audunska

• Skogvoll, Vidar; Angheluta, Luiza; Skaugen, Audun; Salvalaglio, Marco & Viñals, Jorge (2022). A phase field crystal theory of the kinematics of dislocation lines. Journal of the Mechanics and Physics of Solids. ISSN 0022-5096. 166, s. 1–19. doi: 10.1016/j.jmps.2022.104932. Fulltekst i vitenarkiv Vis sammendrag

  We introduce a dislocation density tensor and derive its kinematic evolution law from a phase field description of crystal deformations in three dimensions. The phase field crystal (PFC) model is used to define the lattice distortion, including topological singularities, and the associated configurational stresses. We derive an exact expression for the velocity of dislocation line determined by the phase field evolution, and show that dislocation motion in the PFC is driven by a Peach–Koehler force. As is well known from earlier PFC model studies, the configurational stress is not divergence free for a general field configuration. Therefore, we also present a method (PFCMEq) to constrain the diffusive dynamics to mechanical equilibrium by adding an independent and integrable distortion so that the total resulting stress is divergence free. In the PFCMEq model, the far-field stress agrees very well with the predictions from continuum elasticity, while the near-field stress around the dislocation core is regularized by the smooth nature of the phase-field. We apply this framework to study the rate of shrinkage of an dislocation loop seeded in its glide plane.

• Skogvoll, Vidar; Skaugen, Audun; Angheluta, Luiza & Viñals, Jorge (2021). Dislocation nucleation in the phase-field crystal model. Physical review B (PRB). ISSN 2469-9950. 103(1), s. 014107-1–014107-8. doi: 10.1103/PhysRevB.103.014107. Fulltekst i vitenarkiv Vis sammendrag

  We use the phase-field crystal model to study nucleation of edge dislocations in two dimensions under an applied stress field. A dislocation dipole nucleates under the applied stress, consistent with Burgers vector conservation. The phase field correctly accounts for elastic energy storage prior to nucleation and for dissipative relaxation during the nucleation event. We show that a lattice incompatibility field is a sensitive diagnostic of the location of the nucleation event and of the Burgers vector and slip direction of the dislocations that will be nucleated above threshold. A direct calculation of the phase-field energy accurately correlates with the nucleation event, as signaled by the lattice incompatibility field. We show that a Schmid-like criterion concerning the resolved stress at the nucleation site correctly predicts the critical nucleation stress. Finally, we present preliminary results for a three-dimensional, bcc lattice. The phase field allows direct computation of the lattice incompatibility tensor for both dislocation lines and loops.

• Skogvoll, Vidar; Skaugen, Audun & Angheluta, Luiza (2021). Stress in ordered systems: Ginzburg-Landau-type density field theory. Physical review B (PRB). ISSN 2469-9950. 103(22). doi: 10.1103/PhysRevB.103.224107. Fulltekst i vitenarkiv Vis sammendrag

  We present a theoretical method for deriving the stress tensor and elastic response of ordered systems within a Ginzburg-Landau-type density field theory in the linear regime. This is based on spatially coarse graining the microscopic stress which is determined by the variation of a free energy with respect to mass displacements. We find simple expressions for the stress tensor for phase field crystal models for different crystal symmetries in two and three dimensions. Using tetradic product sums of reciprocal lattice vectors, we calculate elastic constants and show that they are directly related to the symmetries of the reciprocal lattices. We also show that except for bcc lattices there are regions of model parameters for which the elastic response is isotropic. The predicted elastic stress-strain curves are verified by numerical strain-controlled bulk and shear deformations. Since the method is independent of a reference state, it extends also to defected crystals. We exemplify this by considering an edge and screw dislocation in the simple cubic lattice.

• Rønning, Jonas; Skaugen, Audun; Hernández-García, Emilio; López, Cristóbal & Angheluta, Luiza (2020). Classical analogies for the force acting on an impurity in a Bose-Einstein condensate. New Journal of Physics. 22. doi: 10.1088/1367-2630/ab95de. Fulltekst i vitenarkiv Vis sammendrag

  We study the hydrodynamic forces acting on a small impurity moving in a two-dimensional Bose–Einstein condensate at non-zero temperature. The condensate is modelled by the damped-Gross Pitaevskii (dGPE) equation and the impurity by a Gaussian repulsive potential coupled to the condensate. For weak coupling, we obtain analytical expressions for the forces acting on the impurity, and compare them with those computed through direct numerical simulations of the dGPE and with the corresponding expressions for classical forces. For non-steady flows, there is a time-dependent force dominated by inertial effects and which has a correspondence in the Maxey–Riley theory for particles in classical fluids. In the steady-state regime, the force is dominated by a self-induced drag. Unlike at zero temperature, where the drag force vanishes below a critical velocity, at low temperatures the impurity experiences a net drag even at small velocities, as a consequence of the energy dissipation through interactions of the condensate with the thermal cloud. This dissipative force due to thermal drag is similar to the classical Stokes' drag. There is still a critical velocity above which steady-state drag is dominated by acoustic excitations and behaves non-monotonically with impurity's speed.

• Skaugen, Audun; Angheluta, Luiza & Vinals, Jorge (2018). Separation of Elastic and Plastic Timescales in a Phase Field Crystal Model. Physical Review Letters. ISSN 0031-9007. 121(25), s. 255501-01–255501-05. doi: 10.1103/PhysRevLett.121.255501. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Skaugen, Audun; Angheluta, Luiza & Vinals, Jorge (2018). Dislocation dynamics and crystal plasticity in the phase-field crystal model. Physical review B (PRB). ISSN 2469-9950. 97(5). doi: 10.1103/PhysRevB.97.054113. Fulltekst i vitenarkiv Vis sammendrag

  A phase-field model of a crystalline material is introduced to develop the necessary theoretical framework to study plastic flow due to dislocation motion. We first obtain the elastic stress from the phase-field crystal free energy under weak distortion and show that it obeys the stress-strain relation of linear elasticity. We focus next on dislocations in a two-dimensional hexagonal lattice. They are composite topological defects in the weakly nonlinear amplitude equation expansion of the phase field, with topological charges given by the standard Burgers vector. This allows us to introduce a formal relation between the dislocation velocity and the evolution of the slowly varying amplitudes of the phase field. Standard dissipative dynamics of the phase-field crystal model is shown to determine the velocity of the dislocations. When the amplitude expansion is valid and under additional simplifications, we find that the dislocation velocity is determined by the Peach-Koehler force. As an application, we compute the defect velocity for a dislocation dipole in two setups, pure glide and pure climb, and compare it with the analytical predictions. © 2018 American Physical Society

• Skaugen, Audun & Angheluta, Luiza (2017). Origin of the inverse energy cascade in two-dimensional quantum turbulence. Physical Review E (PRE). ISSN 2470-0045. 95(5). doi: 10.1103/PhysRevE.95.052144. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Skaugen, Audun & Angheluta, Luiza (2016). Vortex clustering and universal scaling laws in two-dimensional quantum turbulence. Physical Review E (PRE). ISSN 2470-0045. 93(3). doi: 10.1103/PhysRevE.93.032106. Fulltekst i vitenarkiv
• Skaugen, Audun & Angheluta, Luiza (2016). Velocity statistics for nonuniform configurations of point vortices. Physical Review E (PRE). ISSN 2470-0045. 93(4). doi: 10.1103/PhysRevE.93.042137. Fulltekst i vitenarkiv

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• Skaugen, Audun (2018). A unified perspective on two-dimensional quantum turbulence and plasticity. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  We investigate two-dimensional quantum turbulence and plasticity from a common mathematical perspective, focusing on topological defects as the most important degrees of freedom. Quantum turbulence features quantized vortices which tend to cluster into statistically self-similar structures as a result of the inverse energy cascade. Similarly, the strong interaction between dislocations in single crystals under load leads to characteristic patterns, suggesting a common way of studying the complex nonequilibrium dynamics of the two fields. In the field of turbulence, we benefit from a fruitful interplay between models at different scales, from microscopic quantum field theory, via the semiclassical Gross–Pitaevskii equation, to the more phenomenological point vortex models of larger systems, leading to novel statistical signatures of the self-similar structure of vortices in two-dimensional quantum turbulence. In plasticity, the phase-field crystal model plays a similar mesoscale role to the Gross–Pitaevskii equation in quantum turbu-lence, but there are some problems in applying it to realistic crystals. We attempt to alleviate some of these problems through a more detailed understanding of the elastic and plastic behavior of the phase-field crystal.

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