Stripes

    One can remove the confusion by breaking the symmetry.  The following figure shows an evolution sequence at eight times.  Add three lines on top of the same random initial condition (The average concentration is taken to be 0.5.  The initial condition is set to fluctuate randomly within 0.001 from the average), each 3D wide and having concentration C = 0.51.  The three lines provide a direction to line up the stripes.  Observe that concentration waves expand from the three lines and form “seeds” of superlattices.  These seeds grow into stripe colonies by consuming the nearby serpentine structures.

(The time unit in the figures is t.  The size of each figure is 256b´256b.  In the simulation, W and Q are taken to be 2.2 and 1, respectively)

    At t=100, when two stripe colonies meet, an irregular region emerges, reminiscent of dislocations in atomic crystals.  At t=500, well defined dislocations form.  Each dislocation moves by climbing;  the mass of a dislocation diffuses to its neighbors.  The phenomenon is captured from t=500 to t=2000.  We obtain periodic stripes in the entire calculation cell within t=4.0E4.  The present simulation suggests that serpentine structures can transform into an array of stripes if one breaks the symmetry at a coarse scale, e. g., by phopolithography.