Preparation and third-order nonlinear optical properties of self-organized complex oxide Ce: BaTiO3 quantum dots

Pulsed laser ablation epitaxial Strancky-Krastanow growth of self-organized complex oxide Ce:BaTiO₃ quantum dots on MgO(lOO) substrates is demonstrated. Atomic force microscopy and X-ray diffraction are used to observe the structure and the growth process of the self-organized complex oxide quantum dots. The average dimension, height, and the density of self-organized complex oxide Ce:BaTiO₃ quantum dots are given. The nonlinear refractive indexes of the wetting layer and the selforganized ordered quantum dots are determined by the single beam Z-scan method. The mechanisms of the nonlinear effect enhancement for these low-dimensional structure are discussed.     

Preparation and third-order nonlinear optical properties of self-organized complex oxide Ce:BaTiO3 quantum dots

Pulsed laser ablation epitaxial Strancky-Krastanow growth of self-organized complex oxide Ce:BaTiO3 quantum dots on MgO(100) substrates is demonstrated.Atomic force microscopy and X-ray diffraction are used to observe the structure and the growth process of the self-organized complex oxide quantum dots.The average dimension,height,and the density of self-organized complex oxide Ce:BaTiO3 quantum dots are given.The nonlinear refractive indexes of the wetting layer and the self-organized ordered quantum dots are determined by the single beam Z-scan method.The mechanisms of the nonlinear effect enhancement for these low-dimensional structure are discussed.     

Laser molecular-beam epitaxy and second-order optical nonlinearity of BaTiO3/SrTiO3 superlattices

A series of c-axis oriented BaTiO₃/SrTiO₃ superlattices with the atomic-scale precision were epitaxially grown on single-crystal SrTiO₃(l00) substrates using laser molecular-beam epitaxy (LMBE). A periodic modulation of the intensity of reflection high-energy electron diffraction (RHEED) in BaTiO₃ and SrTiO₃ layers was observed and attributed to the lattice-misfit-induced periodic variation of the terrace density in film surface. The relationship between the second-order nonlinear optical susceptibilities and the superlattice structure was systematically studied. The experimental and theoretical fitting results indicate that the second-order nonlinear optical susceptibilities of BaTiO₃/SrTiO₃ superlattices were greatly enhanced with the maximum value being more than one order of magnitude larger than that of bulk BaTiO₃ crystal. The mechanism of the enhancement of the second-order optical nonlinearity was discussed by taking into account the stress-induced lattice distortion and polarization enhancement.     

Heating effect of BaTiO3 in microwave field and microstructure of BaTiO3

Microwave equipment at 2 450 MHz was employed to prepare BaTiO₃. The heating effect of the system in the microwave field, which was influenced by several factors including dielectric properties of synthesis system and thermal insulate structures, was discussed in detail. The heating rates of the synthesis system were mainly determined by BaCO₃ and TiO₂ at low temperature and by TiO₂ and BaTiO₃ at high temperature. The results show that the heating effects in microwave field are greatly different from those in conventional furnace. The reaction of BaCO₃ and TiO₂ only lasts for 3 min at 1 100°C, and the fine, narrow-distributed and well-crystallized powders were prepared. Project supported by the National Natural Science Foundation of China.     

Atomic scale epitaxial growth of BaTiO3 thin films by laser molecular beam epitaxy

By using laser molecular beam epitaxy (L-MBE), atomic scale epitaxid growth of BaTiO₃(BTO) thin films on SrTiO₃ (STO) substrates is achieved. Measurements of reflection high energy electron diffraction (RHEED), X-ray diffraction (XRD), scanning electron microscopy, and transmission electron microscopy reveal that the BTO films arec-axis oriented single crystals with smooth surface. The multi-layer ferroelectric/superconducting heterostructures are also prepared and the ferroelectric properties of BTO films are studied. The results show that by using L-MBE technique, high quality BTO films and improved device performance can be obtained. Project supported by the National Natural Science Foundation of China, the National Department of Finance, and the National Center for R and D on Superconductivity of China.     

Phase conjugator with two coherent beams in a BaTiO3:Ce crystal

A phase conjugator which includes two coherent beams that are incident upon one of afaces of a BaTiO₃: Ce crystal without internal reflection is performed experimentally. Based on the fourwave mixing, the mechanism of this conjugator is investigated numerically. In comparison with the corresponding self-pumped phase conjugator, the phase-conjugate behavior of this conjugator is established much more quickly, its phase conjugate reflectivity is greater in some cases and the intensity threshold is lower by over two orders of magnitude. The configuration of this conjugator is easy to perform because the output response exists over a wide range of angular and lateral positions of the two incident beams on the crystal.     

First-principles calculations on electronic, chemical bonding and optical properties of tetragonal SrHfO3

Electronic, chemical bonding and optical properties of tetragonal SrHfO₃ were investigated using the plane-wave ultrasoft pseudopotential technique based on the first-principles density functional theory (DFT). The optimized equilibrium lattice parameters of tetragonal SrHfO₃ are in good agreement with experimental values. Band structure, densities of states (DOS), charge densities and molecular-orbital bonding structure of tetragonal SrHfO₃ have been obtained. The band structure shows that tetragonal SrHfO₃ has direct band gap. The DOS and charge densities indicate that bonding between Hf and O is mainly covalent due to Hf 5d and O 2p hybridization and that bonding between Sr and O is mainly ionic. The complex dielectric function, absorption coefficient, energy-loss spectrum, complex conductivity function and reflectivity of tetragonal SrHfO₃ have been predicted. The imaginary and real parts of the calculated complex dielectric functions are consistent with the experimental observations.     

On formal quantum group laws

There exist natural generalizations of the concept of formal groups laws for noncommutative power series. This is a note on formal quantum group laws and quantum group law chunks. Formal quantum group laws correspond to noncommutative (topological) Hopf algebra structures on free associative power series algebras ká áx₁,...,x_m ? ?k\langle\! \langle x_1,\dots,x_m \rangle\! \rangle , k a field. Some formal quantum group laws occur as completions of noncommutative Hopf algebras (quantum groups). By truncating formal power series, one gets quantum group law chunks. ¶If the characteristic of k is 0, the category of (classical) formal group laws of given dimension m is equivalent to the category of m-dimensional Lie algebras. Given a formal group law or quantum group law (chunk), the corresponding Lie structure constants are determined by the coefficients of its chunk of degree 2. Among other results, a classification of all quantum group law chunks of degree 3 is given. There are many more classes of strictly isomorphic chunks of degree 3 than in the classical case.     

Comparison of Two-wave Mixing–Self-focusing inDiffusion- and Drift-type Photorefractive Materials

Self-focusing and -defocusing of light in two-wave mixing is investigatedexperimentally for BaTiO₃ and BSO. Amplification and self-focusing of a probe beamare measured as functions of the frequency shift between probe and pump beam. The self-focusingin two-wave mixing in BSO is anisotropic, whereas it is isotropic in BaTiO₃.Consequences of gain saturation for the measurement of self-focusing in BaTiO₃ arediscussed.     

Superstrings,Cantorian-fractal Spacetime and Quantum-like Chaos in Atmospheric Flows

Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with the inverse power law form for spectra of temporal fluctuations. Such non-local connections are ubiquitous to dynamical systems in nature and are identified as signatures of self-organized criticality. A recently developed cell dynamical system model for atmospheric flows predicts the observed self-organized criticality as a natural consequence of quantum-like mechanics governing flow dynamics. The model is based on the concept that spatial integration of enclosed small scale fluctuations results in the formation of large eddy circulations. The model predicts the following: (a) The flow structure consists of an overall logarithmic spiral trajectory with the quasiperiodic Penrose tiling pattern for the internal structure. (b) Conventional power spectrum analysis will resolve such spiral trajectories as a continuum of eddies with progressive increase in phase. (c) Increments in phase are concomitant with increases in period length and also represent the variance, a characteristic of quantum systems identified as Berrys phase. (d) The universal algorithm for self-organized criticality is expressed in terms of the universal Feigenbaum constants, a and d, as 2a²=πd, where the fractional volume intermittency of occurrence πd contributes to the total variance 2a² of fractal structures. (e) The Feigenbaum constants are expressed as functions of the golden mean. ( f) The quantum mechanical constants fine structure constant and ratio of proton mass to electron mass, which are pure numbers and are obtained by experimental observations only, are now derived in terms of the Feigenbaum constant, a. (g) Atmospheric flow structure follows Keplers third law of planetary motion. Therefore, Newtons inverse square law for gravitation also applies to eddy masses. The centripetal acceleration representing the inertial masses (of eddies) are equivalent to gravitational masses. The fractal-Cantorian structure of spacetime can also be visualized as a nested continuum of vortex (eddy) circulations, whose inertial masses obey Newtons inverse square law of gravitation. The model concept resembles a superstring model for subatomic dynamics which incorporates gravitational forces.     

Is nature quantum non-local,complex holistic,or what?: II — Applications

In Part I of this paper [A. Sengupta, Is nature quantum non-local, complex holistic, or what? I–Theory & analysis. Nonlinear Anal.: RWA (2009) (in press)] to be referenced “I-”, we examined the linear–nonlinear divide of the natural world in an attempt to seek a rationale for the question “Is nature interactively nonlinear and holistic, or is it additively linear and reductionist?”: Is Nature governed by entanglements of linear superposition or does it represent the nonlinear holism of emergence, self-organization, and complexity? This second part carries the debate forward to propose that Quantum Mechanics is an effective linear representation of a fully chaotic, maximally illposed, multifunctional negworld that obviously is not just a mirror image of the functional real world we inhabit: in fact we argue that nonlinear complex holism represents a stronger form of entanglement than linear quantum non-locality. The bi-directionality of a self-organized, emergent, engine-pump system is analyzed with reference to the role of gravity as the compressive agent responsible for generation and maintenance of structures and life in Nature; we also explore the applicability of chanoxity to the metaphorical resolution of some of the long-standing paradoxes and puzzles in quantum measurement and non-locality, in Prigoginian intrinsic irreversibility, and in some core issues in cosmology and gravitational black holes.Holism is to be seen as complementing mainstream reductionism–linear science has after all stood the test of the last 400 years as quantum mechanics is acknowledgedly one of the most successful yet possibly one of the most mysterious of scientific theories: the success lies in its capacity to classify and predict the physical world, the mystery in what this physical world must be like to behave quantum mechanically–providing a unified picture of the dialectics of the evolutionary dynamics of Nature.     

Microstructure of a-SiOx:H

A set of a-SiO_x:H (0.52 <x< 1.58) films are fabricated by plasma-enhanced-chemical-vapor-deposition (PECVD) method at the substrate temperature of 250°C. The microstructure and local bonding configurations of the films are investigated in detail using micro-Raman scattering, X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FTIR). It is found that the films are structural inhomogeneous, with five phases of Si, Si₂O:H, SiO:H, Si₂O₃:H and SiO₂ that coexist. The phase of Si is composed of nonhydrogenated amorphous silicon (a-Si) clusters that are spatially isolated. The average size of the clusters decreases with the increasing oxygen concentration x in the films. The results indicate that the structure of the present films can be described by a multi-shell model, which suggests that a-Si cluster is surrounded in turn by the subshells of Si₂O:H, SiO:H, Si₂O₃:H, and SiO₂.     

Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells

This paper presents the report of an investigation into thermoelastic vibration and buckling characteristics of the functionally graded piezoelectric cylindrical, where the functionally graded piezoelectric cylindrical shell is made from a piezoelectric material having gradient change along the thickness, such as piezoelectricity and dielectric coefficient et al. Here, utilizing Hamilton’s principle and the Maxwell equation with a quadratic variation of the electric potential along the thickness direction of the cylindrical shells and the first-order shear deformation theory, and taking into account both the direct piezoelectric effect and the converse piezoelectric effect, the thermoelastic vibration and buckling characteristics of functionally graded piezoelectric cylindrical shells composed of BaTiO₃/PZT − 4, BaTiO₃/PZT − 5A and BaTiO₃/PVDF are, respectively, calculated. The effects of material composition (volume fraction exponent), thermal loading, external voltage applied and shell geometry parameters on the free vibration characteristics are described, and the axial critical load, critical temperature and critical control voltage are obtained.     

Effect of A-site cation substitution on magnetic transition temperature of (LaCa) MnO3

The ferromagnetic transition temperatures have been measured on two bathes of perovskite manganese oxides such as (La_1-x R _x )_2/3Ca_1/3MnO₃(R=Ce, Pr, Nd, etc.) and La_2/3(Ca_1-y Cd _y )_1/3MnO₃. It is found that the (La_1-x R _x )_2/3Ca_1/3MnO₃ samples have obviously different Curie temperatureT _C although their (r_A) (the average A-site cation radius) are almost identical, and theT _C in the system of (La_1-x R _x )_2/3Ca_1/3MnO₃(R=Ce, Pr, Nd, etc.) and La_2/3(Ca_1-y Cd _y )_1/3MnO₃. It is found that the (La_1-x R _x )_2/3Ca_1/3MnO₃ compounds increases with increasingy although (r_A) decreases slightly. It is suggested that the Curie temperature should be influenced by the average local A-site magnetic moment in the ferromagnetic perovskite manganite system. Project supported by the National Natural Science Foundation of China (Grant No. 19504012) and the Chinese Academy of Sciences.     

Finite element simulation of the poling process in BaTiO3–CoFe2O4 multiferroic composites

The theoretical background of nonlinear constitutive magneto-ferroelectric behavior as well as the Finite Element implementation are presented. On this basis the polarization in the ferroelectric matrix (BaTiO₃) with embedded dielectric-magnetostrictive particels (CoFe2O₄) is simulated and the resulting effects are analyzed. Numerical simulations focus on the prediction of local crystal orientations and residual stress going along with the poling process, in the future supplying information on favorable electric-magnetic loading sequences. Further, multifield homogenization procedures enable the prediction of the electromagnetomechanical properties of smart multiferroic composites and supply useful means for their optimization. The resulting final state of a poling simulation can be implemented as a starting condition for approximate linear simulations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Phase transition in layered perovskite-like manganate Ca3Mn2O7 under high pressure

In situ high pressure energy dispersive X-ray diffraction measurements on the layered perovskite-like manganate Ca₃Mn₂O₇ powder under pressures were performed by using the diamond anvil cell with synchrotron radiation. The results show that the structure of layered perovskite-like manganate Ca₃Mn₂O₇ is unstable under pressure due to the easy compression of NaCl-type blocks. The structure of Ca₃Mn₂O₇ underwent two phase transitions under pressures in the range of 0–35 GPa. One was at about 1.3 GPa with the crystal structure changing from tetragonal to orthorhombic. The other was at about 9.5 GPa with the crystal structure changing from orthorhombic back to another tetragonal.     

A Differential Calculus on Z3-Graded Quantum Superspace ${\mathbb R}_{q}(2|1)$

We introduce a Z₃-graded quantum (2+1)-superspace and define Z₃-graded Hopf algebra structure on algebra of functions on the Z₃-graded quantum superspace. We construct a differential calculus on the Z₃-graded quantum superspace, and obtain the corresponding Z₃-graded Lie superalgebra. We also find a new Z₃-graded quantum supergroup which is a symmetry group of this calculus.     

Epitaxial growth and electrical transport properties of La0.5Sr0.5Co03 thin films prepared by pulsed laser deposition

Epitaxial growth of the La_0.5Sr_{0.5 3}(LO) thin films has been realized on Lin3, SrTiC₃ and MgO substrates by pulsed laser deposition. The epitaxial growth behavior and the electrical transport properties of these films were studied systematically. The temperature dependencies of the resistivity of the film have been determined. Studies indicate that close dependencies exist between the crystal structures and the electrical transport properties of the epitaxial LSCO films, and that the epitaxial thin films are of low resistivity and metallic conductive features. The epitaxial films deposited on the LaA10₃ substrates at about 700 °C possess the optimal properties compared with the others. Discussions of the dependencies and the mechanisms of the epitaxial structures on the electrical transport properties of the LSCO films have been made. Project supported by the National Natural Science Foundation of China (Grant No. 19574003 and No. 19674001).     

An Inequality on the Size of a Set in a Cartesian Product

Let Ω be a finite subset of the Cartesian productW₁  ×   × W_nof n sets. ForA    {1, 2, , n }, denote by Ω_Athe projection ofΩ onto the Cartesian product of W_i, i   A. Generalizing an inequality given in an article by Shen, we prove that | Ω |² ≤  |Ω_A1 || Ω_Ak| provided that { A₁, , A_k} is a double cover of {1, 2, , n }. This inequality is applied to give some bounds on the numbers of special subgraphs of a graph.     

More Examples of Algebraic Quantum Hypergroups

We present in this paper a family of algebraic quantum hypergroups. Fix a natural number n?∈??. Let H _n be an infinite-dimensional vector space with a basis {X _p,i , Y _q,j | p, q?∈??, i, j?∈?{0, 1, 2,???n}}. Then we consider the new multiplication on H _n with structure constants $\{c^k_{pij}\mid p\in \mathbb{Z}, i, j, k\in \{0, 1, 2, \dots n\}\}$ and present a new method of constructing algebraic quantum hypergroups which is very different from the one in Van Daele and Wang (Math Scand 108(2):198–222, 2011). Finally, we give an explicit example to explain our procedure.