Implementation

Applying finite differences permits us to implement eqs.(3) [10].

A possibility to test the pressure control is provided by the calculation of the bulk modulus [14]. This method is equivalent to the computation of the heat capacity described as a check for the thermostat.

$$B_s = - V \left( \frac{\partial P}{\partial V} \right)_s = \frac{V k T}{\langle (\delta V)^2\rangle}$$

In fig. 2 and fig. 3 the pressure as a function of time as obtained in the MD simulation is shown. One sees the effects of the coupling constant.

Figure 2: The evolution of pressure with time for the Nosé-Hoover control for too small coupling constant $\tau$

Figure 3: The evolution of pressure with time for the Nosé-Hoover control for different values of the coupling constant $\tau$