Using Periodic Boundary Conditions

Periodic Boundary Conditions

Overview

There are two forms of periodic boundary conditions available in MCell: traditional and mirrored geometry.

With traditional PBCs, molecules simply wrap around when they hit the edge of boundary. For instance, if a molecule hits the the positive X boundary of the periodic box, then it will wrap around to the negative X boundary and continue diffusing from there.

With the mirrored geometry form, the geometry is mirrored in adjacent boxes and molecules do not wrap around. When a molecule hits a boundary, it will continue diffusing in the mirrored adjacent geometry. Note: this mirrored geometry does not actually exist, but is made possible by keeping careful bookkeeping of all the molecules and the location of the virtual box that they are in.

Usage

Defining the Boundaries

Periodic boundary conditions in MCell are used by defining a periodic box.

PERIODIC_BOX
{
  CORNERS = [-0.2, -0.2, -0.2],[0.2, 0.2, 0.2]
  PERIODIC_TRADITIONAL = FALSE
  PERIODIC_X = TRUE
  PERIODIC_Y = TRUE
  PERIODIC_Z = TRUE
}

Like a normal MCell BOX object, the CORNERS define the lower left and upper right points of the box. Setting PERIODIC_TRADITIONAL to FALSE will use the mirrored geometry form of periodic boundaries. Each axis can be set to be periodic or not via the PERIODIC_X/Y/Z keywords.

There can only be one periodic box and you do not need to instantiate it.

Counting in Virtual Boxes

Counting works very similarly to normal counting in MCell. However, if using mirrored geometry, then you need to specify which "virtual" box that you're counting in like this:

{COUNT[vm,Scene.cell,[1,-2,3]]}=> "./vm.000.dat"

Notice the section with the [1,-2,3]. The numbers refer to the X, Y, and Z coordinates of the virtual box respectively. In this example, we are counting all the vm molecules in Scene.cell that is one virtual box over in the positive X direction, two virtual boxes over in the negative Y direction, and three virtual boxes over in the positive Z direction.