A simple question about periodicty

[Refet Ali Yalcin]

Dear All,

I want to ask a question about placing the periodic boundary conditions. I couldn't find a documentation about defining unit cells

I inspected two examples

https://smuthi.readthedocs.io/en/latest/_source/04%20examples/10_periodic_near_field/discussion.html 

https://smuthi.readthedocs.io/en/latest/_source/04%20examples/fifteen_periodic_spheres_in_slab/discussion.html  

in fifteen spheres case:

In 15 spheres example, BCs are defined as:

    # define unit cell
    a1 = np.array([1001, 0, 0], dtype=float)
    a2 = np.array([0, 1001, 0], dtype=float)

Do the upper arrays consider the area with corners
(0,0,0) (1001,0,0) (0,1001,0) (1001,1001,0)? If so, how can it account for the spheres that have negative coordinates?

Here is the location of spheres from the example file.

particle_list = [part.Sphere(position=[-200, -200, 1000], refractive_index=rfidx, radius=150, l_max=lmax, m_max=mmax),
                  part.Sphere(position=[200, 200, 2000], refractive_index=rfidx, radius=100, l_max=lmax, m_max=mmax),
                  part.Sphere(position=[0, 30, 1500], refractive_index=rfidx, radius=120, l_max=lmax, m_max=mmax),
                  part.Sphere(position=[-300, -200, 2700], refractive_index=rfidx, radius=110, l_max=lmax, m_max=mmax),
                  part.Sphere(position=[110, 150, 2720], refractive_index=rfidx, radius=140, l_max=lmax, m_max=mmax),
                  part.Sphere(position=[200, 0, 390], refractive_index=rfidx, radius=120, l_max=lmax, m_max=mmax),
                  part.Sphere(position=[-100, 380, 400], refractive_index=rfidx, radius=100, l_max=lmax, m_max=mmax),
                  part.Sphere(position=[200, -100, 1900], refractive_index=rfidx, radius=100, l_max=lmax, m_max=mmax),
                  part.Sphere(position=[-320, 300, 2050], refractive_index=rfidx, radius=110, l_max=lmax, m_max=mmax),
                  part.Sphere(position=[-360, -360, 220], refractive_index=rfidx, radius=100, l_max=lmax, m_max=mmax),
                  part.Sphere(position=[100, 300, 1160], refractive_index=rfidx, radius=100, l_max=lmax, m_max=mmax),
                  part.Sphere(position=[-150, 300, 2360], refractive_index=rfidx, radius=120, l_max=lmax, m_max=mmax),
                  part.Sphere(position=[-270, -300, 2200], refractive_index=rfidx, radius=130, l_max=lmax, m_max=mmax),
                  part.Sphere(position=[-170, -180, 1470], refractive_index=rfidx, radius=100, l_max=lmax, m_max=mmax),
                  part.Sphere(position=[340, -300, 1500], refractive_index=rfidx, radius=100, l_max=lmax, m_max=mmax)]

Kind regards,

Refet Yalcin

[Amos Egel]

Dear Refet,

The periodicity definition reads

# define unit cell
a1 = np.array([1001, 0, 0], dtype=float)

a2 = np.array([0, 1001, 0], dtype=float)

This means that the geometry is periodic with respect to a shift by [1001, 0, 0] and with respect to a shift by [0, 1001, 0].

So if a particle is placed at position=[-200, -200, 1000], this results in the same geometry as if the particle would have been placed at position=[-200+1001, -200, 1000] or at position=[-200+1001, -200+1001, 1000]. In other words, it is not necessary to place all particles into an xy-square along [0,0], [0, 1001], [1001,0], [1001,1001]. The particles can also for example be located in a square [-500, -500], [-500, 501], [501, -500], [501,501] or any other square with edge lengths [1001, 1001].

@Dominik, is that correct? Maybe you want to clarify?

Best regards, Amos

--
Smuthi project repository: https://gitlab.com/AmosEgel/smuthi
Online documentation https://smuthi.readthedocs.io/en/latest/
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