# Decay relativistic (in the Newton sense) velocity in particle system

I'm making a particle simulation where particles both attract and repel and have an ideal distance where the forces are balanced. I'd like to use it to simulate different types of matter.

The problem is that regardless of the forces between the atoms all the matter that I produce using this idea seems ends up having the consistency of very jittery jello. If I try to just decay the velocity of all particles (in an absolute sense), then it becomes less like jello, but if being propelled through space, slows down as if in some kind of thick gooey ether.

I'm thinking that if I had an algorithm where I am adjusting forces between particles, without using absolute velocity in any way (relative velocity between interacting particles is ok) I could cause the matter to "crystalize" without having it act as if its in a ether.

I have a vague understanding that atoms generate light when they vibrate with too much energy, which slows them down, I assume, and I'm hoping some sort of similar physics laws may help guide me to an algorithm to do this.

Specifically, it's a $2d$ system, written in Web GL, where I encode the particles in 2d graphics textures, so graphics card handles all the interactions. Each particle creates a field around it based on the following equation:

$$f(x) = \frac{k}{[(l+(x-d)^2]c}$$

Where $k, l$, and $d$ are universally constant, $x$ is the distance from the particle. $c$ is constant per particle type. One particle type could have a negative value, and another a positive, creating an attraction between the two. This is explained more below.

$f(x)$ is multiplied to a normalized vector that is pointed away from the particle in question to get a force vector.

This equation creates a kind of force "donut" around the particle, based on the various values of $k,l$ and $d$.

(Right now I only have the above equation, but of course I could add others).

The field the particles live in contains the sum of all the fields generated by the particles. The change in velocity to the particle is determined as follows:

$$g(x) = f*\frac{c}{m}$$

where $f$ is the total field vector at the particles location, $m$ is the particles mass and $c$ is the "field charge" of the particle type, also used in the above equation.

There are a variable number of fields. In the simplest scenario there is only 1 but in general I have 2, one for the electric force and another for a nuclear repelling force.

• Solids simulated in this way should act like jello until the total energy of the molecules drops to a level whee the average vibrational amplitude is much smaller than the inter-molecular distance and the applied forces (averaged over surface molecules at the area of application) are small compared to those needed to displace a molecule by a inter-molecular distance. You will incidentally get a nice model of the elastic modulii. Commented Oct 1, 2016 at 15:52

As far as I know solid state is impossible with quantum mechanics. Using the $1/r^2$ forces that we have with gravity and electrostatics, there is no way to build up a stable solid. If you have a checkerboard pattern of electrons and protons, it might will collapse by the tiniest perturbation. So actually one needs quantum mechanics to have proper bound states.