Excluded volume

This module implements a method to place a number of spheres that have no overlap.

This example shows use of the excluded volume with the placement of 1000 particles at random positions with a diameter of 1 in a cubic box with each edge being 50:

function example()
local random = math.random
math.randomseed(os.time())

local edge = 50
local box = halmd.mdsim.box{length = {edge, edge, edge}}
local excluded = halmd.mdsim.positions.excluded_volume{box = box, cell_length = 1}

local obstacles = {}
local diameter = 1
local repeats = 50
for i = 1, 1000 do
    for j = 1, repeats do
        local r = {edge * random(), edge * random(), edge * random()}
        if excluded:place_sphere(r, diameter) then
            obstacles[i] = r
            excluded:exclude_sphere(r, diameter)
            break
        end
    end
    if not obstacles[i] then
        error(("cannot place obstacle %d after %d repeats"):format(i, repeats))
    end
end

local particle = halmd.mdsim.particle{dimension = box.dimension, particles = #obstacles}

Note

If one uses the random number generator from Lua , this should be done in conjunction with LuaJIT, only. Standard Lua uses the OS-dependent rand() function.

See http://luajit.org/extensions.html#math_random

class halmd.mdsim.positions.excluded_volume(args)

Construct excluded volume instance

Parameters:
  • args (table) – keyword arguments
  • args.box (number) – instance of halmd.mdsim.box
  • args.cell_length (number) – cell length for internal binning (must not be smaller than largest sphere diameter)
exclude_sphere(centre, diameter)

Place a single sphere at centre with a diameter of diameter

exclude_spheres(centres, diameters)

Place a set of spheres with their respective centres and diameters

place_spheres(centre, diameter)

Test if a sphere at centre with diameter diameter can be placed without overlap with any other previously set sphere