### Sensitivity to initial conditions

Introduction

The idea of this simulation is to show that the 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 N = 11 particles that are equally spaced vertically and all traveling with the same velocity to the right. The program solves Newton's second law of motion numerically for each of the particles assuming the Lennard-Jones potential.

In the second part of the simulation, a small perturbation is applied to particle 6, the one in the middle of the display. Its velocity in the horizontal direction is changed from 1.0 to the default value of 1.00001. In the questions we will explore what happens and why.

Problems

1. Run the program with the default initial condition and describe the motion of the particles.
2. After the simulation proceeds for a while, click on the Perturb button. What happens to the motion of the particles? After the simulation proceeds for a while, say t = 0.02, stop the simulation and click the Reverse button, which reverses the velocities of all particles. Does the system return to its initial special state? Is the motion reversible?
3. Proceed as in Problem 2, but wait longer before perturbing the system. Does the system return to its initial state. Why or why not?

Java Classes

• LJgas
• LJgasApp

Updated 28 December 2009.