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ca6aa7a Mar 3, 2017
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Monte Carlo Simulation of a Homogeneous Hard Sphere Fluid

This example contains four versions of the same simulation; a C++ version, a Rust version with no units, and two Rust versions with units that demonstrate different ways to use dimensioned.

Use

To run all versions of the simulation, run

./run_all.sh N len iter

where N is the number of spheres, len is the cell dimension, and iter is the number of iterations for which to run.

Running with

./run_all.sh 100 10 100000

gives a quick timing comparison. Note that the C++ version will have different output from the Rust versions due to floating point differences.

About the simulation

A hard sphere fluid is a fluid made of spherical particles that have only one interaction; they can't be in the same place at the same time. Imagine a box in space with a bunch of billiard balls bouncing around in it -- that's essentially what it is. That is also one way to simulate it, called molecular dynamics. The simulation method invoked here, Monte Carlo, does not do that. We'll get to that in a minute.

We are simulating a homogeneous fluid. That means that it's the same everywhere---there are no interfaces, or particles that are different from eachother, or really anything interesting at all. Basically, instead of a box of billiard balls in space, all of space is filled with billiard balls and only billiard balls. We simulate this by having a finite box with periodic boundary conditions. If a sphere moves out of the box, then it moves back in on the other side, much like a Pacman level. This way, we are simulating all of space being filled with repeating copies of our box. As long as our box isn't too small, this will give the same results as having a box of infinite size.

In a Monte Carlo simulation, we make a random move of each sphere. If a move is valid, we keep it. If not, we reject the move, returning the system to its state before the move. A move is valid if it does not cause any of the spheres to overlap. Once we've attempted moving each sphere, we repeat, ad infinitum.

As the simulation runs, a histogram stores counts of where spheres are seen. This allows us to calculate the density of spheres across space. It will be the same everywhere, and could be calculated just from the simulation inputs, but this gives us an output to ensure the different versions are all getting the exact same results.

I did research for my undergraduate degree in physics with more involved versions of this simulation, so it seemed a good place to start playing with Rust.

The Simulation Versions

0. C++

The C++ version of this simulation is located in cpp-src. It is not the focus of this documentation and will not be mentioned again.

1. Rust with no units

Let's start with the basic simulation. For simplicity, we use a very basic, non-generic 3d vector library, which you can check out here.

The only thing of note is the random number generation, which was done that way only because we wanted identical results for the Rust and C++ code, so they both use the same, basic random number generator.

Consider this the reference version; it explains what's happening in the simulation, whereas the other versions will only their explain differences. If you don't care about the simulation and are only here to look at units, feel free to skim over this or skip it entirely.

Check out the code here.

2. Rust with units outside

In this first version with units, we use the same non-generic vector library. So, we are forced to wrap the vectors in units. This method allows the most flexibility in what other libraries can be used with dimensioned, but isn't quite as convenient to work with as the next version.

Check out the code here.

3. Rust with units inside

In this final version, we treat primitives with units are just primitives, resulting in code that is very similar to the version with no units. It is the ideal way to use dimensioned.

Of course, there's a catch. We need a much more flexibile vector library, which you can view here. Note that it is not enough for the vector library to be generic, it also has to have no contraints on how types change under operations. E.g. When you multiply two vectors over Meter<f64>, you'll end up with a vector over Meter2<f64>, and the library has to allow this.

So, this version has less flexibility in terms of what libraries it can be used with, but allows treating primitives with units as just primitives, which turns out to be really nice.

Check out the code here.