Identification of lagrangian coherent structures in the turbulent boundary layer

Using Finite-Time Lyapunov Exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field obtained by time-resolved 2D PIV measurement. The typical LCSs in the turbulent boundary layer are hairpin-like structures, which are characterized as legs of quasi-streamwise vortices extending deep into the near wall region with an inclination angle θ to the wall, and heads of the transverse vortex tube located in the outer region. Statistical analysis on the characteristic shape of typical LCS reveals that the probability density distribution of θ accords well with t-distribution in the near wall region, but presents a bimodal distribution with two peaks in the outer region, corresponding to the hairpin head and the hairpin neck, respectively. Spatial correlation analysis of FTLE field is implemented to get the ensemble-averaged inclination angle θ _R of typical LCS. θ _R first increases and then decreases along the wall-normal direction, similar to that of the mean value of θ. Moreover, the most probable value of θ saturates at y ⁺=100 with the maximum value of about 24°, suggesting that the most likely position where hairpins transit from the neck to the head is located around y ⁺=100. The ensemble- averaged convection velocity U _c of typical LCS is finally calculated from temporal-spatial correlation analysis of FTLE field. It is found that the wall-normal profile of the convection velocity U _c(y) accords well with the local mean velocity profile U(y) beyond the buffer layer, evidencing that the downstream convection of hairpins determines the transportation properties of the turbulent boundary layer in the log-region and beyond. Supported by the National Natural Science Foundation of China (Grant Nos. 10425207 and 10832001)     

A tunable green alkaline-earth silicon-oxynitride solid solution (Ca1? x Sr x )Si2O2N2:Eu2+ and its application in LED

A series of (Ca_1−x−y Sr _x )Si₂O₂N₂:yEu²⁺ (x=0.0–0.97, y=0.03) phosphors were synthesized by high-temperature solid-state reaction. The XRD patterns confirm the formation of a solid solution of (Ca_1−x−y Sr _x )Si₂O₂N₂:yEu²⁺. An intense tunable green light is observed with the increasing ratio of Sr/Ca. With an increase in x, the excitation and emission spectra show a redshift and blueshift, respectively, due to large centroid shift and small Stokes shift. The temperature dependent luminescence is also investigated in the temperature range of 77–450 K. The Huang–Rhys factor and the thermal-quenching temperature are determined. Intense green LEDs were successfully fabricated based on the (Ca_1−x−y Sr _x )Si₂O₂N₂:yEu²⁺ phosphor and near-ultraviolet (∼395 nm) GaN/blue (460 nm) InGaN chips. All the results indicate that the solid solution (Ca_1−x−y Sr _x )Si₂O₂N₂:yEu²⁺ is a promising phosphor applicable to near-UV and blue LEDs for solid-state lighting.     

Elastic properties of TeO<Subscript>2</Subscript>–B<Subscript>2</Subscript>O<Subscript>3</Subscript>–Ag<Subscript>2</Subscript>O glasses

A series of glasses [(TeO₂) _x (B₂O₃)_1−x ]_1−y [Ag₂O] _y with x = 70 and y = 10, 15, 20, 25 and 30 mol% were synthesised by rapid quenching. Longitudinal and shear ultrasonic velocity were measured at room temperature and at 5 MHz frequency. Elastic properties, Poisson's ratio, microhardness, softening temperature and Debye temperature have been calculated from the measured density and ultrasonic velocity at room temperature. The experimental results indicate that the elastic constants depend upon the composition of the glasses and the role of the Ag₂O inside the glass network is discussed. Estimated parameters based on Makishima–Mackenzie theory and bond compression model were calculated in order to analyse the experimental elastic moduli. Comparison between the experimental elastic moduli data obtained in the study and the calculated theoretically by the mentioned above models has been discussed.     

Flow measurement around a cycloidal propeller

Abstract  

An experimental investigation was conducted to study the flow around a cycloidal propeller. Flow fields were obtained using a particle image velocimetry system whose data acquisition was synchronized with the propeller’s angular position. The chord-based Reynolds number was Re _c = u _r c/υ = 1.4 × 10⁴, where u _r is the rotational velocity of the propeller and c is the chord length of the airfoil. Flow characteristics such as mean velocity, vorticity and the RMS value of velocity fluctuation were derived from the measurements. The results demonstrated the presence of a downwash around the propeller during the generation of lift. Detailed observations around each airfoil visualized distinct vortex shedding and reattaching flow at certain phase angles of the propeller.     

Deformation of viscoelastic coating in a turbulent flow

The rate and amplitude of compliant coating deformation by turbulent pressure pulsations were calculated. Complex compliance determined by a 2D model has two components: along and across the coating. Dependence of the components of dimensionless compliance on the wavelength — coating thickness ratio was determined for 0.3 < λ/H < 30 and dependence of these components on the ratio of flow velocity to velocity of wave propagation was determined for 0.1 < V/C < 10. Deformation amplitude and rate of surface displacement for the hard compliant coatings which can be used in practice were calculated within the range of 5–55 m/s for the water and air turbulent flow. The effects of the loss tangent and Poisson’s ratio of the coating material were also studied. It is shown that the mean-square displacement of their surface does not exceed the thickness of a viscous sublayer. However, the velocity of surface motion is comparable with velocity pulsations in a boundary layer near a wall. This can be a reason for drag reduction on a compliant wall. The calculated value of ratio between energy absorbed by the wall and energy dissipated within the flow because of drag was 10⁻⁴ for water and 10⁻⁶ for air. This estimate does not confirm the hypothesis explaining drag reduction by energy takeoff from the flow.     

POD analysis on the sphere wake at a subcritical Reynolds number

Abstract  

Flow characteristics of turbulent wake behind a sphere at a subcritical flow regime were experimentally investigated. The particle image velocimetry measurements and proper orthogonal decomposition (POD) modal analysis were employed to get detailed flow information such as the wavy structure, swirling motion and coherent structures of the sphere wake. The variation of turbulent intensities of the radial and circumferential velocity components showed the swirling motion of sphere wake in the cross-sectional planes. The relative contribution of the POD mode 1, 2 and 3 in eigenvalues was 26, 11, and 8%, respectively. The general pattern of velocity fields for the POD mode 1 in the near-wake region of x/d = 0.7–1.4 is similar with that of time-averaged mean velocity fields. In addition, the sweeping flow in the region from x/d = 1.5 to x/d = 2.0 possesses wavy structure of the sphere wake. The experimental results of the present study would contribute to the fundamental understanding of the turbulent near-wake behind a sphere.     

A Construction of Blow up Solutions for Co-rotational Wave Maps

The existence of co-rotational finite time blow up solutions to the wave map problem from ${\mathbb{R}^{2+1} \to N}The existence of co-rotational finite time blow up solutions to the wave map problem from \mathbbR²⁺¹ ? N{\mathbb{R}^{2+1} \to N} , where N is a surface of revolution with metric d ρ ² + g(ρ)² dθ², g an entire function, is proven. These are of the form u(t,r)=Q(l(t)t)+R(t,r){u(t,r)=Q(\lambda(t)t)+\mathcal{R}(t,r)} , where Q is a time independent solution of the co-rotational wave map equation −u _tt  + u _rr  + r ⁻¹ u _r  = r ⁻² g(u)g′(u), λ(t) = t ^−1-ν, ν > 1/2 is arbitrary, and R{\mathcal{R}} is a term whose local energy goes to zero as t → 0.     

Passive scalar in a large-scale velocity field

We consider advection of a passive scalar θ(t,r) by an incompressible large-scale turbulent flow. In the framework of the Kraichnan model all PDF’s (probability distribution functions) for the single-point statistics of θ and for the passive scalar difference θ(r ₁)−θ(r ₂) (for separations r ₁−r ₂ lying in the convective interval) are found. Zh. éksp. Teor. Fiz. 115, 920–939 (March 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Weak-link bi-epitaxial Josephson junctions in a YBa2Cu3O7−δ film on BaZrO3/CeO2/SrTiO3

A bi-epitaxial (001)YBa₂Cu₃O_7−δ /(110)BaZrO₃/(001)CeO₂ three-layer heterostructure has been grown on (100)SrTiO₃ by laser ablation. The epitaxial relations between the layers making up the heterostructure were derived from x-ray diffraction data. The I _cR_n product for the bi-epitaxial Josephson junctions thus obtained was within 1–1.5 mV for 4.2 K, and 30–60 μV for 77 K. The normal resistance R _n=(2–5 Ω) was practically independent of temperature. The magnetic field dependences of I _c had typically a clearly pronounced main maximum, followed by distorted subsequent peaks. Interaction of the Josephson ac current with self-induced electromagnetic waves at the 45° grain boundary and with external microwave radiation (f=11 GHz) produced current steps in the I-V characteristics of the bi-epitaxial junctions at the corresponding voltages. Fiz. Tverd. Tela (St. Petersburg) 39, 1732–1738 (October 1997)     

N-Vortex Equilibria for Ideal Fluids in Bounded Planar Domains and New Nodal Solutions of the sinh-Poisson and the Lane-Emden-Fowler Equations

We prove the existence of equilibria of the N-vortex Hamiltonian in a bounded domain ${\Omega\subset\mathbb{R}^2}We prove the existence of equilibria of the N-vortex Hamiltonian in a bounded domain W ì \mathbbR²{\Omega\subset\mathbb{R}^2} , which is not necessarily simply connected. On an arbitrary bounded domain we obtain new equilibria for N = 3 or N = 4. If Ω has an axial symmetry we obtain a symmetric equilibrium for each N ? \mathbbN{N\in\mathbb{N}} . We also obtain new stream functions solving the sinh-Poisson equation -Dy = rsinhy{-\Delta\psi=\rho\sinh\psi} in Ω with Dirichlet boundary conditions for ρ > 0 small. The stream function y_r{\psi_\rho} induces a stationary velocity field v_r{v_\rho} solving the Euler equation in Ω. On an arbitrary bounded domain we obtain velocitiy fields having three or four counter-rotating vortices. If Ω has an axial symmetry we obtain for each N a velocity field v_r{v_\rho} that has a chain of N counter-rotating vortices, analogous to the Mallier-Maslowe row of counter-rotating vortices in the plane. Our methods also yield new nodal solutions for other semilinear Dirichlet problems, in particular for the Lane-Emden-Fowler equation -Du=|u|^p-1u{-\Delta u=|u|^{p-1}u} in Ω with p large.     

Generalized holographic and Ricci dark energy models

In this paper, we consider generalized holographic and Ricci dark energy models where the energy densities are given as ρ _R =3c ² M _pl² Rf(H ²/R) and ρ _h =3c ² M _pl² H ² g(R/H ²), respectively; here f(x), g(y) are positive defined functions of the dimensionless variables H ²/R or R/H ². It is interesting that holographic and Ricci dark energy densities are recovered or recovered interchangeably when the function f(x)=g(y)≡1 or f(x)=Id and g(y)=Id are taken, respectively (for example f(x),g(x)=1−ε(1−x), ε=0or1, respectively). Also, when f(x)≡xg(1/x) is taken, the Ricci and holographic dark energy models are equivalent to a generalized one. When the simple forms f(x)=1−ε(1−x) and g(y)=1−η(1−y) are taken as examples, by using current cosmic observational data, generalized dark energy models are considered. As expected, in these cases, the results show that they are equivalent (ε=1−η=1.312), and Ricci-like dark energy is more favored relative to the holographic one where the Hubble horizon was taken as an IR cut-off. And the suggested combination of holographic and Ricci dark energy components would be 1.312R−0.312H ², which is 2.312H²+1.312[(H)\dot]2.312H^{2}+1.312\dot{H} in terms of H ² and [(H)\dot]\dot{H} .     

Visualization of turbulent flow around a sphere at subcritical reynolds numbers

The shear layer evolution and turbulent structure of near-wake behind a sphere atRe= 11,000 and 5,300 were investigated using a smoke-wire visualization method. A laminar flow separation was found to occur near the equator. The smooth laminar shear layers appeared to be axisymmetrically stable to the downstream location of aboutx/d=1.0 atRe=11,000 andx/d= 1.7∼1.8 atRe=5,300, respectively. At Re=11,000, the vortex ring-shaped protrusions were observed with the onset of shear layer instability. Moreover, the transition from laminar to turbulence in the separated flow region occurred earlier at the hiher Reynolds number ofRe=11,000 than atRe=5,300. The PIV measurements in the streamwise and cross-sectional planes atRe=11,000 clearly revealed the turbulent structures of the sphere wake such as recirculating flow, shear layer instability, vortex roll-up, and small-scale turbulent eddies.     

Local structure and electrochemistry of LiNi y Mn y Co1 − 2y O2 electrode materials for Li-ion batteries

A series of LiNi _x Mn _y Co _z O₂ (x = y, z = 1 − 2y) oxides have been synthesized by “chimie douce” and investigated as positive electrodes in rechargeable lithium batteries. Layered LiNi _y Mn _y Co_1 − 2y O₂ materials with high homogeneity and crystallinity were synthesized using the wet-chemical method assisted by carboxylic acid as the polymeric agent. The long range and local structural properties are investigated with experiments including X-ray diffraction, Fourier transform infrared spectroscopy, and electron paramagnetic resonance spectroscopy. The evolution of the structure is discussed as a function of the cobalt content that confers layer-like behavior on the framework. Electrochemical performance of LiNi _y Mn _y Co_1 − 2y O₂ oxides is tested in cells using nonaqueous 1 M LiPF₆ dissolved in ethylene carbonate–diethyl carbonate. Charge–discharge profiles are investigated as a function of the rate capability and the voltage window. A relation is found between the gravimetric capacity and the cation disorder of the positive electrode as indicated by structural analysis. Fast lithium extraction attributed to the larger interslab space has been observed in the cobalt-rich oxides. Paper presented at the 11th Euro-Conference on Science and Technology of Ionics, Batz-sur-Mer, France, 9–15 Sept. 2007.     

Temperature dependence of magnetic properties and change of specific heat in perovskite ErCrO3 chromites

In this paper, the temperature dependence of magnetic properties and specific heat are systematically investigated for perovskite ErCrO₃ chromites. The results show that there exists a strong temperature dependence of magnetic ordering and phase coexistence in the region of low temperature. Specifically, ErCrO₃ possesses the long-range antiferromagnetic ordering and the appearance of weak ferromagnetism, occurring at T _N =133 K. In the range of higher temperature, above 133.0 K, the reciprocal of magnetic susceptibility χ ⁻¹ behaves linearly, indicating a typical Curie–Weiss behavior fitted. The effective magnetic moment μ _eff=10.57μ _B and asymptotic paramagnetic Curie temperature T _cw=−30 K, which suggests the predominance of antiferromagnetic interactions in ErCrO₃ chromites. Around T _SR≈22 K, ErCrO₃ undergoes a spin reorientation from \varGamma ₄(G_x,A_y,F_z;F^R_z)\varGamma _{4}(G_{x},A_{y},F_{z};F^{R}_{z}) to \varGamma ₁(A_x,G_y,C_z;C^R_z)\varGamma _{1}(A_{x},G_{y},C_{z};C^{R}_{z}) or Γ ₁(0). Also, the stability of the ferromagnetic Γ ₄ phase increases with increasing applied field. Furthermore, the ac susceptibilities exhibit frequency-independent anomalies near 133 K and the coexistence of the magnetic configuration \varGamma ₂(F_x,G_y,C_z;F^R_x,C^R_y)\varGamma _{2}(F_{x},G_{y},C_{z};F^{R}_{x},C^{R}_{y}) and Γ ₄. Combining the magnetic properties and the specific-heat measurements, this current magnetization can be interpreted from the interaction between C ^r3+–Cr³⁺, Cr³⁺–Er³⁺ and Er³⁺–Er³⁺.     

Superionic conductivity of the heterovalent solid solutions R 1−x M x F 3−x (R=REE, M=Ca, Ba) with tysonite-type structure

The fluorine-ion conductivity of anion-deficient solid solutions R _1−x Ca_xF_3−x and R _1−x Ba_xF_3−x having the tysonite (LaF₃) structure was investigated by the impedance spectroscopy method. R _1−x Ca_xF_3−x (R=La, Pr, Nd, Sm, Gd, Tb, Dy, Ho) and R _1−x Ba_xF_3−x (R=La, Pr, Nd) single crystals were grown from the melt by the Bridgman-Stockbarger method. The electrophysical measurements were performed in the frequency range 5−5×10⁵ and temperature range 300–700 K. The temperature dependences of the electrical conductivity for the crystals studied is determined by the migration of fluorine anions along various structural positions. It is shown that, from the standpoint of increasing the conductivity of tysonite matrices RF₃ (R=La, Pr, Nd), doping by CaF₂ and BaF₂ is less promising than SrF₂. Fiz. Tverd. Tela (St. Petersburg) 41, 638–640 (April 1999)     

Comparative analysis of the effect of La and Co on the superconductivity and energyband spectrum of YBa2Cu3Oy for different oxygen contents

Temperature dependences of the resistivity and Seebeck coefficient of Y(Ba_1−x La_x)₂Cu₃O_y and YBa₂Cu_3−x Co_xO_y samples (x=0–0.25) have been measured under maximum sample saturation with oxygen, as well as following their anneal in an oxygen-deficient atmosphere. The T _c (x) dependences for as-prepared samples were found to pass through a maximum at x=0.05, which persists after annealing for Y(Ba_1−xLa_x)₂Cu₃O_y and disappears for YBa₂Cu_3−x Co_xO_y. A phenomenological model of the band spectrum in normal phase has been used to determine the parameters of the conduction band and of the carrier system, and to analyze their variation with the dopant type and content, as well as with annealing. Despite the differences observed in the T _c (x) dependence, the critical temperatures for all the sample series studied were found to correlate with the conduction-band effective width. The mechanism of the effect of impurities on the band-structure parameters and the reasons for the different influence of annealing on the properties of Y(Ba_1−x La_x)₂Cu₃O_y and YBa₂Cu_3−x Co_xO_y are discussed. Fiz. Tverd. Tela (St. Petersburg) 41, 389–394 (March 1997)     

Structure, electrical properties and temperature characteristics of?Bi0.5Na0.5TiO3–Bi0.5K0.5TiO3–Bi0.5Li0.5TiO3 lead-free piezoelectric ceramics

(1−x−y)Bi_0.5Na_0.5TiO₃–xBi_0.5K_0.5TiO₃– yBi_0.5Li_0.5TiO₃ lead-free piezoelectric ceramics have been prepared by an ordinary sintering technique, and their structure, electrical properties, and temperature characteristics have been studied systematically. The ceramics can be well-sintered at 1050–1150 °C. The increase in K⁺ concentration decreases the grain-growth rate and promotes the formation of grains with a cubic shape, while the addition of Li⁺ decreases greatly the sintering temperature and assists in the densification of BNT-based ceramics. The results of XRD diffraction show that K⁺ and Li⁺ diffuse into the Bi_0.5Na_0.5TiO₃ lattices to form a solid solution with a pure perovskite structure. As x increases from 0.05 to 0.50, the ceramics transform gradually from rhombohedral phase to tetragonal phase and consequently a morphotropic phase boundary (MPB) is formed at 0.15≤x≤0.25. The concentration y of Li⁺ has no obvious influence on the crystal structure of the ceramics. Compared with pure Bi_0.5Na_0.5TiO₃, the partial substitution of K⁺ and Li⁺ for Na⁺ lowers greatly the coercive field E _c and increases the remanent polarization P _r of the ceramics. Because of the MPB, lower E _c and large P _r, the piezoelectricity of the ceramics is improved significantly. For the ceramics with the compositions near the MPB (x=0.15–0.25 and y=0.05–0.10), the piezoelectric properties become optimum: piezoelectric coefficient d ₃₃=147–231 pC/N and planar electromechanical coupling factor k _P=20.2–41.0%. In addition, the ceramics exhibit relaxor characteristic, which probably results from the cation disordering in the 12-fold coordination sites. The depolarization temperature T _d shows a strong dependence on the concentration x of K⁺ and reaches the lowest values at the MPB. The temperature dependences of the ferroelectric and dielectric properties at high temperatures may imply that the ceramics may contain both the polar and non-polar regions at temperatures above T _d.     

Viscous fluids and Gauss–Bonnet modified gravity

We study effects of cosmic fluids on finite-time future singularities in modified f (R, G)-gravity, where R and G are the Ricci scalar and the Gauss–Bonnet invariant, respectively. We consider the fluid equation of state in the general form, ω = ω(ρ), and we suppose the existence of a bulk viscosity. We investigate quintessence region (ω > −1) and phantom region (ω < −1) and the possibility to change or avoid the singularities in f (R, G)-gravity. Finally, we study the inclusion of quantum effects in large curvature regime.     

Er<Superscript>3+</Superscript> as glass structure modifier of Ga–Ge–S chalcogenide system

Er³⁺ clustering phenomenon in Ga–Ge–S chalcogenide system is studied using Raman spectroscopy. The Raman spectra from 10 to 500 cm⁻¹ for glasses (100−y)[15Ga₂S₃–85GeS₂]–yEr₂S₃ (y=0.08−5.00 mol. %) have been analyzed. To reveal the influence of the chemical composition on the glass structure the intensity of the peak corresponding to Ge–Ge (Ga–Ga) homopolar bonds has been examined. The peak intensity increase with Er₂S₃ concentration change in the region 0<C(Er₂S₃)<2 mol. % has been interpreted in terms of the sulphur deficiency in the glass resulting in the formation of S₃Ge–GeS₃ (S₃Ga-GaS₃) structural units. The further increase in concentration beyond 2 mol. % reduces the sulphur deficiency, which can be attributed to the formation of the ternary compound Er₃GaS₆. The structural units Er₃GaS₆ contain a large mol. fraction of Er³⁺ or, in other words, Er³⁺ clusters. The data obtained from the low-frequency Raman spectra (boson band) indicate strong variations of the medium-range order (MRO) in the glasses induced by Er³⁺. The observed behavior of the MRO size (the correlation length) with increasing of Er₂S₃ concentration provides for additional evidence of the Er³⁺ clustering.     

The Unusual Magnetic Resonance Properties of Trigonal Prismatic Tc and Re Complexes

The electron paramagnetic resonance (EPR) spectra of the trigonal prismatic complexes Tc(abt)₃, Tc(bdt)₃, Re(abt)₃ and Re(bdt)₃ (abt, O-aminobenzenethiol; bdt, benzene-1,2-dithiol) in dilute frozen solution are interpreted in terms of an axially symmetric spin Hamiltonian, with g values close to two, principal hyperfine couplings of |A ^Tc| ~ 5–12 × 10⁻⁴ cm⁻¹, nuclear quadrupole couplings of |P ^Tc| ~ 0.3–0.35 × 10⁻⁴ cm⁻¹ and the unusual values 5 × 10⁻⁴ cm⁻¹ ~ |A _zz ^Re| < |P ^Re| ~ |A _xx ^Re| ~ |A _yy ^Re| ~ 25 × 10⁻⁴ cm⁻¹. Similar magnitudes of the parameters have been obtained by simulation of the previously published spectra of Re(pda)₃, Re(tdt)₃ and Re(pdt)₃ (pda, O-phenylenediamine; tdt, toluene-3,4-dithiol; pdt, cis-1,2-diphenylethene-1,2-dithiol) by other authors. The unexpectedly large value of P relative to A is a common feature of all the Re tris-dithiolato and related trigonal prismatic complexes studied by EPR and is attributed to the high degree of delocalization of the unpaired electron onto the ligands and the distortion of the electron charge cloud. These factors are less evident in the complexes Tc(abt)₃ and Tc(bdt)₃. Intermolecular dipolar interactions, narrowed by weak exchange, are responsible for some of the spectral features observed in the solid state and concentrated (≫1 mM) frozen solutions, although there is no evidence for specific solute–solute interactions.