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

From SklogWiki
Jump to: navigation, search
m (moved Martyna-Tuckerman-Klein barostat to Martyna-Tuckerman-Tobias-Klein barostat: Added Tobias as Douglas J. Tobias appears as a co-author.)
m (tmp save)
 
(4 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
{{Stub-general}}
 
{{Stub-general}}
 
'''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

Simeq0.png This article is a 'stub' page, it has no, or next to no, content. It is here at the moment to help form part of the structure of SklogWiki. If you add sufficient material to this article then please remove the {{Stub-general}} template from this page.

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]