3维Ginzburg-Landau方程涡旋集的结构

在假定外加磁场|h_(ex)|=o(|lnε|)以及涡旋能量以|lnε|阶爆破的前提下,借助几何测度论工具,分析了三维Ginzburg-Landau超导方程涡旋集的结构．粗略地说,它是由线段构成的一维可求长集合．     

磁弹性耦合效应引起的铁磁直杆磁场中振动频率的改变

基于磁弹性广义变分原理和Hamilton原理,对处于外加磁场中的软铁磁体,建立了磁弹性动力学理论模型．分别通过关于铁磁杆磁标势和弹性位移的变分运算,获得了包含磁场和弹性变形的所有基本方程,并给出描述磁弹性耦合作用的磁体力和磁面力．采用摄动技术和Galerkin方法,将所建立的磁弹性理论模型用于外加磁场中铁磁直杆的振动分析．结果表明,由于磁弹性耦合效应,外加磁场将对铁磁杆的振动频率产生影响:当铁磁杆的振动位移沿着磁场方向时,其频率减小并出现磁弹性屈曲失稳;当铁磁杆的振动位移垂直于磁场方向时,其频率将会增大．理论模型能够很好地解释已有实验观测的振动频率改变现象．     

再论高温超导体的E-j关系

对高温超导体磁弛豫尚未达到平衡态和达到平衡态的情况,考虑了磁通热激活的正、反向跃迁(反向跃迁即为从低势能向高势能跃迁),在Bean模型下,严格求解了外加磁场与外加电流时的高温超导板的E-j关系.理论指出电流产生的磁场方向与外加磁场方向相同的板的一侧lnE-lnj只有正曲率;相反的一侧在特定的磁场范围lnE-lnj在同一条曲线上可以呈现正、负曲率,并给以理论证明.还讨论了出现正、负曲率对临界电流密度、外加磁场和温度的要求.     

Ginzburg-Landau方程极小能量解存在性的新证明

对R~2上带有外磁场或一般流源场的Ginzburg-Landau方程组,借助于Hardy型不等式,利用直接变分的方法重新证明了其极小能量解的存在性,且该解满足Coulomb规范.     

3维Ginzburg-Landau方程涡旋集的结构

在假定外加磁场|hex|=o(|lnε|)以及涡旋能量以|lnε|阶爆破的前提下,借助几何测度论工具,分析了三维Ginzburg-Landau超导方程涡旋集的结构.粗略地说,它是由线段构成的一维可求长集合.     

考虑磁通流动效应的超导薄膜基底结构界面断裂行为研究北大核心CSCD

超导薄膜是一种采用化学涂层制备而成的多层薄膜结构,作为性能优越的导电功能结构材料,其载流能力与结构完整性直接相关.在超导薄膜制备过程中,超导层与金属基底之间的界面裂纹很难避免.因此,在载流运行过程中,由于外磁场的存在,这类界面裂纹的强度问题成为关键.为此,该文针对超导薄膜结构,以磁通量子穿透薄膜理论和线弹性断裂理论为基础,建立了研究超导层与基底界面裂纹强度问题的解析模型.深入分析了外加磁场作用下界面裂纹强度问题,得到了超导磁通流动对裂纹尖端应力场和能量释放率的影响.结果表明:磁通流动速度越大,界面裂纹尖端处应力越大且能量释放率越大,这将导致界面更容易发生裂纹破坏.该文所得结果有助于分析相关的界面裂纹问题.     

论高温超导体的E-j关系 *

在高温超导体中 ,磁弛豫接近平衡态情况下 ,外加电流时 ,考虑了磁通热激活的正、反向跃迁 (反向跃迁即为从低势能向高势能跃迁 ) ,严格求解了在外加磁场与外加电流下的高温超导板的E-j关系 ,指出lnE-lnj曲线存在正曲率 ,并与其他几种理论模型进行了比较 .还对j→0时 ,ρ是趋向于零还是有限值的问题进行了讨论.     

横向磁场中真空电弧的腐蚀角

实验发现,在横向磁场中,由大量连续引发的真空电弧在同一阴极表面上所产生的合腐蚀图案,形成一个以一固定触发点为顶点的角度(腐蚀角),该角度的大小与外加磁场有关,与电弧电流无关(直至70A)。 本文提出了一个物理模型,以解释横向磁场中真空电弧的腐蚀角。按照此模型理论上算出的腐蚀角与外磁场的函数关系定量地与报道的实验结果相符合。     

朝向产热或吸热伸展平面的MHD驻点流动

分析了微极流体朝向加热伸展平面的磁流体动力学(MHD)驻点流动,考虑了粘性耗散和内部产热/吸热对流动的影响.讨论了指定表面温度(PST)和指定热通量(PHF)两种情况,采用同伦分析方法(HAM)求解边界层流动和能量方程.通过图表的显示,研究了感兴趣物理量的变化.注意到高伸展参数时解的存在与外加应用磁场密切相关.     

目标流形为Heisenberg群能量极小映射的逆Poincardé不等式

研究目标流形为Heisenberg群能量极小映射的性质,得到关于能量极小映射的逆Poincaré不等式.     

ESTIMATES OF LOWER CRITICAL MAGNETIC FIELD AND VORTEX PINNING BY INHOMOGENEITIES IN TYPE Ⅱ SUPERCONDUCTORS

The effect of an applied magnetic field on an inhomogeneous superconductor is studied and the value of the lower critical magnetic field Hc1 at which superconducting vortices appear is estimated. In addition, the authors locate the vortices of local minimizers, which depends on the inhomogeneous term a(x).     

Stochastic dynamo in critical situations

Based on the functional method of consecutive approximations, we consider the problem of magnetic field excitation (stochastic dynamo) by a random velocity field with a finite temporal correlation radius. In critical situations, in the first (diffusion) approximation, the Lyapunov characteristic parameter of the magnetic field energy vanishes. This implies the absence of structure formation (clustering) in realizations of the magnetic field in that approximation. Critical situations occur in problems of magnetic field diffusion in an equilibrium thermal and random pseudoequilibrium and acoustic (in the absence of dissipation) velocity fields. The sign of the Lyapunov characteristic parameter in the second-order approximation determines the possibility of clustering of the magnetic field energy. We show that energy clustering does not occur in a thermal velocity field. In the cases of pseudoequilibrium and acoustic velocity fields, clustering occurs with probability one, i.e., in almost every realization. We evaluate the characteristic time for clustering to be established.     

Quantized planary dynamics in orthogonal magneto-electrostatic fields

At the first quantization level, we deal with the planary dynamics of a charged scalar evolving in static orthogonal magnetic and electric fields. Working in a relativistic approach, we get the quantum eigenstates and the energy spectrum exhibiting a non-linear dependence on the exterior fields and the particle momentum parameter. Analyzing the generalized Landau-type energy levels, we point out a shift of the Larmor pulsation, due to the electrostatic field and derive a critical induction-energy spectrum. The same has been done for strong magnetic fields and a compulsory relation between the particle momentum and the electric field intensity has been obtained. For quasi-on-shell particles, moving in either strong or weak magnetic field, we derive the completely possible momentum spectrum. It turns out that, in extremely faint electrostatic fields, it yields the same momentum quantization.     

Neutral Fermion with a Magnetic Moment in External Electromagnetic Fields

The interaction between a massive neutral fermion with a static (spin) magnetic dipole moment and an external electromagnetic field is described by the Dirac–Pauli equation. Exact solutions of this equation are obtained along with the corresponding energy spectrum for an axially symmetric external magnetic field and for some centrally symmetric electric fields. It is shown that the spin–orbital interaction of a neutral fermion with a magnetic moment determines both the characteristic properties of the quantum states and the fermion energy spectrum. It is found that (1) the discrete energy spectrum of a neutral fermion depends on the projection of the fermion spin on a certain quantization axis, (2) the ground energy level of a fermion in these electric fields as well as the energy levels of all bound states with a fixed value of the quantum number characterizing the projection of the fermion spin in the electric field E = er is degenerate and the degeneration order is countably infinite, and (3) the energy spectra of neutral fermions and antifermions with spin magnetic moments are symmetric in centrally symmetric fields. Bound states of a neutral fermion with a magnetic moment in an external electric field do exist even if the Dirac–Pauli equation does not explicitly contain the term with the fermion mass. In addition, in centrally symmetric electric fields, there exist a countably infinite set of pairs of isolated charge-conjugate zero-energy solutions of the Dirac–Pauli equation.     

ESTIMATE OF THE UPPER CRITICAL FIELD AND CONCENTRATION FOR SUPERCONDUCTOR

The effect of an applied magnetic field on an inhomogeneous superconductor is studied and the value of the upper critical magnetic field Hc3 at which superconductivity can nucleate is estimated. In addition, the authors locate the concentration of the order parameter, which depends on the inhomogeneous term a(x). Unlikely to the homogeneous case, the order parameter may concentrate in the interior of the superconducting material, due to the influence of the inhomogeneous term a(x).     

A (2+1)-dimensional fermion in the Coulomb and magnetic field backgrounds

In the problem of a two-dimensional hydrogen-like atom in a magnetic field background, we construct quasi-classical solutions and the energy spectrum of the Dirac equation in a strong Coulomb field and in a weak constant homogeneous magnetic field in 2+1 dimensions. We find some “exact” solutions of the Dirac and Pauli equations describing the “spinless” fermions in strong Coulomb fields and in homogeneous magnetic fields in 2+1 dimensions. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 1, pp. 105–118, April, 1999.     

Nucleation of bulk superconductivity close to critical magnetic field

We consider the two-dimensional Ginzburg–Landau functional with constant applied magnetic field. For applied magnetic fields close to the second critical field HC₂ and large Ginzburg–Landau parameter, we provide leading order estimates on the energy of minimizing configurations. We obtain a fine threshold value of the applied magnetic field for which bulk superconductivity contributes to the leading order of the energy. Furthermore, the energy of the bulk is related to that of the Abrikosov problem in a periodic lattice. A key ingredient of the proof is a novel L^∞-bound which is of independent interest.     

Moving domain walls in magnetic nanowires

This paper investigates the reversal of magnetic nanowires via a perturbation argument from the static case. We consider the gradient flow equation of the micromagnetic energy including the nonlocal stray field energy. For thin wires and weak external magnetic fields we show the existence of travelling wave solutions. These travelling waves are almost constant on the cross section and can thus be seen as moving domain walls of a type called transverse wall.     

Combined free and forced convection effects on the magnetohydrodynamic flow through a porous channel

The combined effect of free and forced convection on the flow of an electrically conducting liquid between two horizontal parallel porous walls has been studied. There is a transverse magnetic field at the walls. The equations of motion and energy have been solved by a small perturbation method. The flow phenomenon has been characterized by the non-dimensional numbers like R (cross-flow Reynolds number), K (Brinkman number), G (Grashof number), M (magnetic number) and the effects of these numbers on the velocity and temperature fields, induced magnetic field, electric field and shearing stress at the walls have been studied.     

矩形铁磁板的磁弹性弯曲与稳定性

本文对于在外加磁场中的矩形软铁磁弹性板的磁弹性弯曲现象进行了定量模拟;建立了能反映磁弹性相互耦合作用的数值计算程序;揭示了铁磁板弯曲变形与磁(场)力的非线性特征关系,并据此讨论了磁弹性失稳临界磁场随倾斜角变化的规律.