Note

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2.1.4 Plotting a nematic field

This example shows how to visualize a nematic tensor field \(\boldsymbol Q = S(\boldsymbol n \otimes \boldsymbol n - \mathbb{1}/2)\). The field shown here contains a \(+\frac12\) defect at the origin, where the director \(\boldsymbol n\) rotates by \(\pi\) around the defect and the nematic order \(S\) vanishes.

Nematic field with a $+1/2$ defect
from pde import CartesianGrid, Tensor2Field

grid = CartesianGrid([[-2, 2], [-2, 2]], 24)

order = "tanh(2 * sqrt(x**2 + y**2))"  # nematic order vanishing at the defect
q_xx = f"0.5 * {order} * x / sqrt(x**2 + y**2)"
q_xy = f"0.5 * {order} * y / sqrt(x**2 + y**2)"
field = Tensor2Field.from_expression(grid, [[q_xx, q_xy], [q_xy, f"-({q_xx})"]])

field.plot(kind="nematic", title="Nematic field with a $+1/2$ defect")

Total running time of the script: (0 minutes 0.321 seconds)