under conditions that the droplet volume does not exceed a certain value, it is demonstrated that when the nucleation of the solid starts at the solid-liquid-vapor triple line, a relatively large droplet volume and low wetting angle favor the formation of the wurtzite structure. We show that the effective V/III flux ratio is the primary parameter controlling the structure.