不可压缩流动的并行数值方法

不可压缩流动的数值模拟是计算流体力学的重要组成部分. 基于有限元离散方法, 本文设计了不可压缩Navier-Stokes (N-S)方程支配流的若干并行数值算法. 这些并行算法可归为两大类: 一类是基于两重网格离散方法, 首先在粗网格上求解非线性的N-S方程, 然后在细网格的子区域上并行求解线性化的残差方程, 以校正粗网格的解; 另一类是基于新型完全重叠型区域分解技巧, 每台处理器用一局部加密的全局多尺度网格计算所负责子区域的局部有限元解. 这些并行算法实现简单, 通信需求少, 具有良好的并行性能, 能获得与标准有限元方法相同收敛阶的有限元解. 理论分析和数值试验验证了并行算法的高效性     

Levi problem and semistable quotients

A complex space X is in class 𝒬 _G if it is a semistable quotient of the complement to an analytic subset of a Stein manifold by a holomorphic action of a reductive complex Lie group G. It is shown that every pseudoconvex unramified domain over X is also in 𝒬 _G .     

Influence of exchange coupling on current-driven domain wall motion in a nanowire

In this study, the effect of exchange stiffness constant on current-driven domain wall motion in nanowires with in-plane magnetic anisotropy (IMA) and perpendicular magnetic anisotropy (PMA) has been investigated using micromagnetic simulation. The critical current density in a nanowire with IMA decreases as the exchange stiffness constant decreases because the domain wall width at the upper edge of the nanowire narrows according to the decrease of the exchange stiffness constant. On the other hand, the critical current density in a nanowire with PMA slightly decreases contrary to that of IMA although the domain wall width reasonably decreases as the exchange stiffness constant decreases. The slight reduction rate of the critical current density is due to the increase of the effective hard-axis anisotropy of PMA nanowire.     

Geometrical confinement effects on the magnetization and polarization response in resonant magneto-optic rotator waveguides

Control of magnetization is central to the performance of magneto-optical switches and isolators. Photonic crystal technology on these devices can yield significant improvements in polarization rotation efficiency and an overall reduction in device dimensions. The optical response and field reversal characteristics of resonant magneto-optic polarization rotators fabricated on chip are presented herein and analyzed by micromagnetic simulation. By introducing domain-strip structures into the resonant cavity of Bragg gratings formed on magnetic garnet films, a bi-stable magnetic state is demonstrated and the enhancement of characteristic saturation field is studied. Domain closure loops between the strips affect the hysteresis response in the resonant cavity. Large magneto-optic rotations exceeding 45° are produced near resonance between 1500 and 1580 nm in the stop-bands, although the presence of linear birefringence in these gyrotropic waveguides strongly suppresses the Faraday rotation outside the stop-bands and degrades the linearity of the output polarization.     

Vector method for studying the second-harmonic-generation light derived from complex periodic ferroelectric domains

In this Letter, in order to overcome the disadvantages of controlling the second-harmonic-generation (SHG) light derived from the traditional one-dimensional (1D) periodic ferroelectric domains we propose a kind of so-called complex periodic ferroelectric structure (CPFS), which unit cell is composed of even layers of positive and negative domains arranged alternatively following aperiodic sequence. It is found that comparing with the traditional periodic structure, CPFS cannot offer more reciprocal vector compensations for the mismatching phase, but CPFS may provide larger effective nonlinear coefficients (ENCs) in high-order quasi-phase-matching (QPM) and possesses advantages of the amplitude modulation for SHG peaks. In this Letter we study CPFS by use of vector method (VM), where the contribution to ENC for each domain or each unit cell will be treated as a vector and the QPM condition for CPFS and the modulation effect of aperiodic unit cells have been obtained. Without any Fourier transformation VM treats the grating function in real space and will be very convenient and intuitive. Both VM and CPFS would possess potential applications in the field of SHG investigations.     

Field polarity dependent nucleation of superconductivity in quasi-one-dimensional magnetic templates

We investigate the nucleation of superconductivity in an Al/Al₂O₃/Py trilayer system by electrical transport measurements. Magnetic force microscopy images taken at room temperature show that the 0.7 μm thick Py-film form stripes of magnetic domains with alternating out-of-plane stray field. After applying a strong out of plane magnetic field H the superconductor/normal phase boundary becomes asymmetric with respect to H = 0. This lack of field polarity symmetry results from the unbalanced size distribution of domains with opposite polarity.     

Analysis of local polarity change around Cys34 in bovine serum albumin during N→B transition by a polarity-sensitive fluorescence probe

The change trend of the local environment of Cys34 domain in bovine serum albumin has been studied as a function of pH value by using thiol-specific and polarity-sensitive fluorescent probe 3-(4-chloro-6-p-maleimidylphenoxyl-1,3,5-triazinylamino)-7-dimethylamino-2-methyl-phenazine. The local polarity of the Cys34 domain is found to rise with the increase of pH values, and the corresponding dielectric constant is raised from 12.8 at pH 6.0 to 23.3 at pH 9.1. The result shows that the environment of the Cys34 domain is rather hydrophobic in normal state at pH 6.0 and becomes a little hydrophilic in the course of N→B transition, which may be attributed to the slight unfolding of the protein and thus the increasing of exposure of the previously relatively buried Cys34. In addition, the increased dielectric constant (23.3) is much lower than that (80.1) of water, suggesting that the unfolding of bovine serum albumin does not cause the full exposure of the Cys34 to the aqueous media during the transition.     

On suboperators with codimension one domains

The question of the existence of a proper closed densely defined suboperator whose domain contains a given linear space is answered. Such suboperators with codimension one domains are described. The motivation for studying this topic comes from the theory of extremal extensions of (non-densely defined) positive operators.     

Meromorphic functions sharing values in an angular domain

In this paper we study the problems of meromorphic functions sharing values in an angular domain and obtain some uniqueness results which are the improvement of the well-known five-value theorem and four-value theorem given by Nevanlinna.     

Growth estimates in the Hardy-Sobolev space of an annular domain with applications

We give an explicit estimate on the growth of functions in the Hardy-Sobolev space Hk,2(Gs) of an annulus. We apply this result, first, to find an upper bound on the rate of convergence of a recovery interpolation scheme in H1,2(Gs) with points located on the outer boundary of Gs. We also apply this result for the study of a geometric inverse problem, namely we derive an explicit upper bound on the area of an unknown cavity in a bounded planar domain from the difference of two electrostatic potentials measured on the boundary, when the cavity is present and when it is not.