Steady-State MHD Flows in Nozzles with an External Longitudinal Magnetic Field

Steady-state MHD flows in channels of the nozzle type in the presence of an external longitudinal magnetic field can be divided into two significantly different classes. Subcritical flows, in which the Alfvén velocity calculated from the longitudinal magnetic field is less than the plasma velocity, have mainly the same properties as flows in a transverse magnetic self-field and their quantitative characteristics depend only slightly on the longitudinal magnetic field strength. Supercritical flows with the opposite inequality for the velocities correspond to strong longitudinal magnetic field. The main difference is the transitions between different forms of energy (kinetic, thermal, and electromagnetic). The present study contains a classification of possible flows, namely, sub- and supercritical and sub-, super-, and transonic flows with respect to the fast and slow magnetosonic and Alfvén velocities. Examples of these flows are given. The effect of the problem parameters on the flow properties is investigated.     

Quasi-Periodic Solutions for the Generalized Ginzburg-Landau Equation with Derivatives in the Nonlinearity

In this paper, we discuss the existence of time quasi-periodic solutions for the generalized Ginzburg-Landau equation under periodic boundary conditions. By constructing a KAM theorem for dissipative systems with unbounded perturbations and multiple normal frequencies, we obtain a Cantorian branch of 2-dimensional invariant tori for the generalized Ginzburg-Landau equation.     

Stress State of a Soft Ferromagnetic with an Ellipsoidal Cavity in a Homogeneous Magnetic Field

The stress problem is solved for an infinite elastic magnetically soft ferromagnetic containing an ellipsoidal cavity. The body is in a homogeneous magnetic field directed along the shortest axis of the ellipsoid. The main stress-strain and magnetic characteristics of the body are determined. The stress distribution over the cavity surface is analyzed__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 3, pp. 70–78, March 2005.     

The Stress State of a Ferromagnetic with an Elliptic Crack in a Homogeneous Magnetic Field

The problem on the stress–strain state of an infinite isotropic body made of a magnetically soft material and containing an elliptic crack is considered. It is assumed that the body is under an external magnetic field perpendicular to the crack plane. The basic characteristics of the stress–strain state and the magnetic field induced are determined and their singularities near the elliptic crack are studied. Formulas are given for the stress intensity factors for the force and magnetic fields near the crack tip     

Melt Motion Due to Peltier Marking during Bridgman Crystal Growth with an Axial Magnetic Field

This paper treats a liquid-metal flow inside an electrically insulating cylinder with electrically conducting solids above and below the liquid region. There is a uniform axial magnetic field, and there is an electric current through the liquid and both solids. Since the lower liquid-solid interface is concave into the solid and since the liquid is a better electrical conductor than the adjacent solid, the electric current is locally concentrated near the centerline. The return to a uniform current distribution involves a radial electric current which interacts with the axial magnetic field to drive an azimuthal flow. The axial variation of the centrifugal force due to the azimuthal velocity drives a meridional circulation with radial and axial velocities. This problem models the effects of Peltier marking during the vertical Bridgman growth of semiconductor crystals with an externally applied magnetic field, where the meridional circulation due to the Peltier current may produce important mixing in the molten semiconductor. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stress Concentration in a Soft Ferromagnetic with an Elliptic Inclusion in a Homogeneous Magnetic Field

The paper addresses a stress–strain problem for an infinite soft ferromagnetic body with an elliptic inclusion. The body is in a homogeneous magnetic field B ₀₁. The basic stress–strain characteristics and induced magnetic field in the body and inclusion are determined and their features in the neighborhood of the inclusion are studied. The magnetoelastic and Maxwell stresses are plotted against the ratio of ellipse axes and the latitude angle. Maximum stresses versus magnetic induction and mechanical and magnetic properties of the material are tabulated     

The Stress–Strain State of an Elastic Ferromagnetic Medium with an Ellipsoidal Inclusion in a Homogeneous Magnetic Field

A stress–strain problem is solved for an infinite elastic magnetically soft medium with an ellipsoidal inclusion in an external magnetic field. The main characteristics of the stress–strain state and induced magnetic fields in the medium and the inclusion are determined and their distribution over the surface of the inclusion is analyzed     

Convection in a Porous Medium with Variable Gravity Field and Magnetic Field Effects

The problem of convection in a variable gravity field with magnetic field effect is studied using methods of linear instability theory and non-linear energy theory. Then, the accuracies of both the linear instability and global non-linear energy stability thresholds are tested using a three-dimensional simulation. The strong stabilizing effect of gravity field and magnetic field is shown. Moreover, the results support the assertion that the linear theory is very accurate in predicting the onset of convective motion, and thus regions of stability.     

Stress State of a Transversely Isotropic Ferromagnetic with an Elliptic Crack in a Homogeneous Magnetic Field

The magnetoelastic stress-strain problem for a transversely isotropic ferromagnetic body with an elliptical crack in the isotropy plane is solved explicitly. The body is in an external magnetic field perpendicular to the isotropy plane. The magnetic field induces elastic strains and an internal magnetic field in the body. The main characteristics of stress-strain state and induced magnetic field are determined and their features in the neighborhood of the crack are analyzed. Formulas for the stress intensity factors of the mechanical and magnetic fields near the crack tip are presented__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 48–59, January 2005.     

Asymptotic Behavior of Minimizers for the Ginzburg-Landau Functional with Weight. Part I

(Accepted July 23, 1996)     

The Ginzburg–Landau Functional with Vanishing Magnetic Field

Archive for Rational Mechanics and Analysis - We study the infimum of the Ginzburg–Landau functional in a two dimensional simply connected domain and with an external magnetic field allowed...     

Asymptotic Behavior of Minimizers for the Ginzburg-Landau Functional with Weight. Part II

(Accepted July 23, 1996)     

Deformation of an Inviscid Magnetizable Liquid Drop in a Non-Stationary Magnetic Field

Fluid Dynamics - Variation in the shape of a magnetizable liquid drop suspended in another immiscible magnetizable liquid in the presence of a non-stationary uniform magnetic field is theoretically...     

Localization and approximation of attractors for the Ginzburg-Landau equation

This paper studies the long-term behavior of solutions to the Ginzburg-Landau partial differential equation. For each positive integerm we explicitly produce a sequence of approximate inertial manifolds _m,j ,j = 1, 2,..., of dimensionm and associate with each manifold a thin neighborhood into which the orbits enter with an exponential speed and in a finite time. Of course this neighborhood contains the universal attractor which embodies the large time dynamics of the equations. The thickness of these neighborhoods decreases with increasingm for a fixed orderj; however, for a fixedm no conclusion can be made about the thickness of the neighborhoods associated to two differentj's. The neighborhoods associated to the manifolds localize the universal attractor and provide computabie large time approximations to solutions of the Ginzburg-Landau equation.     

A Stable Rapidly Oscillating Periodic Solution for an Equation with State-Dependent Delay

We exhibit a differential delay equation with state-dependent delay

$$\begin{aligned} x'(t) = f(x(t - h(x_t))) \end{aligned}$$

for which the familiar non-increasing “oscillation speed” is defined and for which there exists an asymptotically stable rapidly oscillating periodic solution.

     

Similarity Solution of Unsteady Boundary Layer Equations with a Magnetic Field

The unsteady laminar incompressible boundary layer flow of an electricallyconducting fluid in the stagnation region of two-dimensional and axisymmetricbodies with an applied magnetic field has been studied. The boundary layerequations which are parabolic partial differential equations with threeindependent variables have been reduced to a system of ordinary differential equations by using suitable transformations and then solved numerically using a shooting method. Here, we have obtained new solutions which are solutions of both the boundary layer and Navier-Stokes equations.     

Forces Exerted on a Plate in a Magnetic Fluid Located in a Magnetic Field with Exponential Inhomogeneity

The hydrostatic force exerted on a nonmagnetic body in the form of an extended flat plate immersed in a magnetic fluid occupying a vessel with plane walls parallel to the plate surfaces is measured. The vessel is located in a nonuniform magnetic field whose absolute value decreases exponentially in the direction normal to the plate. Approximate models which take into account, in particular, perturbations of the field induced by the fluid and the nonlinearity of the law of fluid magnetization are developed to describe this force theoretically.     

电感式磨粒监测传感器的磁场均匀性研究

在介绍电感式磨粒监测传感器结构原理的基础上 ,提出可采用检测线圈内部磁场均匀性的方法来弥补颗粒运动轨迹和流型变化带来的检测误差 ,以提高检测灵敏度 .通过分析不同几何尺寸的线圈中轴线上磁场的变化情况 ,并借助直螺线管的径向和轴向公式 ,对轴外磁场均匀性进行了探讨 .数学模型和优化结果表明 :在检测传感器线圈中部范围内为非匀强磁场 ,且呈非线性变化 ,细长管磁场相对均匀 ;当选取 R/ L <0 .2 ,磁场在线圈轴向长度范围内 ,径向在90 %范围内可近似看作均匀磁场 .所得结果可以确定传感器检测区域的磁场均匀性范围 ,为设计电感式磨粒监测传感器提供依据 .     

Plane Sources of Waves in the Presence of Magnetic Field

In this paper the generation of harmonic waves in an elastic magneticmaterial, which is a perfect conductor of electricity, isconsidered. It has been assumed that an infinite body is subjected tothe action of an initially constant magnetic fieldH = (H,0,0) and in the plane ax+by=0 acts a source ofdistortion. It has been shown that this source may produce bothtransverse and longitudinal waves and each of them consists of two parts,which propagate with different speeds. The amplitudes and speeds in dependence on theangle between the direction of wave propagation and the magnetic fieldintensity H have been discussed.