Boundary value problems for differential-algebraic equations

This paper shows how certain regularization methods can be used to determine the solution structure of linear differential systems subject to linear constraints and boundary conditions. Attention is restricted to the relatively straightforward index-one problems and to certain index-two problems, where endpoint jumps are related to the underlying boundary layer structure of the corresponding singular perturbation problems.     

X-Ray Diffraction by Liquid Crystals

Following a very brief historical review, x-ray diffraction by nematic and smectic liquid crystals is critically examined in terms of the data available and the structural models and molecular theories that have been proposed to explain it. Studiesof TBBA are used to illustrate some of the principal mesophases that have been distinguished. Other types of liquid crystals and their phase transitions are also briefly reviewed.

This analysis shows that careful experimental work is still needed to decide the kinds of models that best describe the various types of mesophases that have been shown to exist.     

Poisson Algebras of Block-Upper-Triangular Bilinear Forms and Braid Group Action

In this paper we study a quadratic Poisson algebra structure on the space of bilinear forms on ${\mathbb{C}^{N}}$ C N with the property that for any ${n, m \in \mathbb{N}}$ n , m ∈ N such that n m = N, the restriction of the Poisson algebra to the space of bilinear forms with a block-upper-triangular matrix composed from blocks of size ${m \times m}$ m × m is Poisson. We classify all central elements and characterise the Lie algebroid structure compatible with the Poisson algebra. We integrate this algebroid obtaining the corresponding groupoid of morphisms of block-upper-triangular bilinear forms. The groupoid elements automatically preserve the Poisson algebra. We then obtain the braid group action on the Poisson algebra as elementary generators within the groupoid. We discuss the affinisation and quantisation of this Poisson algebra, showing that in the case m = 1 the quantum affine algebra is the twisted q-Yangian for ${\mathfrak{o}_{n}}$ o n and for m = 2 is the twisted q-Yangian for ${(\mathfrak{sp}_{2n})}$ ( sp 2 n ) . We describe the quantum braid group action in these two examples and conjecture the form of this action for any m > 2. Finally, we give an R-matrix interpretation of our results and discuss the relation with Poisson–Lie groups.     

In situ Raman spectroscopic study of the pressure induced structural changes in ammonia borane

The effect of static compression up to 65 GPa at ambient temperature on ammonia borane, BH(3)NH(3), has been investigated using in situ Raman spectroscopy in a diamond anvil cells. Two phase transitions were observed at approximately 12 GPa and previously not reported transition at 27 GPa. It was demonstrated that ammonia borane behaves differently under compression at quasi-hydrostatic and non-hydrostatic conditions. The ability of BH(3)NH(3) to generate second harmonic of the laser light observed up to 130 GPa suggests that the non-centrosymmetric point group symmetry is preserved in the material up to very high pressures.     

The 57Fe Synchrotron Mössbauer Source at the ESRF

The design of a ⁵⁷Fe Synchrotron Mössbauer Source (SMS) for energy‐domain Mössbauer spectroscopy using synchrotron radiation at the Nuclear Resonance beamline (ID18) at the European Synchrotron Radiation Facility is described. The SMS is based on a nuclear resonant monochromator employing pure nuclear reflections of an iron borate (⁵⁷FeBO₃) crystal. The source provides ⁵⁷Fe resonant radiation at 14.4 keV within a bandwidth of 15 neV which is tunable in energy over a range of about ±0.6 µeV. In contrast to radioactive sources, the beam of γ‐radiation emitted by the SMS is almost fully resonant and fully polarized, has high brilliance and can be focused to a 10 µm × 5 µm spot size. Applications include, among others, the study of very small samples under extreme conditions, for example at ultrahigh pressure or combined high pressure and high temperature, and thin films under ultrahigh vacuum. The small cross section of the beam and its high intensity allow for rapid collection of Mössbauer data. For example, the measuring time of a spectrum for a sample in a diamond anvil cell at ～100 GPa is around 10 min, whereas such an experiment with a radioactive point source would take more than one week and the data quality would be considerably less. The SMS is optimized for highest intensity and best energy resolution, which is achieved by collimation of the incident synchrotron radiation beam and thus illumination of the high‐quality iron borate crystal within a narrow angular range around an optimal position of the rocking curve. The SMS is permanently located in an optics hutch and is operational immediately after moving it into the incident beam. The SMS is an in‐line monochromator, i.e. the beam emitted by the SMS is directed almost exactly along the incident synchrotron radiation beam. Thus, the SMS can be easily utilized with all existing sample environments in the experimental hutches of the beamline. Owing to a very strong suppression of electronic scattering for pure nuclear reflections (～10^?9), SMS operation does not required any gating of the prompt electronic scattering. Thus, the SMS can be utilized in any mode of storage ring operation.     

Thin silica films on Ru(0001): monolayer, bilayer and three-dimensional networks of [SiO4] tetrahedra

The atomic structure of thin silica films grown over a Ru(0001) substrate was studied by X-ray photoelectron spectroscopy, infrared reflection absorption spectroscopy, low energy electron diffraction, helium ion scattering spectroscopy, CO temperature programmed desorption, and scanning tunneling microscopy in combination with density functional theory calculations. The films were prepared by Si vapor deposition and subsequent oxidation at high temperatures. The silica film first grows as a monolayer of corner-sharing [SiO(4)] tetrahedra strongly bonded to the Ru(0001) surface through the Si-O-Ru linkages. At increasing amounts of Si, the film forms a bilayer of corner-sharing [SiO(4)] tetrahedra which is weakly bonded to Ru(0001). The bilayer film can be grown in either the crystalline or vitreous state, or both coexisting. Further increasing the film thickness leads to the formation of vitreous silica exhibiting a three-dimensional network of [SiO(4)]. The principal structure of the films can be monitored by infrared spectroscopy, as each structure shows a characteristic vibrational band, i.e., ～1135 cm(-1) for a monolayer film, ～1300 cm(-1) for the bilayer structures, and ～1250 cm(-1) for the bulk-like vitreous silica.     

Aromaticity in heterocyclic analogues of benzene: comprehensive analysis of structural aspects, electron delocalization and magnetic characteristics

The degree of aromaticity of six-membered monoheterocycles with IV-VI group heteroatoms (C(6)H(5)X, where X = SiH, GeH, N, P, As, O(+), S(+), Se(+)) was analyzed using the results of ab initio calculations at the MP2/cc-pvtz level. Values of common aromaticity indices including those based on electronic delocalization properties, structural-dynamic features and magnetic properties all indicate high aromaticity of all considered heterocycles. A decrease in aromaticity is observed with increasing atomic number of the heteroatom, except in the case of the pyrylium cation. However, not all types of indices or even different indices within the same type correlate well among each other. Ring currents have been obtained at the HF/cc-pvdz level using the ipsocentric formulation. Ring current maps indicate that in the case of cationic heterocycles the ring current persists in all molecules under consideration. The different conclusions reached depending on the type of index used are a manifestation of the fact that when not dealing with hydrocarbons, aromaticity is ill-defined. One should always express explicitly which property of the molecules is considered to establish a degree of "aromaticity".     

Remarkable nanoconfinement effects on chemical equilibrium manifested in nucleotide dimerization and H-D exchange reactions

Nanoconfinement entropic effects on chemical equilibrium involving a small number of molecules, which we term NCECE, are revealed by two widely diverse types of reactions. Employing statistical-mechanical principles, we show how the NCECE effect stabilizes nucleotide dimerization observed within self-assembled molecular cages. Furthermore, the effect provides the basis for dimerization even under an aqueous environment inside the nanocage. Likewise, the NCECE effect is pertinent to a longstanding issue in astrochemistry, namely the extra deuteration commonly observed for molecules reacting on interstellar dust grain surfaces. The origin of the NCECE effect is elucidated by means of the probability distributions of the reaction extent and related variations in the reactant-product mixing entropy. Theoretical modelling beyond our previous preliminary work highlights the role of the nanospace size in addition to that of the nanosystem size, namely the limited amount of molecules in the reaction mixture. Furthermore, the NCECE effect can depend also on the reaction mechanism, and on deviations from stoichiometry. The NCECE effect, leading to enhanced, greatly variable equilibrium "constants", constitutes a unique physical-chemical phenomenon, distinguished from the usual thermodynamical properties of macroscopically large systems. Being significant particularly for weakly exothermic reactions, the effects should stabilize products in other closed nanoscale structures, and thus can have notable implications for the growing nanotechnological utilization of chemical syntheses conducted within confined nanoreactors.     

Pulse EPR and ENDOR study of 1,2,3-benzodithiazolyl, 2,1,3-benzothiaselenazolyl and 1,2,3-benzodiselenazolyl radicals

1,2,3-Benzodithiazolyl, 2,1,3-benzothiaselenazolyl and 1,2,3-benzodiselenazolyl radicals were generated by the reduction of the corresponding cations and investigated by pulse EPR and ENDOR in frozen CHCl(3) solutions at 30 and 80 K. These methods, in combination with density functional theory calculations, were used to study the magnetic parameters of the radicals, namely the principal values of the nitrogen and proton hyperfine interactions and g-tensors. The spin density distribution was shown to be nearly the same for all investigated radicals and, therefore, replacement of sulfur by selenium leads to a limited perturbation of the radicals' electronic structure. A high anisotropy of the g-tensors was found for the selenium-containing radicals.     

Selective ablation of Xe from silicon surfaces: molecular dynamics simulations and experimental laser patterning

The mechanism of laser-induced removal of Xe overlayers from a Si substrate has been investigated employing MD simulations and evaluated by buffer layer assisted laser patterning experiments. Two distinct regimes of overlayer removal are identified in the simulations of a uniform heating of the Si substrate by a 5 ns laser pulse: The intensive evaporation from the surface of the Xe overlayer and the detachment of the entire Xe overlayer driven by explosive boiling in the vicinity of the hot substrate. Simulations of selective heating of only a fraction of the silicon substrate suggest that the lateral heat transfer and bonding to the unheated, colder regions of the Xe overlayer is very efficient and suppresses the separation of a fraction of the overlayer from the substrate. Interaction with surrounding cold Xe is responsible for significant increase in the substrate temperature required for achieving the spatially selective ablation of the overlayer. The predictions of the MD simulations are found to be in a qualitative agreement with the results of experimental measurements of the threshold laser power required for the removal of Xe overlayers of different thickness and the shapes of metallic stripes generated by buffer-assisted laser patterning.