7.4 Exercises

Gauss Dynamics:

Write a Gaussian MD program to simulate the following system:
3 particles without pairwise interaction are moving in a one-dimensional harmonic potential. The sum of their kinetic energies is kept constant. Draw the $x,\dot{x}$ trajectory of the first particle. Use Runge-Kutta.

Nosé-Hoover thermostat:

The equations of motion of the Nosé oscillator with $k=m=E_{0}=1$ are

$$\dot{x} = v$$ (7.23)

$$\dot{v} = -x-\zeta v$$ (7.24)

$$\dot{\zeta} = \frac{1}{Q} \left[ v^{2}-2\right]$$ (7.25)

Integrate this set of equations, using Runge-Kutta, and draw the $x,v$ trajectory.