Crystal Structure and Non-Hydrostatic Stress-Induced Phase Transition of Urotropine Under High Pressure

High-pressure behavior of hexamethylenetetramine (urotropine) was studied in situ using angle-dispersive single-crystal synchrotron X-ray diffraction (XRD) and Fourier-transform infrared absorption (FTIR) spectroscopy. Experiments were conducted in various pressure-transmitting media to study the effect of deviatoric stress on phase transformations. Up to 4 GPa significant damping of molecular librations and atomic thermal motion was observed. A first-order phase transition to a tetragonal structure was observed with an onset at approximately 12.5 GPa and characterized by sluggish kinetics and considerable hysteresis upon decompression. However, it occurs only in non-hydrostatic conditions, induced by deviatoric or uniaxial stress in the sample. This behavior finds analogies in similar cubic crystals built of highly symmetric cage-like molecules and may be considered a common feature of such systems. DFT computations were performed to model urotropine equation of state and pressure dependence of vibrational modes. The first successful Hirshfeld atom refinements carried out for high-pressure diffraction data are reported. The refinements yielded more realistic C−H bond lengths than the independent atom model even though the high-pressure diffraction data are incomplete.     

Using FFT-based techniques in polynomial and matrix computations: recent advances and applicatons

Computations with univariate polynomials, like the evaluation of product, quotient, remainder, greatest common divisor, etc, are closely related to linear algebra computations performed with structured matrices having the Toeplitz-like or the Hankel-like structures.

The discrete Fourier transform, and the FFT algorithms for its computation, constitute a powerful tool for the design and analysis of fast algorithms for solving problems involving polynomials and structured matrices.

We recall the main correlations between polynomial and matrix computations and present two recent results in this field: in particular, we show how Fourier methods can speed up the solution of a wide class of problems arising in queueing theory where certain Markov chains, defined by infinite block Toeplitz matrices in generalized Hessenberg form, must be solved. Moreover, we present a new method for the numerical factorization of polynomials based on a matrix generalization of Koenig's theorem. This method, that relies on the evaluation/interpolation technique at the Fourier points, reduces the problem of polynomial factorization to the computation of the LU decomposition of a banded Toeplitz matrix with its rows and columns suitably permuted. Numerical experiments that show the effectiveness of our algorithms are presented     

Moduli of curves and spin structures via algebraic geometry

Here we investigate some birational properties of two collections of moduli spaces, namely moduli spaces of (pointed) stable curves and of (pointed) spin curves. In particular, we focus on vanishings of Hodge numbers of type and on computations of Kodaira dimension. Our methods are purely algebro-geometric and rely on an induction argument on the number of marked points and the genus of the curves.

     

A fast implicit QR eigenvalue algorithm for companion matrices

An implicit version of the shifted QR eigenvalue algorithm given in Bini et al. [D.A. Bini, Y. Eidelman, I. Gohberg, L. Gemignani, SIAM J. Matrix Anal. Appl. 29(2) (2007) 566-585] is presented for computing the eigenvalues of an n×n companion matrix using O(n²) flops and O(n) memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method.     

Role of doping and CuO segregation in improving the giant permittivity of CaCu3Ti4O12

The dopant role on the electric and dielectric properties of the perovskite-type CaCu₃Ti₄O₁₂ (CCTO) compound is evidenced. Impedance spectroscopy measurements show that the relevant permittivity value attributed to sintered CCTO is due to grain boundary (g.b.) effects. The g.b. permittivity value of the pure CCTO can be increased of 1-2 orders of magnitude by cation substitution on Ti site and/or segregation of CuO phase, while the bulk permittivity keeps values 90<ε_r<180. Bulk and g.b. conductivity contributions are discussed: electrons are responsible for the charge transport and a mean bulk activation energy of 0.07 eV is obtained at room temperature for all the examined samples. The g.b. activation energy ranges between 0.54 and 0.76 eV. Defect models related to the transport properties are proposed, supported by electron paramagnetic resonance measurements.