http://mech.spbstu.ru/api.php?action=feedcontributions&user=78.25.122.228&feedformat=atomDepartment of Theoretical and Applied Mechanics - User contributions [en]2024-03-28T19:28:54ZUser contributionsMediaWiki 1.27.3http://mech.spbstu.ru/?title=Nos%C3%A9%E2%80%93Hoover_thermostat&diff=6248Nosé–Hoover thermostat2015-10-26T18:07:37Z<p>78.25.122.228: </p>
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<div>[[Virtual laboratory]] > '''Nosé–Hoover thermostat''' <HR><br />
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== Description of the model == <br />
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Nosé–Hoover thermostat is used to keep the temperature constant in the system. Equations of motion of the thermostated harmonic oscillator have the form:<br />
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::<math><br />
\left\{ <br />
\begin{array}{ll}<br />
\dot{v} =\omega^2_{\rm 0} x - \gamma v \\<br />
\displaystyle \dot{\gamma} = \frac{1}{\tau^2} \left( \frac{T}{T_{\rm 0}} - 1\right)\\<br />
\end{array}<br />
\right.<br />
</math><br />
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where<br />
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* <math> {\omega}_{\rm 0} = \sqrt{ \frac{c}{m}} </math> is the eigen frequency<br />
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* <math> {T_{\rm 0}} </math> is the initial kinetic temperature of the system<br />
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* <math> {T} </math> is the current kinetic temperature of the system <br />
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* <math> {v} </math> is the velocity<br />
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* <math> {\tau} </math> is the relaxation time<br />
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* <math> {tau}_{\rm 0} = 1 </math> - scale for <math> {\tau} </math><br />
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* <math> {c}_{\rm 0} = 1 </math> - scale of stiffness for <math> {c} </math><br />
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== Phase-space trajectory of thermostated harmonic oscillator == <br />
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:<br />
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1) tau = <math> {\tau} </math> is the relaxation time<br />
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2) stiff = <math> {c} </math> is the stiffness <br />
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3) scale is a scale parameter for a plot <br />
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'''The last slider allows to choose the number of pre-configured experiment.''' <br />
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{{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Markov/Nose%E2%80%93Hoover%20thermostat/Thermostat_en.html |width=1000 |height=720 |border=0 }}<br />
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== Authorship ==<br />
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This stand has been developed by [http://tm.spbstu.ru/Nikolai_Markov Nikolai Markov].<br />
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== References ==<br />
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* S. Nosé (1984). "A unified formulation of the constant temperature molecular-dynamics methods". J. Chem. Phys. 81 (1): 511–519. <br />
* W.G. Hoover, (1985). "Canonical dynamics: Equilibrium phase-space distributions". Phys. Rev. A, 31 (3): 1695–1697.<br />
* D.J. Evans, B.L. Holian (1985) The Nose–Hoover thermostat. J. Chem. Phys. 83, 4069.<br />
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== Links ==<br />
* [[Virtual laboratory]]<br />
* [http://williamhoover.info/ William Hoover's Homepage]</div>78.25.122.228