## BubbleBath.jl

Generate loose packings of spheres in orthorhombic domains, in 2 and 3 dimensions.
Author mastrof
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Updated Last
1 Year Ago
Started In
December 2022

# BubbleBath.jl

Generate loose packings of spheres in orthorhombic domains, in 2 and 3 dimensions.

## Features

• Fill a domain with spheres from a given distribution of radii to reach a target packing fraction, or from already-sampled radii.
• Control minimum allowed distance between spheres.
• Decide whether spheres can cross through domain boundaries or not.

`BubbleBath.jl` just employs the trivial brute-force method, with the only peculiarity that spheres are introduced in order of decreasing radius. Dense packings are obtained with reasonable performance, but spatial correlations between sphere sizes are introduced.

This is not an algorithm to generate tight, space-filling packings.

## Example usage

The package exports a `Sphere{D}` type, which is just a wrapper around a position `pos::NTuple{D,Float64}` and a radius `radius::Float64`, and the `bubblebath` function, which creates a loose packing of spheres in a domain.

To generate a (2D) distribution of spheres with radii uniformly distributed within 1 and 5, in a rectangular domain of edges 100 and 50, with a packing fraction 0.4, we can do

```using BubbleBath
using Distributions: Uniform

extent = (100, 50)
ϕ_max = 0.4

If we want to impose a minimal distance between the surface of spheres, the `min_distance` keyword can be used

```radius_pdf = Uniform(1,5)
extent = (100, 50)
ϕ_max = 0.4
min_distance = 2.0
bath = bubblebath(radius_pdf, ϕ_max, extent; min_distance)```

Again, the procedure in 3D is identical

```radius_pdf = Uniform(10,25)
extent = (100, 100, 100)
ϕ_max = 0.3
min_distance = 10.0
bath = bubblebath(radius_pdf, ϕ_max, extent; min_distance)```

We can verify that the generated radii closely match the chosen distribution, even at relatively high packing fractions.

```using Distributions: Exponential
θ = 3.0 # average radius
extent = ntuple(_->300, 3)
# this can take a while
r1 = map(s -> s.radius, bath1)
r2 = map(s -> s.radius, bath2)```

Finally, `bubblebath` also has an in-place version `bubblebath!`, which can operate on pre-initialised vectors of `Sphere`s. For example, to produce the `BubbleBath.jl` logo:

```using Distributions: Exponential
# initialise vector with three spheres at desired locations
Lx = 400
Ly = 400
extent = (Lx,Ly)
R = 50
D = 60
spheres = [
Sphere((Lx/2-D,Ly/2-D), R),
Sphere((Lx/2+D,Ly/2-D), R),
Sphere((Lx/2,Ly/2+3D/4), R)
]