Investigation of spin transition in GdCoO3 by measuring the electric field gradient at Co sites

In the present work, the time differential perturbed angular correlation (PAC) technique was used to study the temperature dependence of electric field gradient (efg) in GdCoO₃ perovskite using ¹¹¹Cd and ¹⁸¹Ta nuclear probes. The radioactive parent nuclei ¹¹¹In and ¹⁸¹Hf were introduced in the oxide lattice through chemical process during sample preparation and were found to occupy only the Co sites in GdCoO₃. The efg's at ¹¹¹Cd and ¹⁸¹Ta show temperature dependence with two different fractions each that change with temperature. In the case of ¹¹¹Cd the quadrupole frequency slowly decreases, with corresponding increase of the temperature and shows a peak like structure at around 200 K and a discontinuity at 700 K. These changes have been interpreted as thermally activated spin-state transitions from low-spin ground state configuration to the intermediate-spin state and from intermediate-spin to high-spin state of Co³⁺${\mathrm{Co}}^{3+}$ ion similar to LaCoO₃ compound. Indication of a Jahn–Teller distortion, which stabilizes the intermediate-spin state with orbital ordering, is also pointed out.     

Well-posedness of a class of perturbed optimization problems in Banach spaces

Let X be a Banach space and Z a nonempty subset of X. Let J:Z→R be a lower semicontinuous function bounded from below and p?1. This paper is concerned with the perturbed optimization problem of finding z₀∈Z such that ‖x−z₀p^‖+J(z₀)=infz∈Z{‖x−zp^‖+J(z)}, which is denoted by minJ(x,Z). The notions of the J-strictly convex with respect to Z and of the Kadec with respect to Z are introduced and used in the present paper. It is proved that if X is a Kadec Banach space with respect to Z and Z is a closed relatively boundedly weakly compact subset, then the set of all x∈X for which every minimizing sequence of the problem minJ(x,Z) has a converging subsequence is a dense Gδ-subset of X?Z₀, where Z₀ is the set of all points z∈Z such that z is a solution of the problem minJ(z,Z). If additionally p>1 and X is J-strictly convex with respect to Z, then the set of all x∈X for which the problem minJ(x,Z) is well-posed is a dense Gδ-subset of X?Z₀.     

Exact multiplicity of solutions and S-shaped bifurcation curves for the p-Laplacian perturbed Gelfand problem in one space variable

We study exact multiplicity of positive solutions and the bifurcation curve of the p-Laplacian perturbed Gelfand problem from combustion theory

     

Effects of Zr impurity on microscopic behavior of Hf metal

Hf metal with ∼ 3 wt% Zr impurity has been reinvestigated by perturbed angular correlation (PAC) spectroscopy using a LaBr₃(Ce)–BaF₂ detector set up to understand the microscopic behavior of this metal with temperature. From present measurements, five quadrupole interaction frequencies have been found at room temperature where both pure hcp fraction (∼33%) with 12 nearest neighbor Hf surrounding the probe ¹⁸¹Hf atom and the probe–impurity fraction (∼33%) corresponding to 11 nearest neighbor Hf plus one dissimilar Zr atom are clearly distinguished. At room temperature, the results for quadrupole frequency and asymmetry parameter are found to be ω_Q=51.6(4) Mrad/s, η=0.20(4) for the impurity fraction and ω_Q=46.8(2) Mrad/s, η=0 for the pure fraction with values of frequency distribution width δ=0 for both components. At 77 K, only 1 NN Zr impurity (∼93%) and pure hcp (∼7%) components have been found with a value of δ ∼ 10% for the impurity fraction. A drastic change in microstructural configuration of Hf metal is observed at 473 K where the impurity fraction increases to ∼ 50% and the pure hcp fraction reduces to ∼ 15% with abrupt changes in quadrupole frequencies for both components. The pure fraction then increases with temperature and enhances to ∼50% at 973 K. In the temperature range 473–973 K, quadrupole frequencies for both components are found to decrease slowly with temperature. Using the Arrhenius relation, binding energy (B) for the probe–impurity pair and the entropy of formation are measured from temperature dependent fractions of probe–impurity and pure hcp in the temperature range 473–773 K. The three other minor components found at different temperatures are attributed to crystalline defects.     

Third-Order Dispersion in Linearly Chirped Bragg Gratings and Its Compensation

When fiber optics' quadratic dispersion is compensated, the cubic dispersion determines the transmission quality in an optical link. Although the third-order dispersion coefficient is small in standard fiber optics at the third window, it is not in the linearly chirped grating used to the second-order dispersion equalization. The influence of the grating parameters on its third-order dispersion value is systematically studied and an efficient and low-cost device is proposed thatis numerically proven to cancel the global third-order dispersion that arises from the optical link.     

Natural examples of Valdivia compact spaces

We collect examples of Valdivia compact spaces, their continuous images and associated classes of Banach spaces which appear naturally in various branches of mathematics. We focus on topological constructions generating Valdivia compact spaces, linearly ordered compact spaces, compact groups, L¹ spaces, Banach lattices and noncommutative L¹ spaces.     

不同波长的散射介质后向散射光偏振度特性

基于Stockes矢量,通过测量以线偏振光和圆偏振光入射时脂肪乳剂后向散射光的偏振度,研究了532nm、650nm和780nm三个波长的光与散射粒子粒径为325nm的脂肪乳剂溶液作用后,其后向散射光的偏振度特性.研究结果表明,对于入射线偏振光,780nm波长后向散射光中的线偏振光成分多于圆偏振光成分,而532nm波长则相反;对于入射圆偏振光,三个波长后向散射光中的圆偏振光成分均多于线偏振光成分;532nm波长的总偏振度高于650nm和780nm两个波长各自的总偏振度;线偏振光的保偏性优于圆偏振光的保偏性,但偏振光在散射介质中的穿透深度较小.因此,后向散射成像技术适用于物体表层成像,而且选择波长略大于粒径的线偏振光可以提高成像质量.     

Three-dimensional flow of a Jeffery fluid over a linearly stretching sheet

This investigation reports the three-dimensional flow of Jeffrey fluid over a linearly stretching surface. Transformation method has been utilized for the reduction of partial differential equations into the ordinary differential equations. The solutions of the nonlinear systems are presented by a homotopy analysis method (HAM). The reported graphical results are analyzed. A comparative study with the previous results of viscous fluid in the literature is made.     

Can a linearly polarized light beam polarize atomic spin?

Lax et al. [Phys. Rev. 11 (1975) 1365] discovered that a light beam in vacuum is not a transverse wave but does have a longitudinal field component. We investigate atomic and molecular electric dipole transitions induced by such a light beam, in particular, linearly polarized in a transverse plane. We derive the selection rules and the transition rates for various quantization axes using the paraxial approximation up to the first order of 1/kw, where k is the wave number and w is the transverse size of the light beam. The light beam is able to yield atomic spin polarization in the direction perpendicular to both the optical axis and the transverse electric field, and its magnitude is approximately 1/kw times that generated by a circularly polarized light wave with the similar intensity.