Geometric analysis on H ‐type groups related to division algebras

The present article applies the method of Geometric Analysis to the study H ‐type groups satisfying the J² condition and finishes the series of works describing the Heisenberg group and the quaternion H ‐type group. The latter class of H ‐type groups satisfying the J² condition is related to the octonions. The relations between the group structure and the boundary of the corresponding Siegel upper half space are given. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coupled nano-plasmons

High aspect-ratio nanochannels were fabricated by irradiating polyimide films with swift heavy ions of 2.2 GeV energy and subsequently sensitising and etching the ion tracks in hydrogen peroxide and sodium hypochloride, respectively. The nanochannels were analysed by means of small angle X-ray scattering in combination with a new form factor model that considers bi-conical channel geometry. This approach allows us to tune the etching parameters for controlled channel shape adjustment.     

Group additivity methods without group values

The conventional group additivity (GA) formalism may be identically reduced to a stoichiometric and thermochemical analysis of a special class of reactions referred to as GA reactions, that is, reactions that preserve the type and number of groups. Within this approach, the performance (error) of a GA scheme is determined by the stoichiometry and enthalpy changes of the GA reactions. That is, the lower the enthalpy changes of the GA reactions, the better the performance of a GA scheme. Ideally, an exact GA scheme would imply any conceivable GA reaction to be precisely thermoneutral, that is, have a zero enthalpy change. A somewhat surprising result is that, additionally, the performance of GA methods is influenced by a purely stoichiometric factor of GA reactions. These findings do not improve the performance of a given GA scheme. Rather, it is an interpretation that leads to a deeper understanding of the performance of a GA scheme and may be used in designing more accurate GA schemes.     

Analysis of tapered front‐coupling X‐ray waveguides

The coupling and propagation of electromagnetic waves through planar X‐ray waveguides (WG) with vacuum gap and Si claddings are analyzed in detail, starting from the source and ending at the detector. The general case of linearly tapered WGs (i.e. with the entrance aperture different from the exit one) is considered. Different kinds of sources, i.e. synchrotron radiation and laboratory desk‐top sources, have been considered, with the former providing a fully coherent incoming beam and the latter partially coherent beams. It is demonstrated that useful information about the parameters of the WG can be derived, comparing experimental results with computer simulation based on analytical solutions of the Helmholtz equation which take into account the amplitude and phase matching between the standing waves created in front of the WG, and the resonance modes propagating into the WG.     

Giant proximity effect in a phase-fluctuating superconductor

When a tunneling barrier between two superconductors is formed by a normal material that would be a superconductor in the absence of phase fluctuations, the resulting Josephson effect can undergo an enormous enhancement. We establish this novel proximity effect by a general argument as well as a numerical simulation and argue that it may underlie recent experimental observations of the giant proximity effect between two cuprate superconductors separated by a barrier made of the same material rendered normal by severe underdoping.     

Norm calculations of a class of integral operators

In this paper we calculate the norm of a special class of integral operators acting on Lp (Cn,dvs), where dvs is the Gaussian measure on Cn.     

"Cooking the sample": radiofrequency induced heating during solid-state NMR experiments

Dissipation of radiofrequency (RF) energy as heat during continuous wave decoupling in solid-state NMR experiment was examined outside the conventional realm of such phenomena. A significant temperature increase could occur while performing dynamic NMR measurements provided the sample contains polar molecules and the sequence calls for relatively long applications of RF power. It was shown that the methyl flip motion in dimethylsulfone (DMS) is activated by the decoupling RF energy conversion to heat during a CODEX pulse sequence. This introduced a significant bias in the correlation time–temperature dependency measurement used to obtain the activation energy of the motion. By investigating the dependency of the temperature increase in hydrated lead nitrate on experimental parameters during high-power decoupling one-pulse experiments, the mechanisms for the RF energy deposition was identified. The samples were heated due to dissipation of the energy absorbed by dielectric losses, a phenomenon commonly known as “microwave” heating. It was thus established that during solid-state NMR experiments at moderate B₀ fields, RF heating could lead to the heating of samples containing polar molecules such as hydrated polymers and inorganic solids. In particular, this could result in systematic errors for slow dynamics measurements by solid-state NMR.     

Reaction route graphs. III. Non-minimal kinetic mechanisms

The concept of reaction route (RR) graphs introduced recently by us for kinetic mechanisms that produce minimal graphs is extended to the problem of non-minimal kinetic mechanisms for the case of a single overall reaction (OR). A RR graph is said to be minimal if all of the stoichiometric numbers in all direct RRs of the mechanism are equal to +/-1 and non-minimal if at least one stoichiometric number in a direct RR is non-unity, e.g., equal to +/-2. For a given mechanism, four unique topological characteristics of RR graphs are defined and enumerated, namely, direct full routes (FRs), empty routes (ERs), intermediate nodes (INs), and terminal nodes (TNs). These are further utilized to construct the RR graphs. One algorithm involves viewing each IN as a central node in a RR sub-graph. As a result, the construction and enumeration of RR graphs are reduced to the problem of balancing the peripheral nodes in the RR sub-graphs according to the list of FRs, ERs, INs, and TNs. An alternate method involves using an independent set of RRs to draw the RR graph while satisfying the INs and TNs. Three examples are presented to illustrate the application of non-minimal RR graph theory.