Numerical simulations of single and multiple scattering by fractal ice clusters

We consider the scattering model in the form of a vertically and horizontally homogeneous particulate slab of an arbitrary optical thickness composed of widely separated fractal aggregates built of small spherical ice monomers. The aggregates are generated by applying three different approaches, including simulated cluster-cluster aggregation (CCA) and diffusion-limited aggregation (DLA) procedures. Having in mind radar remote-sensing applications, we report and analyze the results of computations of the backscattering circular polarization ratio obtained using efficient superposition T-matrix and vector radiative-transfer codes. The computations have been performed at a wavelength of 12.6 cm for fractal aggregates with the following characteristics: monomer refractive index m=1.78+i0.003, monomer radius r=1 cm, monomer packing density p=0.2, overall aggregate radii R in the range 4≤R≤10 cm and fractal dimensions D_f=2.5 and 3.We show that for aggregates generated with simulated CCA and DLA procedures, the respective values of the backscattering circular polarization ratio differ weakly for D_f=2.5, but the differences can increase somewhat for D_f=3, especially in case of an optically semi-infinite medium. For aggregates with a spheroidal overall shape, the dependence of the circular polarization ratio on the cluster morphology can be quite significant and increases with increasing the aspect ratio of the circumscribing spheroid.     

Light-scattering properties of fractal aggregates: numerical calculations by a superposition technique and the discrete-dipole approximation

Dust particles in space often grow by mutual collisions and appear to be an agglomeration of individual grains, the morphology of which can be described by the concept of fractals. In this paper, we study light scattering by fractal aggregates of identical spheres (monomers) using the superposition technique incorporated into the T-matrix method where the orientationally averaged scattering matrix is analytically obtained. We also apply the discrete-dipole approximation, in which the dipole polarizability of spherical monomers is determined by the first term of the scattering coefficients in the Mie theory. Two cases of the ballistic aggregation process (particle–cluster and cluster–cluster aggregations) are considered to model fractal aggregates consisting of silicate or carbon material. The dependences of light-scattering properties on the monomer sizes, aggregate structures and material compositions are intensively investigated. The light-scattering properties of the fractal aggregates strongly depend on the size parameters of the monomers. The difference in the scattering function between the particle–cluster and cluster–cluster aggregates can be seen in the case of monomers much smaller than the wavelength of incident radiation. When the size parameter of monomers exceeds unity, the material composition of the monomers influences the light-scattering properties of the aggregates, but different morphologies result in similar scattering and polarization patterns. We show that silicate aggregates consisting of submicron-sized monomers, irrespective of the aggregate size and morphology, produce a backscattering enhancement and a negative polarization observed for dust in the solar system.     

GPU-based single-cluster algorithm for the simulation of the Ising model

We present the GPU calculation with the common unified device architecture (CUDA) for the Wolff single-cluster algorithm of the Ising model. Proposing an algorithm for a quasi-block synchronization, we realize the Wolff single-cluster Monte Carlo simulation with CUDA. We perform parallel computations for the newly added spins in the growing cluster. As a result, the GPU calculation speed for the two-dimensional Ising model at the critical temperature with the linear size L = 4096 is 5.60 times as fast as the calculation speed on a current CPU core. For the three-dimensional Ising model with the linear size L = 256, the GPU calculation speed is 7.90 times as fast as the CPU calculation speed. The idea of quasi-block synchronization can be used not only in the cluster algorithm but also in many fields where the synchronization of all threads is required.     

The impact of ice particle roughness on the scattering phase matrix

The goal of this study is to explore the influence of ice particle habit (or shape) and surface roughness on the scattering phase matrix. As an example, reported here are the results for two wavelengths: 0.67 and 1.61 μm. For this effort, a database of single-scattering properties has been computed for a set of habits including hexagonal plates, hollow and solid columns, hollow and solid 3D bullet rosettes, droxtals, aggregates of solid columns, and aggregates of plates. The database provides properties for each of the habits at 101 wavelengths between 0.45 and 2.24 μm for smooth, moderately roughened, and severely roughened particles. At each wavelength, the scattering properties are provided at 233 discrete particle diameters ranging from 2 to 10,000 μm. A single particle size distribution from a very cold ice cloud sampled during the CRYSTAL-FACE field campaign (T_cld=–76 °C) is used to illustrate the influence of habit and roughness on the phase matrix. In all, four different habit mixtures are evaluated. The nonzero elements of the phase matrix are shown to be quite sensitive to the assumed habit, particularly in the case of ?P₁₂/P₁₁ that is associated with the degree of linear polarization of scattered radiation. Surface roughness is shown to smooth out maxima in the scattering phase function and in the other elements of the phase matrix, consistent with other studies. To compare with the theoretical simulations of the phase matrix for smooth and roughened particles, a full year of cloud-aerosol lidar with orthogonal polarization (CALIOP) data from 2008 is analyzed to provide global statistics on the values of P₁₁ and P₂₂/P₁₁ in the backscattering direction. In a comparison of two of the habit mixtures (one used for MODIS Collection 5 and another that incorporates new habits including hollow bullet rosettes and aggregates of plates) with the CALIOP data, the values for P₁₁ are higher regardless of the degree of particle surface roughness, and the values for P₂₂/P₁₁ are lower than those for CALIOP. Further investigation is warranted to better understand this discrepancy.     

Current carrying capability of HTS Roebel cable

We have developed a numerical technique to estimate the current carrying capability of HTS Roebel cable composed from coated conductor strands. The influence of self-field on the critical current density is studied computationally for a Roebel cable using a realistic field and angle dependence behaviour of critical current. The computations are carried out for N/2 (number of strands/strand width in mm), and N/5 Roebel cable for N = 2–15. The local current distribution in each strand satisfies the self-consistent criteria J = J_c(B(J)) except for a small region where the current density is set to zero to maintain the condition of equal currents in all strands. The variation of critical current with vertical and horizontal separation between the strands is also investigated. Results are compared with the measured values of critical current for some of our cables. The comparison shows an error of up to 10% which we attribute mostly to the model not accounting for the spread in I_c values of the constituent strands.     

Preparation,thermal expansion,chemical compatibility,electrical conductivity and polarization of A2−αA′αMO4 (A = Pr,Sm; A′ = Sr; M = Mn,Ni; α = 0.3, 0.6) as a new cathode for SOFC

A_2−αA′_αMO₄ (A = Pr, Sm, A′ = Sr, M = Ni, Mn) with K₂NiF₄-type structure were synthesized by solid reaction. Their chemical stability, electrical conductivity and thermal expansion behavior as well as cathodic polarization were investigated in relation to the cathode of SOFC. The results showed that A_2−αA′_αMO₄ exhibited a low reactivity with yttria stabilized zirconia (YSZ) electrolyte. The thermal expansion coefficient (TEC) values were changed with the ionic radius of A. The specific conductivities of the nickelates were higher than those of manganites. While the nickelates showed a lower cathodic polarization in comparison with manganites.     

Dependence of the AES backscattering correction factor on the experimental configuration

We present an analysis of the dependence of the backscattering correction factor (BCF) in Auger-electron spectroscopy (AES) on the analyzer acceptance angle. Illustrative BCF calculations are presented for Pd M₅N₄₅N₄₅ Auger electrons as a function of primary-electron energy for primary-electron angles of incidence, θ₀, of 0° and 80° and for various values of the analyzer acceptance angle. It was necessary to generalize the BCF definition for the case of an analyzer with an arbitrarily large acceptance angle; this was done with a new function, the integral emission depth distribution function. BCFs calculated from an advanced model of electron transport in the surface region of the Pd sample varied weakly with analyzer half-cone angle for θ₀ = 0° but more strongly for θ₀ = 80° where there were BCF differences varying between 19% at a primary energy of 1 keV and 6% at a primary energy of 5 keV. These BCF differences are due in part to variations of the BCF with emission angle and in part to variations of the density of inner-shell ionizations within the information depth for the detected Auger electrons. The latter variations are responsible for differences larger than 10% between BCFs from the widely used simplified BCF model and those from the more accurate advanced model for primary energies less than about 5 keV for θ₀ = 80°. For normal incidence of the primary beam, differences greater than 10% between BCFs from the simplified and advanced models were found for primary energies between 1 keV and 4 keV. These BCF differences indicate that the simplified model can provide only approximate BCF values. In addition, the simplified model does not provide any BCF dependence on Auger-electron emission angle or analyzer acceptance angle.     

Anomalous scaling behaviour of cobalt cluster size distributions on graphite,epitaxial graphene and carbon-rich (6√3 × 6√3)R30°

The influence of the underlying interface on adsorption of cobalt (Co) is investigated by comparing the nucleation and growth of Co at room temperature on three carbon (C) surfaces, i.e. highly oriented pyrolytic graphite (HOPG), epitaxial graphene/SiC(0001) (hereafter abbreviated as EG) and precursor of EG i.e. C-rich (6√3 × 6√3)R30°/SiC(0001) (hereafter abbreviated as 6√3). On all three surfaces, Co adopts Volmer–Weber growth mode via formation of three-dimensional dome-shaped nanoclusters. Co clusters formed on 6√3 surface are smaller but denser than Co/HOPG or Co/EG. Scaling analysis reveals a critical nucleus size, i* = 1 (atom) and the smallest stable cluster (i* + 1) would be a dimer. Co/HOPG and Co/EG have the same order of magnitude for their cluster densities and sizes. Scaling analyses however show that the i* for Co/EG (i* = 3) is larger than Co/HOPG (i* = 0) and in this respect the smallest stable cluster would be tetramer and monomer respectively. This difference is attributed to the influence of an interface situated between graphene and SiC bulk. It appears that EG is more inert than HOPG towards the adsorption of Co and may act as a better substrate to host Co clusters.     

Self-induced polarization rotation of laser beam in fullerene (C70) solutions

Nonlinear self-rotation of elliptically polarized laser pulses (λ = 532 nm, τ_FWHM ~ 12 ns) in toluene, benzene and binary mixture (toluene + ethanol) solutions of fullerene C₇₀ has been investigated experimentally. Absolute values and signs of the nonlinear refractive indices (n₂) and nonlinear optical susceptibilities χ⁽³⁾(ω, ? ω, ω) of C₇₀ solutions in toluene and benzene at different values of polarization ellipse (θ = 0.2 ÷ 0.8) have been determined. High-resolution transmission electron microscope studies of C₇₀ solutions showed that in toluene + ethanol mixtures ball-shaped C₇₀ clusters are formed with particle sizes in the range ~ 100 ÷ 500 nm. It has been demonstrated, that the clusters sizes depend on the C₇₀ concentration and volume fraction of ethanol in toluene. Correlation between the processes of C₇₀ clusters formation in solutions and the values of polarization self-rotation angle of transmitted laser beam has been demonstrated. Physical mechanisms of laser induced optical activity in fullerene solutions have been discussed.     

Polarization properties of stochastic spatially and spectrally partially coherent electromagnetic flat-topped pulses

The propagation behavior of the spectral degree of polarization of stochastic spatially and spectrally partially coherent electromagnetic flat-topped pulses in free space is studied. Numerical calculation results are given to illustrate the dependence of spectral degree of polarization on the beam order, pulse frequency, temporal coherence length, pulse duration and spatial correlation length. It is shown that with increasing beam order M the position z of the on-axis spectral degree of polarization P = 0 decreases, and the distribution of spectral degree of polarization is different for different values of M.     

Numerical and perturbative computations of solitary waves of the Benjamin–Ono equation with higher order nonlinearity using Christov rational basis functions

Computation of solitons of the cubically-nonlinear Benjamin–Ono equation is challenging. First, the equation contains the Hilbert transform, a nonlocal integral operator. Second, its solitary waves decay only as O(1/∣x∣²). To solve the integro-differential equation for waves traveling at a phase speed c, we introduced the artificial homotopy H(u_XX) ? c u + (1 ? δ)u² + δu³ = 0, δ ∈ [0, 1] and solved it in two ways. The first was continuation in the homotopy parameter δ, marching from the known Benjamin–Ono soliton for δ = 0 to the cubically-nonlinear soliton at δ = 1. The second strategy was to bypass continuation by numerically computing perturbation series in δ and forming Padé approximants to obtain a very accurate approximation at δ = 1. To further minimize computations, we derived an elementary theorem to reduce the two-parameter soliton family to a parameter-free function, the soliton symmetric about the origin with unit phase speed. Solitons for higher order Benjamin–Ono equations are also computed and compared to their Korteweg–deVries counterparts. All computations applied the pseudospectral method with a basis of rational orthogonal functions invented by Christov, which are eigenfunctions of the Hilbert transform.     

A novel polarization splitter in ZnTe tellurite glass three-core photonic crystal fiber

A kind of polarization splitter in ZnTe tellurite glass three-core photonic crystal fiber has been proposed. The polarization splitter is based on the phenomenon of resonant tunneling. We use the finite element method and the full-vector beam propagating method to analyze the characteristics of three-core photonic crystal fiber. Compare with the silica glass three-core PCF, the ZnTe tellurite glass three-core PCF have higher extinction ratios and lower coupling loss, the extinction ratios ERA = ? 164.2681 dB and ERC = ? 37.1742 dB at the wavelength λ = 1.55 μm, and the coupling loss is lower than 0.02 dB. The 8.7983-mm-long splitter is proposed to achieve extinction ratio better than ? 20 dB and a bandwidthof 20 nm.     

A ceria layer as diffusion barrier between LAMOX and lanthanum strontium cobalt ferrite along with the impedance analysis

A thin interlayer of samarium doped ceria (SDC) is applied as diffusion barrier between La_1 ? xSr_xCo_yFe_1 ? yO₃ x = 0.1–0.4, y = 0.2–0.8 (LSCF) cathode and La_1.8Dy_0.2Mo_1.6W_0.4O₉ (LDMW82) electrolyte to obstruct Mo–Sr diffusion and solid state reaction in the intermediate temperature range of SOFC. We demonstrate the effectiveness of the diffusion barrier through contrasting the clearly defined interfaces of LSCF/SDC/LDMW82 against a rugged growing product layer of LSCF/LDMW82 in 800 °C thermal annealing, and analyze the product composition and the probable new phase. In addition, the measured polarization resistance is considerably lower for the half-cell with a diffusion barrier. Therefore, the electrochemical performance of the LSCF cathode is investigated on the SDC-protected LDMW82. The cell with LSCF (x = 0.4) persistently outperforms the one with x = 0.2 in polarization resistance because of its small low-frequency contribution. The activation energy of polarization resistance is also lower for La_0.6Sr_0.4Co_yFe_1 ? yO₃ (112–135 kJ/mol), than that for La_0.8Sr_0.2Co_yFe_1 ? yO₃ (156–164 kJ/mol). La_0.6Sr_0.4Co_yFe_1 ? yO₃ y = 0.4–0.8 is the proper composition for the cathode interfaced to SDC/LDMW82.     

Flow versus permeability weighting in estimating the forward volumetric transfer constant (Ktrans) obtained by DCE-MRI with contrast agents of differing molecular sizes

PurposeTo quantify the differential plasma flow- (F_p-) and permeability surface area product per unit mass of tissue- (PS-) weighting in forward volumetric transfer constant (K^trans) estimates by using a low molecular (Gd-DTPA) versus high molecular (Gadomer) weight contrast agent in dynamic contrast enhanced (DCE) MRI.Materials and methodsDCE MRI was performed using a 7T animal scanner in 14 C57BL/6J mice syngeneic for TRAMP tumors, by administering Gd-DTPA (0.9 kD) in eight mice and Gadomer (35 kD) in the remainder. The acquisition time was 10 min with a sampling rate of one image every 2 s. Pharmacokinetic modeling was performed to obtain K^trans by using Extended Tofts model (ETM). In addition, the adiabatic approximation to the tissue homogeneity (AATH) model was employed to obtain the relative contributions of F_p and PS.ResultsThe K^trans values derived from DCE-MRI with Gd-DTPA showed significant correlations with both PS (r² = 0.64, p = 0.009) and F_p (r² = 0.57, p = 0.016), whereas those with Gadomer were found only significantly correlated with PS (r² = 0.96, p = 0.0003) but not with F_p (r² = 0.34, p = 0.111). A voxel-based analysis showed that K^trans approximated PS (< 30% difference) in 78.3% of perfused tumor volume for Gadomer, but only 37.3% for Gd-DTPA.ConclusionsThe differential contributions of F_p and PS in estimating K^trans values vary with the molecular weight of the contrast agent used. The macromolecular contrast agent resulted in K^trans values that were much less dependent on flow. These findings support the use of macromolecular contrast agents for estimating tumor vessel permeability with DCE-MRI.     

Luminescence of Eu2+–vc− dipoles and their associates in CsI:Eu crystals

Spectral-kinetics properties of photo-scintillation excited with single light pulses of a nitrogen laser (λ=337.1 nm, t_1/2=5 ns, Q=1 mJ) have been studied in CsI:Eu crystals at temperature within 80–300 K. It is found that the exponential decay of 463 nm emission band has a time constant which grows from 0.85 μs at 78 K to 1.6 μs at 380 K. Such an anomalous temperature behavior of 463 nm emission decay kinetics is discussed in terms of the crystal thermal expansion. It has been proposed that 463 nm emission is caused by a cluster center consisting of three dipoles Eu²⁺v_c^? bounded with each other in a hexagon. Owing to the exchange resonance in the cluster, the energy passes from an excited dipole to a non-excited one and the distance between them gets longer due to thermal expansion of the crystal.     

Scaling behavior of polished (1 1 0) single-crystal nickel surfaces

The kinetic surface roughening of the polished (1 1 0) plane of a single-crystal nickel is investigated using atomic force microscopy. The polished (1 1 0) surfaces exhibit the scaling behavior characterized by the roughness exponent α=0.83±0.05, the growth exponent β=0.83±0.07 and the skewness=−0.52±0.06, whose values are compared with the theoretical values in statistical growth models in deposition. These characteristics indicate that the scaling behavior of the polished nickel surfaces can be related to a statistical growth model of nonlinear diffusion dynamics in deposition.     

Assessment of the patellofemoral cartilage: Correlation of knee pain score with magnetic resonance cartilage grading and magnetization transfer ratio asymmetry of glycosaminoglycan chemical exchange saturation transfer

PurposeBiochemical imaging of glycosaminoglycan chemical exchange saturation transfer (gagCEST) could predict the depletion of glycosaminoglycans (GAG) in early osteoarthritis. The purpose of this study was to evaluate the relationship between the magnetization transfer ratio asymmetry (MTR_asym) of gagCEST images and visual analog scale (VAS) pain scores in the knee joint.Materials and methodsThis retrospective study was approved by the institutional review board. A phantom study was performed using hyaluronic acid to validate the MTR_asym values of gagCEST images. Knee magnetic resonance (MR) images of 22 patients (male, 9; female, 13; mean age, 50.3 years; age range; 25–79 years) with knee pain were included in this study. The MR imaging (MRI) protocol involved standard knee MRI as well as gagCEST imaging, which allowed region-of-interest analyses of the patellar facet and femoral trochlea. The MTR_asym at 1.0 ppm was calculated at each region. The cartilages of the patellar facets and femoral trochlea were graded according to the Outerbridge classification system. Data regarding the VAS scores of knee pain were collected from the electronic medical records of the patients. Statistical analysis was performed using Spearman's correlation.ResultsThe results of the phantom study revealed excellent correlation between the MTR_asym values and the concentration of GAGs (r = 0.961; p = 0.003). The cartilage grades on the MR images showed significant negative correlation with the MTR_asym values in the patellar facet and femoral trochlea (r = −0.460; p = 0.031 and r = −0.543; p = 0.009, respectively). The VAS pain scores showed significant negative correlation with the MTR_asym values in the patellar facet and femoral trochlea (r = −0.435; p = 0.043 and r = −0.671; p = 0.001, respectively).ConclusionThe pain scores were associated with the morphological and biochemical changes in articular cartilages visualized on knee MR images. The biochemical changes, visualized in terms of the MTR_asym values of the gagCEST images, exhibited greater correlation with the pain scores than the morphological changes visualized on conventional MR images; these results provide evidence supporting the theory regarding the association of patellofemoral osteoarthritis with knee pain scores.     

Modelling of corona discharge in cylinder-wire-plate electrode configuration

Numerical computation of the electric field strength and ionic space charge density in electrode systems consisting of ionizing wire and non-ionizing cylinder, connected to the same DC high-voltage supply and facing a grounded plate, is a difficult problem, which is of interest to several electrostatic processes applications. In a previous study a simple numerical method has been proposed to calculate the spatial distributions of electric field and ionic space charge in a case of a continuum and uniform corona discharge originating at the surface of the wire. The aim of the present paper is to improve the physical model of the corona discharge in this particular electrode configuration, by assuming a more realistic law of charge injection on the wire circumference. The computations were carried out for an ionizing wire of radius r=0.1 mm, located at different distances h from a metallic tubular support of radius R=13.4 mm.The initial conditions of the corona discharge took into account the non-uniformity of the charge injection around the ionizing wire electrode. The computational results were compared with those obtained under the assumption of uniform corona discharge. The comparison pointed out that neither the non-uniformity of the electric field nor that of the charge injection can be neglected. They depend on the geometry of the electrode system and affect the distribution of the electric field and of the space charge density in the inter-electrode gap.     

Low loss broadband polarization independent fishnet negative index metamaterial at 40 GHz

We present a polarization independent fishnet negative index metamaterial at 40 GHz. The structure is investigated theoretically using finite element method simulations and experimentally by measuring the amplitude and phase of the S-parameters. The experimental setup for free space measurements of both transmission and reflection is hereby introduced. The internal properties are thereafter retrieved and show the double-negative behavior of the structure. This negative index metamaterial exhibits very high transmission (?0.13 dB), low reflection (?33.1 dB) and a high figure of merit (FOM = |Re(n)/Im(n)| = 42), where the real part of the refractive index is nearly ?1 (Re(n) = ?0.93) at 40 GHz.     

Photoionization studies of the atmospherically important species N and OH at the Elettra synchrotron radiation source

In this paper angularly resolved photoelectron spectra (PES) and constant-ionic-state (CIS) spectra are presented for the atmospherically important species N and OH.The natural width Γ, line shape parameters q and ρ² and discrete oscillator strengths f have been measured for the members of the N*[2s2p³(⁵S), np] (⁴P) ← N(⁴S) autoionizing resonances for n = 5–10. The n = 5 parameters calculated in this work are in good agreement with the values obtained previously whereas for the resonances with n = 6–10 the values of these parameters are reported for the first time. The asymmetry parameter (β) for the first band of N atoms, the N⁺(³P) ← N(⁴S) ionization, has also been measured in the photon energy range of the above autoionizing resonances.For OH, CIS spectra have been recorded for the first photoelectron band corresponding to the ionization OH⁺(X³Σ⁻, v⁺ = 0) ← OH(X²Π, v″ = 0). In these spectra, rotationally partially resolved bands associated with OH*(a¹Δ3d, v′ = 0) ← OH(X²Π, v″ = 0) resonances have been observed. Suggestions for their assignment are made on the basis of their positions and band simulations which use rotational line strength calculations.