Effects of 3D sampling in (k, t)-space on temporal qualities of dynamic MRI

3D (kx, ky, t)-space analysis is invoked to provide insights into dynamic magnetic resonance imaging (DMRI) with arbitrary k-space sampling trajectories. The effects of 3D sampling in (kx, ky, t) are analyzed theoretically and verified with computer simulation. The analyses show that a 3D sampling pattern that is more isotropic in (kx, ky, t)-space and denser around the (kx=0, ky=0, t)-line likely results in improved temporal qualities of DMRI. The isotropy of 3D sampling is quantified using Voronoi 3D cells and the isoperimetric theorem. This 3D sampling perspective provides a theoretical framework for understanding the temporal qualities of various DMRI methods.     

爆轰加载下弹塑性固体Richtmyer-Meshkov流动的扰动增长规律

研究了冲击波加载弹塑性材料扰动自由面的动力学演化过程,分析了高能炸药爆轰驱动时初始扰动与材料性质对扰动增长的影响.研究结果表明:初始扰动的振幅与波长之比越高,扰动越易增长,强度越高的材料扰动增长幅度越小;扰动增长被抑制时,尖钉的最大振幅与增长速度无量纲数之间存在线性近似关系,进一步理论分析表明尖钉的振幅增长因子与加载压力、初始扰动形态和材料强度有关,该理论关系作为扰动增长规律的线性近似在一定范围内适用于多种金属材料.     

On the Structure of the Mixing Zone at an Unstable Contact Boundary

The interface between two media of different densities (contact boundary) moving with an acceleration directed from the less dense medium to the more dense one is unstable (Rayleigh–Taylor instability) [1, 2]. The initial perturbations of the interface grow indefinitely and, as a result, a medium mixing zone growing with time is formed at the interface. The structure of such a mixing zone at gas–gas and gas–liquid interfaces is discussed on the basis of laboratory experiments on shock tubes of various types. It is concluded that the regions of turbulent and laminar flows are combined in the mixing zone.     

Metastability at the displacement of a fluid in a Hele-Shaw cell

The displacement of silicon oil by air (with a constant flow rate) in a radial Hele-Shaw cell has been studied experimentally. The initially circular air-oil interface is perturbed controllably by a harmonic law. The sub-sequent evolution of such perturbations has been examined. It has been shown that there are three characteristic regions in the displacement process: stable, metastable (where perturbation can either disappear or grow), and unstable. It has been found that the width of the metastable region increases with the amplitude of perturbation. The results quantitatively confirm the theoretical values of the binodal and spinodal (boundaries of the metastable region) previously predicted for this morphological transition.     

Effects of Hall Currents and Gyroviscosity on the Instability of a Self-Gravitating Stratified Plasma

The instability in a horizontal layer of a partially ionized self gravitating plasma has been studied to include simultaneously the effects of Hall currents, viscosity and finiteness of Larmor radius (FLR). The ambient magnetic field is assumed to be uniform and vertical. Proper solutions have been obtained through the variational methods for a semi-infinite plasma in which the density has an exponential gradient along the vertical. The dispersion relation obtained has been solved numerically and it is found that the growth rate of unstable perturbations decreases with the effects of viscosity, neutral gas friction and FLR. The influence of effects of viscosity, neutral gas friction and FLR are consequently stabilizing. It is found that the Hall currents have a destabilizing influence as the growth rate is found to increase with this effect.     

Parametric excitation of spin waves in ferromagnets by longitudinal pumping localized in space

The equations of motion for the slowly varying complex amplitudes of spin waves parametrically excited by a localized pumping magnetic field have been derived. A solution of these equations satisfying given boundary and initial conditions has been obtained. The energy dissipated by spin waves decreases with the pumping intensity beyond a certain pumping power, which can be termed the regeneration threshold. The losses vanish and change sign at the instability threshold. Both thresholds depend heavily on the linear dimension L of the pumping zone, increasing with decreasing L. Owing to the regeneration process, the dissipation length of spin waves increases without bound as the pumping power approaches the instability threshold. Consequently, perturbations of a uniform state due to the boundary penetrate throughout the pumping zone, regardless of the dimension L. As a result, the full pattern of parametric instability is strongly affected by the zone boundary: 1) the spatial distribution of wave amplitudes becomes nonuniform everywhere inside the zone; 2) the amplitude growth rate in the unstable regime decreases at all points when perturbations due to the boundary reach these points; 3) the instability threshold is independent of the spin-wave frequency offset from the parametric resonance frequency. The calculated minimum instability threshold as a function of the bias magnetic field (the “butterfly” curve) changes shape with L, in agreement with the available experimental data. Zh. éksp. Teor. Fiz. 111, 199–219 (January 1997)     

高精度有限差分法模拟Kelvin-Helmholtz不稳定性

WENO有限差分格式有较高的分辨精度,适合复杂流场的计算,在国际上被广泛采用。本文利用WENO有限差分格式求解2维守恒型欧拉方程,实现了对无粘流体中Kelvin-Helmholtz不稳定性的数值模拟。速度剪切方向采用周期边界条件;扰动增长方向采用嵌边出流边界条件,一个不稳定波长分布64个网格。数值模拟给出的扰动幅值线性增长率与线性稳定性分析给出的结果很好符合,显示了该格式的有效性和精度。数值模拟给出了清晰的密度等值线,表明该方法还具有较好的界面变形捕捉能力。     

高精度有限差分法模拟Kelvin-Helmholtz不稳定性

 WENO有限差分格式有较高的分辨精度,适合复杂流场的计算,在国际上被广泛采用。本文利用WENO有限差分格式求解2维守恒型欧拉方程,实现了对无粘流体中Kelvin-Helmholtz不稳定性的数值模拟。速度剪切方向采用周期边界条件;扰动增长方向采用嵌边出流边界条件,一个不稳定波长分布64个网格。数值模拟给出的扰动幅值线性增长率与线性稳定性分析给出的结果很好符合,显示了该格式的有效性和精度。数值模拟给出了清晰的密度等值线,表明该方法还具有较好的界面变形捕捉能力。     

The instability of streaming Walters' viscoelastic fluid B′ in porous medium

The instability of streaming Walters' elastico-viscous fluid B in porous medium is considered. The case of two uniform streaming fluids separated by a horizontal boundary is considered. It is found that for the special case when perturbations in the direction of streaming are ignored, the system can be stable or unstable, depending upon kinematic viscoelasticity, medium porosity and medium permeability, for both potential unstable and potentially stable configurations. In every other direction, a minimum value of wave-number has been found and the system is unstable for all wave-numbers greater than this minimum wave number.     

分析半透明单晶生长传热过程的边界元方法

论文发展了一个能求解带相变运动界面非定常传热和非线性热物理特性问题的双倒易边界元方法。数值模拟了半透明单晶生长中热过程的一个例子。由于方法是纯边界积分方法,计算量与计算内存都大大减少。获得了单晶生长过程瞬态温度场分布和固液相界面形状时间推进的一些结果。     

Two-dimensional perturbations in a scalar model for shear banding

We present an analytical study of a toy model for shear banding, without normal stresses, which uses a piecewise linear approximation to the flow curve (shear stress as a function of shear rate). This model exhibits multiple stationary states, one of which is linearly stable against general two-dimensional perturbations. This is in contrast to analogous results for the Johnson-Segalman model, which includes normal stresses, and which has been reported to be linearly unstable for general two-dimensional perturbations. This strongly suggests that the linear instabilities found in the Johnson-Segalman can be attributed to normal stress effects.     

Excitation of slow EM waves in a waveguide having a thin, annularplasma sheet

A thin, annular plasma sheet in a waveguide slows down the phase velocity of electromagnetic modes in a plasma density window for frequencies below the electron cyclotron frequency via Cerenkov interaction. At lower densities, the plasma is not effective enough to reduce the phase velocity of the EM wave below c. At higher densities the plasma expels the radiation field, leading to enhancement of phase velocity. The lowest mode having azimuthal number l=0 is most unstable. The radial mode having amplitude maximum at r=a, viz the plasma boundary, has the largest growth rate     

磁化等离子体中静电漂移波和剪切阿耳芬波的非线性耦合

本文采用Hasegawa-Wakatani方程组研究磁化等离子体中静电漂移波和剪切阿耳芬波的非线性耦合。求得非线性方程组的偶极涡旋解。这些解属于本性电磁涡旋,对应的扰动磁场和纵向电流在涡旋边界上是连续的。 关键词：     

Kink stability of self-similar solutions of scalar field in 2 + 1 gravity

The kink stability of self-similar solutions of a massless scalar field with circular symmetry in 2 + 1 gravity is studied, and found that such solutions are unstable against the kink perturbations along the sonic line (self-similar horizon). However, when perturbations outside the sonic line are considered, and taking the ones along the sonic line as their boundary conditions, we find that non-trivial perturbations do not exist. In other words, the consideration of perturbations in the whole spacetime limits the unstable mode of the perturbations found along the sonic line, and the kink instability rises because of the incomplete treatment of the problem. As a result, the critical solution for the scalar collapse remains critical even after the kink perturbations are taken into account.     

Linear instability of planar shear banded flow

We study the linear stability of planar shear banded flow with respect to perturbations with wave vector in the plane of the banding interface, within the nonlocal Johnson-Segalman model. We find that perturbations grow in time, over a range of wave vectors, rendering the interface linearly unstable. Results for the unstable eigenfunction are used to discuss the nature of the instability. We also comment on the stability of phase separated domains to shear flow in model H.     

Hydromagnetic Stability of a Self-Gravitating Composite Plasma in the Presence of Finite Larmor Radius

The hydromagnetic stability of a self-gravitating composite plasma has been studied to include the effects of ion viscosity and the finiteness of the ion Larmor radius. The whole medium is embedded in a uniform horizontal magnetic field. The F. L. R. effects have been included through the stress tensor. An explicit solution for a semi-infinite plasma of finite depth and with an exponential density variation along the vertical is obtained by means of a variational principle characterizing the problem. Numerical calculations show that the influence of the effects of ion viscosity and F. L. R. is to reduce the growth rate of unstable perturbations. On the other hand the effects of neutral gas collisions have been found to be both stabilizing as well as destabilizing.     

Scattering of electromagnetic wave by perfect electromagnetic conductor (PEMC) sphere placed in chiral media

A theoretical investigation has been carried out for electromagnetic waves scattering from a perfect electromagnetic conductor (PEMC) sphere which is placed in chiral media. The formulation of the problem is realized by expanding the incident as well as the scattered electromagnetic fields in terms of left circularly polarized (LCP) and right circularly polarized (RCP) waves. By applying the boundary conditions at the chiral-PEMC interface, eight simultaneous equations are generated, which yield the scattering coefficients associated with the Left and Right electromagnetic waves. The relative contribution of Co-polarized and Cross-polarized components of fields to the calculations of scattering cross-section is presented. The effect of admittance parameter and the effect of chirality parameter in cases of lossless, lossy permittivity and lossy permeability on Co and Cross components of scattering cross sections are observed. The results are also compared with available published literatures which are in good agreement.     

A moving boundary model motivated by electric breakdown: II. Initial value problem

An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be formulated as a Laplacian growth model regularized by a ‘kinetic undercooling’ boundary condition. Using this model we study both the linearized and the full nonlinear evolution of small perturbations of a uniformly translating circle. Within the linear approximation analytical and numerical results show that perturbations are advected to the back of the circle, where they decay. An initially analytic interface stays analytic for all finite times, but singularities from outside the physical region approach the interface for t→∞, which results in some anomalous relaxation at the back of the circle. For the nonlinear evolution numerical results indicate that the circle is the asymptotic attractor for small perturbations, but larger perturbations may lead to branching. We also present results for more general initial shapes, which demonstrate that regularization by kinetic undercooling cannot guarantee smooth interfaces globally in time.     

The wave flow effect on a plane boundary between vacuum and an optical medium with a quasi-zero refractive index

A boundary problem in which a plane electromagnetic wave is reflected and refracted at a plane boundary of a semi-infinite optical medium with a quasi-zero refractive index has been solved. Such a medium has a random refractive index taking values in an interval from zero to some finite value less than unity. It means that the concept of a sharp interface between two media loses its meaning, the boundary of the medium becomes inhomogeneous, and laws of reflection and refraction of light become non-Fresnelian. Formulas for non-Fresnelian amplitudes of reflection and refraction have been derived. It is shown that a surface wave arises near the boundary of a medium with a quasi-zero refractive index. The wave propagates both on the inside and outside of the boundary.