A fast directional algorithm for high-frequency electromagnetic scattering

This paper is concerned with the fast solution of high-frequency electromagnetic scattering problems using the boundary integral formulation. We extend the O(N log N) directional multilevel algorithm previously proposed for the acoustic scattering case to the vector electromagnetic case. We also detail how to incorporate the curl operator of the magnetic field integral equation into the algorithm. When combined with a standard iterative method, this results in an almost linear complexity solver for the combined field integral equations. In addition, the butterfly algorithm is utilized to compute the far field pattern and radar cross section with O(N log N) complexity.     

Fast stray field computation on tensor grids

A direct integration algorithm is described to compute the magnetostatic field and energy for given magnetization distributions on not necessarily uniform tensor grids. We use an analytically-based tensor approximation approach for function-related tensors, which reduces calculations to multilinear algebra operations. The algorithm scales with N^4/3 for N computational cells used and with N^2/3 (sublinear) when magnetization is given in canonical tensor format. In the final section we confirm our theoretical results concerning computing times and accuracy by means of numerical examples.     

Effective threshold energy for pair production in nonpolar semiconductors

A streaming model (high field) analysis is given for the average energy for and the probability of electron-hole pair production in a semiconductor when a quadratically energy dependent impact ionization cross-section exists above a threshold energy and competes with a nonpolar optical phonon scattering mechanism. A power series expansion method and tabulated results are provided to treat the resulting probability integrals of the form ∫₀^∞xⁿ exp {?(βx + x³)}dx.     

Transport of a Passive Tracer by an Irregular Velocity Field

The trajectories of a passive tracer in a turbulent flow satisfy the ordinary differential equation x′(t)=V(t,x(t)), where V(t,x) is a stationary random field, the so-called Eulerian velocity. It is a nontrivial question to define the dynamics of the tracer in the case when the realizations of the Eulerian field are only spatially Hölder regular because the ordinary differential equation in question lacks then uniqueness. The most obvious approach is to regularize the dynamics, either by smoothing the velocity field (the so-called ε-regularization), or by adding a small molecular diffusivity (the so-called κ-regularization) and then pass to the appropriate limit with the respective regularization parameter. The first procedure corresponds to the Prandtl number Pr=∞, while the second to Pr=0. In the present paper we consider a two parameter family of Gaussian, Markovian time correlated fields V(t,x), with the power-law spectrum. Using the infinite dimensional stochastic calculus we show the existence and uniqueness of the law of the trajectory process corresponding to a given field V(t,x) for a certain regime of parameters characterizing the spectrum of the field. Additionally, this law is the limit, in the sense of the weak convergence of measures, of the laws obtained as a result of any of the described regularizations. The so-called Kolmogorov point, that corresponds to the parameters characterizing the relaxation time and energy spectrum of a turbulent, three dimensional flow, belongs to the boundary of the parameter regime considered in the paper.     

Quasiparticle band structure and optical spectrum of LiBr

The electronic structures of the Fe-doped perovskite ruthenates BaRu_1?x Fe _x O₃ with x = 0, 0.25, 0.5, 0.625, 0.75, and 1 are investigated through density-functional calculations. Large exchange splitting and small crystal field splitting are found in BaFeO₃, and a contrary scenario can take place on BaRuO₃ as expected since the Ru atom has a highly extended 4d orbital. The small exchange splitting and extended 4d states are the reasons why the obtained spin magnetic moment (0.628μ _B ) is significantly lower than the spin only value (2μ _B ) for the t _2g 3↑ t _2g 1↓ electronic configuration for Ru⁴⁺ ion. Further investigations suggest that Fe substitution at the Ru sites can suppress the bandwidths of Ru 4d orbital, leading to the half-metallic behaviour in BaRu_1?x Fe _x O₃ with x = 0.625 and 0.75. The different orbital feature of the Ru⁴⁺ ions in BaRu_0.375Fe_0.625O₃ is presented, which reflects the influence of Fe dopant on Ru 4d orbitals.     

Replica symmetry breaking in and around six dimensions

Two, replica symmetry breaking specific, quantities of the Ising spin glass — the breakpoint x₁ of the order parameter function and the Almeida-Thouless line — are calculated in six dimensions (the upper critical dimension of the replicated field theory used), and also below and above it. The results confirm that replica symmetry breaking does exist below d=6, and also the tendency of its escalation for decreasing dimension continues. As a new feature, x₁ has a nonzero and universal value for d<6 at criticality. Near six dimensions we have x1c=3(6−d)+O[²(6−d)]. A method to expand a generic theory with replica equivalence around the replica symmetric one is also demonstrated.     

Phase rule for critical coexistence manifolds

In high-dimensional phase diagrams there appear variations of singular manifolds other than coexistence and critical manifolds, e.g. the critical endpoint. The general singular manifold can be taken as a manifold on which p phases coexist and each phase of the order O_j, whereas O_j = 1 for an ordinary phase. In an n-dimensional phase diagram, the dimension of the singular manifold d has been shown to satisfy d ? n + p + 1–2Σ^p_j = 1 O_j. This is the general phase rule including those of coexistence points and critical points as special cases.     

A note on traversal time for tunneling

A simple approach to study the traversal time for tunneling is given. By using the WKB wave function to evaluate the velocity field of particles in the barrier region, an expression for the traversal time τ=εdx[m/2(V(x)-E)]^1/2 is obtained in conformity with the recent results.     

Analysis of the electronic structure of ZrO2 by Compton spectroscopy

The electronic structure of ZrO₂ is studied using the Compton scattering technique. The first-ever Compton profile measurement on polycrystalline ZrO₂ was obtained using 59.54 keV gamma-rays emanating from the ²⁴¹Am radioisotope. To explain the experimental data, we compute theoretical Compton profile values using the method of linear combination of atomic orbitals in the framework of density functional theory. The correlation scheme proposed by Perdew-Burke-Ernzerhof and the exchange scheme of Becke are considered. The ionic-model-based calculations for a number of configurations, i.e., Zr^+x (O^?x/2)₂ (0 ≤ x ≤ 2), are also performed to estimate the charge transfer on compound formation, and the study supports transfer of 1.5 electrons from Zr to O atoms.     

Evolution of the optical properties and the electrical resistivity of CaMnO3 during the substitution of Mo for Mn ions

The reflectance, the optical density, and the optical conductivity spectra of CaMn_{1 ? x} Mo _x O₃ (x ≤ 0.07) polycrystals are studied over a wide spectral region. The substitution of Mo⁶⁺ ions for Mn⁴⁺ ions leads to a strong decrease in the first high-energy phonon band, which is related to vibrations in the MnO₆ octahedron. The appearance of band-type charge carriers is detected in CaMn_{1 ? x} Mo _x O₃ with x ≤ 0.04, and carrier localization is observed in CaMn_0.93Mo_0.07O₃. This localization increases at T < 160 K, i.e., during the transition from the paramagnetic to the antiferromagnetic state with orbital ordering and a monoclinic structure. The optical conductivity spectrum of CaMn_0.93Mo_0.07O₃ exhibits a strong shift of fundamental absorption bands, which is associated with a change in the band structure because of a decrease in the splitting of the 3d levels of Mn in the crystal field.     

Low temperature specific heat studies on the pairing states of high-Tc superconductors: a brief review

Low temperature specific heat (LTSH) data on a variety of high-T_c superconductors, such as YBa₂Cu₃O₇, La_1−xSr_xCuO₄, Bi₂Sr₂CaCu₂O₈, and Ba_0.6K_0.4BiO₃ are reviewed. The agreement between the experimental data and theoretical predictions, such as T²-dependence of specific heat at zero magnetic field and H^1/2-dependence of electronic specific heat is widely discussed within the scenario of d-wave superconductivity. Impurity scattering effects and scaling model on d-wave superconductivity are verified using Zn- and Ni-doped La_1−xSr_xCuO₄. The low energy quasiparticle density of states N(E)=N(0)+E^1/2 are deduced from dirty d-wave superconductors. Absence of paramagnetic contribution to LTSH is found both in superconducting and non-superconducting underdoped samples suggesting that a mechanism beyond Kondo screening model maybe required to explain its magnetic property.     

A multilevel Cartesian non-uniform grid time domain algorithm

A multilevel Cartesian non-uniform grid time domain algorithm (CNGTDA) is introduced to rapidly compute transient wave fields radiated by time dependent three-dimensional source constellations. CNGTDA leverages the observation that transient wave fields generated by temporally bandlimited and spatially confined source constellations can be recovered via interpolation from appropriately delay- and amplitude-compensated field samples. This property is used in conjunction with a multilevel scheme, in which the computational domain is hierarchically decomposed into subdomains with sparse non-uniform grids used to obtain the fields. For both surface and volumetric source distributions, the computational cost of CNGTDA to compute the transient field at N_s observation locations from N_s collocated sources for N_t discrete time instances scales as O(N_tN_slogN_s) and O(N_tN_slog²N_s) in the low- and high-frequency regimes, respectively. Coupled with marching-on-in-time (MOT) time domain integral equations, CNGTDA can facilitate efficient analysis of large scale time domain electromagnetic and acoustic problems.     

Fast evaluation of Helmholtz potential on graphics processing units (GPUs)

This paper presents a parallel algorithm implemented on graphics processing units (GPUs) for rapidly evaluating spatial convolutions between the Helmholtz potential and a large-scale source distribution. The algorithm implements a non-uniform grid interpolation method (NGIM), which uses amplitude and phase compensation and spatial interpolation from a sparse grid to compute the field outside a source domain. NGIM reduces the computational time cost of the direct field evaluation at N observers due to N co-located sources from O(N²) to O(N) in the static and low-frequency regimes, to O(N log N) in the high-frequency regime, and between these costs in the mixed-frequency regime. Memory requirements scale as O(N) in all frequency regimes. Several important differences between CPU and GPU implementations of the NGIM are required to result in optimal performance on respective platforms. In particular, in the CPU implementations all operations, where possible, are pre-computed and stored in memory in a preprocessing stage. This reduces the computational time but significantly increases the memory consumption. In the GPU implementations, where handling memory often is a critical bottle neck, several special memory handling techniques are used to accelerate the computations. A significant latency of the GPU global memory access is hidden by implementing coalesced reading, which requires arranging many array elements in contiguous parts of memory. Contrary to the CPU version, most of the steps in the GPU implementations are executed on-fly and only necessary arrays are kept in memory. This results in significantly reduced memory consumption, increased problem size N that can be handled, and reduced computational time on GPUs. The obtained GPU–CPU speed-up ratios are from 150 to 400 depending on the required accuracy and problem size. The presented method and its CPU and GPU implementations can find important applications in various fields of physics and engineering.     

Ligand field splitting of d orbitals in nine-coordinated sites of capped antiprism structure: Application to monazite

The splitting of the energy levels of d¹ ions in a field of nine ligands arranged in a capped antiprism is calculated for both the regular and distorted structure. In the regular capped antiprism, the ground state is found to be the degenerate state dxy, dx²-y²; in the distorted structure, the ground state is dx²-y². The results are consistent with experimental ESR data on the V⁴⁺: CePO₄ system.     

Transferred hyperfine fields at 119Sn in Fe1−xMxSn [M≡Mn, Co and Ni]

The transferred hyperfine fields at ¹¹⁹Sn, using Mössbauer spectroscopy are reported for the hexagonal B-35 compounds with a general formula Fe_1?xM_xSn, where MMn, Co and Ni. In these compounds, Sn atoms occupy two crystallographically inequivalent sites. For FeSn the observed spectrum consists of a quadrupole doublet and a magnetic pattern corresponding to 2(d) and 2(a) sites respectively. The data have been analysed to resolve the controversy regarding hyperfine parameters. On replacing Fe by Mn atoms, additional lines appear in the higher velocity region of the Mössbauer spectrum and the intensity of the nuclear Zeeman pattern increases at the expense of quadrupole doublet. The resulting Mössbauer spectra have been analysed by taking only the nearest neighbour interactions into account. This analysis shows that on replacing each Fe atom by a Mn atom, the hyperfine field at 1(a) Sn site increases by about 40 kOe and a field of about 35 kOe is produced at the 2(d) Sn sites. Further, from the nuclear Zeeman pattern for 2(d) sites, the sign of quadropole splitting for these sites could also be determined and was found to be positive. However, the substitution of Co and Ni in place of Fe atoms results in a broad unresolved pattern suggesting that the hyperfine field at the 1(a) sites decreases and a finite field develops at the 2(d) site. The origin of transferred hyperfine fields at the two inequivalent Sn sites is discussed, the magnetic transition temperatures of these compounds have been estimated and the magnetic moments of M-atoms have been inferred.     

Photoluminescence in MgxSr1−xAl2O4:Eu, Ndand electron-vibrational interaction in the Eu 5d states

Green phosphor compositions Mg_xSr_1−xAl₂O₄:Eu, Nd (with x=0.05-0.25) were prepared by solid state reaction method. The effect of Mg substitution on photoluminescence characteristics was investigated. The photoluminescence show intense green emission for MgSrAl₂O₄:Eu²⁺, Nd³⁺ with long persistence. This green emission corresponds to transitions from 4f⁶5d¹ to 4f⁷ of Eu²⁺ ion. Comparative analysis of the excitation and emission spectra were used to evaluate the crystal field splitting of the 5d states of Eu²⁺ and the parameters of electron-vibrational interaction, such as Huang-Rhys factor, effective phonon energy, and zero-phonon line position.     

On the theory of collective motion in nuclei. I. Classical theory

From the assumption that the collective Hamiltonian be invariant under the orthogonal group O(A ? 1, $\text{R}$) it is concluded that classical collective dynamics can be formulated on a symplectic manifold. This manifold is shown to be a coset space of the symplectic group $\text{L}$h(6, $\text{R}$) of dimension 12, 16 or 18. The first case corresponds to the dequantization of closed-shell collective dynamics and is described in terms of six complex s- and d-quasiparticles. In the limit A ? 1 it is shown that a transformation leads to interacting s- and d-bosons with the symmetry group $\text{u}$ (6) in the collective phase space.     

Motional narrowing in the electron-spin-resonance-spectrum of pentavalent vanadium-compounds

The activation energy of the hopping frequency of the vanadium-3d ¹-electron is derived from the temperature dependence of the ESR linewidth in the following semiconducting, pentavalent vanadium-compounds: Na_xV₂O₅, Li_xV₂O₅ (x <0.02), V₂O₅ weakly doped with WO₃ or MoO₃ (E _a ≈0.07 eV). In V₂MoO₈, vanadium-3d ₁-electrons are responsible for the electronic conductivity, too.     

Luminescent properties of red-emitting LiSr4B3O(9−3x/2)Nx:Eu2+ phosphor for white-LEDs

An Eu²⁺-activated oxynitride LiSr_(4?y)B₃O_(9?3x/2)N_x:yEu²⁺ red-emitting phosphor was synthesized by solid-state reactions. The synthesized phosphor crystallized in a cubic system with space group Ia–3d. The LiSr₄B₃O_(9?3x/2)N_x:Eu²⁺ phosphors exhibited a broad red emission band with a peak at 610 nm and a full width at half maximum of 106 nm under 410 nm excitation, which is ascribed to the 4f⁶5d¹→4f⁷ transition of Eu²⁺. The optimal doped nitrogen concentration was observed to be x=0.75. The average decay times of two different emission centers were estimated to be 568 and 489 ns in the LiSr_3.99B₃O_8.25N_0.5:0.01Eu²⁺ phosphors, respectively. Concentration quenching of Eu²⁺ ions occurred at y=0.07, and the critical distance was determined as 17.86 Å. The non-radiative transitions via dipole–dipole interactions resulted in the concentration quenching of Eu²⁺-site emission centers in the LiSr₄B₃O₉ host. These results indicate LiSr₄B₃O_(9?3x/2)N_x:Eu²⁺ phosphor is promising for application in white near-UV LEDs.