Difference between revisions of "Nosé–Hoover thermostat"
From Department of Theoretical and Applied Mechanics
(Created page with "== Description == Nosé–Hoover thermostat is used to keep the temperature constant in the system. Thermostat is given by: ::<math> \left\{ \begin{array}{ll} v' =\omega^2...") |
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| − | + | [[Virtual laboratory]] > '''Nosé–Hoover thermostat''' <HR> | |
| − | Nosé–Hoover thermostat is used to keep the temperature constant in the system. | + | |
| + | == 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> | ::<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 28: | 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 == | ||
| − | * [[ | + | |
| − | * [ | + | * 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] | ||
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 time
2) stiff = 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[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.
