# Balls In A Box

The Balls in a Box model shows that the phase-space trajectory of a system of particles is very sensitive to its initial conditions. In general, an isolated system of many particles that is prepared in a nonrandom configuration will change in time so as to approach its most random configuration where it is in equilibrium. What happens if we choose the initial conditions in a very special way?

The default initial condition corresponds to eight stationary particles perfectly aligned on the x-axis. Two particles approach from the left and the right. What happens when these particles collide with the eight stationary particles? The Ejs model solves Newton's second law of motion numerically but pauses when a collision is detected. This is called an Ejs event. Conservation of energy and momentum are applied at the event and the simulation is resumed.

- Perturb one of the stationary particles ever so slightly and observe the resulting trajectories.
- Select other pre-programmed experiments and observe the motion.
- Simulations accumulate error due to both the finite precision of computer arithmetic and the approximate nature of finite-difference algorithms. How do these errors manifest themselves in this simulation?

## Reference:

Gould and Tobochnik Statistic and Thermal Physics p19 to be published by Princeton University Press (2010). Draft chapters are available online at <http://stp.clarku.edu/>.

### Note:

This simulation was created by Wolfgang Christian using the Easy Java Simulations (Ejs) modeling tool. It is based on a Java program from the Statistical and Thermal Physics Project. You can modify this simulation if you have Ejs installed by right-clicking within a plot and selecting "Open Ejs Model" from the pop-up menu item. Information about Ejs is available at: <http://www.um.es/fem/Ejs/>.