Berendsen thermostat: Difference between revisions
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The '''Berendsen thermostat''' is a method for controlling the [[temperature]] in a [[molecular dynamics]] simulation. | |||
The Berendsen [[thermostats |thermostat]] uses a weak coupling <math>(\gamma_i)</math> to an external heat bath of temperature <math>T_0</math>. This results in the modified equation of motion (Ref. 1 Eq. 8): | |||
:<math>m_i \frac{{\mathrm d} {\mathbf {v}}_i}{{\mathrm d} t} = {\mathbf {F}}_i + m_i \gamma \left( \frac{T_0}{T} -1\right){\mathbf {v}}_i </math>. | |||
This represents a proportional scaling of the velocities per [[time step]] from <math>{\mathbf {v}}</math> to <math>\lambda {\mathbf {v}}</math>, where (Ref. 1 Eq. 11) | |||
:<math>\lambda = \left[1 + \frac{\Delta t}{\tau_T} \left( \frac{T_0}{T} -1\right)\right]^{1/2}</math> | |||
where <math>\tau_T</math> is a time constant associated with the coupling. | |||
==References== | ==References== | ||
#[http://dx.doi.org/10.1063/1.448118 H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. R. Haak "Molecular dynamics with coupling to an external bath", Journal of Chemical Physics '''81''' pp. 3684-3690 (1984)] | #[http://dx.doi.org/10.1063/1.448118 H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. R. Haak "Molecular dynamics with coupling to an external bath", Journal of Chemical Physics '''81''' pp. 3684-3690 (1984)] | ||
[[category: molecular dynamics]] | [[category: molecular dynamics]] | ||
Revision as of 17:16, 26 March 2008
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The Berendsen thermostat is a method for controlling the temperature in a molecular dynamics simulation. The Berendsen thermostat uses a weak coupling Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (\gamma_i)} to an external heat bath of temperature Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_0} . This results in the modified equation of motion (Ref. 1 Eq. 8):
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m_i \frac{{\mathrm d} {\mathbf {v}}_i}{{\mathrm d} t} = {\mathbf {F}}_i + m_i \gamma \left( \frac{T_0}{T} -1\right){\mathbf {v}}_i } .
This represents a proportional scaling of the velocities per time step from to Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lambda {\mathbf {v}}} , where (Ref. 1 Eq. 11)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lambda = \left[1 + \frac{\Delta t}{\tau_T} \left( \frac{T_0}{T} -1\right)\right]^{1/2}}
where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau_T} is a time constant associated with the coupling.