Extremal stochastic integrals: a parallel between max-stable processes and α-stable processes

We construct extremal stochastic integrals of a deterministic function with respect to a random Fréchet () sup-measure. The measure is sup-additive rather than additive and is defined over a general measure space , where is a deterministic control measure. The extremal integral is constructed in a way similar to the usual stable integral, but with the maxima replacing the operation of summation. It is well-defined for arbitrary , and the metric metrizes the convergence in probability of the resulting integrals.This approach complements the well-known de Haan's spectral representation of max-stable processes with Fréchet marginals. De Haan's representation can be viewed as the max-stable analog of the LePage series representation of stable processes, whereas the extremal integrals correspond to the usual stable stochastic integrals. We prove that essentially any strictly stable process belongs to the domain of max-stable attraction of an Fréchet, max-stable process. Moreover, we express the corresponding Fréchet processes in terms of extremal stochastic integrals, involving the kernel function of the stable process. The close correspondence between the max-stable and stable frameworks yields new examples of max-stable processes with non-trivial dependence structures.This research was partially supported by a fellowship of the Horace H. Rackham School of Graduate Studies at the University of Michigan and the NSF Grant DMS-0505747 at Boston University.     

Analysis of the magnetic bubble collapse method

In the bubble collapse technique the domain wall mobility is evaluated by measuring the shortest time for which a magnetic bubble collapses. The way in which this evaluation should be carried out is discussed.     

Magnetic force microscopy characterization of heat and current treated Fe40Ni38Mo4B18 amorphous ribbons

The domain structure of a magnetostrictive Fe₄₀Ni₃₈Mo₄B₁₈ amorphous ribbon has been studied using magnetic force microscopy (MFM) at room temperature. First, the evolution of the magnetic domain patterns as a function of the annealing temperature has been investigated. In samples heat treated at 250 and 450 °C for 1 h, a transformation from 90° to 180° domain wall has been clearly observed, while the sample heat treated at 700 °C for 1 h showed a magnetic phase fixed by the crystalline anisotropy. Additionally, the evolution of the magnetic domain structure by applying a DC current was recorded by the MFM technique. For current annealed samples at 1 A for 1, 30 and 60 min, a transformation between different domain patterns has been observed. Finally, in samples treated by the current annealing method under simultaneous stress, an increase of the annealing time gives rise to a different magnetic structure arising from the development of transverse magnetic anisotropy.     

Field-driven creep motion of a composite domain wall in a Pt/Co/Pt/Co/Pt multilayer wire

We have studied the field-driven motion of a pair of coupled Bloch domain walls in a perpendicular magnetic anisotropy Pt/Co/Pt/Co/Pt multilayer Hall bar. The nucleation of an isolated but coincident pair of walls in the two Co layers, observed by Kerr microscopy, took place at an artificial nucleation site created by Ga⁺ ion irradiation. The average velocity v of the wall motion was calculated from time-resolved magnetotransport measurements at fixed driving field H, where the influence of the extraordinary Hall effect leads to the observation of voltages at the longitudinal resistance probes. We observed a good fit to the scaling relation lnv∝H^−1/4, consistent the motion of a single 1-dimensional wall moving in a 2-dimensional disordered medium in the creep regime: the two walls are coupled together into a 1-dimensional composite object.     

The influence of wire width on the charge distribution of transverse domain walls and their stray field interactions

We present here a numerical study of the magnetostatic charge distribution of transverse Néel type domain wall in permalloy nanowires. The calculations indicate that not only is the distribution highly non-uniform within a given transverse wall but it also varies dramatically with respect to the wire width. The implications of this for magnetostatic domain wall pinning are analyzed by considering the stray field interaction between a wall and another extended magnetic body for a particular domain wall chirality, where two distinct depinning mechanisms are observed depending on the wire width.     

Magnetoresistance due to domain wall bulging

The effect of bulging of domain wall (DW) on the magnetoresistance (MR) is investigated. With taking into account the auto-correlation between the points of the interface, one can formulate the mobility within the relaxation time approximation scheme. The results show that the bulging of DW, evaluated with the commonly accepted magnetic parameters for typical ferromagnetic materials of Co, Fe and Ni, has a countable role into the MR.     

Low-scale leptogenesis and the domain wall problem in models with discrete flavor symmetries

We propose a new mechanism for leptogenesis, which is naturally realized in models with a flavor symmetry based on the discrete group A₄$A_4$, where the symmetry breaking parameter also controls the Majorana masses for the heavy right-handed (RH) neutrinos. During the early universe, for T?TeV$T?\text{TeV}$, part of the symmetry is restored, due to finite temperature contributions, and the RH neutrinos remain massless and can be produced in thermal equilibrium even at temperatures well below the most conservative gravitino bounds. Below this temperature the phase transition occurs and they become massive, decaying out of equilibrium and producing the necessary lepton asymmetry. Unless the symmetry is broken explicitly by Planck-suppressed terms, the domain walls generated by the symmetry breaking survive till the quark–hadron phase transition, where they disappear due to a small energy splitting between the A₄$A_4$ vacua caused by the QCD anomaly.     

A conservative parallel difference method for 2-dimension diffusion equation

In this paper, a conservative parallel difference scheme, which is based on domain decomposition method, for 2-dimension diffusion equation is proposed. In the construction of this scheme, we use the numerical solution on the previous time step to give a weighted approximation of the numerical flux. Then the sub-problems with Neumann boundary are computed by fully implicit scheme. What is more, only local message communication is needed in the program. We use the method of discrete functional analysis to give the proof of the unconditional stability and second-order convergence accuracy. Some numerical tests are given to verify the theory results.     

相容连续Domain的不变性

引入了Scott相容连续映射与商相容Domain等概念,研究了Scott相容连续映射保局部基与保waybelow序及保局部基与保紧元之间的关系,证明了相容连续Domain或相容代数Domain在保局部基的Scott相容连续满映射下保持不变.