Nosé–Hoover thermostat en

for Russian press here

Description of the model

Nosé–Hoover thermostat is used to keep the temperature constant in the system. Equations of motion of the thermostated harmonic oscillator have the form:

[math] \left\{ \begin{array}{ll} \dot{v} =\omega^2_{\rm 0} x - \gamma v \\ \displaystyle \dot{\gamma} = \frac{1}{\tau^2} \left( \frac{T}{T_{\rm 0}} - 1\right)\\ \end{array} \right. [/math]

where

• [math] {\omega}_{\rm 0} = \sqrt{ \frac{c}{m}} [/math] is the eigen frequency

• [math] {T_{\rm 0}} [/math] is the initial kinetic temperature of the system

• [math] {T} [/math] is the current kinetic temperature of the system

• [math] {v} [/math] is the velocity

• [math] {\tau} [/math] is the relaxation time

• [math] {tau}_{\rm 0} = 1 [/math] - scale for [math] {\tau} [/math]

• [math] {c}_{\rm 0} = 1 [/math] - scale of stiffness for [math] {c} [/math]

Phase-space trajectory of thermostated harmonic oscillator

The plot shows the trajectory of the thermostated harmonic oscillator in the phase-space. The equations of motion are solved numerically using leap-frog integration scheme. The followng three parameters can be changed by the user:

1) tau = [math] {\tau} [/math] is the relaxation time

2) stiff = [math] {c} [/math] is the stiffness

3) scale is a scale parameter for a plot

The last slider allows to choose the number of pre-configured experiment.

Authorship

This stand has been developed by Nikolai Markov.

References

• S. Nosé (1984). "A unified formulation of the constant temperature molecular-dynamics methods". J. Chem. Phys. 81 (1): 511–519.
• W.G. Hoover, (1985). "Canonical dynamics: Equilibrium phase-space distributions". Phys. Rev. A, 31 (3): 1695–1697.
• D.J. Evans, B.L. Holian (1985) The Nose–Hoover thermostat. J. Chem. Phys. 83, 4069.

Links

• Virtual laboratory
• William Hoover's Homepage