Aggregation models with limited choice and the multiplicative coalescent

The percolation phase transition and the mechanism of the emergence of the giant component through the critical scaling window for random graph models, has been a topic of great interest in many different communities ranging from statistical physics, combinatorics, computer science, social networks and probability theory. The last few years have witnessed an explosion of models which couple random aggregation rules, that specify how one adds edges to existing configurations, and choice, wherein one selects from a “limited” set of edges at random to use in the configuration. While an intense study of such models has ensued, understanding the actual emergence of the giant component and merging dynamics in the critical scaling window has remained impenetrable to a rigorous analysis. In this work we take an important step in the analysis of such models by studying one of the standard examples of such processes, namely the Bohman‐Frieze model, and provide first results on the asymptotic dynamics, through the critical scaling window, that lead to the emergence of the giant component for such models. We identify the scaling window and show that through this window, the component sizes properly rescaled converge to the standard multiplicative coalescent. Proofs hinge on a careful analysis of certain infinite‐type branching processes with types taking values in the space of cadlag paths, and stochastic analytic techniques to estimate susceptibility functions of the components all the way through the scaling window where these functions explode. Previous approaches for analyzing random graphs at criticality have relied largely on classical breadth‐first search techniques that exploit asymptotic connections with Brownian excursions. For dynamic random graph models evolving via general Markovian rules, such approaches fail and we develop a quite different set of tools that can potentially be used for the study of critical dynamics for all bounded size rules. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 55–116, 2015     

FeCo基磁芯螺线管巨磁阻抗效应与磁芯长度关系的研究

研究了Fe₃₆Co₃₆Nb₄Si_4.8B_19.2合金薄带为磁芯的螺线管(FeCo基磁芯螺线管)的巨磁阻抗效应与磁芯长度之间的关系.研究结果表明,磁芯长度是影响FeCo基磁芯螺线管巨磁阻抗效应的重要因素.当磁芯长度小于螺线管长度时,磁芯螺线管巨磁阻抗的最大值(ΔZ/Z)_max与磁芯长度呈线性关系,其线性相关系数可以根据电磁学理论推导得到;当磁芯的长度大于螺线管的长度时,由于漏磁作用,(ΔZ/Z)_max与磁芯长度的关系偏离了线性关系,(ΔZ/Z)_max与磁芯长度的关系曲线中有一个极值点,(ΔZ/Z)_max在极值点达到最大.磁芯螺线管巨磁阻抗效应曲线的尖刺部分高度(ΔZ/Z)_T与磁芯长度的关系也有类似的极值点,(ΔZ/Z)_T在极值点达到最大值.磁芯螺线管巨磁阻抗效应曲线的尖刺部分对弱磁场敏感,受磁芯退磁场的影响明显,磁芯的退磁场与磁芯长度呈负指数关系. 关键词： 磁芯螺线管 FeCo基合金薄带 巨磁阻抗效应 磁芯长度     

Optical Super-Resonances in Mesoscale Dielectric Cenosphere: Giant Magnetic Field Generations

Resonant light scattering by mesoscale dielectric spheres has received enormous attention and found many interesting applications. The recently emerged field of Mesotronics provides novel opportunities for wavelength-scaled optics and new fundamental aspects are still being uncovered. It has recently been demonstrated that high-order Mie resonances can be excited in homogeneous low-dissipation mesoscale dielectric spheres, leading to the generation of intense magnetic fields. This article describes a simple and effective way to drastically enhance the superresonance effect. Proof-of-principle results for the first time show that yet one more novel phenomenon of increasing the intensity of the magnetic field without changing the resonant Mie size parameter of the sphere by introducing an air cavity. In such a dielectric cenosphere (from two Greek words “kenos”-hollow and “sphaira”-sphere), by correct choice of the air cavity size, it is possible to increase the intensity of the electromagnetic fields at the poles of the sphere by an order of magnitude due to increasing of the amplitude of resonant partial wave coefficient.     

基于巨磁电阻效应的多功能测量仪

利用巨磁电阻传感器设计了多功能测量仪器,实验表明该测量仪能够精确测量物体的转速和转角,直观地演示行驶车辆对地磁场的扰动.     

Effect of thermal deformation on giant magnetoresistance of flexible spin valves grown on polyvinylidene fluoride membranes

We fabricated flexible spin valves on polyvinylidene fluoride(PVDF) membranes and investigated the influence of thermal deformation of substrates on the giant magnetoresistance(GMR) behaviors. The large magnetostrictive Fe_(81)Ga_(19)(Fe Ga) alloy and the low magnetostrictive Fe_(19)Ni_(81)(Fe Ni) alloy were selected as the free and pinned ferromagnetic layers.In addition, the exchange bias(EB) of the pinned layer was set along the different thermal deformation axes α_(31) or α_(32) of PVDF. The GMR ratio of the reference spin valves grown on Si intrinsically increases with lowering temperature due to an enhancement of spontaneous magnetization. For flexible spin valves, when decreasing temperature, the anisotropic thermal deformation of PVDF produces a uniaxial anisotropy along the α_(32) direction, which changes the distribution of magnetic domains. As a result, the GMR ratio at low temperature for spin valves with EB α_(32)becomes close to that on Si, but for spin valves with EB α_(31)is far away from that on Si. This thermal effect on GMR behaviors is more significant when using magnetostrictive Fe Ga as the free layer.     

Asymptotic normality in random graphs with given vertex degrees

We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model and then, by a conditioning argument, for the simple uniform random graph with the given degree sequence. Such conditioning is standard for convergence in probability, but much less straightforward for convergence in distribution as here. The proof uses the method of moments, and is based on a new estimate of mixed cumulants in a case of weakly dependent variables. The result on small components is applied to give a new proof of a recent result by Barbour and Röllin on asymptotic normality of the size of the giant component in the random multigraph; moreover, we extend this to the random simple graph.     

LC共振型巨磁阻抗效应的研究

采用化学镀方法成功制备了自带电容构成LC共振回路的CoP/Insulator/BeCu复合结构丝. 研究了这种新型复合结构丝产生LC共振型巨磁阻抗效应的特征,长度为l_m=95 cm的复合结构丝,当驱动电流频率为LC共振频率f_r=290 MHz时,LC共振型巨磁阻抗效应为4875%,磁场灵敏度为046%/A·m^-1,大于常规复合结构丝;远离此频率时的巨 关键词： 复合结构丝 LC共振')" href="#">LC共振 等效电路模型 巨磁阻抗效应     

Theory of Electron Transport in FeRh-Based Natural Magnetic Multilayers

The electronic structure and the residual resistivity of random FeRh-based alloys in the CsCl structure are calculated from first principles. The calculations are performed for different spin structures using the tight-binding linear muffin-tin orbital method in the atomic sphere approximation. The effect of late transition-metal impurities (Pd, Rh) is taken into account by means of the coherent potential approximation generalized to inhomogeneous systems. It is shown that impurity scattering leads to giant magnetoresistance effects in qualitative agreement with experiment.     

Magnetic Properties of Permalloy/Cu-Au Multilayers

The interlayer exchange coupling and GMR effect of (permalloy/Cu _x Au_1-x )30 (Py = Ni₈₃Fe₁₇; 0.29x0.75) sputtered multilayers (MLs) were investigated. The strength of the antiferromagnetic (AF) interlayer coupling J _AF was determined from M(H) and/or R(H) curves. GMR effect and AF coupling was found in entire investigated concentration range of Cu _x Au_1-x . For x<0.65 the J _AF values at the first maximum of AF coupling (1.3t _Cu-Au1.6 nm) were smaller than 3×10^-6 J/m² and for x>0.65 J _AF increased to a value characteristic of Py/Cu MLs (J _AF10^-5 J/m²). The second maximum of AF coupling (J _AF10^-7 J/m²) was only found for x0.75 at t _Cu-Au2.6 nm.