Effects of orientation and interaction of grains on coercivity for sintered NdFeB magnets

The coercivity of NdFeB magnets is determined by the coercivity of individual grains and the interaction between the grains composed of the magnets. The coercivity of individual grains and the intergrain interaction depend on the degree of the grain alignment, “tanθ type” Gaussian function is applied to describing the degree of the grain alignment. According to different coercivity mechanisms, there are different formula on the coercivity and the angular dependence of coercivity. The interaction between grains can be classified as the long-range magnetostatic interaction and the exchange-coupling interaction of neighboring grains. For the sintered magnet, the grain size is large and the grain boundaries are mostly separated by the non-magnetic phase. So, the long-range magnetostatic interaction is much stronger than the exchange coupling interaction and it makes the coercivity of the magnet composed of misaligned grains be bigger than that of the magnet composed of ideally aligned grains. The effects of coercivity of individual grains and the intergrain interactions are taken into account, and the starting field theory is in agreement with the experimental result for the coercivity of sintered NdFeB magnets. Project supported by the National Natural Science Foundation of China (Grant No. 59571017).     

Magnetic field effects on Newtonian and non-Newtonian ferrofluid flow past a circular cylinder

The changes in the flow properties under the action of electromagnetic body forces are investigated numerically for ferrofluid flow past a circular cylinder. Ferrofluid is modeled as both a Newtonian and a non-Newtonian Power-Law fluid. Magnetic forces are applied by placing magnets at different locations on the surface of the cylinder. The magnetostatic effects on the structure of the wake region, on drag reduction and on vortex formation length and frequency are shown and compared in terms of Reynolds number, interaction parameter, Power-Law index and magnet location. It is shown that the increase in the interaction parameter reduces drag for both Newtonian and non-Newtonian model. This decrease is observed to be higher for shear thinning and lower for shear thickening fluid compared to Newtonian case. It is also shown that vortex street formation in the wake region behind the cylinder may be delayed under high magnetic effects. The Strouhal number is higher for shear thinning case at both low and high Reynolds numbers, and lower for shear thickening case at high Reynolds numbers, compared to Newtonian fluid. The vortex formation frequency also decreases under the action of the magnetic field in all cases, however the vortex formation length increases. Placing the magnet towards the front region of the cylinder increases considerably the drag coefficient for both Newtonian and non-Newtonian model. This increase in drag coefficient is higher in the shear thinning fluid and lower in the shear thickening fluid compared to the Newtonian case.     

Magnetic properties and microstructure of HDDR isotropic Nd-Dy-Fe-Co-B bonded magnets with high coercivity

The effect of small amount of Co and Dy addition on the magnetic properties of HDDR isotropic Nd-Dy-Fe-Co-B bonded magnets was investigated. The experimental results show that the intrinsic coercivity H_cj and the reversible temperature coefficient of remanence of (Nd_0.65 Dy_0.35)_12.5-(Fe_0.9Co_0.1)₈₁B_6.5 magnet were 1.53 MA·m^-1(19.3 kOe) and -0.059%/°C (25–155°C), respectively. The high coercivity and low temperature coefficient of the magnet are due to the enhanced anisotropy field, increased Curie temperature and improved microstructure by Dy and Co addition.     

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．     

One approach to a magnetostatic problem for bodies with inclusions in an inhomogeneous external field

A direct magnetostatic problem for magnets with a finite-size inclusion is considered in an integrodifferential form. An approach is used that, under certain conditions, reduces the problem to a single integral equation on a two-dimensional manifold-the inclusion surface. As an important illustrative example, finite formulas are derived to compute the resulting field of a magnetic half-space with a spherical cavity in an arbitrary external field.     

Asymptotic analysis of simultaneous damages in spatial Boolean models

A notion of the positive spatial association is introduced in this paper to analyze spatial dependence of Boolean models with the focus on estimating the long-range spatial dependence. The explicit tail estimates for probabilities of simultaneous damage to two distant spatial regions are obtained using the regular variation method, and the long-range spatial covariance for the Boolean models with heavy-tailed grains is shown to decay at the power-law rate that is smaller than the tail decay rate of grains. Examples and applications to spatial reliability modeling are also discussed.     

On the McKean-Vlasov Limit for Interacting Diffusions

For a system of diffusions in a domain of R^d with long-range weak interaction the behavior of the associated empirical process is studied. Under mild growth and smoothness assumptions on the drift and diffusion coefficients such as coercivity and monotonicity conditions the law of large numbers and the propagation of chaos are proved. Existence and uniqueness of the weak solution to the McKean - Vlasov equation and the associated non-linear martingale problem are investigated.     

Vector potential formulation for magnetostatics and modelling of permanent magnets

A very general magnetostatic problem involving inhomogeneousanisotropic materials filling irregular regions and with mixedboundary conditions is formulated in terms of magnetic vectorpotential. Some restrictions inherent to the introduction ofa vector potential become apparent and additional conditionsfor the uniqueness of the vector potential naturally arise.The modelling of permanent magnets is introduced in both thevector potential and the field formulations by weakening theregularity requirements on the source term. The vector potentialformulation is also shown to be equivalent to a penalized formulationwidely used in numerical applications.     

Electromagnetic forces in high field magnet coils

There has been considerable study in recent years of the mechanical effects of the electromagnetic forces in large high field magnet coils. The problem of supporting the electromagnetic forces acting on the windings has become a limiting factor in the design of such magnets. Caldwell has already obtained a mathematical model representing the stress distribution in magnet windings but a number of simplifying assumptions were made in deriving the equations. This paper checks the accuracy of this method by comparing it with homogeneous thick cylinder theory which involves the calculation of stresses by solving the Timoshenko stress equations. Thus values of the circumferential stress are compared for two different coil configurations and reasonable agreement is obtained.     

A magnet spring model

The paper discusses an elementary spring model representing the motion of a magnet suspended from the ceiling at one end of a vertical spring which is held directly above a second magnet fixed on the floor. There are two cases depending upon the north–south pole orientation of the two magnets. The attraction or repelling force induced by the magnets follow an inverse quartic law and thus we are led to a nonlinear model suitable for discussion in a beginning differential equations course. Spring models are common fare in such courses, but usually only linear models with simple sinusoidal forcing are considered. The resultant model is autonomous and thus an energy approach permits a full phase portrait of the resultant motions in the phase plane. These phase portraits show interesting behaviour of the system, reinforcing one's natural physical intuition. The computer algebra system Mathematica is employed here, although almost any other system would suffice. Such a system permits almost effortless calculations and can generate the graphics needed to thoroughly investigate the model.     

Permanent magnet system of alpha magnetic spectrometer

Alpha magnetic spectrometer (AMS) is the first large magndtic spectrometer in space. Its precursor flioht was completed successfully in June 1998. The key part of AMS is the permanent magnet system, which was built by the lnstitute of Electric Engineering, the institute of High Energy Physics and the Chinese Academy of Launch Vehicle Technology. This system includes a permanent magnet made of high grade NdFeB and a support structure. The unique design of the permanent magnet based on the magic ring fulfills the severe requirements on the magnetic field leakage and the dipole moment for space experiments. The permanent magnet weighs about 2 tons, and provides a geometric acceptance of 0.6 m² · sr and an analyzing powerBL ² of 0.135 T · m². It works up to 40°C without demagnetization. The main structure is a thin double shell, which undergoes the strong magnetic force and torque of the permanent magnet, as well as the large load during launching and landing. The permanent magnet system fulfills the requirements from AMS, and satisfies the strict safety standards of NASA.     

Estimation of penalty parameters for symmetric interior penalty Galerkin methods

This paper presents computable lower bounds of the penalty parameters for stable and convergent symmetric interior penalty Galerkin methods. In particular, we derive the explicit dependence of the coercivity constants with respect to the polynomial degree and the angles of the mesh elements. Numerical examples in all dimensions and for different polynomial degrees are presented. We show the numerical effects of loss of coercivity.     

Two-dimensional magnetic solitons and thermodynamics of quasi-two-dimensional magnets

The article reviews two-dimensional magnetic solitons in a classical weakly-anisotropic Heisenberg magnets. Topological classification, structure, dynamical properties and thermodynamical contribution of 2D solitons to response functions of the magnet are discussed. Based on effective equations of motion we calculated the soliton contribution to the dynamical structure factor of ferromagnets and antiferromagnets both for localized topological solitons and magnetic vortices.     

各向异性双晶和三晶体晶界附近应力场分析

采用率相关晶体滑移有限元程序对不同取向晶粒构成的双晶体和三晶体在晶界和三晶交点附近的应力集中特性进行了计算分析．双晶体的数值结果表明,不同取向晶粒的晶界附近应力场具有较大的应力梯度,存在应力集中现象;三晶体由于晶界之间的相互作用使得三晶交点可能造成应力集中地,也可能不造成应力集中,晶界附近的应力结构与双晶体晶界附近的应力结构亦不相同,这主要取决于三个晶粒的晶体取向．对双晶体和三晶体的分析说明,不同取向的晶粒具有不同的变形规律．因此研究金属材料的损伤、断裂问题至少需要采用晶体滑移理论从细观的角度分析不同晶粒之间的相互作用．     

热扩散和电场对风沙流发展过程的影响

建立了描述在来流水平风场和由于地表热扩散产生的垂向风场联合作用下的风沙流发展过程的基本方程．通过定量分析表明:地表热扩散和风沙电场对风沙流发展过程的影响十分明显．在此基础上,给出地表热扩散和风沙电场对风沙流中的沙粒跃移轨迹、输沙率以及风沙流达到充分发展的时间等的影响规律．     

2014“高教社杯”全国大学生数学建模竞赛颁奖仪式在海军航空工程学院青岛校区举行

<正>2014年12月20日,2014"高教社杯"全国大学生数学建模竞赛颁奖仪式暨工作会议在海军航空工程学院青岛校区隆重举行。全国大学生数学建模竞赛组委会主任、复旦大学李大潜院士,海军航空工程学院政委龚理华少将,山东省教育厅宋承祥副厅长,高等教育出版社林金安副总编辑,中国科学院袁亚湘院士,全国大学生数学建模竞赛组委会副主任、专家组组长、浙江大学陈叔平教授等160余人出席了颁奖仪式。颁奖仪式由全国组委会秘书长、清华大学谢金星教授主持。颁奖仪式上,学院龚理华     

2014全国大学生数学建模竞赛“高教社杯”获奖感言

<正>尊敬的各位领导、老师,亲爱的同学们:大家好!室外数九隆冬,室内春意阵阵。在这温暖如春的颁奖仪式现场,我的内心既高兴又激动。让我高兴的是,我能参加"高教社杯"全国大学生数学建模竞赛;让我激动的是,自己能作为获奖者的代表在此发言。我是来自信阳师范学院数学与信息科学学院2012级的学生程双泽,我们能获得今年的高教社杯,是和无数人的关心和帮助分不开的。所以我想真诚地对他们说声-谢谢。感谢全国数学建模竞赛组委会及所有为数学建模付出心血的领导和老师们,是你们为全国广大学子提供了一个展现自我风采的平     

纳米单晶与多晶铜薄膜力学行为的数值模拟研究

通过对不同温度下单晶薄膜的拉伸性能的分子动力学模拟，从微观角度揭示了温度效应对材料性能的影响. 结果表明温度效应对材料的变形机理影响很大.0K温度下由于缺乏热激活软化的影响, 粒子运动所受到的阻碍较大, 薄膜的强度较高, 塑性变形主要来自于粒子的短程滑移.温度升高，粒子的热运动加剧，屈服强度降低, 塑性变形将主要来自于大范围的位错长程扩展.多晶薄膜的模拟结果表明, 虽然其晶粒形状较为特殊, 但是它仍然遵循反Hall-Petch关系.在模拟过程中，侧向应力最大值比拉伸方向应力的最大值滞后出现.位错只会从晶界产生并向晶粒内部传播，晶粒间界滑移是多晶薄膜塑性变形的主要来源.     

Creep damage modeling of a polycrystalline material

A polycrystalline material is investigated under creep conditions within the framework of continuum micromechanics. Geometrical 3D model of a polycrystalline microstructure is represented as a unit cell with grains of random crystallographical orientation and shape. Thickness of the plains, separating neighboring grains in the unit cell, can have non-zero value. Obtained geometry assigns a special zone in the vicinity of grain boundaries, possessing unordered crystalline structure. A mechanical behavior of this zone should allow sliding of the adjacent grains. Within the grain interior crystalline structure is ordered, what prescribes cubic symmetry of a material. The anisotropic material model with the orthotropic symmetry is implemented in ABAQUS and used to assign elastic and creep behavior of both the grain interior and grain boundary material. Appropriate parameters set allows transition from the orthotropy to the cubic symmetry for the grain interior. Material parameters for the grain interior are identified from creep tests for single crystal copper. Model parameters for the grain boundary are set from the physical considerations and numerical model validation according to the experimental data of the grain boundary sliding in a polycrystalline copper [2]. As the result of analysis representative number of grains and grain boundary thickness in the unit cell are recommended. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)