On the Construction of Composite Wannier Functions

We give a constructive proof for the existence of a Bloch basis of rank \({N}\) which is both smooth (real analytic) and periodic with respect to its \({d}\)-dimensional quasi-momenta, when \({1\leq d\leq 2}\) and \({N\geq 1}\). The constructed Bloch basis is conjugation symmetric when the underlying projection has this symmetry, hence the corresponding exponentially localized composite Wannier functions are real. In the second part of the paper, we show that by adding a weak, globally bounded but not necessarily constant magnetic field, the existence of a localized basis is preserved.     

Extraction of molybdenum and technetium with diamides of dipicolinic acid from nitric acid solutions

The concentration of molybdenum(VI) in dissolved spent nuclear fuel is comparable with the concentrations of Tc, and the minor actinides (Np, Am). Therefore it is of great interest to understand its behavior under conditions imposed by separation processes. The simultaneous extraction ability of ortho, meta, and para isomers of N,N′-diethyl-N,N′-ditolyl-dipicolinamide (EtTDPA) for molybdenum and technetium were investigated in a large range of nitric and hydrochloric acid conditions. Molybdenum shows no increase in extraction at higher concentrations of nitric acid giving a solvate number n=0 with all isomers of EtTDPA, while Mo shows great extractability from HCl. Technetium distribution ratios decrease with increasing concentrations of nitrate showing indication of ion exchange occurring between TcO₄ ⁻ and NO₃ ⁻ anions. Et(m)TDPA and Et(p)TDPA show the greatest extractability, with 60% of the total technetium extracted into the organic phase at 1M HNO₃.     

Chemoselective Boron–Carbon Bond Cleavage by Hydroboration of Borirenes

We report on the hydroboration of 1‐[bis(trimethylsilyl)amino]‐2,3‐diethylborirene ( 3 ) with 9‐borabicyclo[3.3.1]nonane (9‐BBN), which led through ring‐opening to an amino(vinyl)borane. The viscous borane was subsequently converted into a crystalline borate on treatment with MeLi. Both compounds were fully characterized by multinuclear NMR spectroscopy and in case of the latter by single‐crystal X‐ray diffraction analysis. To elucidate the reaction mechanism of the unexpected boron‐carbon bond cleavage, DFT calculations of energy minima and transition states for the hydroboration were carried out.     

Electroglottographic wavegrams: a technique for visualizing vocal fold dynamics noninvasively

A method for analyzing and displaying electroglottographic (EGG) signals (and their first derivative, DEGG) is introduced: the electroglottographic wavegram ("wavegram" hereafter). To construct a wavegram, the time-varying fundamental frequency is measured and consecutive individual glottal cycles are identified. Each cycle is locally normalized in duration and amplitude, the signal values are encoded by color intensity and the cycles are concatenated to display the entire voice sample in a single image, similar as in sound spectrography. The wavegram provides an intuitive means for quickly assessing vocal fold contact phenomena and their variation over time. Variations in vocal fold contact appear here as a sequence of events rather than single phenomena, taking place over a certain period of time, and changing with pitch, loudness and register. Multiple DEGG peaks are revealed in wavegrams to behave systematically, indicating subtle changes of vocal fold oscillatory regime. As such, EGG wavegrams promise to reveal more information on vocal fold contacting and de-contacting events than previous methods.     

Use of a kinetic energy orifice as a probe of metastable dissociation in Fourier transform ion cyclotron resonance mass spectrometry

Although Fourier transform ion cyclotron resonance mass spectrometry is a powerful tool in the qualitative observation of gas phase reactions, ion detection is on the millisecond time scale, orders of magnitude longer than typically found when using a sector instrument. Observations of short-lived species such as chemically activated adduct ions can be accomplished using selective ion excitation as a probe of intermediate lifetime. Whereas ion elimination has been shown to be effective in monitoring ion lifetimes on the microsecond time scale, problems associated with detecting ions produced with high kinetic energies limits the technique. Use of a kinetic energy orifice as an ion skimmer effectively eliminates ions near the center of the ion cell at relatively low kinetic energies. By modifying a single section cell to include a kinetic energy orifice, the lifetimes of chemically activated adduct ions have been investigated.     

Invariant Manifolds,Nonclassical Normal Modes,and Proper Orthogonal Modes in the Dynamics of the Flexible Spherical Pendulum

It is shown that the flexible spherical pendulum undergoes purely slow motions with master and slaved components. The family of slow motions is realized as a three-dimensional invariant manifold in phase space. This manifold is computed analytically by applying the method of geometric singular perturbations. This manifold is nonlinear and for all energy and angular momentum levels is characterized precisely by three PO (proper orthogonal) modes. Its submanifold of zero angular momentum is a two-dimensional invariant manifold; it is the geometric realization of a nonclassical nonlinear normal mode. This normal mode is characterized precisely by two PO modes. The slaved slow dynamics are characterized precisely by a single PO mode. The stability of the slow invariant manifold as well as interactions between fast and slow dynamics are considered.