Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, 3j Symbols, and Character Localization

In this paper, we employ a technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index J) of generic Wigner matrix elements D^J_MM￠(g){D^{J}_{MM'}(g)} . We use this result to derive asymptotic formulae for the character χ ^J (g) of an SU(2) group element and for Wigner’s 3j symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for χ ^J (g) is in fact exact. The result hints at a “Duistermaat-Heckman like” localization property for discrete sums.     

Polymer Lamellae as Reaction Intermediates in the Formation of Copper Nanospheres as Evidenced by In Situ X‐ray Studies

The classical nucleation theory (CNT) is the most common theoretical framework used to explain particle formation. However, nucleation is a complex process with reaction pathways which are often not covered by the CNT. Herein, we study the formation mechanism of copper nanospheres using in situ X‐ray absorption and scattering measurements. We reveal that their nucleation involves coordination polymer lamellae as pre‐nucleation structures occupying a local minimum in the reaction energy landscape. Having learned this, we achieved a superior monodispersity for Cu nanospheres of different sizes. This report exemplifies the importance of developing a more realistic picture of the mechanism involved in the formation of inorganic nanoparticles to develop a rational approach to their synthesis.     

Tree Quantum Field Theory

We propose a new formalism for quantum field theory (QFT) which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e., it computes correlation functions through convergent rather than divergent expansions. It applies both to Fermionic and Bosonic theories. It is compatible with the renormalization group, and it allows to define non-perturbatively differential renormalization group equations. It accommodates any general stable polynomial Lagrangian. It can equally well treat noncommutative models or matrix models such as the Grosse–Wulkenhaar model. Perhaps most importantly it removes the space-time background from its central place in QFT, paving the way for a non-perturbative definition of field theory in non-integer dimension.     

Colored Group Field Theory

Random matrix models generalize to Group Field Theories (GFT) whose Feynman graphs are dual to higher dimensional topological spaces. The perturbative development of the usual GFT’s is rather involved combinatorially and plagued by topological singularities (which we discuss in great detail in this paper), thus very difficult to control and unsatisfactory.     

A dispersive regularization of the modulational instability of stratified gravity waves

We derive high-order corrections to a modulation theory for the propagation of internal gravity waves in a density-stratified fluid with coupling to the mean flow. The methodology we use allows for strong modulations of wavenumber and mean flow, extending previous approaches developed for the quasi-monochromatic regime. The wave mean flow modulation equations consist of a system of nonlinear conservation laws that may be hyperbolic, elliptic or of mixed type. We investigate the regularizing properties of the asymptotic correction terms in the case when the system becomes unstable and ill-posed due to a change of type (loss of hyperbolicity). A linear analysis reveals that the regularization by the added correction terms does so by introducing a short-wave cut-off of the unstable wavenumbers. We perform various numerical experiments that confirm the regularizing properties of the correction terms, and show that the growth of unstable modes is tempered by nonlinearity. We also find an excellent agreement between the solution of the corrected modulation system and the modulation variables extracted from the numerical solution of the nonlinear Boussinesq equations.     

Unusual Structure,Fluxionality, and Reaction Mechanism of Carbonyl Hydrosilylation by Silyl Hydride Complex [(ArN)Mo(H)(SiH2Ph)(PMe3)3]

The reactions of bis(borohydride) complexes [(RN?)Mo(BH₄)₂(PMe₃)₂] ( 4 : R=2,6‐Me₂C₆H₃; 5 : R=2,6‐iPr₂C₆H₃) with hydrosilanes afford new silyl hydride derivatives [(RN?)Mo(H)(SiR′₃)(PMe₃)₃] ( 3 : R=Ar, R′₃=H₂Ph; 8 : R=Ar′, R′₃=H₂Ph; 9 : R=Ar, R′₃=(OEt)₃; 10 : R=Ar, R′₃=HMePh). These compounds can also be conveniently prepared by reacting [(RN?)Mo(H)(Cl)(PMe₃)₃] with one equivalent of LiBH₄ in the presence of a silane. Complex 3 undergoes intramolecular and intermolecular phosphine exchange, as well as exchange between the silyl ligand and the free silane. Kinetic and DFT studies show that the intermolecular phosphine exchange occurs through the predissociation of a PMe₃ group, which, surprisingly, is facilitated by the silane. The intramolecular exchange proceeds through a new non‐Bailar‐twist pathway. The silyl/silane exchange proceeds through an unusual Mo^VI intermediate, [(ArN?)Mo(H)₂(SiH₂Ph)₂(PMe₃)₂] ( 19 ). Complex 3 was found to be the catalyst of a variety of hydrosilylation reactions of carbonyl compounds (aldehydes and ketones) and nitriles, as well as of silane alcoholysis. Stoichiometric mechanistic studies of the hydrosilylation of acetone, supported by DFT calculations, suggest the operation of an unexpected mechanism, in that the silyl ligand of compound 3 plays an unusual role as a spectator ligand. The addition of acetone to compound 3 leads to the formation of [trans‐(ArN)Mo(OiPr)(SiH₂Ph)(PMe₃)₂] ( 18 ). This latter species does not undergo the elimination of a Si? O group (which corresponds to the conventional Ojima′s mechanism of hydrosilylation). Rather, complex 18 undergoes unusual reversible β‐CH activation of the isopropoxy ligand. In the hydrosilylation of benzaldehyde, the reaction proceeds through the formation of a new intermediate bis(benzaldehyde) adduct, [(ArN?)Mo(η²‐PhC(O)H)₂(PMe₃)], which reacts further with hydrosilane through a η¹‐silane complex, as studied by DFT calculations.     

Measurement of the sputter yield after mild ion erosion of a pristine Cu(001) surface

Using the STM technique we have determined the sputter yield on a pristine Cu(001) surface after mild (fluence less than 0.044 ions per surface atom) bombardment of the pristine surface with 800 eV Ar⁺ions at normal incidence. The experiments have been performed at substrate temperatures ranging from 200 to 350 K. Making use of the positional correlation of adatoms and surface vacancies, at 200 K and 325 K, we concluded that about 1/3 of the surface adatoms originate from interstitials arriving at the surface and they give a direct indication of the buried bulk vacancies. A careful analysis of the different areas for surface vacancies and adatom then allowed a quantitative evaluation of the sputter yield at 1.2 Cu atoms per 800 eV Ar⁺ ion.     

The effect of copper ions addition on structural and optical properties of zinc borate glasses

Glasses in the ternary system xCuO?(100 ? x)[55B₂O₃·45ZnO] (0 ≤ x ≤ 20 mol%) have been prepared by melting at 1200 °C and rapidly cooling at room temperature. The effect of copper ions addition in 55B₂O₃·45ZnO glass matrix together with the matrix effect on paramagentic behavior has been investigated using X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, differential thermal analysis (DTA), electron paramagnetic resonance (EPR), ultraviolet–visible (UV–VIS) spectroscopy and density measurements. The increase of the number of non-bridging oxygen (NBO) atoms as a function of CuO content in these glasses leads to the decrease of glass polymerization which reduces the stability of the glasses and favors the association of copper ions in clusters. This leads to the major changes of structural and optical properties of the studied glasses as can be seen from the data obtained by FTIR and EPR spectroscopies.     

XRD and EPR structural investigation of some zinc borate glasses doped with iron ions

Glasses in the system xFe₂O₃·(100?x) [45ZnO·55B₂O₃] (0≤x≤10 mol%) have been prepared by melting at 1200 °C and rapidly cooling at room temperature. The obtained samples were submitted to an additional thermal treatment at 570 °C for 12 h in order to relax the glass structure as well as to improve the local order. The as cast and heat treated samples were investigated using X-ray diffraction (XRD) and electron paramagnetic resonance (EPR) measurements. The XRD patterns of all the studied samples show their vitreous nature. Structural modifications occurring in the heat treated samples compared to the untreated ones have been pointed out. EPR spectra of untreated and heat treated samples revealed resonance absorptions centered at g≈2.0, g≈4.3 and g≈6.4. The compositional variation of the line intensity and linewidth of the absorptions from g≈4.3 and g≈2.0 have been interpreted in terms of the variation in the concentration of the Fe³⁺ ions and the interaction between the iron ions. The EPR spectra of the untreated samples containing 5 mol% Fe₂O₃ have been studied at different temperatures (110–290 K). The line intensity of the resonance signals decreases with increase in temperature whereas the linewidth is found to be independent of temperature. It was also found that the temperature variation of reciprocal line intensity obeys the Boltzmann law.