Depinning Exponents of Thin Film Domain Walls Depend on Disorder Strength.

Domain wall dynamics in ferromagnets is complicated by internal degrees of freedom of the domain walls. We develop a model of domain walls in disordered thin films with perpendicular magnetic anisotropy capturing such features, and use it to study the depinning transition. For weak disorder, excitations of the internal magnetization are rare, and the depinning transition takes on exponent values of the quenched Edwards-Wilkinson equation. Stronger disorder results in disorder-dependent exponents concurrently with nucleation of an increasing density of Bloch lines within the domain wall.

Separation of Elastic and Plastic Timescales in a Phase Field Crystal Model.

A consistent small-scale description of plasticity and dislocation motion in a crystalline solid is presented based on the phase field crystal description. By allowing for independent mass motion and lattice distortion, the crystal can maintain elastic equilibrium on the timescale of plastic motion. We show that the singular (incompatible) strains are determined by the phase field crystal density, while the smooth distortions are constrained to satisfy elastic equilibrium. A numerical implementation of the model is presented and used to study a benchmark problem: the motion of an edge dislocation dipole in a triangular lattice. The time dependence of the dipole separation agrees with continuum elasticity with no adjustable parameters.

Origin of the inverse energy cascade in two-dimensional quantum turbulence.

We establish a statistical relationship between the inverse energy cascade and the spatial correlations of clustered vortices in two-dimensional quantum turbulence. The Kolmogorov spectrum k^{-5/3} on inertial scales r corresponds to a pair correlation function between the vortices with different signs that decays as a power law with the pair distance given as r^{-4/3}. To test these scaling relations, we propose a forced and dissipative point vortex model that captures the turbulent dynamics of quantized vortices by the emergent clustering of same-sign vortices. The inverse energy cascade developing in a statistically neutral system originates from this vortex clustering that evolves with time.

Velocity statistics for nonuniform configurations of point vortices.

Within the point-vortex model, we compute the probability distribution function of the velocity fluctuations induced by same-sign vortices scattered within a disk according to a fractal distribution of distances to the origin ∼r^{-α}. We show that the different random configurations of vortices induce velocity fluctuations that are broadly distributed and follow a power-law tail distribution P(V)∼V^{α-2} with a scaling exponent determined by the α exponent of the spatial distribution. We also show that the range of the power-law scaling regime in the velocity distribution is set by the mean density of vortices and the exponent α of the vortex density distribution.

Vortex clustering and universal scaling laws in two-dimensional quantum turbulence.

We investigate numerically the statistics of quantized vortices in two-dimensional quantum turbulence using the Gross-Pitaevskii equation. We find that a universal -5/3 scaling law in the turbulent energy spectrum is intimately connected with the vortex statistics, such as number fluctuations and vortex velocity, which is also characterized by a similar scaling behavior. The -5/3 scaling law appearing in the power spectrum of vortex number fluctuations is consistent with the scenario of passive advection of isolated vortices by a turbulent superfluid velocity generated by like-signed vortex clusters. The velocity probability distribution of clustered vortices is also sensitive to spatial configurations, and exhibits a power-law tail distribution with a -5/3 exponent.