- #1
Gerard Westendorp
I was playing with a 2D model with point particles and gravitational
attraction. To avoid particles going off to infinity, I thought I might
turn the 2D space into a topological torus: connect x=L = x=0 and y=L to
y=0.
But now a problem occurs: What is the distance between 2 points?
Because of the periodic boundary, you get for the distance (s):
s^2 = (x2-x1+i*L)^2 + (y2-y1+j*L)^2
You could set i = j = 0, but that would destroy translation symmetry, it
would make the coordinates at 0 and L physically different from other
points.
So there are a multitude of distances, a grid of them described by the
integers (i,j).
But that does seem a bit weird. Any comments on this?
Gerard
attraction. To avoid particles going off to infinity, I thought I might
turn the 2D space into a topological torus: connect x=L = x=0 and y=L to
y=0.
But now a problem occurs: What is the distance between 2 points?
Because of the periodic boundary, you get for the distance (s):
s^2 = (x2-x1+i*L)^2 + (y2-y1+j*L)^2
You could set i = j = 0, but that would destroy translation symmetry, it
would make the coordinates at 0 and L physically different from other
points.
So there are a multitude of distances, a grid of them described by the
integers (i,j).
But that does seem a bit weird. Any comments on this?
Gerard