Difference between revisions of "Martyna-Tuckerman-Tobias-Klein barostat"

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(New page: ==References== # G. J. Martyna, M. E. Tuckerman, D. J. Tobias and M. L. Klein "Explicit reversible integrators for extended systems dynamics", Molecular Physics '''87''' pp. 1117-1157 (19...)
 
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'''Martyna-Tuckerman-Tobias-Klein barostat''' <ref>[http://dx.doi.org/10.1063/1.467468 Glenn J. Martyna, Douglas J. Tobias, and Michael L. Klein "Constant pressure molecular dynamics algorithms", Journal of Chemical Physics '''101''' pp. 4177-4189 (1994)]</ref>
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<ref>[http://dx.doi.org/10.1080/00268979600100761 G. J. Martyna, M. E.  Tuckerman, D. J. Tobias and M. L. Klein "Explicit reversible integrators for extended systems dynamics", Molecular Physics '''87''' pp. 1117-1157 (1996)]</ref> has the following equations of motion (Eq.13):
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:<math> \dot{\mathbf {r}}_i = \frac{{\mathbf {p}}_i}{m_i} + \frac{\overline{\mathbf {p}}_g}{W_g} {\mathbf {r}}_i </math>
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:<math> \dot{\mathbf {p}}_i =  {\mathbf {F}}_i  - \frac{\overline{\mathbf {p}}_g}{W_g} {\mathbf {p}}_i - \left(\frac{1}{N_f}\right)  \frac{\mathrm{Tr}[ \overline{\mathbf {p}}_g ]}{W_g} - \frac{p_{\xi}}{Q} {\mathbf {p}}_i</math>
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:<math>\dot{\overline{\mathbf {h}}} =  \frac{\overline{\mathbf {p}}_g {\overline{\mathbf {h}}} }{W_g}</math>
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:<math> \dot{\overline{\mathbf {p}}}_g = V \left({\overline{\mathbf {p}}}_{\mathrm {int}}  - {\overline{\mathbf {I}}} P_{\mathrm {ext}} \right) + \left[ \frac{1}{N_f}  \sum_{i=1}^N  \frac{{\mathbf {p}}_i^2 }{m_i}  \right] {\overline{\mathbf {I}}}  - \frac{p_{\xi}}{Q}{\overline{\mathbf {p}}}_g</math>
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:<math>\dot\xi= \frac{p_{\xi}}{Q}</math>
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:<math>\dot p_{\xi} =  \sum_{i=1}^N \frac{{\mathbf {p}}_i^2 }{m_i} + \frac{1}{W_g} \mathrm{Tr}\left[ {\overline{\mathbf {p}}}_g^t {\overline{\mathbf {p}}}_g \right] - (N_f + d^2) kT</math>
 
==References==
 
==References==
# G. J. Martyna, M. E.  Tuckerman, D. J. Tobias and M. L. Klein "Explicit reversible integrators for extended systems dynamics", Molecular Physics '''87''' pp. 1117-1157 (1996)
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<references/>
 
[[category: molecular dynamics]]
 
[[category: molecular dynamics]]

Latest revision as of 17:44, 31 January 2014

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Martyna-Tuckerman-Tobias-Klein barostat [1] [2] has the following equations of motion (Eq.13):

 \dot{\mathbf {r}}_i = \frac{{\mathbf {p}}_i}{m_i} + \frac{\overline{\mathbf {p}}_g}{W_g} {\mathbf {r}}_i
 \dot{\mathbf {p}}_i =  {\mathbf {F}}_i  - \frac{\overline{\mathbf {p}}_g}{W_g} {\mathbf {p}}_i - \left(\frac{1}{N_f}\right)  \frac{\mathrm{Tr}[ \overline{\mathbf {p}}_g ]}{W_g} - \frac{p_{\xi}}{Q} {\mathbf {p}}_i
\dot{\overline{\mathbf {h}}} =  \frac{\overline{\mathbf {p}}_g {\overline{\mathbf {h}}} }{W_g}
 \dot{\overline{\mathbf {p}}}_g = V \left({\overline{\mathbf {p}}}_{\mathrm {int}}  - {\overline{\mathbf {I}}} P_{\mathrm {ext}} \right) + \left[ \frac{1}{N_f}  \sum_{i=1}^N  \frac{{\mathbf {p}}_i^2 }{m_i}  \right] {\overline{\mathbf {I}}}  - \frac{p_{\xi}}{Q}{\overline{\mathbf {p}}}_g
\dot\xi= \frac{p_{\xi}}{Q}
\dot p_{\xi} =   \sum_{i=1}^N \frac{{\mathbf {p}}_i^2 }{m_i} + \frac{1}{W_g} \mathrm{Tr}\left[ {\overline{\mathbf {p}}}_g^t {\overline{\mathbf {p}}}_g \right] - (N_f + d^2) kT

References[edit]