A unified perspective on two-dimensional quantum turbulence and plasticity
AbstractWe 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.
List of papers
|Paper I: Vortex clustering and universal scaling laws in two-dimensional quantum turbulence. Audun Skaugen and Luiza Angheluta. Physical Review E 93, 032106 (2016). DOI: 10.1103/PhysRevE.93.032106. The article is inckuded in the thesis. Also available at https://doi.org/10.1103/PhysRevE.93.032106|
|Paper II: Velocity statistics for nonuniform configurations of point vortices. Audun Skaugen and Luiza Angheluta. Physical Review E 93, 042137 (2016). DOI: 10.1103/PhysRevE.93.042137. The article is inckuded in the thesis. Also available at https://doi.org/10.1103/PhysRevE.93.042137|
|Paper III: Origin of the inverse energy cascade in two-dimensional quantum turbulence. Audun Skaugen and Luiza Angheluta. Physical Review E 95, 052144 (2017). DOI: 10.1103/PhysRevE.95.052144. The article is inckuded in the thesis. Also available in DUO http://urn.nb.no/URN:NBN:no-65759|
|Paper IV: Dislocation dynamics and crystal plasticity in the phase-field crystal model. Audun Skaugen, Luiza Angheluta and Jorge Viñals. Physical Review B 97, 054113 (2018). DOI: 10.1103/PhysRevB.97.054113. The article is inckuded in the thesis. Also available in DUO http://urn.nb.no/URN:NBN:no-68582|
|Paper V: Mesoscale model of dislocation motion and crystal plasticity. Audun Skaugen, Luiza Angheluta and Jorge Viñals. Submitted to Physical Review Letters, arXiv:1807.10245. Published as: Separation of Elastic and Plastic Timescales in a Phase Field Crystal Model. Phys. Rev. Lett. 121, 255501. DOI: 10.1103/PhysRevLett.121.255501. The paper is included in the thesis. Also available in DUO http://hdl.handle.net/10852/66180|