Flows of inelastic non-Newtonian fluids through arrays of aligned cylinders. Part 2. Inertial effects for square arrays

Numerical simulations are presented for flows of inelastic non-Newtonian fluids through periodic arrays of aligned cylinders. The truncated power-law fluid model is used for the relationship between the viscous stress and the rate-of-strain tensor. Results for the drag coefficient for creeping flows of such fluids have been presented in a companion paper [1]. In this second part the effects of finite fluid inertia are investigated for flows through square arrays. It is shown that the Reynolds-number dependence of the drag coefficient of a cylinder in the array is of the form C _d≡ F/(ηU) = k ₀ + k ₂ Re²+ .. for small values of the Reynolds number Re ≡ ρaU/η, where F is the drag force, U is the averaged velocity in the array, η = K (U/a)^n-1 is a viscosity scale with K and n the power-law coefficient and index and a the cylinder radius, and k ₀ is the drag coefficient for creeping flows. The proportionality constant k ₂ depends on the way the drag coefficient and the Reynolds number are defined. It is shown that the observed strong dependence of k ₂ on n can almost be eliminated by using length scales different from a in the viscosity scales η used in the definition of Re and in the definition of the drag coefficient. Numerical simulation results are also presented for the velocity variance components. Results for flows at moderate Reynolds number, of order 100, are also presented; these are qualitatively similar to those for Newtonian fluids. The value of the Reynolds number beyond which the flow becomes unsteady was related to the Newtonian fluid case by rescaling. These results for moderate-Reynolds-number flow are compared against previously published experimental data.     

Magnetic shielding behavior of YBCO cylinders— A universal scaling property

Magnetic shielding studies have been carried out to investigate the usefulness of high-T _c YBCO ceramics for EMS applications. The starting materials were single-phase YBCO powder. The cylinders were prepared by uniaxial compresssion and isostatic compression, with and without Ag additive. The shielding fieldH ^*, defined as the value of the applied field at which a detectable field will be seen inside the superconducting shield, was 12 G for the shield prepared by uniaxial compression and around 17 G for shields prepared by isostatic compression. Measurements were done in both ac and dc fields. The field inside the shield for the sinusoidal ac applied field is highly distorted, showing the presence of three higher harmonics. The penetrated waveform was Fourier-analyzed to yield the rms value ofB _in. When the normalized value ofB was plotted against the normalized value ofH with respect toH ^*, all the points corresponding to different shields fall on the same curve.     

Effects of local characteristics on the performance of full length Bi2223 multifilamentary tapes

The effects of local characteristics on the performance of full length Bi2223 multifilamentary tapes are investigated computationally and experimentally at 77 K and self-field. Generally the current-voltage characteristics of superconductors are described by the standard power law model with parameters such as critical current I_c and index n. By measuring the critical current {I_ci} and index {n_i} values of local tapes, we can get the critical current I_c and n value of full length tapes by means of statistical method. The results show that the distribution of local critical currents are non-uniform, and local critical currents have important effect on the performance of the entire tapes. The critical current of the entire tape is different from the mean value of local critical current based on Gaussian statistical distribution along the long tape.     

The enhanced magneto-optical Kerr effect in Co/TiO2 multilayer films

Spectral dependences of the polarization plane rotation angle (??_k) in the polar Kerr effect in Co/TiO₂ multilayer nanocomposite films have been studied in the 400?C1000 nm wavelength range. It is established that the sign, magnitude, and shape of the magneto-optical spectrum depend on the dielectric spacer thickness and the number of layers in the structure. The Kerr rotation angle in Co/TiO₂ multilayers is significantly greater than that in homogeneous Co films of the same thickness. The angle of rotation of the polarization plane reaches a record high value of 2??_k = 7.3° in the Co(5 nm)/TiO₂(17 nm) multilayer structure with number of layers n = 8 at a wavelength of 540 nm.     

Vortex Dynamics in a Superconducting Film with a Kagome and?a?Honeycomb Pinning Landscape

The vortex dynamics in a superconducting thin Al film with a periodic Honeycomb or Kagome array of antidots has been investigated by electrical transport measurements. The large values of the superconducting coherence length and penetration depth of the Al films guarantee a maximum of one flux quantum trapped per pinning site. This allows us to directly compare the experimental results with previous theoretical investigations based on molecular dynamics simulations. For the Kagome lattice, two submatching features not anticipated theoretically at H/H ₁=1/3 and 2/3, where H ₁ is the field at which the number of vortices coincides with the number of pinning sites, are observed. Possible corresponding stable vortex patterns are suggested. For the Honeycomb pinning landscape, the commensurability effects are in agreement with the theoretical expectations. A preliminary analysis of the vortex mobility in this lattice shows the presence of a weak vortex guidance.     

Neutron diffraction study of p-phenylene oligomer molecules adsorbed onto graphite

Neutron scattering experiments have been carried out on low-coverage films of the aromatic p-phenylene oligomer molecules (p-nP, C_6nH_{10 + 4(n − 2)}, where n indicates the number of phenyl units per molecule) physisorbed onto the surface of graphite. The molecular arrangement within these films has been determined as a function of temperature, number of molecular layers, and molecular length. Analysis of the diffraction data reveals two-dimensional film structures consistent for molecules having their long-axis parallel to the underlying substrate. The experimental measurements provide evidence for a melting transition in a monolayer film and thermal expansion of a bilayer film of p-terphenyl (p-3P). The planes of the phenyl rings are approximately parallel to the substrate in the monolayer structure but rotate out of this plane by 60 ± 20° in the bilayer film of p-3P. As the number of phenyl units is increased from n = 3 to n = 6, bilayer structures are observed having similar packing arrangements of the molecules but with lattice parameters that scale with molecular length.     

Near-infrared reflection from periodically aluminium-doped zinc oxide thin films

Multilayers of aluminium-doped zinc oxide (Al:ZnO) as a heat-reflection material were prepared by a reactive sputtering method with intermittent Al doping or Al content modulation. A drop in the refractive indices n around the plasma wavelength λ_p of 1456 nm for the optimally-doped Al:ZnO layers formed the periodic distribution of n in the multilayers. The periodic n provided selective reflection of approximately 60% under λ_p and shielded near-infrared solar radiation containing high energy, which was impossible to be reflected from the Al:ZnO monolayer. The selective reflection was accompanied by infrared reflection above λ_p, low emissivity and no subsequent visible reflection, which allowed the multilayers to achieve compatibility between the solar heat gain coefficient of 0.6 and the visible transmittance of nearly 80%.     

Evaluation of the NBS Unit of Resistance Based on a Computable Capacitor

An evaluation of the unit of resistance maintained at the National Bureau of Standards, based on the prototype standards of length and time, is described. The evaluation is based on a nominally one-picofarad capacitor whose value may be calculated from its mechanical dimensions to high accuracy. This capacitor is used to calibrate an 0.01-microfarad capacitor. A frequency-dependent bridge involving this capacitor establishes the value of a 10⁴-ohm resistor. Comparison of that resistor with the bank of one-ohm resistors maintaining the NBS unit of resistance establishes that this unit is Ω_EU = 1.000002₃ ohms ± 2.1ppm.The indicated uncertainty is an estimated 50 percent error of the reported value based on the statistical uncertainty of the measurements and allowing for known sources of possible systematic errors other than in the speed of light, assuming that the speed of light c=2.997925×10¹⁰cm/sec.     

Evaluation of a voltage source with three calculable RMS outputs

This paper describes a voltage source which generates three different waveforms. Measurement techniques with such a source are proposed, with emphasis on the uncertainty of each waveform used, when the ac amplitude is defined with a dc calibration of the source. The instrument circuitry and operation is described. Measurement results are also discussed. Emphasis is given to selected parameters of waveforms and to their effect on the measured rms value     

The critical layer number of Stranski-Krastanov growth mode epitaxial growth for bcc metallic thin films

Based on the classical elastic theory and a thermodynamic model for surface energy, the critical layer number n_c of Stranski-Krastanov growth mode epitaxial growth for bcc metallic thin films is calculated. n_c is determined by the consideration that the sum of the surface energy of a film and the lattice mismatch elastic energy between a substrate and the film is equal to the surface energy of the substrate. When the film layer number n is larger than n_c, a flat growth of the film on the substrate will transform to an island growth. Our predictions on several metallic films are in agreement with experimental results.     

Uncertainties in the Realization of Thermodynamic Temperature Above the Silver Point

Recent advances in high-temperature thermometry have opened up the possibility of realizing and disseminating thermodynamic temperatures above the silver point by means of both primary radiometry and radiation thermometry with the aid of high-temperature fixed points with known thermodynamic temperatures. A variety of realization schemes, denoted n = 0, 1, 2, 3, 3+, where n refers to the number of fixed points used in the realization, are described in new sections of the ??Mise en pratique for the definition of the kelvin.?? A major advantage of this approach is flexibility, accommodating the varying resources and needs of a wide range of laboratories and/or users. This article outlines the uncertainty analysis for each of the n ?? 0 schemes, which provides a means for assessing the suitability of any particular scheme and for selection of the appropriate fixed points. In all cases, the analysis is based on a modified Sakuma?CHattori model of the radiometer response. This model allows simple analytical expressions to be derived for all sensitivity coefficients, identification of the dominant uncertainty components, and each scheme to be easily compared. Current best estimates for each uncertainty component are given, and these are propagated to give a total uncertainty for each scheme.     

Magneto-optical studies of low-dimensional organic conductors

Abstract

Our periodic orbit resonance (POR) results on quasi-two-dimensional (q2D), highly anisotropic q2D and quasi-one-dimensional (q1D) organic conductors are reviewed together with our rotational cavity magneto-optical measurement system. Higher order POR up to seventh order has been observed in the q2D system (BEDT-TTF)₂Br(DIA), and the experimental conditions to observe POR and the cyclotron resonance (CR) are discussed. Highly anisotropic q2D Fermi surface (FS) in β″-(BEDT-TTF)(TCNQ), which was considered to have q1D FS previously, is proposed by our POR measurements, and the possible interpretations of other experimental results of β″-(BEDT-TTF)(TCNQ) are discussed assuming the highly anisotropic q2D FS. Finally, detailed q1D FS of (DMET)₂I₃, obtained from our POR results, is discussed in connection with the typical q1D system (TMTSF)₂ClO₄.     

Static Magnetic Flux Dynamics in One-Dimensional (1D) Josephson Lattices

We investigated static magnetic flux dynamical properties of one-dimensional lattices of Josephson junctions. The discretized wave equations of the Josephson junction lattice were solved using a generalized relaxation iteration algorithm. Numerical simulations indicated that transitions between periodic state and chaotic state will occur as the physical parameters and geometric parameters such as external current y _n, magnetic field h ₀, h, and the length of Josephson junction _n and d _n , varied. A shot length of the Josephson junction favors stable periodic states.     

Influence of Structural Anisotropy on the Irreversibility Line of High-T c Cuprates

From zero-field-cooled and field-cooled magnetic response, we have determined the irreversibility lines for a number of high-T _c oxides, viz., La(Sr)-214, Nd-223, Dy(Tb)-124, (Tl, Pb)-1212, and Tl-11112, in the H–T plane, which fit the relation H=A(1 –T/T _c ) ⁿ . Our results are consistent with a correlation between the anisotropy of the structure and the value of n, is in agreement with the Josephson decoupling model [1].     

Two results on stable rapidly oscillating periodic solutions of delay differential equations

In 1999 Ivanov and Losson [A.F. Ivanov and J. Losson, Stable rapidly oscillating solutions in delay differential equations with negative feedback, Differ. Int. Eqns 12 (1999), pp. 811–832] presented a computer assisted proof that a particular delay differential equation (with negative feedback) admits a stable rapidly oscillating periodic solution (ROPS). In this article the delay equation of Ivanov and Losson is embedded in a five-parametric class of differential equations. Conditions on the parameters are given such that the delay equation admits a stable ROPS. Moreover, it is shown that for odd n?>?1 the delay equation admits a stable ROPS with n humps per unit time if the parameters satisfy some explicitly given conditions. The delay equation of Ivanov and Losson satisfies all conditions on the five parameters. This gives an analytic proof and a considerable generalization of the result of Ivanov and Losson. The conditions on the parameters are believed to be sharp in a certain sense. The second result proves part of a conjecture in Stoffer [D. Stoffer, Delay equations with rapidly oscillating stable periodic solutions, J. Dyn. Differ. Eqns 20(1) (2008), pp. 201–238]. For a class of stiff delay differential equations with piecewise constant nonlinearity (positive or negative feedback) and for every n the following holds: if the stiffness parameter is sufficiently large then there are 2a(n) essentially different stable ROPSs with n humps per time unit. a(n) is the number of essentially different binary n-stage shift register sequences.     

Magneto-optical studies of low-dimensional organic conductors

Our periodic orbit resonance (POR) results on quasi-two-dimensional (q2D), highly anisotropic q2D and quasi-one-dimensional (q1D) organic conductors are reviewed together with our rotational cavity magneto-optical measurement system. Higher order POR up to seventh order has been observed in the q2D system (BEDT-TTF)₂Br(DIA), and the experimental conditions to observe POR and the cyclotron resonance (CR) are discussed. Highly anisotropic q2D Fermi surface (FS) in β″-(BEDT-TTF)(TCNQ), which was considered to have q1D FS previously, is proposed by our POR measurements, and the possible interpretations of other experimental results of β″-(BEDT-TTF)(TCNQ) are discussed assuming the highly anisotropic q2D FS. Finally, detailed q1D FS of (DMET)₂I₃, obtained from our POR results, is discussed in connection with the typical q1D system (TMTSF)₂ClO₄.     

Localized Pair Breaking Effect in the Quasi-multilayers of YBa2Cu3O7?δ /La0.88Ca0.12MnO3

Quasi-multilayers consisting of superconducting YBa₂Cu₃O_7??? (YBCO) and ferromagnetic La_0.88Ca_0.12MnO₃ (LCMO), namely p×(YBCO(m)/LCMO(n)) (p: repetition periods, m: YBCO pulse number, and n: LCMO pulse number) are prepared on single crystal LaAlO₃ (LAO) by pulsed laser deposition (PLD). X-ray diffraction measurements reveal that both in-plane and out-of-plane textures of the quasi-multilayers are as good as in the pure YBCO films. Nevertheless, the present quasi-multilayer system shows significant modifications in the superconducting properties, as evidenced by the suppressed superconducting transition temperature as well as the critical current density. This indicates that a special pair breaking effect emerges at YBCO/LCMO interfaces, and it is believed to arise from the spin scattering by the local exchange field due to the insulating nature of the ferromagnetic LCMO.     

Estimation of the number of true null hypotheses when conducting a multiple testing

Application of the standard hypothesis test with no adjustment for the multiple testing leads to a large number of false discoveries. The most convenient error measure in multiple testing is False Discovery Rate, FDR. However, calculation of FDR requires good estimation of the number of true null hypotheses, n₀, (or equivalently, of π₀ = n₀/n, where n denotes the number of all tested hypotheses). Estimation of π₀ is a non-trivial problem and it can be done under several assumptions about input data. In our study, several approaches to the estimation of π₀ values are compared for the different data models (independent features, block-correlated data and mixture models). The presented results give evidence that general dependence of the features leads to a very doubtful estimation of their significance.     

Excitons in organic-inorganic hybrid compounds (CnH2n + 1NH3)2PbBr4 (n = 4, 5, 7 and 12)

Thin films of microcrystalline (C_nH_2n + 1NH₃)₂PbBr₄ (n = 4, 5, 7 and 12) have been prepared by a modified spin-coating method, and the effect of the number of carbon atoms of the alkyl chain length (n) on optical properties has been investigated. Absorption spectra reveal that (C_nH_2n + 1NH₃)₂PbBr₄ films show stable excitons with a binding energy of a few hundred meV. The excitonic structure of (C_nH_2n + 1NH₃)₂PbBr₄ varies with the number of carbon atoms. The lowest-energy exciton splits into a few fine-structure levels at low temperature. (C_nH_2n + 1NH₃)₂PbBr₄ films (n = 5, 7 and 12) show not only singlet excitons but also triplet excitons at low temperature, while (C₄H₉NH₃)₂PbBr₄ films show only singlet excitons. The intersystem crossing from excited singlet state to triplet state plays an important role in the relaxation process of excitons.