http://mech.spbstu.ru/api.php?action=feedcontributions&user=78.25.122.228&feedformat=atom Department of Theoretical and Applied Mechanics - User contributions [en] 2022-09-27T14:14:19Z User contributions MediaWiki 1.27.3 http://mech.spbstu.ru/?title=Nos%C3%A9%E2%80%93Hoover_thermostat&diff=6248 Nosé–Hoover thermostat 2015-10-26T18:07:37Z <p>78.25.122.228: </p> <hr /> <div>[[Virtual laboratory]] &gt; '''Nosé–Hoover thermostat''' &lt;HR&gt;<br /> <br /> <br /> == Description of the model == <br /> <br /> 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 /> <br /> ::&lt;math&gt;<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 /> &lt;/math&gt;<br /> <br /> where<br /> <br /> * &lt;math&gt; {\omega}_{\rm 0} = \sqrt{ \frac{c}{m}} &lt;/math&gt; is the eigen frequency<br /> <br /> * &lt;math&gt; {T_{\rm 0}} &lt;/math&gt; is the initial kinetic temperature of the system<br /> <br /> * &lt;math&gt; {T} &lt;/math&gt; is the current kinetic temperature of the system <br /> <br /> * &lt;math&gt; {v} &lt;/math&gt; is the velocity<br /> <br /> * &lt;math&gt; {\tau} &lt;/math&gt; is the relaxation time<br /> <br /> * &lt;math&gt; {tau}_{\rm 0} = 1 &lt;/math&gt; - scale for &lt;math&gt; {\tau} &lt;/math&gt;<br /> <br /> * &lt;math&gt; {c}_{\rm 0} = 1 &lt;/math&gt; - scale of stiffness for &lt;math&gt; {c} &lt;/math&gt;<br /> <br /> == 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 /> <br /> 1) tau = &lt;math&gt; {\tau} &lt;/math&gt; is the relaxation time<br /> <br /> 2) stiff = &lt;math&gt; {c} &lt;/math&gt; is the stiffness <br /> <br /> 3) scale is a scale parameter for a plot <br /> <br /> '''The last slider allows to choose the number of pre-configured experiment.''' <br /> <br /> {{#widget:Iframe |url=http://tm.spbstu.ru/htmlets/Markov/Nose%E2%80%93Hoover%20thermostat/Thermostat_en.html |width=1000 |height=720 |border=0 }}<br /> <br /> == Authorship ==<br /> <br /> This stand has been developed by [http://tm.spbstu.ru/Nikolai_Markov Nikolai Markov].<br /> <br /> == References ==<br /> <br /> * S. Nosé (1984). &quot;A unified formulation of the constant temperature molecular-dynamics methods&quot;. J. Chem. Phys. 81 (1): 511–519. <br /> * W.G. Hoover, (1985). &quot;Canonical dynamics: Equilibrium phase-space distributions&quot;. 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 /> <br /> == Links ==<br /> * [[Virtual laboratory]]<br /> * [http://williamhoover.info/ William Hoover's Homepage]</div> 78.25.122.228