Particles interacting via Fields

CS 493 Lecture, Dr. Lawlor

A common style in physics and simulation is a set of particles, that interact via a force field. Sometimes the particles are actual discrete objects, like moose or electrons; but often the particles are just a convenient way to discretize some finer material, like chunks of a galaxy or bullet.

Subject	Particles	Interaction / Force
Semiconductor current flow	electrons	electromagnetic field
Cosmological dynamics	chunks of galaxy	gravitational field
Meshless metal deformation	chunks of bullet	mechanical forces
Fluid dynamics (SPH)	smoothed fluid parcels	hydrodynamics (navier-stokes)
Ecological simulation	moose and wolves	predator visibility field

In each of these cases, there are several ways to calculate the field-particle interactions:

The O(n²) approach is to calculate each particle's influence on every other particle.
An O(n lg n) approach uses a tree to find nearby particles, and only calculate interactions with nearby particles (or some lumped version of distant particles).
A rasterization scheme can reach O(n+p), where p is the number of pixels used to draw the field. The advantage of this approach is its excellent fit to graphics hardware, where we can render (or "splat") particles on the screen as quads. It is possible to either keep lists of particles in each pixel, which allows coarser pixels but requires more computation per pixel; or to draw the interaction force directly to the pixel, which requires finer pixels but each pixel is simpler. One drawback of this approach is the number of pixels p does not scale well, especially in 3D.

Here's a short, typical mechanical engineering paper on mesh-free metal deformation, with a giant bullet-like object smashing into a flat armor-like object:
     http://www.ijmer.com/papers/Vol3_Issue1/DS31568573.pdf

There's a beautiful PhysX (CUDA) fluid library based on particles, with amazing video, but few technical details shown here:
    http://physxinfo.com/news/11109/introduction-to-position-based-fluids/

Here's a 2D game engine based on fluids simulated via particles. They adjust the size of a particle based on nearby particle density, and render the mass onscreen using a splat-and-threshold technique:
    http://www.gdcvault.com/play/1012447/Go-With-the-Flow-Fluid