View source for Nosé–Hoover thermostat

[[Virtual laboratory]] > '''Nosé–Hoover thermostat'''  <HR>


== 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.''' 

{{#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 ==

* 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]]
* [http://williamhoover.info/  William Hoover's Homepage]