Construction of Equilibrium Magnetic Vector Potentials

In [9] we introduced the notion of equilibrium surface current JdS_x on the closed C smooth surfaces in R ³ as a generalization of electric solenoid, and proved their existence. We here show an algorithm for JdS_x starting from a given surface current J dS_x on .     

Nonlinear Evolution of Magnetic Islands in the Magnetopause Curent Sheet

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Magnetic susceptibilities of orthopyroxenes in the Frantz Isodynamic separator

Frantz Isodynamic Separator was calibrated with substances of known magnetic susceptibilities. From the calibration graph, magnetic susceptibilities of the orthopyroxenes were deduced. The investigated orthopyroxenes ranged in composition from En₈₇Fs₁₃ to En₅₁Fs₄₉ and varied in magnetic susceptibilities from 12·18 to 54·49 × 10^?6 e.m.u./gram at 30° C. Magnetic susceptibilities were found to decrease with increase in the En content. A graph drawn with current strengths and the compositions of the orthopyroxenes shows a linear relationship between them.     

Semiclassical Pseudodifferential Calculus and the Reconstruction of a Magnetic Field

We give a procedure for reconstructing a magnetic field and electric potential from boundary measurements given by the Dirichlet to Neumann map for the magnetic Schrödinger operator in R ⁿ , n ≥ 3. The magnetic potential is assumed to be continuous with L ^∞ divergence and zero boundary values. The method is based on semiclassical pseudodifferential calculus and the construction of complex geometrical optics solutions in weighted Sobolev spaces.     

磁拱的运动学无力场

本文首先推导了完全导电流体内运动学磁拱无力场的基本方程，接着考虑了静态解和不定常相似性解．     

Multipolarons in a Constant Magnetic Field

The binding of a system of N polarons subject to a constant magnetic field of strength B is investigated within the Pekar–Tomasevich approximation. In this approximation, the energy of N polarons is described in terms of a non-quadratic functional with a quartic term that accounts for the electron–electron self-interaction mediated by phonons. The size of a coupling constant, denoted by α, in front of the quartic term is determined by the electronic properties of the crystal under consideration, but in any case it is constrained by 0 < α < 1. For all values of N and B, we find an interval α _N,B <  α <  1 where the N polarons bind in a single cluster described by a minimizer of the Pekar–Tomasevich functional. This minimizer is exponentially localized in the N-particle configuration space ${\mathbb{R}^{3N}}$ .     

Magnetic Susceptibility of a Diluted Ising Magnet

Theoretical and Mathematical Physics - for the Ising model with nonmagnetic dilution, we consider a method for constructing the “pseudochaotic” impurity distribution based on the...     

Effective Dynamics of a Magnetic Vortex in a Local Potential

We study a simplified mean field model of superconductor dynamics in the presence of impurities or for variable superconductor depth. This model is given by the gradient-flow version of the Ginzburg-Landau equations (Gorkov-Eliashberg equations) with an addition of a potential term. We find a dynamical law of motion of the vortex center, involving the potential, such that for datum close to a (static) magnetic vortex the solution is close, for all times, to a magnetic vortex whose center obeys this law.     

恒磁场对刚性圆直管中脉动流的影响*

本文研究了恒磁场对于刚性圆直管中脉动流的影响,并根据现有的实验资料考虑了磁场对于血液粘度的影响,给出了恒磁场作用下刚性圆直管脉动流的分析解以及恒磁场对刚性圆直管中的流速分布、流量以及阻抗的影响的计算结果.这些结果对于深入研究磁场对于血液动力学的影响具有一定参考价值.     

磁性刚体航天器的混沌姿态运动

研究在地球万有引力场和磁场中的磁性刚体航天器在圆轨道上的混沌姿态运动。利用动量矩原理建立了系统的动力学模型。应用Melnikov方法证明了存在复杂非游荡Cantor集。分别采用时间历程、功率谱、Poincaré映射和Liapunov指数对系统动力学行为进行了数值研究。数值仿真表明,随着磁场力矩的增强,系统准周期环面破裂而出现混沌。     

Wave Propagation in a Layer of Magnetic Liquid

A linearized equation for the propagation of surface gravitational waves in a layer of magnetized liquid of finite depth is examined. The liquid is assumed to be inviscid, incompressible, and to possess magnetization properties in the absence of electrical conductivity, while the motion is assumed to be irrotational. Travelling wave solutions are obtained. The dependences of the phase and group velocities of the magnetic liquid on the magnetic parameters are studied. It is shown that for some values of the magnetic parameters there is an interval of short wavelengths for which the group velocity is negative, which indicates that the wave energy propagates in the negative direction.     

Semiclassical Spectral Series of a Helium-like Atom in a Magnetic Field

We apply the complex WKB method (the Maslov complex germ theory) to the model of two electrons in a field with a fixed center. We construct semiclassical spectral series of the Pauli operator eigenvalues in the external magnetic field with the spin–orbital and spin–spin interactions and the quadrupole moment of the nucleus taken into account. These series correspond to a new type of closed phase trajectories, the relative equilibrium positions of the corresponding classical nonintegrable system. Explicit effective formulas are derived for the fine (Zeeman effect) and the hyperfine splitting of semiclassical energy levels of a helium-like ion with an arbitrary nucleus charge Z in the entire range of the magnetic field magnitude, including the extreme cases of weak and ultrastrong fields.     

The Cauchy Problem for the Average Field Equation Describing a Model of a Magnetic Solid

We study a model of a magnetic solid treated as a system of particles with mechanical moment $\vec s,\vec s \in S^2$ , and magnetic moment $\vec \mu ,\vec \mu = \vec s$ , interacting with one another via the magnetic field, which determines variations in the mechanical moment of each particle. We study the system of integro-differential equations describing the evolution of the one-particle distribution function for this system of particles. We prove existence and uniqueness theorems for the generalized and the classical solution of the Cauchy problem for this system of equations. We also prove that the generalized solution continuously depends on the initial conditions.     

矩形永磁体磁场分布的解析表达式

从分子环流模型出发,利用毕奥-萨伐尔定理,对于仅在一个方向均匀完全充磁的矩形永磁块体,导出了其外部空间磁场分布的解析表达式．该解析式能精确描述一块至多块按极性相反并列放置时矩形永磁体外部空间的磁场分布．针对单块永磁体,还分析了磁场分布与永磁体几何尺寸之间的依赖关系,以及磁场大小随外部空间点离开永磁体表面距离之间的关系;定量分析了横向磁场的强度均匀度和分布均匀度随永磁体几何尺寸和离开永磁体表面距离的变化规律．     

Magnetic field in a turbulent conducting fluid

The problem of magnetic field in conducting turbulent, incompressible fluid is considered. The velocity of the fluid is taken to be independent of the magnetic field and is described by a Gaussian field, ‘white noise’ in time with smooth space correlation. The main result is that no fast dynamo (by which is meant almost sure exponential growth of magnetic field) can exist for an incompressible fluid when the magnetic viscosity is positive. For d = 2, sharper results are obtained; the magnetic field dies out when the magnetic viscosity is strictly positive. Furthermore, when d = 2, existence and characterization of invariant measure are given for d = 2 when the magnetic viscosity is zero. The results are compared to those discussed by Baxendale and Rosovskii in [2]     

Magnetic inelastic scattering of neutrons by a ferromagnetic crystal

This paper deals with a theoretical investigation of the energy spectrum of thermal neutrons inelastically scattered by a ferromagnetic crystal. The method of double-time temperature-dependent Green’s functions is used. Formulæ are derived for the line width and for an asymmetry parameter leading to a deviation from the Lorentzian form. The results are discussed and compar d with earlier work. Special attention is paid to the question of the deviation of the energy distribution from the purely Lorentzian form.     

Magnetic Suppression of Thermocapillary Convection in a Cylindrical Specimen

Convective flows may adversely affect the homogeneity of semiconductor crystals grown by the floating-zone method. The intensity of the convective flow can be reduced by an external magnetic field. The study simulates the convective flow in a cylindrical specimen. The mathematical model consists of the system of quasihydrodynamic (QHD) equations for a quasineutral electrically conducting fluid in an external electromagnetic field. The numerical results show how the convective flow velocities and configurations depend on the magnetic field strength.     

On the Temporal and the Spatial Kelvin-Helmholtz Instability of a Hypersonic Jet Confined by a Longitudinal Magnetic Field

Both the temporal and the spatial Kelvin-Helmholtz instability of a hypersonic jet confined by a longitudinal magnetic field are investigated. The reflection modes are calculated for a set of typical jet parameters. Analytical treatments for both temporal and spatial resonant modes, i.e., the most important reflection modes with the local maximum growth rates, are given. Various properties of the resonant modes are plotted against the jet temperature. The growth rates of the temporal and the spatial resonant modes are connected by the group velocity. The astrophysical implications of the present investigation are discussed.     

Travelling Waves with a Singularity in Magnetic Nanowires

We model the evolution of the magnetization in an infinite cylinder by harmonic map heat flow with an additional external field. Using variational methods, we prove the existence of corotationally symmetric travelling wave solutions with a moving vortex. We moreover show that for weak and strong fields the travelling waves connect the original state anti-parallel to the external magnetic field with the totally reversed state in direction of the external field. Our results match numeric simulations. For thicker wires several groups have found a reversal mode where a domain wall with a corotational symmetry and a vortex is propagating through the wire.