Consolidation of hydrogenation–disproportionation–desorption–recombination processed Nd–Fe–B magnets by spark plasma sintering

We have successfully consolidated hydrogenation–disproportionation–desorption–recombination (HDDR) processed Nd–Fe–Co–Zr–B–Ga powder by spark plasma sintering (SPS). The field compacted samples were sintered at different temperatures (T_S) from 550 to 600 °C with compressive pressure of 80 MPa for 20 min. Microstructural investigations by transmission electron microscopy indicated that the sintered specimen exhibits Nd₂Fe₁₄B grains of ~300 nm with Nd-rich grain boundary phase. The optimum magnetic properties of B_r: 1.22 T, H_c: 928 kA/m, _BH_c: 600 kA/m, (BH)_max: 210 kJ/m³ were obtained in the sample sintered at 550 °C. The strategy for further improving the coercivity and remanence is discussed based on the microstructure-property relationships.     

Photoionization and electron–ion recombination of Cr I

Using the unified method, the inverse processes of photoionization and electron–ion recombination are studied in detail for neutral chromium, (), for the ground and excited states. The unified method based on close-coupling approximation and R-matrix method (i) subsumes both the radiative recombination (RR) and dielectronic recombination (DR) for the total rate and (ii) provides self-consistent sets of photoionization cross sections σ_PI and recombination rates α_RC. The present results show in total photoionization of the ground and excited states an enhancement in the background at the first excited threshold, state of the core. One prominent phot-excitation-of-core (PEC) resonance due to one dipole allowed transition (⁶S-⁶P^o) in the core is found in the photoionization cross sections of most of the valence electron excited states. Structures in the total and partial photoionization, for ionization into various excited core states and ground state only, respectively, are demonstrated. Results are presented for the septet and quintet states with n≤10 and l≤9 of Cr I. These states couple to the core ground state ⁶S and contribute to the recombination rates. State-specific recombination rates are also presented for these states and their features are illustrated. The total recombination rate shows two DR peaks, one at a relatively low temperature, at 630 K, and the other around 40,000 K. This can explain existence of neutral Cr in interstellar medium. Calculations were carried out in LS coupling using a close-coupling wave function expansion of 40 core states. The results illustrate the features in the radiative processes of Cr I and provide photoionization cross sections and recombination rates with good approximation for this astrophysically important ion.     

Electrical characteristics of a metal–insulator–semiconductor memory structure containing Ge nanocrystals

A metal–insulator–semiconductor structure device with Ge nanocrystals in SiO₂ was synthesized and the electrical characteristics were investigated. Capacitance–voltage (C–V) curves show hysteresis and the measurements indicate that the device has charge storage effects and stores more holes than electrons. For decreasing measurement frequencies from 1 MHz to 500 Hz, both branches of the C–V hysteresis shift in the positive voltage direction. The slope of the left flank of the C–V hysteresis curve becomes stretched out with decreasing frequency. The slope of the right one appears frequency independent, while there is a small hump/step on the right flank of the C–V hysteresis curve for the lower frequency cases (500 Hz and 1 kHz). The role of Si/SiO₂ interface states is discussed.     

Karhunen–Loève decomposition of peripheral blood flow signal

The Karhunen–Loève expansion is applied to scalar signals and the effect of window length (t_w), time lag (τ) and embedding dimension (d) is analysed for periodic signals and for signals modeled by the Lorenz equations. For τ≠k/2f_i (f_i are characteristic frequencies of the signal, k is positive integer), we obtain 2m modes from an m-periodic signal. For a large set of parameters a finite number of modes was not obtained from the Lorenz system. It is further shown that, on the time scale of a minute, the peripheral blood flow signal contains oscillatory modes that occur in pairs thereby confirming that the blood flow through the cardiovascular system is oscillatory. Some of the difficulties of applying Karhunen–Loève expansion to scalar signals are pointed out.     

Scattering and bound states of spinless particles in a mixed vector–scalar smooth step potential

Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is mapped into the Schrödinger-like equation with an effective Rosen–Morse potential. It is shown that the scalar uniform background present subtle and trick effects for the scattering states and reveals itself a high-handed element for formation of bound states. In that process, it is shown that the problem of solving a differential equation for the eigenenergies is transmuted into the simpler and more efficient problem of solving an irrational algebraic equation.     

Phase Separation in the Neutral Falicov–Kimball Model

The Falicov–Kimball model consists of spinless electrons and classical particles (ions) on a lattice. The electrons hop between nearest neighbor sites, while the ions do not. We consider the model with equal numbers of ions and electrons and with a large on-site attractive force between ions and electrons. For densities 1/4 and 1/5, the ion configuration in the ground state had been proved to be periodic. We prove that for density 2/9 it is periodic as well. However, for densities between 1/4 and 1/5 other than 2/9 we prove that the ion configuration in the ground state is not periodic. Instead there is phase separation. For densities in (1/5, 2/9) the ground-state ion configuration is a mixture of the density 1/5 and 2/9 ground-state ion configurations. For the interval (2/9, 1/4) it is a mixture of the density 2/9 and 1/4 ground states.     

Aharonov–Bohm effect in Kane-type semiconductor quantum wire

In the present study, the Aharonov–Bohm effect for bound states in Kane-type quantum wire is analysed. It is demonstrated that the wave function and the energy spectra of carriers depend on the magnetic flux. The energy and the g factor of electrons are of a periodic function of the magnetic flux. The statistical property of the orbital magnetism of electrons at low temperatures and strong magnetic fields is presented. It is shown that the magnetisation of electron oscillations depends on the magnetic flux.     

Multigrid algorithms for high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations

Multigrid algorithms are developed for systems arising from high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations on unstructured meshes. The algorithms are based on coupling both p- and h-multigrid (ph-multigrid) methods which are used in nonlinear or linear forms, and either directly as solvers or as preconditioners to a Newton–Krylov method.The performance of the algorithms are examined in solving the laminar flow over an airfoil configuration. It is shown that the choice of the cycling strategy is crucial in achieving efficient and scalable solvers. For the multigrid solvers, while the order-independent convergence rate is obtained with a proper cycle type, the mesh-independent performance is achieved only if the coarsest problem is solved to a sufficient accuracy. On the other hand, the multigrid preconditioned Newton–GMRES solver appears to be insensitive to this condition and mesh-independent convergence is achieved under the desirable condition that the coarsest problem is solved using a fixed number of multigrid cycles regardless of the size of the problem.It is concluded that the Newton–GMRES solver with the multigrid preconditioning yields the most efficient and robust algorithm among those studied.     

Towards Drinfeld–Sokolov reduction for quantum groups

In this paper we study the Poisson–Lie version of the Drinfeld–Sokolov reduction defined in [E. Frenkel, N. Reshetikhin, M.A. Semenov-Tian-Shansky, Drinfeld–Sokolov reduction for difference operators and deformations of W-algebras. I. The case of Virasoro algebra, Comm. Math. Phys. 192 (1998) 605; M.A. Semenov-Tian-Shansky, A.V. Sevostyanov, Drinfeld–Sokolov reduction for difference operators and deformations of W-algebras. II. General semisimple case, Comm. Math. Phys. 192 (1998) 631]. Using the bialgebra structure related to the new Drinfeld realization of affine quantum groups we describe reduction in terms of constraints. This realization of reduction admits direct quantization.As a byproduct we obtain an explicit expression for the symplectic form associated to the twisted Heisenberg double and calculate the moment map for the twisted dressing action. For some class of infinite-dimensional Poisson–Lie groups we also prove an analogue of the Ginzburg–Weinstein isomorphism.     

The factor of nonparaxial Hermite–Gaussian beams and related problems

On the basis of the second-order moment of the power density and in the use of the series expansion, the expressions for the beam width, far-field divergence angle and M² factor of nonparaxial Hermite–Gaussian (H–G) beams are derived and expressed in a sum of the series of the Gamma function. The theoretical results are illustrated with numerical examples. The M² factor of nonparaxial H–G beams depends not only on the beam order m, but also on the waist-width to wavelength ratio w₀/λ. The far-field divergence angles of nonparaxial H–G beams with even and odd orders approach their upper limits θ_max=63.435 and 73.898, respectively, which results in M²<1 as w₀/λ→0. For the special case of m=0 our results reduce to those of nonparaxial Gaussian beams. Some problems related to the characterization of the nonparaxial beam quality are also discussed.     

Vortex pinning properties of –Ba–Cu–O and –Ba–Cu–O superconducting bulks

We have studied the effect of a small amount of Y-site substitution by La or Pr ions on the vortex pinning in the Y–Ba–Cu–O system. (Y_1-xLa_x)–Ba–Cu–O and (Y_1-xPr_x)–Ba–Cu–O bulks were fabricated by the melt-textured growth, in which x was varied from 0 to 0.01. The critical current density J_c at 77 K is improved in magnetic fields parallel to the c-axis above 2–4.5 T and the corresponding irreversibility field, H_irr, shifts to the higher value in both bulks.     

Exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions

The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with δ-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering method. Many interesting features appear in the system. For example, the wave function has the SU(2|2) supersymmetry. It is also found that the ground state of the system is partial polarized, where the fermions form a spin singlet state and the bosons are totally polarized. From the solution of Bethe ansatz equations, it is shown that all the momentum, spin and isospin rapidities at the ground state are real if the interactions between the particles are repulsive; while the fermions form two-particle bounded states and the bosons form one large bound state, which means the bosons condensed at the zero momentum point, if the interactions are attractive. The charge, spin and isospin excitations are discussed in detail. The thermodynamic Bethe ansatz equations are also derived and their solutions at some special cases are obtained analytically.     

Numerical algorithm for the time fractional Fokker–Planck equation

Anomalous diffusion is one of the most ubiquitous phenomena in nature, and it is present in a wide variety of physical situations, for instance, transport of fluid in porous media, diffusion of plasma, diffusion at liquid surfaces, etc. The fractional approach proved to be highly effective in a rich variety of scenarios such as continuous time random walk models, generalized Langevin equations, or the generalized master equation. To investigate the subdiffusion of anomalous diffusion, it would be useful to study a time fractional Fokker–Planck equation. In this paper, firstly the time fractional, the sense of Riemann–Liouville derivative, Fokker–Planck equation is transformed into a time fractional ordinary differential equation (FODE) in the sense of Caputo derivative by discretizing the spatial derivatives and using the properties of Riemann–Liouville derivative and Caputo derivative. Then combining the predictor–corrector approach with the method of lines, the algorithm is designed for numerically solving FODE with the numerical error O(k^min{1+2α,2})+O(h²), and the corresponding stability condition is got. The effectiveness of this numerical algorithm is evaluated by comparing its numerical results for α=1.0 with the ones of directly discretizing classical Fokker–Planck equation, some numerical results for time fractional Fokker–Planck equation with several different fractional orders are demonstrated and compared with each other, moreover for α=0.8 the convergent order in space is confirmed and the numerical results with different time step sizes are shown.     

Proca Effect in Kerr–Newman Metric

The Proca effect of an electric field is studied in curved space. A Kerr–Newman metric with the photon rest mass can be presented by the analytic continuation (Xu, C. M. (....). General Relativity and Modern Cosmology, Nanking Normal University) in a short range. It yields the correction in the Kerr–Newman space.     

Schrödinger Operators with Few Bound States

We show that whole-line Schrödinger operators with finitely many bound states have no embedded singular spectrum. In contradistinction, we show that embedded singular spectrum is possible even when the bound states approach the essential spectrum exponentially fast. We also prove the following result for one- and two-dimensional Schrödinger operators, H, with bounded positive ground states: Given a potential V, if both H±V are bounded from below by the ground-state energy of H, then V≡0.D. D. was supported in part by NSF grant DMS–0227289.R. K. was supported in part by NSF grant DMS–0401277.B. S. was supported in part by NSF grant DMS–0140592.     

Composite fermion picture for multi-component plasmas in 2D electron–hole systems in a strong magnetic field

Low-lying states of a 2D electron–hole system contain electrons and one or more types of charged excitonic complexes. Binding energies and angular momenta of these excitonic ions, and the pseudopotentials describing their interactions with electrons and with one another are obtained from numerical studies of small systems. Incompressible fluid ground states of such multi-component plasmas are found in exact numerical diagonalizations. A generalized composite fermion (CF) picture involving Chern–Simons charges and fluxes of different types is proposed and shown to predict the low-lying states at any value of the magnetic field.     

Bound polaron in a wurtzite GaN/AlxGa1 − xN ellipsoidal finite-potential quantum dot

A variational method is used to study the ground state of a bound polaron in a weakly oblate wurtzite GaN/Al_xGa_1 − xN ellipsoidal quantum dot. The binding energy of the bound polaron is calculated by taking the electron couples with both branches of LO-like and TO-like phonons due to the anisotropic effect into account. The interaction between impurity and phonons has also been considered to obtain the binding energy of a bound polaron. The results show that the binding energy of bound polaron reaches a peak value as the quantum dot radius increases and then diminishes for the finite potential well. We found that the binding energy of bound polaron is reduced by the phonons effect on the impurity states, the contribution of LO-like phonon to the binding energy is dominant, the anisotropic angle and ellipticity influence on the binding energy are small.     

Far-field properties and beam quality of vectorial Hermite–Laguerre–Gaussian beams beyond the paraxial approximation

The far-field properties and beam quality of vectorial nonparaxial Hermite–Laguerre–Gaussian (HLG) beams are studied in detail, where, instead of the second-order-moments-based M² factor, the extended power in the bucket (PIB) and βparameter are used to characterize the beam quality in the far field and the intensity in the formulae is replaced by the z component of the time-averaged Poynting vector S_z. It is found that the S_z PIB and βparameter of vectorial nonparaxial HLG beams depend on the mode indices n, m, αparameter and waist-width-to-wavelength ratio w₀/λ and the PIB and βparameter are additionally dependent on the bucket's size taken.     

A new form of the Sutton–Chen potential for the Cu–Ag alloys

The analytic construction of a many-body potential inspired from the Sutton–Chen parametrization is presented for copper and silver. A new approach is used to model the cross interaction for the Cu–Ag alloys. The parameters are fitted to first principles calculations based on the full potential linear plane wave method. The structural properties of the order and disorder Cu–Ag alloys in the B₂and fcc structures are presented for different concentration.     

Exploring ground states and excited states of spin-1 Bose–Einstein condensates by continuation methods

A pseudo-arclength continuation method (PACM) is employed to compute the ground state and excited state solutions of spin-1 Bose–Einstein condensates (BEC). The BEC is governed by the time-independent coupled Gross–Pitaevskii equations (GPE) under the conservations of the mass and magnetization. The coupling constants that characterize the spin-independent and spin-exchange interactions are chosen as the continuation parameters. The continuation curve starts from a ground state or an excited state with very small coupling parameters. The proposed numerical schemes allow us to investigate the effect of the coupling constants and study the bifurcation diagrams of the time-independent coupled GPE. Numerical results on the wave functions and their corresponding energies of spin-1 BEC with repulsive/attractive and ferromagnetic/antiferromagnetic interactions are presented. Furthermore, we reveal that the component separation and population transfer between the different hyperfine states can only occur in excited states due to the spin-exchange interactions.