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Skyrmion dynamics in a chiral magnet driven by periodically varying spin currents
In this work, we investigated the spin dynamics in a slab of chiral magnets
induced by an alternating (ac) spin current. Periodic trajectories of the
skyrmion in real space are discovered under the ac current as a result of the
Magnus and viscous forces, which originate from the Gilbert damping, the spin
transfer torque, and the -nonadiabatic torque effects. The results are
obtained by numerically solving the Landau-Lifshitz-Gilbert equation and can be
explained by the Thiele equation characterizing the skyrmion core motion
Central Limit Theorems for Supercritical Superprocesses
In this paper, we establish a central limit theorem for a large class of
general supercritical superprocesses with spatially dependent branching
mechanisms satisfying a second moment condition. This central limit theorem
generalizes and unifies all the central limit theorems obtained recently in
Mi{\l}o\'{s} (2012, arXiv:1203:6661) and Ren, Song and Zhang (2013, to appear
in Acta Appl. Math., DOI 10.1007/s10440-013-9837-0) for supercritical super
Ornstein-Uhlenbeck processes. The advantage of this central limit theorem is
that it allows us to characterize the limit Gaussian field. In the case of
supercritical super Ornstein-Uhlenbeck processes with non-spatially dependent
branching mechanisms, our central limit theorem reveals more independent
structures of the limit Gaussian field
Central Limit Theorems for Super-OU Processes
In this paper we study supercritical super-OU processes with general
branching mechanisms satisfying a second moment condition. We establish central
limit theorems for the super-OU processes. In the small and crtical branching
rate cases, our central limit theorems sharpen the corresponding results in the
recent preprint of Milos in that the limit normal random variables in our
central limit theorems are non-degenerate. Our central limit theorems in the
large branching rate case are completely new. The main tool of the paper is the
so called "backbone decomposition" of superprocesses
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