An algorithm for spectral factorization using random search techniques

An approximation method for the energy spectrum of a stationary stochastic dynamical system is presented, which allows approximate functional rational factorization.This paper is in three parts. The first deals with a theoretical problem of approximation in Hardy Spaces, whose main result is the following:Let S⁽ⁱⁿ⁾, S be positive functions belonging to L¹(R_gw), such that log S⁽ⁿ⁾ and log S belong to L¹(R_ω, dω/1 + ω²).Let h⁽ⁿ⁾, h be the outer functions of the Hardy Space H²(Π₊) such that S^(g) = |h⁽ⁿ⁾|² and S = |h|² on iR.If S⁽ⁿ⁾ n^→∝ S in L¹(R_ω), and log S⁽ⁿ⁾ n^→∝ log S in L¹(R_ω, dω/1 + ω²), then: h⁽ⁿ⁾ n^→∝ h in H²(Π₊).The second part describes an effective algorithm, using random search methods, and gives an almost sure convergence result for it.The third part treats numerically two examples, permitting comparison of this algorithm with others (whenever there are…): the first example is a problem of approximation for a nonrational process (turbulence) that was considered in Ref. 22: the second example is a problem of model reduction (automatic) considered in Ref. 4.     

Performance comparisons of space borne cryostats

We discuss the performance of liquid helium cryostats that have flown in space or are planned for space flight. Usual figures of merit are total cryostat mass or depletion rate of the cryogen. These often fail to accurately represent other important characteristics which affect cryostat performance such as the method used to survive launch lock-up or the temperature of the cryostat vacuum shell obtained by radiative cooling. To address these issues, we define the ratio, H/R in W day/l as metric to judge cryostat performance. The parameter H=σ_BA_tank(T⁴_shell−T⁴_tank) is the Stefan Boltzmann law for energy transfer to the helium tank, where σ_B is the Stefan Boltzmann constant, A_tank is the surface area of the cryogen tank and T_shell and T_tank are the vacuum shell and cryogen temperatures. The average cryogen depletion rate R=V_f/t is computed using the total cryogen volume, V_f, at the last fill before launch, including the volume of ‘booster tank' cryogen if used and the cryogen lifetime, t, to depletion on-orbit. Cryostats launched on the Space Shuttle have the same H/R≈60 W day/l whether the cryogen was liquid helium or solid neon, and for a broad range of vacuum shell temperatures 113<T_shell<300 K, cryogen volumes 2200>V_f>85 l, and mission times, 9 days to >2 years. Cryostats launched on unmanned rockets have a higher H/R≈300 W day/l. Only one, the X-Ray Spectrometer (XRS), out of the four solid neon and two solid hydrogen cryostats showed a clear advantage of using a cryogen other than liquid helium.     

VUV spectroscopy of wide bandgap materials

In this paper we will present VUV spectroscopy experiments performed at the Superlumi station of Hasylab, DESY, Hamburg, on samples of BaF₂ crystals activated with Ce and BaF₂, (Ba,La)F₂ crystals activated with Er. The results of these experiments include time resolved luminescence and luminescence excitation spectra obtained under wavelength selective VUV and UV excitation by pulsed synchrotron radiation.We will reveal the information provided by the VUV/UV excitation spectra of the Ce³⁺ 5d → 4f as well as Er³⁺ 4fⁿ⁻¹5d → 4fⁿ and 4fⁿ → 4fⁿ emissions on energy transfer mechanisms from the fluoride host to the rare earth ion. We will demonstrate that the fast energy transfer channels involve bound excitons while the generation of free electrons and holes leads to slower processes dependant on hole and/or electron trapping.We will demonstrate that differences between the excitation spectra of the 5d → 4f emission in Ce and 4f¹⁰5d → 4f¹¹ emission in Er activated BaF₂ are generated by the coupling of the 4f → 5d transition to the 4f¹⁰ core of the Er³⁺ ion. We will also identify the additional band, absent for Ce, which is due to the exchange split high spin (HS) state of the 4f¹⁰5d configuration responsible for the slow decay of the excited Er³⁺ ions in BaF₂ and (Ba,La)F₂.Finally we will provide evidence and explain why the dominant VUV 4f¹⁰5d → 4f¹¹ Er³⁺ emission in BaF₂ is spin-forbidden and slow while in the mixed (Ba,La)F₂ crystals it is spin-allowed and fast.     

Spectral analysis of RE (RE = Sm, Dy, and Tm): P2O5–Al2O3–Na2O glasses

Phosphate glasses in the compositions of 70P₂O₅–15Al₂O₃–14Na₂O–1RE³⁺ (RE = Sm, Dy, and Tm) (mol%) were prepared by melt-quenching technique and characterized optically. The differential thermal analysis (DTA) profile of the host glass was carried out to confirm its thermal stability. For all the glasses absorption, photoluminescence and decay measurements have also been carried out. These glasses have shown strong emission and absorption bands in visible and near-infrared (NIR) region. From the measured absorption spectra, Judd–Ofelt (J–O) intensity parameters (Ω₂, Ω₄ and Ω₆) have been calculated for all the studied ions. For Sm³⁺ doped glass, four emission bands centered at 562 nm (⁴G_5/2 → ⁶H_5/2), 598 nm (⁴G_5/2 → ⁶H_7/2), 644 nm (⁴G_5/2 → ⁶H_9/2), and 704 nm (⁴G_5/2 → ⁶H_11/2) have been observed with 402 nm (⁶H_5/2 → ⁴F_7/2) excitation wavelength. Of them, 598 nm (⁴G_5/2 → ⁶H_7/2) has shown a bright orange emission. With regard to Dy³⁺ doped glass, a blue emission band centered at 486 nm (⁴F_9/2 → ⁶H_15/2) and a bright yellow emission at 575 nm (⁴F_9/2 → ⁶H_13/2) have been observed, apart from 662 nm (⁴F_9/2 → ⁶H_11/2) emission transition with an excitation at 388 nm (⁶H_15/2 → ⁴I_13/2,⁴F_7/2) wavelength. Emission bands of 650 nm (¹G₄ → ³F₄) and 785 nm (¹G₄ → ³H₅) transitions for the Tm³⁺ doped glass, with an excitation wavelength at 466 nm (³H₆ → ¹G₄), have also been observed. The stimulated emission cross-sections of all the emission bands of RE³⁺ glasses (RE = Sm, Dy, and Tm) have been computed based on their measured full-width at half maximum (FWHM, Δλ) and measured lifetimes (τ_m).     

UV–VUV spectroscopy of rare earth doped persistent luminescence materials

The electronic and defect energy level structure of polycrystalline SrAl₂O₄:Eu²⁺,R³⁺ persistent luminescence materials were studied with thermoluminescence and UV–VUV synchrotron radiation emission and excitation spectroscopy. Theoretical calculations using the density functional theory (DFT) were carried out simultaneously with the experimental work. The experimental band gap energy (E_g) value of 6.6 eV agrees very well with the DFT value of 6.4 eV. The 4f⁷ → 4f⁶5d¹ excitation bands of Eu²⁺ were found rather similar irrespective of the R³⁺ co-dopant. The trap level energy distribution depended strongly on the R³⁺ co-dopant except for the shallowest trap energy above the room temperature remaining the same, however. The different processes in the mechanism of persistent luminescence from SrAl₂O₄:Eu²⁺,R³⁺ was constructed and discussed.     

Magneto-optical activity of f–f transitions in elpasolite Rb2NaDyF6

Absorption and magnetic circular dichroism (MCD) spectra of f–f transitions ⁶H_15/2 → ⁶F_3/2, ⁶F_5/2, ⁶(F_7/2 + H_5/2) have been measured in cubic crystal Rb₂NaDyF₆ with Dy³⁺ ions in centrosymmetrical O_h positions. Magneto-optical activities (MOA) of the transitions (the ratio of zero moments of the MCD and absorption bands) have been obtained from the corresponding spectra. Origins of the transitions MOA have been analyzed and theoretical estimations of the MOA values have been made. It turned out, that MOA of the transitions in the centrosymmetrical crystal Rb₂NaDyF₆ (being allowed by odd vibrations) are noticeably larger than those in non-centrosymmetrical compounds, where f–f transitions are allowed by static odd components of crystal field.     

Disk Resonators as Nonlinear Surface Impedance Measurement Tools

The edge-current–free rotational symmetric disk resonator mode, TM₀₁₀, was used as characterization tool for nonlinear surface impedance measurement of Y₁Ba₂Cu₃O_7–x (YBCO) thin films. The microwave surface resistance of high quality epitaxial YBCO thin films as a function of frequencies and rf surface magnetic field H _rf was measured using the circular disk resonator technique. Using this technique the properties degradation of the resonators by edge current crowding effect was avoided. The measured R _s values are divided into three regions. In the low field region (H _rf H _c1J), R _s is independent of H _rf. In the intermediate H _rf region, R _s can be well fitted to the formula of R _s(H _rf) = a(f) + b(f) H _rf ², and b(f) is proportional to f ². This form of microwave surface resistance quantitatively agrees with the modified coupled-grain model with the idea that the materials are composed of identical superconducting grains coupled together by identical intergranular regions that function as Josephson junctions. The experimental results show that the loss mechanisms are extrinsic properties resulting from defects in the films.     

Determination of the half-life of the spontaneous fission of240PU

Two metallic²⁴⁰Pu sources were certified as reference standards of spontaneous-fission activity and neutron flux. The certification results were used to determine the ratio T_&#x03B1;T_s&f of the alpha-decay and spontaneousfission half-lives of²⁴⁰Pu. The ratio was found to be (5.68&#x002B;-0.11)&#x00B7;10^&#x2212;8, which corresponds to T_s&f =(1.16&#x002B;0.02)&#x00B7;1011 yr for an assumed value T_&#x03B1;=6563&#x002B;7yr.Translated from Izmeritel'naya Tekhnika, No. 2, pp. 57&#x2013;58, February, 1995.     

Emission analysis of RE (Dy or Tb):Ca3Ln(Y,Gd)(VO4)3 powder phosphors

This paper reports on the photoluminescence results of Dy³⁺ or Tb³⁺ ions in Ca₃Ln(Y,Gd)(VO₄)₃ powder phosphors. Emission spectra of Dy³⁺:Ca₃Ln(Y,Gd)(VO₄)₃ powder phosphors have shown blue emissions (⁴F_9/2 → ⁶H_15/2) at 481 nm, yellow emissions (⁴F_9/2 → ⁶H_13/2) at 572 nm and a weak red emissions (⁴F_9/2 → ⁶H_11/2) at 661 nm upon excitation with λ_exci = 310 nm (⁶H_15/2 → ⁴L_19/2). Similarly photoluminescence spectra of Tb³⁺:Ca₃Ln(Y,Gd)(VO₄)₃ have shown green emissions (⁵D₄ → ⁷F₅) at 545 nm with λ_exci = 312 nm. For these phosphors XRD, FTIR, SEM and EDAX measurements have also been carried out.     

Emission spectra of lanthanide ions in hexafluoroelpasolite lattices excited by synchrotron radiation

Emission spectra at 10 K employing synchrotron radiation have been recorded for the tripositive lanthanide ions, Ln = Sm, Gd, Tb, Ho, and Er situated at octahedral (or nearly octahedral) site symmetry in hexafluoroelpasolite Cs₂NaMF₆ (M = Y, Sc, or Ga) lattices. Interconfigurational 5d → 4f transitions are only observed for Er³⁺, and the intensity ratio of 4f¹⁰5d → 4f¹¹ emission, compared with 4f¹¹ → 4f¹¹ emission, with excitation into 5d levels, is greater for M = Ga than M = Sc. The highest energy intraconfigurational emission is from ⁴G_5/2 (Sm³⁺), ⁶P_7/2 (Gd³⁺), ⁵D₃ (Tb³⁺), ⁵G₄ (Ho³⁺), and ²F(2)_7/2 (Er³⁺). Detailed energy level assignments have been given for Ln = Sm, Gd, and the remaining spectra are assigned as multiplet–multiplet transitions.     

Effect of Mg and Ti doping on the luminescence of Y2O2S:Eu

The Y₂O₂S:Eu³⁺,Mg²⁺,Ti^IV (x_Eu = 0.028, x_Mg = 0.086, x_Ti = 0.03) materials were prepared with the flux fusion method. According to X-ray powder diffraction, the materials had the hexagonal crystal structure. The emission of Y₂O₂S:Eu³⁺,Mg²⁺,Ti^IV was centered at 627 nm (λ_exc : 250 nm) due to the ⁵D₀ → ⁷F₂ transition of Eu³⁺. The excitation spectra (λ_em : 627 nm) showed broad bands at 240 and 320 nm due to the O²⁻ → Eu³⁺ and S²⁻ → Eu³⁺ charge transfer transitions, respectively. The latter band can also overlap with the Ti → Eu³⁺ energy transfer. In the excitation spectra with synchrotron radiation, in addition to the O²⁻ → Eu³⁺ and S²⁻ → Eu³⁺ charge transfer transitions, excitation over the band gap was observed at 4.8 eV (258 nm). The red persistent luminescence due to the ⁵D₀ → ⁷F₂ emission from Eu³⁺ residing in the regular Y³⁺ site of the host was ca. 10 min with 1 min fluorescent lamp irradiation. In addition, a very broad band was observed at 600 nm probably due to the Ti³⁺ emission.     

Fabrication and optical properties of NUV-emitting SiO2–SrB4O7:Eu glass–ceramic thin films

SiO₂–SrB₄O₇:Eu²⁺ glass–ceramic thin films were fabricated for possible application in near ultraviolet (NUV) emitting devices. Nano-sized SrB₄O₇:Eu²⁺ powders were prepared by a Pechini-type sol–gel method and a subsequent ball-milling treatment. The powders showed NUV emissions centered at 367 nm, upon irradiation with UV of shorter wavelengths, due to an allowed 4f⁶5d¹ → 4f⁷ electronic transition of Eu²⁺ ions. The glass–ceramic thin films were prepared by dip-coating of tetraethylorthosilicate (TEOS) solutions dispersed with the nano-sized SrB₄O₇:Eu²⁺ powders and a subsequent heat-treatment. It was found that the glass–ceramic thin films had relatively high thermal stability up to 800 °C in terms of the Eu²⁺ emissions. SiO₂ layers surrounding SrB₄O₇:Eu²⁺ appeared to be effective for the surface passivation of the phosphor particles.     

Compositional dependence of spectroscopic parameters of Dy ions in Ge–Ga–Se glasses

Dy³⁺ doped chalcogenide glasses from Ge–Ga–Se system were prepared and spectroscopic parameters of Dy³⁺ ions in these glasses were studied on the basis of Judd–Ofelt theory. We have found that the values of Judd–Ofelt intensity parameters Ω_t (t = 2, 4, 6) have maximal values at the GeSe₂–Ga₂Se₃ tie-line. Largest values of spectroscopic parameters of 1.3 µm Dy³⁺ transition (⁶F_11/2, ⁶H_9/2 → ⁶H_15/2), localized again at the GeSe₂–Ga₂Se₃ tie-line, confirm the importance of the stoichiometry of amorphous matrix for optical properties of doping rare-earth ions.     

Fluorescence and nonlinear optical properties of non-aggregating hexadeca-substituted phthalocyanine

Highly non-aggregating hexadeca-substituted phthalocyanine (Pc) complexes were prepared and their fluorescence and nonlinear optical properties were studied. Three visible fluorescence bands were observed when the Pc complexes were excited at 355 nm and found to be concentration dependent. They are attributed to the optical transitions S₂ → S₀ at 415 nm, T₂ → T₁ at 630 nm, and S₂ → S₁ at 755 nm. Nonlinear absorptive and refractive effects were measured with the help of Z-scan technique. Saturation absorption was observed at 632.8 nm where the nonlinear absorption coefficient is found to be very large (β = −2.8 × 10⁻² cm/W) and the refractive nonlinear coefficient γ = −9.5 × 10⁻¹¹ cm²/W. In the transparency domain at 532 nm, reverse absorption saturation is observed and β and γ are found to be 17.5 and 15.5 times smaller, respectively. Optical limiting performances are measured in the absorption and transparency domains. Purely refractive-based optical limiting at 632.8 nm is found to have a threshold of 0.16 kW/cm², lower than the reverse absorption saturation and refractive-based optical limiting of 0.90 kW/cm² at 532 nm.     

Fabrication and photoluminescence of thin films of lanthanide–polyoxometalates grafted on colloid silica sphere

In this paper, two lanthanide–polyoxometalates Na₉LnW₁₀O₃₆ (Ln=Eu, Dy, LnW₁₀) were grafted on 400 nm amine-functionalized spherical Stöber silica. The monolayer thin films of hybrid particles were fabricated on quartz by spin-coating method. The hybrid particles and thin films obtained were characterized by IR, UV–vis spectra, scanning electron microscopy, transmission electron microscope and luminescent spectra, respectively. The hybrid particles show strong luminescence which could be seen by naked eyes. The excitation spectra of hybrid particles and thin films show both abroad ligand to metal charge band and the excitation lines of rare earth ions. The transition ⁵D₀→⁷F₀ could be seen in the emission of hybrid EuW₁₀/SiO₂ spheres and thin films, which could not be found in spectrum of EuW₁₀ solid. It is noticed that the intensity ratio of red (⁵D₀→⁷F₂) to orange (⁵D₀→⁷F₁) of Eu³⁺ and the yellow to blue (⁴F_9/2→⁶H_13/2: ⁴F_9/2→⁶H_15/2) of Dy³⁺ in LnW₁₀/SiO₂ particles and thin films are quite different from those of LnW₁₀ solids. The different shapes and ratios between characteristic emissions of hybrid particles and thin films indicated the various symmetry of sites occupied by Ln³⁺ ions.     

Algebraic model of turbulent boundary layer on a convex curvilinear surface

A simple algebraic model of turbulent boundary layer on convex curvilinear surfaces is suggested that is based on the generalization of the two-layer one-parameter algebraic model for a flat plate [ 1 ]. The model is tested in a wide range of variation of the curvature parameter (0.01 ≤ δ₀/R _w ≤ 0.09, where δ₀ is the thickness of the boundary layer at the initial cross section of the curvilinear region andR _w is the curvature radius of the surface), the results of which are indicative of a good agreement between the experimental and calculated data on the integral characteristics of the boundary layer, namely, the friction coefficientC _f , the displacement thickness δ^* and momentum thickness δ^**, and the form parameterH = δ^*/δ^**. Based on the comparison between the calculated and experimental data on the distribution of tangential turbulent stresses, a conclusion is made that the model predicts a much lower effect of the curvature on the suppression of turbulence in the outer region of boundary layers at a mild curvature of the surface (δ ₀ /R _w = 0.01) than in experiments. However, this difference has a tendency to decrease as the surface curvature increases. An analysis of the calculated and experimental velocity profiles plotted in the variables of the wall law leads to a conclusion that the generalized Townsend wall law is partially realized on a curvilinear surface.     

Up-conversion luminescence properties of Y2O2S:Yb,Er nanophosphors

Up-converting yttrium oxysulfide nanomaterials doped with ytterbium and erbium (Y₂O₂S:Yb³⁺,Er³⁺) were prepared with the flux method. The precursor oxide materials were prepared using the combustion synthesis. The morphology of the oxysulfides was characterized with transmission electron microscopy (TEM). The particle size distribution was 10–110 nm, depending on the heating temperature. According to the X-ray powder diffraction (XPD), the crystal structure was found hexagonal and the particle sizes estimated with the Scherrer equation agreeded with the TEM images. Upon the 970 nm infrared (IR) laser excitation, the materials yield moderate green ((²H_11/2, ⁴S_3/2) → ⁴I_15/2 transition) and strong red (⁴F_9/2 → ⁴I_15/2) luminescence. The green luminescence was enhanced with respect to the red one by an increase in both the crystallite size and erbium concentration due to the cross-relaxation (CR) processes. The most intense up-conversion luminescence was achieved with x_Yb and x_Er equal to 0.10 and 0.005, respectively. Above these concentrations, concentration quenching occurred.     

Up-conversion processes in NaLaF4:Er

Structural and spectroscopic investigation of NaLaF₄:Er³⁺ material at different doping concentrations is presented. X-ray diffraction patterns, up-conversion luminescence spectra and decay curves for ²H_9/2 → ⁴I_15/2, ⁴S_3/2 → ⁴I_15/2 and ⁴F_9/2 → ⁴I_15/2 optical transitions in the material are shown and possible excitation routes are discussed. Raman spectrum for the undoped material is presented and the effective phonon energy of the material is estimated. Based on the obtained results application of rare-earth doped NaLaF₄ in the field of up-conversion phosphors is evaluated.     

A Fast Pulsed Source of Ballistic R− Rotons in Superfluid 4He

Superfluid ⁴ He is unique in having well-defined excitations (R ^– rotons) with momentum oppositely directed to their velocity. If a beam of R ^– rotons can be produced, it could be unambiguously detected by quantum evaporation because the atoms will emerge in the opposite quadrant to that for atoms evaporated by R ⁺ rotons and phonons. Previous work shows that a heated metal film which is immersed in superfluid ⁴ He only creates phonons and R ⁺ rotons. A sponge-like heater does appear to produce R ^– rotons but, because it has a long time constant, it cannot be used in time of flight studies. We have developed a source that produces fast pulses of R ^– rotons suitable for time of flight measurements. The method uses interactions between R ⁺ rotons to create R ^– rotons, so a transient high density of R ⁺ rotons in a small confined volume is needed. The source appears to operate as we expect from a model of the evolution of the R ⁺ and R ^– roton populations.