# Difference between revisions of "Nosé–Hoover thermostat"

From Department of Theoretical and Applied Mechanics

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\left\{ | \left\{ | ||

\begin{array}{ll} | \begin{array}{ll} | ||

− | v | + | \dot{v} =\omega^2_{\rm 0} x - \gamma v \\ |

− | \displaystyle \gamma | + | \displaystyle \dot{\gamma} = \frac{1}{\tau^2} \left( \frac{T}{T_{\rm 0}} - 1\right)\\ |

\end{array} | \end{array} | ||

\right. | \right. |

## Revision as of 19:15, 24 October 2015

Virtual laboratory >**Nosé–Hoover thermostat**

## Contents

## 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:

where

- is the eigen frequency

- is the initial kinetic temperature of the system

- is the current kinetic temperature of the system

- is the velocity

- is the relaxation time

- - scale for

- - scale of stiffness for

## Phase-space trajectory of thermostated harmonic oscillator

The plot shows the phase space, i.e. the dependence

. The followng three parameters can be changed by the user:1) tau =

is the relaxation time2) stiff =

is the stiffness3) scale is a scale parameter for a plot

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

## 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.