Ordering processes and pattern formation in systems far from equilibrium

In this work, we present our investigations into two different systems, both far from equilibrium. We first present the relaxation and ordering processes in magnetic skyrmion systems. This is followed by a study of the behavior of many species interacting on a spatially heterogeneous lattice. Magnetic skyrmions have been a subject of great interest in recent years. They have been proposed to be at the heart of next-generation computing and information storage devices. One interesting feature of magnetic skyrmions is the presence of the non-dissipative Magnus force. The Magnus force causes the skyrmions to be deflected from their direction of motion. In this work, we examine the effect the strength of this Magnus force has on the late-time ordering behavior of magnetic skyrmions. We show that the late-time ordering also shows enhanced relaxation with an increase in the Magnus force. We also studied the behavior of magnetic skyrmions when confined to a narrow channel. We show that, like before, the Magnus force helps the system order faster while experiencing a constant drive. Interestingly, when the drive was periodic, the Magnus force inhibited the relaxation in the system. Interacting populations have been a topic of scientific interest since the late eighteenth century. We studied the effect of spatial heterogeneity on a two-dimensional lattice. Using cyclic predator-prey interaction schemes, we numerically simulated the effect of asymmetric predation rates inside "habitats." We show that, due to the non-linearity of the system, the species that had a chance to escape predation did not see the largest benefit from this change. Instead, the predator of this prey saw the largest benefit from this change. The material on skyrmion systems is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award Number DE-SC0002308. The population dynamics research was sponsored by the Army Research Office and was accomplished under Grant No. W911NF17-1-0156.