Adaptive numerical schemes for a parabolic problem with blow-up

In this paper we present adaptive procedures for the numericalstudy of positive solutions of the following problem: u_t = u_xx (x, t) (0, 1) x [0, T), u_x(0, t) = 0 t [0, T), u_x(1, t) = u^p(1, t) t [0, T), u(x, 0) = u₀(x) x (0, 1), with p > 1. We describe two methods. The first one refinesthe mesh in the region where the solution becomes bigger ina precise way that allows us to recover the blow-up rate andthe blow-up set of the continuous problem. The second one combinesthe ideas used in the first one with moving mesh methods andmoves the last points when necessary. This scheme also recoversthe blow-up rate and set. Finally, we present numerical experimentsto illustrate the behaviour of both methods.     

Formation and structure of self-assembled silica nanoparticles in basic solutions of organic and inorganic cations

The phase behavior of silica solutions containing organic and inorganic cations was studied at room temperature using conductivity, pH, and small-angle scattering experiments. A critical aggregation concentration (cac) was observed at approximately 1:1 ratio of SiO(2)/OH(-) for all cation solutions from conductivity and pH studies. From this cac, a phase diagram of the system was developed with three distinct phase regions in pseudoequilibrium: a monomer/oligomer region (I), a monomer/oligomer/nanoparticle region (II), and a gel region (III). Small-angle X-ray and neutron scattering (SAXS and SANS) on solutions of region II formed with tetrapropylammonium hydroxide (TPAOH) revealed that the nanoparticles have a core-shell structure. Structure analysis of the SAXS and SANS data was best fit by a core-shell oblate ellipsoid model. A polydisperse set of core-shell spheres also fit the data well although with lower agreement factors. Similar nanoparticle morphologies were found in solutions of TMAOH, CsOH, and NaOH.     

Kinetic study of the reaction between hydroxylated polybutadienes and isocyanates. II. Reaction with 3-isocyanatomethyl-3,5,5-trimethylcyclohexylisocyanate (IPDI) and dimer diacid diisocyanate (DDI)

A comparative kinetic study of the reaction of three different hydroxylated liquid poly-butadienes (M?_n ? 3000)–R-45M, R-45HT and H-034–with 3-isocyanatomethyl–3,5,5-trimethylclohexylisocyanate (IPDI) and dimer diacid diisocyanate (DDI) was carried out in toluene solution. An analytical method was used to follow the kinetics of the reactions, at four different temperatures. In the second-order plots, a discontinuity was observed in the reaction with IPDI, in contrast to the reactions with DDI which showed straight-line plots. In all studied reactions, the R-45M polybutadiene was about twice as reactive as R-45HT and H-034. The latter hydroxylated polybutadienes (R-45HT and H-034) showed similar reactivities.     

The Carleman-smithies theory of integral operators for reflexive Orlicz spaces

The Carleman inequalities for Hilbert-Schmidt integral operators on L₂ are shown to hold for their counterpart on reflexive Orlicz spaces. This solves a problem posed by Zaanen. A refined version of Schur's inequality for the ₂-norm of eigenvalues is also proved in this context.     

Stereoselective Michael addition of 6-amino-1,3-dimethyl-2,4-pyrimidinedione to the exocyclic methylene of three sesquiterpene lactones. 1H and 13C NMR evidence of a new C-C bond and lactam formation

The Stereoselective addition of the pyrimidine derivative 1 to the exocyclic methylene of the α,β unsaturated dehydrocostus lactone 2, Ivalin acetate 3 and Zaluzanin A diacetate 4, was achieved resulting in a new C-C bond formation. In the cases of compounds 3 and 4, after the addition, the lactone was cleaved followed by reclosure into a lactam ring system.     

Physical basis for the formation and stability of silica nanoparticles in basic solutions of monovalent cations

The colloidal stability, phase behavior, and solubility of silica nanoparticles (3-10 nm) that are formed in basic solutions of monovalent cations (primarily tetrapropylammonium) are investigated using a combination of chemical equilibria and electrostatic models. The free-energy gain associated with the formation of an electric double layer surrounding the nanoparticle was obtained by solving the Poisson-Boltzmann equation. This free energy is an important contribution to the total free energy of the particle and is second only to the formation of Si-O-Si bonds. The free energy of formation of the nanoparticles becomes increasingly negative with an increase in particle size and density, which explains the lower solubility of nanoparticles compared to that of amorphous silica. There is a minimum in the free energy of condensation as a function of size that qualitatively explains why the formation of small particles with a uniform size (<5 nm) is energetically favorable. The electrostatic models provide an estimate for the nanoparticle surface potential, which is significantly higher (-120 to -170 mV) than that of zeolite silicalite-1 (-60 to -80 mV) prepared in similar solutions. This result explains the stability of such small particles in solution. It is also shown that a condensation model that is based on silica solubility can describe the phase diagram for nanoparticle formation reported by Fedeyko et al. (J. Phys. Chem. B 2004, 108, 12271) over a wide range of pH and, in conjunction with a complexation model, provides an approximate equilibrium constant (pKa = 8.4) for the dissociation of nanoparticle silanol groups.     

Intra- vs intermolecular hydrogen bonding. The crystal structure of 5-methyl-2-hydroxyacetophenone thiosemicarbazone monohydrate and salicylaldehyde-2-methylthiosemicarbazone monohydrate

The crystal structure of 5-methyl-acetophenonethiosemicarbazone monohydrate,A, and salicylaldehyde-2-methylthiosemicarbazone monohydrate,B, were determined using single crystal X-ray diffraction.A crystallizes in the monoclinic space groupC2/c, with lattice parametersa=14.161(2),b=15.753(1) Å,c=11.084(1) Å, β=112.59(1)° andZ=4, yielding a calculated density ofD _calc=1.352 mg/m³.B crystallizes in the triclinic space groupP1, witha=7.233(2) Å,b=7.371(2) Å,c=11.841(2) Å, α=82.77(2)°, β=78.33(2)°, γ=63.06(2)° andD _calc=1.371 mg/m³ forZ=2,. In bothA andB the immine nitrogen and the sulfur atom areanti with respect to N2-C8. WhileA presents the usual intramolecular six membered hydrogen bond ring,B has instead an intermolecular hydrogen bond between the hydroxy moiety of the salicyladehyde and a water molecule. AM1 calculations agree with the experimental conformations observed in both compounds.     

Propane dehydrogenation over extra-framework In(i) in chabazite zeolites

Indium on silica, alumina and zeolite chabazite (CHA), with a range of In/Al ratios and Si/Al ratios, have been investigated to understand the effect of the support on indium speciation and its corresponding influence on propane dehydrogenation (PDH). It is found that In₂O₃ is formed on the external surface of the zeolite crystal after the addition of In(NO₃)₃ to H-CHA by incipient wetness impregnation and calcination. Upon reduction in H₂ gas (550 °C), indium displaces the proton in Brønsted acid sites (BASs), forming extra-framework In⁺ species (In-CHA). A stoichiometric ratio of 1.5 of formed H₂O to consumed H₂ during H₂ pulsed reduction experiments confirms the indium oxidation state of +1. The reduced indium is different from the indium species observed on samples of 10In/SiO₂, 10In/Al₂O₃ (i.e., 10 wt% indium) and bulk In₂O₃, in which In₂O₃ was reduced to In(0), as determined from the X-ray diffraction patterns of the product, H₂ temperature-programmed reduction (H₂-TPR) profiles, pulse reactor investigations and in situ transmission FTIR spectroscopy. The BASs in H-CHA facilitate the formation and stabilization of In⁺ cations in extra-framework positions, and prevent the deep reduction of In₂O₃ to In(0). In⁺ cations in the CHA zeolite can be oxidized with O₂ to form indium oxide species and can be reduced again with H₂ quantitatively. At comparable conversion, In-CHA shows better stability and C₃H₆ selectivity (∼85%) than In₂O₃, 10In/SiO₂ and 10In/Al₂O₃, consistent with a low C₃H₈ dehydrogenation activation energy (94.3 kJ mol⁻¹) and high C₃H₈ cracking activation energy (206 kJ mol⁻¹) in the In-CHA catalyst. A high Si/Al ratio in CHA seems beneficial for PDH by decreasing the fraction of CHA cages containing multiple In⁺ cations. Other small-pore zeolite-stabilized metal cation sites could form highly stable and selective catalysts for this and facilitate other alkane dehydrogenation reactions.

Indium-containing chabazite zeolites show better stability and C₃H₆ selectivity for propane dehydrogenation than In₂O₃, In/SiO₂ and In/Al₂O₃. Extra-framework In⁺ is identified as the stable active site upon reduction of an impregnated sample.     

Effects of precursors on nucleation in atomic layer deposition of HfO2

Atomic layer deposition of hafnium dioxide (HfO₂) on silicon substrates was studied. It was revealed that due to low adsorption probability of HfCl₄ on silicon substrates at higher temperatures (450–600 °C) the growth was non-uniform and markedly hindered in the initial stage of the HfCl₄–H₂O process. In the HfI₄–H₂O and HfI₄–O₂ processes, uniform growth with acceptable rate was obtained from the beginning of deposition. As a result, the HfI₄–H₂O and HfI₄–O₂ processes allowed deposition of smoother, more homogeneous and denser films than the HfCl₄–H₂O process did. The crystal structure developed, however, faster at the beginning of the HfCl₄–H₂O process.