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The '''Andersen thermostat''' | The '''Andersen thermostat''' (Ref. 1, section IV) couples the system to a heat bath via stochastic forces that modify the kinetic energy of the atoms or molecules. | ||
The time between collisions, or the number of collisions in some (short) time interval is decided [[random numbers |randomly]], with the following [[Poisson distribution]] (Eq. 4.1): | The time between collisions, or the number of collisions in some (short) time interval is decided [[random numbers |randomly]], with the following [[Poisson distribution]] (Ref. 1 Eq. 4.1): | ||
:<math>P(t) = \nu e^{-\nu t}.</math> | :<math>P(t) = \nu e^{-\nu t}.</math> | ||
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where <math>\nu</math> is the stochastic collision frequency. | where <math>\nu</math> is the stochastic collision frequency. | ||
Between collisions the system evolves at constant energy, i.e. business as usual. Upon a 'collision event' the new momentum of the lucky atom (or molecule) is chosen at random from a [[Boltzmann distribution]] at [[temperature]] <math>T</math>. | Between collisions the system evolves at constant energy, i.e. business as usual. Upon a 'collision event' the new momentum of the lucky atom (or molecule) is chosen at random from a [[Boltzmann distribution]] at [[temperature]] <math>T</math>. | ||
In principle <math>\nu</math> can adopt any value. However, there does exist an optimum choice (Eq. 4.9): | In principle <math>\nu</math> can adopt any value. However, there does exist an optimum choice (Ref. 1 Eq. 4.9): | ||
:<math>\nu = \frac{2a \kappa V^{1/3}}{3 k_BN} = \frac{2a \kappa}{3 k_B\rho^{1/3}N^{2/3}}</math> | :<math>\nu = \frac{2a \kappa V^{1/3}}{3 k_BN} = \frac{2a \kappa}{3 k_B\rho^{1/3}N^{2/3}}</math> | ||
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where <math>a</math> is a dimensionless constant, <math>\kappa</math> is the [[thermal conductivity]], <math>V</math> is the volume, <math>k_B</math> is the [[Boltzmann constant]], and <math>\rho</math> is the [[number density]] of particles; <math>\rho:=N/V</math>. | where <math>a</math> is a dimensionless constant, <math>\kappa</math> is the [[thermal conductivity]], <math>V</math> is the volume, <math>k_B</math> is the [[Boltzmann constant]], and <math>\rho</math> is the [[number density]] of particles; <math>\rho:=N/V</math>. | ||
Note: the Andersen thermostat should only be used for time-independent properties. Dynamic properties, such as the [[diffusion]], should not be calculated if the system is thermostated using the Andersen algorithm | Note: the Andersen thermostat should only be used for time-independent properties. Dynamic properties, such as the [[diffusion]], should not be calculated if the system is thermostated using the Andersen algorithm (Ref. 2) | ||
==See also== | ==See also== | ||
*[[Lowe-Andersen thermostat]] | *[[Lowe-Andersen thermostat]] | ||
==References== | ==References== | ||
#[http://dx.doi.org/10.1063/1.439486 Hans C. Andersen "Molecular dynamics simulations at constant pressure and/or temperature", Journal of Chemical Physics '''72''' pp. 2384-2393 (1980)] | |||
#[http://dx.doi.org/10.1063/1.445020 H. Tanaka, Koichiro Nakanishi, and Nobuatsu Watanabe "Constant temperature molecular dynamics calculation on Lennard-Jones fluid and its application to water", Journal of Chemical Physics '''78''' pp. 2626-2634 (1983)] | |||
[[Category: Molecular dynamics]] | [[Category: Molecular dynamics]] | ||