# Difference between revisions of "Nosé–Hoover thermostat"

From Department of Theoretical and Applied Mechanics

(→Links) |
|||

(4 intermediate revisions by one other user not shown) | |||

Line 2: | Line 2: | ||

− | == Description == | + | == Description of the model == |

− | Nosé–Hoover thermostat is used to keep the temperature constant in the system. | + | 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> | ::<math> | ||

\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. | ||

</math> | </math> | ||

− | + | where | |

− | * <math> {\omega}_{\rm 0} = \sqrt{ \frac{c}{m}} </math> | + | * <math> {\omega}_{\rm 0} = \sqrt{ \frac{c}{m}} </math> is the eigen frequency |

− | * <math> {T_{\rm 0}} </math> | + | * <math> {T_{\rm 0}} </math> is the initial kinetic temperature of the system |

− | * <math> {T} </math> | + | * <math> {T} </math> is the current kinetic temperature of the system |

− | * <math> {v} </math> | + | * <math> {v} </math> is the velocity |

− | * <math> {\tau} </math> | + | * <math> {\tau} </math> is the relaxation time |

* <math> {tau}_{\rm 0} = 1 </math> - scale for <math> {\tau} </math> | * <math> {tau}_{\rm 0} = 1 </math> - scale for <math> {\tau} </math> | ||

Line 31: | Line 31: | ||

* <math> {c}_{\rm 0} = 1 </math> - scale of stiffness for <math> {c} </math> | * <math> {c}_{\rm 0} = 1 </math> - scale of stiffness for <math> {c} </math> | ||

− | == | + | == Phase-space trajectory of thermostated harmonic oscillator == |

− | The | + | 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> | + | 1) tau = <math> {\tau} </math> is the relaxation time |

− | 2) stiff = <math> {c} </math> | + | 2) stiff = <math> {c} </math> is the stiffness |

− | 3) scale | + | 3) scale is a scale parameter for a plot |

− | ''' | + | '''The last slider allows to choose the number of pre-configured experiment.''' |

− | + | {{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Markov/Nose%E2%80%93Hoover%20thermostat/Thermostat_en.html |width=1000 |height=720 |border=0 }} | |

− | + | == Authorship == | |

+ | |||

+ | This stand has been developed by [http://tm.spbstu.ru/Nikolai_Markov Nikolai Markov]. | ||

== References == | == References == |

## Latest revision as of 21:07, 26 October 2015

Virtual laboratory >**Nosé–Hoover thermostat**

## Contents

## Description of the model[edit]

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[edit]

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 =

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.**

## Authorship[edit]

This stand has been developed by Nikolai Markov.

## References[edit]

- 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.