Determination of titanium NMR parameters of ATiO3 compounds: correlations with structural distortion

Solid state ^47,49Ti NMR spectra have been obtained for a number of perovskite and ilmenite ATiO₃ compounds. The ⁴⁹Ti quadrupole coupling constant varies from 2.75 MHz (CaTiO₃) to 15.5 MHz (MgTiO₃) and the electric field gradient at the titanium site was found to correlate well with the shear strain, independent of structure. The chemical shift in the perovskite structures varies by 160 ppm and correlates well with the mean Ti–O distance. The ²⁵Mg and ¹¹³Cd NMR parameters are also reported for the relevant compounds.     

Singularly Perturbed Semilinear Systems

Solutions of a singularly perturbed vector boundary-value problem are studied under the principal assumption that the trivial solution of the unperturbed equation is stable in certain senses. This is accomplished by constructing special invariant regions in which solutions display the kind of nonuniformity known as boundary-layer behavior.     

Global Asymptotics of the Second Painlevé Equation in Okamoto’s Space

We study the solutions of the second Painlevé equation (P II) in the space of initial conditions first constructed by Okamoto, in the limit as the independent variable, x, goes to infinity. Simultaneously, we study solutions of the related equation known as the thirty-fourth Painlevé equation (P 34). By considering degenerate cases of the autonomous flow, we recover the known special solutions, which are either rational functions or expressible in terms of Airy functions. We show that the solutions that do not vanish at infinity possess an infinite number of poles. An essential element of our construction is the proof that the union of exceptional lines is a repeller for the dynamics in Okamoto’s space. Moreover, we show that the limit set of the solutions exists and is compact and connected.     

Gyrokinetic simulations of solar wind turbulence from ion to electron scales

A three-dimensional, nonlinear gyrokinetic simulation of plasma turbulence resolving scales from the ion to electron gyroradius with a realistic mass ratio is presented, where all damping is provided by resolved physical mechanisms. The resulting energy spectra are quantitatively consistent with a magnetic power spectrum scaling of k(-2.8) as observed in in situ spacecraft measurements of the "dissipation range" of solar wind turbulence. Despite the strongly nonlinear nature of the turbulence, the linear kinetic Alfvén wave mode quantitatively describes the polarization of the turbulent fluctuations. The collisional ion heating is measured at subion-Larmor radius scales, which provides evidence of the ion entropy cascade in an electromagnetic turbulence simulation.     

Preparation, structural analysis and dielectric properties of Bi x La1−x FeO3 perovskite

Rare earth element substituted bismuth ferrites (BiFeO₃) are of enormous importance as magnetoelectric materials. The polycrystalline samples of Bi _x La_1−x FeO₃ (x=0, 0.2, 0.4, 0.6, 0.8) were prepared by solid-state reaction using standard ceramic method. The single-phase formation of these compounds was confirmed by X-ray diffraction (XRD) studies. The samples with x=0, 0.2, 0.4, 0.6 are found to be orthorhombic while the sample with x=0.8 is triclinic. The dielectric constant (ε′) and dissipation factor (tan δ) were measured in the frequency range 100 Hz to 1 MHz at room temperature and as a function of temperature at certain fixed frequencies (1 kHz, 10 kHz, 100 kHz, 1 MHz). All the samples showed dielectric dispersion. The dielectric constant with temperature shows a broad peak; the peak temperature shifts with frequency which reflects the relaxor-type behavior. The peak above 600 K in the measured temperature range corresponds to antiferromagnetic ordering temperature (Néel temperature). The broadness of the peak changes with composition. The ac conductivity as well as ε′ are found to be maximum for the sample x=0.2 at room temperature.     

A Model Nonlinear Problem Having a Continuous Locus of Singular Points

The asymptotic behavior of solutions of a singularly perturbed boundary value problem whose reduced equation has continuous bran,ches of singular points is investigated. In particular, unexpected limiting values of solutions for certain choices of the boundary conditions are found by means of a priori estimates.     

Singularly Perturbed Semilinear Robin Problems

Several phenomena of current interest in catalytic reaction theory can be phrased in terms of solutions of singularly perturbed, second-order, semilinear differential equations satisfying boundary conditions of Robin type. This paper offers a mathematical theory for such problems in both the scalar and the vector case, and treats some examples involving the pseudo-steady-state hypothesis and a parallel reaction inside of a porous catalyst pellet.