Matrix differential equations and scalar polynomials satisfying higher order recursions

We show that any scalar differential operator with a family of polyno- mials as its common eigenfunctions leads canonically to a matrix differen- tial operator with the same property. The construction of the correspond- ing family of matrix valued polynomials has been studied in [D1, D2, DV] but the existence of a differential operator having them as common eigen- functions had not been considered This correspondence goes only one way and most matrix valued situations do not arise in this fashion. We illustrate this general construction with a few examples. In the case of some families of scalar valued polynomials introduced in [GH] we take a first look at the algebra of all matrix differential operators that share these common eigenfunctions and uncover a number of phenomena that are new to the matrix valued case

Hexaaquazinc(II) dinitrate bis[5-(pyridinium-3-yl)tetrazol-1-ide]

Indexación: Scopus.Funding for this research was provided by: Fondecyt Regular (award No. 1151527); Proyecto REDES ETAPA INICIAL, Convocatoria 2017 (award No. REDI170423); Millennium Institute for Research in Optics (MIRO); Basal USA (award No. 1799).Hexaaquazinc(II) dinitrate 5-(pyridinium-3-yl)tetrazol-1-ide, [Zn(H2 O)6](NO 3)2 ·2C6H5 N 5, crystallizes in the space group P. The asymmetric unit contains one zwitterionic 5-(pyridinium-3-yl)tetrazol-1-ide molecule, one NO3-anion and one half of a [Zn(H2 O)6]2+ cation (symmetry). The pyridinium and tetrazolide rings in the zwitterion are nearly coplanar, with a dihedral angle of 5.4 (2)°. Several O-H..N and N-H..O hydrogen-bonding interactions exist between the [Zn(H2 O)6]2+ cation and the N atoms of the tetrazolide ring, and between the nitrate anions and the N-H groups of the pyridinium ring, respectively, giving rise to a three-dimensional network. The 5-(pyridinium-3-yl)tetrazol-1-ide molecules show parallel-displaced π-π stacking interactions; the centroid-centroid distance between adjacent tetrazolide rings is 3.6298 (6) Å and that between the pyridinium and tetrazolide rings is 3.6120 (5) Å. © 2018 Chi-Duran et al.http://journals.iucr.org/e/issues/2018/09/00/cq2025/index.htm

Synthesis of Y1Ba2Cu3O(sub x) superconducting powders by intermediate phase reaction

One of the more striking problems for the synthesis of the Y1Ba2Cu3Ox compound is the high-temperature decomposition of the BaCO3. This compound is present as raw material or as an intermediate compound in chemical processes such as amorphous citrate, coprecipitation oxalate, sol-gel process, acetate pyrolisis, etc. This fact makes difficult the total formation reaction of the Y1Ba2Cu3Ox phase and leads to the presence of undesirable phases such as the BaCuO2 phase, the 'green phase', Y2BaCuO5 and others. Here, a new procedure to overcome this difficulty is studied. The barium cation is previously combined with yttrium and/or copper to form intermediate compounds which can react between them to give Y1Ba2Cu3Ox. BaY2O4 and BaCu2O3 react according to the equation BaY2O4+3BaCu2O3 yields 2Y1Ba2Cu3Ox. BaY2O4 is a stable compound of the Y2O3-BaO system; BaCu2O3 is an intimate mixture of BaCuO2 and uncombined CuO. The reaction kinetics of these phases have been established between 860 and 920 C. The phase evolution has been determined. The crystal structure of the Y1Ba2Cu3Ox obtained powder was studied. According to the results obtained from the kinetics study the Y1Ba2Cu3Ox the synthesis was performed at temperatures of 910 to 920 C for short treatment times (1 to 2 hours). Pure Y1Ba2Cu3Ox was prepared, which develops orthorombic type I structure despite of the cooling cycle. Superconducting transition took place at 91 K. The sintering behavior and the superconducting properties of sintered samples were studied. Density, microstructure and electrical conductivity were measured. Sintering densities higher than 95 percent D(sub th) were attained at temperatures below 940 C. Relatively fine grained microstructure was observed, and little or no-liquid phase was detected

Effect of friction in a toy model of granular compaction

We proposed a toy model of granular compaction which includes some resistance due to granular arches. In this model, the solid/solid friction of contacting grains is a key parameter and a slipping threshold Wc is defined. Realistic compaction behaviors have been obtained. Two regimes separated by a critical point Wc* of the slipping threshold have been emphasized : (i) a slow compaction with lots of paralyzed regions, and (ii) an inverse logarithmic dynamics with a power law scaling of grain mobility. Below the critical point Wc*, the physical properties of this frozen system become independent of Wc. Above the critical point Wc*, i.e. for low friction values, the packing properties behave as described by the classical Janssen theory for silos

Velocity Distribution in a Viscous Granular Gas

We investigate the velocity relaxation of a viscous one-dimensional granular gas, that is, one in which neither energy nor momentum is conserved in a collision. Of interest is the distribution of velocities in the gas as it cools, and the time dependence of the relaxation behavior. A Boltzmann equation of instantaneous binary collisions leads to a two-peaked distribution with each peak relaxing to zero velocity as 1/t while each peak also narrows as 1/t. Numerical simulations of grains on a line also lead to a double-peaked distribution that narrows as 1/t. A Maxwell approximation leads to a single-peaked distribution about zero velocity with power-law wings. This distribution narrows exponentially. In either case, the relaxing distribution is not of Maxwell-Boltzmann form

Ripples in Tapped or Blown Powder

We observe ripples forming on the surface of a granular powder in a container submitted from below to a series of brief and distinct shocks. After a few taps, the pattern turns out to be stable against any further shock of the same amplitude. We find experimentally that the characteristic wavelength of the pattern is proportional to the amplitude of the shocks. Starting from consideration involving Darcy's law for air flow through the porous granulate and avalanche properties, we build up a semi-quantitative model which fits satisfactorily the set of experimental observations as well as a couple of additional experiments.Comment: 7 pages, four postscript figures, submitted PRL 11/19/9

Synthesis of Y1BaCu3O(x) superconducting powders by intermediate phase reactions

A procedure for synthesizing Y1Ba2Cu3O(x) by solid state reactions was developed. The method is based on the use of barium compounds, previously synthesized, as intermediate phases for the process. The reaction kinetics of this procedure were established between 860 C and 920 C. The crystal structure and the presence of second phases were studied by means of XRD. The sintering behavior and ceramic parameters were also determined. The orthorhombic type-I structure was obtained on the synthesized bodies after a cooling cycle in an air atmosphere. Superconducting transition took place at 91 K. Sintering densities higher than 95 percent D sub th were attained at temperatures below 940 C