Finite Dimensional Behaviors of the Primitive Equations Under Small Depth Assumption

In this article, we study the asymptotic degrees of freedom for solutions to the primitive equation (PEs for brevity). More precisely, we will prove that the long-time behavior of solutions to PEs is determined by the set of either finite Fourier modes, line elements, or volume elements. Our results show that the long-time behavior of the PEs is determined by the baro-tropic flows that are independent of the vertical direction in ?³. This study builds upon the previous article by the author concerning the existence and uniqueness of strong solutions to the PEs in thin domains.     

Analysis and Numerical Simulation of Viscous Burgers Equation

This work is concerned with the viscous Burgers equation inside a time dependent domain. We establish theoretical and numerical analysis such as existence and uniqueness of solutions, asymptotic behavior to the energy, and numerical discretization by Finite difference and Finite element methods.     

A Smooth Embedding Domain Method Based On the Penalty Approach

It is well known that convergence of the fictitious domain formulation with boundary Lagrange multipliers is slow due to the lower global regularity of its solution. This article presents a smoothed variant of this approach which is based on a formulation in the form of a state constraint optimal control problem. The convergence rate is increased as seen from a model example.     

Analysis of the Fictitious Domain Method with an L 2-Penalty for Elliptic Problems

The L ²-penalty fictitious domain method is based on a reformulation of the original problem in a larger simple-shaped domain by introducing a discontinuous reaction term with a penalty parameter ε > 0. We first derive regularity results and some a priori estimates and then prove several error estimates. We also give several error estimates for discretization problems by the finite element and finite volume methods.     

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.