Martyna-Tuckerman-Tobias-Klein barostat: Difference between revisions
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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> | '''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> | ||
<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>. | <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): | ||
:<math> \dot{\mathbf {r}}_i = \frac{{\mathbf {p}}_i}{m_i} + \frac{\overline{\mathbf {p}}_g}{W_g} {\mathbf {r}}_i </math> | |||
:<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> | |||
:<math>\dot{\overline{\mathbf {h}}} = \frac{\overline{\mathbf {p}}_g {\overline{\mathbf {h}}} }{W_g}</math> | |||
:<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> | |||
:<math>\dot\xi= \frac{p_{\xi}}{Q}</math> | |||
:<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== | ||
<references/> | <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):
![{\displaystyle {\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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/047bebf5a66e401b154a0b8a23ac0d2cad4d422b)
![{\displaystyle {\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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/44de86d15a6d2135673a4ca48cc3847978088631)
![{\displaystyle {\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}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7f5f62291bbc47e174e19150dbc279935a0ebad6)
References[edit]
- ↑ Glenn J. Martyna, Douglas J. Tobias, and Michael L. Klein "Constant pressure molecular dynamics algorithms", Journal of Chemical Physics 101 pp. 4177-4189 (1994)
- ↑ 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)