No abstract

Abstract. Some new statistics are proposed to test the uniformity of random samples in the multidimensional unit cube [0, 1] d (d ≥ 2). These statistics are derived from number-theoretic or quasi-Monte Carlo methods for measuring the discrepancy of points in [0, 1] d . Under the null hypothesis that the samples are independent and identically distributed with a uniform distribution in [0, 1] d , we obtain some asymptotic properties of the new statistics. By Monte Carlo simulation, it is found that the finite-sample distributions of the new statistics are well approximated by the standard normal distribution, N (0, 1), or the chi-squared distribution, χ 2 (2). A power study is performed, and possible applications of the new statistics to testing general multivariate goodness-of-fit problems are discussed.

Chi-square statistic, mean and covariance structures, EM algorithm, maximum likelihood, multivariate normal distribution, two-level structural equation models,

The study of skyrmion/antiskyrmion motion in magnetic materials is very important in particular for the spintronics applications. In this work, we study the dynamics of isolated skyrmions and antiskyrmions in frustrated magnets driven by magnetic field gradient, using the Landau-Lifshitz-Gilbert simulations on the frustrated classical Heisenberg model on the triangular lattice. A Hall-like motion induced by the gradient is revealed in bulk system, similar to that in the well-studied chiral magnets. More interestingly, our work suggests that the lateral confinement in nanostripes of the frustrated system can completely suppress the Hall motion and significantly speed up the motion along the gradient direction. The simulated results are well explained by Thiele theory. It is demonstrated that the acceleration of the motion is mainly determined by the Gilbert damping constant, which provides useful information for finding potential materials for skyrmion-based spintronics.

No abstract