2016/04/29 by David J. B. Lloyd, Lloyd, David J. B., Arnd Scheel +1
Computer Science · Materials Science · Physics and Astronomy · #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS) #Solidification and crystal growth phenomena #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1604.08766
openalex publication_date 2016/04/29 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We study grain boundaries between striped phases in the prototypical\nSwift-Hohenberg equation. We propose an analytical and numerical far-field-core\ndecomposition that allows us to study existence and bifurcations of grain\nboundaries analytically and numerically using continuation techniques. This\ndecomposition overcomes problems with computing grain boundaries in a large\ndoubly periodic box with phase conditions. Using the spatially conserved\nquantities of the time-independent Swift-Hohenberg equation, we show that\nsymmetric grain boundaries must select the marginally zig-zag stable stripes.\nWe find that as the angle between the stripes is decreased, the symmetric grain\nboundary undergoes a parity-breaking pitchfork bifurcation where dislocations\nat the grain boundary split into disclination pairs. A plethora of asymmetric\ngrain boundaries (with different angles of the far-field stripes either side of\nthe boundary) is found and investigated. The energy of the grain boundaries is\nthen mapped out. We find that when the angle between the stripes is greater\nthan a critical angle, the symmetric grain boundary is energetically preferred\nwhile when the angle is less than the critical angle, the grain boundaries\nwhere stripes on one side are parallel to the interface are energetically\npreferred. Finally, we propose a classification of grain boundaries that allows\nus to predict various non-standard asymmetric grain boundaries.\n