We investigate the properties of two distinct disordered systems: the two-species predator-prey Lotka-Volterra model with rate variability, and an elastic line model to simulate vortex lines in type-II superconductors. We study the effects of intrinsic demographic variability with inheritance in the reaction rates of the Lotka-Volterra model via zero-dimensional Monte Carlo simulations as well as two-dimensional lattice simulations. Individuals of each species are assigned inheritable predation efficiencies during their creation, leading to evolutionary dynamics and thus population-level optimization. We derive an effective subspecies mean-field theory and compare its results to our numerical data. Furthermore, we introduce environmental variability via quenched spatial reaction-rate randomness. We investigate the competing effects and relative importance of the two types of variability, and find that both lead to a remarkable enhancement of the species densities, while the aforementioned optimization effects are essentially neutral in the densities. Additionally, we collected extinction time histograms for small systems and find a marked increase in the stability of the populations against extinction due to the presence of variability. We employ an elastic line model to investigate the steady-state properties and non-equilibrium relaxation kinetics of magnetic vortex lines in disordered type-II superconductors. To this end, we developed a versatile and efficient Langevin molecular dynamics simulation code, allowing us to do a careful study of samples with or without vortex-vortex interactions or disorder allows us to disentangle the various complex relaxational features present in this system and investigate their origin. In particular, we compare disordered samples with randomly distributed point defects versus correlated columnar defects. We extract two-time quantities such as the mean-square displacement, the height and density correlations, to investigate the relaxation kinetics of the system of flux lines. Additionally, we compare the steady-state mean velocity and gyration radius as a function of an external driving current in the presence of point-like and columnar disorder. We validate our simulation algorithm by matching our results against a previously-used Monte Carlo algorithm, verifying that these microscopically quite distinct methods yield similar results even in out-of-equilibrium settings. / Ph. D.

We numerically investigate the dynamical properties of driven magnetic flux vortices in disordered type-II superconductors for a variety of temperatures, types of disorder and sample thicknesses. We do so with the aid of Langevin molecular dynamics simulations of a coarsegrained elastic line model of flux vortices in the extreme London limit. Some original findings of this doctoral work include the discovery that flux vortices driven through random point disorder show simple aging following drive quenches from the moving lattice state to both the pinned glassy state (non-universal aging) and near the critical depinning region (universal aging); estimations of experimentally consistent critical scaling exponents for the continuous depinning phase transition of vortices in three dimensions; and an estimation of the boundary curve separating regions of linear and non-linear electrical transport for flux lines driven through planar defects via novel direct measurements of vortex excitations. / Ph. D. / The works contained in this dissertation were undertaken with the goal of better understanding the dynamics of driven magnetic flux lines in type-II superconductors under different conditions of temperature, material defects and sample thickness. The investigations were conducted with the aid of computer simulations of the flux lines which preserve physical aspects of the system relevant to long-time dynamics while discarding irrelevant microscopic details. As a result of this work, we found (among other things) that when driven by electric currents, flux lines display very different dynamics depending on the strength of the current. When the current is weak, the material defects strongly pin the flux lines leaving them in a disordered glassy state. Sufficiently high current overpowers the defect pinning and results in the flux lines forming into a highly ordered crystal-like structure. In the intermediate critical current regime, the competing forces become comparable resulting in very large fluctuations of the flux lines and a critical slowing down of the flux line dynamics.

We investigate the relaxation properties of two distinct systems: magnetic vortex lines in disordered type-II superconductors and charge carriers in the Coulomb glass in disordered semiconductors. We utilize an elastic line model to simulate magnetic flux lines in disordered type-II superconductors by performing Langevin molecular dynamics simulations. We study the non-equilibrium relaxation properties of flux lines in the presence of uncorrelated point-like disorder or extended linear defects analyzing the effects of rapid changes in the system's temperature or magnetic field on these properties. In a previously-equilibrated system, either the temperature is suddenly changed or the magnetic field is abruptly altered by adding or removing random flux lines to or from the system. One-time observables such as the radius of gyration are measured to characterize steady-state properties, and two-time correlation functions such as the vortex line height autocorrelations are computed to investigate the relaxation dynamics in the aging regime and therefore distinguish the complex relaxation features that result from the different types of disorder in the system. This study allows us to test the sensitivity of the system's non-equilibrium aging kinetics to the selection of initial states and to make closer contact to experimental setups. Furthermore, we employ Monte Carlo simulations to study the relaxation properties of the two-dimensional Coulomb glass in disordered semiconductors and the two-dimensional Bose glass in type-II superconductors in the presence of extended linear defects. We investigate the effects of adding non-zero random on-site energies from different distributions on the properties of the correlation-induced Coulomb gap in the density of states and on the non-equilibrium aging kinetics highlighted by the autocorrelation functions. We also probe the sensitivity of the system's equilibrium and non-equilibrium relaxation properties to instantaneous changes in the density of charge carriers in the Coulomb glass or flux lines in the Bose glass. / Ph. D.