# Plotting topological defects with VectorPlot

I have been trying to create a table with the graphs of the lowest winding number topological defects that can appear in a nematic Liquid Crystal.

That is what I have been able to do so far:

ρ[x_, y_] := Sqrt[x^2 + y^2];
Θ[x_, y_] := ArcTan[x, y];

OptStrSt = {{Red, AbsoluteThickness[3]}};

points = Join[{#, -1.} & /@ Range[-1, 1, .2], {#, 1.} & /@
Range[-1, 1, .2]];

Table[VectorPlot[{Cos[Θ[x, y] q],
Sin[Θ[x, y] q]}, {x, -1, 1}, {y, -1, 1},
VectorPoints -> 10, StreamStyle -> OptStrSt,
StreamPoints -> {points, Automatic, 2}, StreamScale -> None,
Frame -> False, VectorStyle -> OptVecSt, VectorScale -> 0.06,
ImageSize -> Medium], {q, 1/2, 2, 1/2}]


And this is the output:

Now, I would like to have more uniform distribution of streamlines. I am happy with their thickness and the fact that they are continuous across the $x$-axes, but I would need the streamlines to extend to those regions that are white at the moment.

Any ideas?

Also, it would be nice to be able to use manipulate to vary the following settings:

• number of vectors,
• density of streamlines,
• thickness of vectors and streamlines,

but, especially for the second one, I have no idea how to proceed. Thanks in advance!

• You could change the branch cut to be on the positive $x$-axis by using VectorPlot[{Cos[(Θ[-x, -y] + π) q], Sin[(Θ[-x, -y] + π) q]}, ...] and then switch to StreamPoints -> Coarse. i.stack.imgur.com/ZdHY1.png – user484 Jun 30 '16 at 15:44
• This is definitely helpful, thanks! – usumdelphini Jun 30 '16 at 15:48
• It doesn't give the desired result for q=1/2 though. Any ideas? – usumdelphini Jun 30 '16 at 16:11
• Isn't q=1/2 the leftmost image? It looks fine to me, how is it different from the desired result? i.stack.imgur.com/ZdHY1.png – user484 Jun 30 '16 at 16:38
• P.S. In retrospect instead of changing VectorPlot it would be better to just change Θ[x_, y_] := ArcTan[-x, -y] + π. – user484 Jun 30 '16 at 16:40