Modulated patchy Lennard-Jones model - Revision history

Carl McBride: /* References */ Added a recent publication

2012-06-07T12:58:36Z

References: Added a recent publication

← Older revision		Revision as of 14:58, 7 June 2012
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	==References==		==References==
	<references/>		<references/>
			;Related reading
			*[http://dx.doi.org/10.1063/1.4722477 Emanuela Bianchi, Günther Doppelbauer, Laura Filion, Marjolein Dijkstra, and Gerhard Kahl "Predicting patchy particle crystals: Variable box shape simulations and evolutionary algorithms", Journal of Chemical Physics '''136''' 214102 (2012)]
	[[category: models]]		[[category: models]]

Carl McBride: Added equation numbers

2010-05-14T11:02:30Z

Added equation numbers

← Older revision		Revision as of 13:02, 14 May 2010
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	The '''modulated patchy Lennard-Jones model''' is given by		The '''modulated patchy Lennard-Jones model''' is given by
	<ref>[http://dx.doi.org/10.1039/b614955c Jonathan P. K. Doye, Ard A. Louis, I-Chun Lin, Lucy R. Allen, Eva G. Noya, Alex W. Wilber, Hoong Chwan Kok and Rosie Lyus "Controlling crystallization and its absence: proteins, colloids and patchy models", Physical Chemistry Chemical Physics '''9''' pp. 2197-2205 (2007)]</ref>		<ref>[http://dx.doi.org/10.1039/b614955c Jonathan P. K. Doye, Ard A. Louis, I-Chun Lin, Lucy R. Allen, Eva G. Noya, Alex W. Wilber, Hoong Chwan Kok and Rosie Lyus "Controlling crystallization and its absence: proteins, colloids and patchy models", Physical Chemistry Chemical Physics '''9''' pp. 2197-2205 (2007)]</ref> (Eqs. 4.3 and 4.4)

	:<math>u_{\mathrm {patchy}}({\mathbf r}_{ij},{\mathbf \Omega}_i,{\mathbf \Omega}_j) =		:<math>\Phi_{\mathrm {patchy}}({\mathbf r}_{ij},{\mathbf \Omega}_i,{\mathbf \Omega}_j) =
	\left\{ \begin{array}{lll}		\left\{ \begin{array}{lll}

	u_{\mathrm {LJ}}(r_{ij}) & ; & r_{ij} < \sigma_{\mathrm {LJ}} \\		\Phi_{\mathrm {LJ}}(r_{ij}) & ; & r_{ij} < \sigma_{\mathrm {LJ}} \\

	u_{\mathrm{LJ}}(r_{ij}) \exp \left(-\frac{\theta_{k_{min},ij}^2}{2\sigma^2 } \right) \exp \left(-\frac{\theta_{l_{min},ji}^2}{2\sigma^2 } \right)		\Phi_{\mathrm{LJ}}(r_{ij}) \exp \left(-\frac{\theta_{k_{min},ij}^2}{2\sigma^2 } \right) \exp \left(-\frac{\theta_{l_{min},ji}^2}{2\sigma^2 } \right)
	& ; & r_{ij} \ge \sigma_{\mathrm{LJ}}		& ; & r_{ij} \ge \sigma_{\mathrm{LJ}}

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	</math>		</math>

	where <math>u_{\mathrm {LJ}}(r_{ij})</math> is the [[Lennard-Jones model \| Lennard-Jones potential]] and		where <math>\Phi_{\mathrm {LJ}}(r_{ij})</math> is the [[Lennard-Jones model \| Lennard-Jones potential]] and
	[[Image:patchy_model.png\|center]]		[[Image:patchy_model.png\|center]]
	==References==		==References==

Carl McBride: New page: The '''modulated patchy Lennard-Jones model''' is given by [http://dx.doi.org/10.1039/b614955c Jonathan P. K. Doye, Ard A. Louis, I-Chun Lin, Lucy R. Allen, Eva G. Noya, Alex W. Wilbe...

2010-05-14T09:22:41Z

New page: The '''modulated patchy Lennard-Jones model''' is given by <ref>[http://dx.doi.org/10.1039/b614955c Jonathan P. K. Doye, Ard A. Louis, I-Chun Lin, Lucy R. Allen, Eva G. Noya, Alex W. Wilbe...

New page

The '''modulated patchy Lennard-Jones model''' is given by
<ref>[http://dx.doi.org/10.1039/b614955c Jonathan P. K. Doye, Ard A. Louis, I-Chun Lin, Lucy R. Allen, Eva G. Noya, Alex W. Wilber, Hoong Chwan Kok and Rosie Lyus "Controlling crystallization and its absence: proteins, colloids and patchy models", Physical Chemistry Chemical Physics '''9''' pp. 2197-2205 (2007)]</ref>

:<math>u_{\mathrm {patchy}}({\mathbf r}_{ij},{\mathbf \Omega}_i,{\mathbf \Omega}_j) =
\left\{ \begin{array}{lll}

u_{\mathrm {LJ}}(r_{ij}) & ; & r_{ij} < \sigma_{\mathrm {LJ}} \\

u_{\mathrm{LJ}}(r_{ij}) \exp \left(-\frac{\theta_{k_{min},ij}^2}{2\sigma^2 } \right) \exp \left(-\frac{\theta_{l_{min},ji}^2}{2\sigma^2 } \right)
& ; & r_{ij} \ge \sigma_{\mathrm{LJ}}

\end{array} \right.
</math>

where <math>u_{\mathrm {LJ}}(r_{ij})</math> is the [[Lennard-Jones model | Lennard-Jones potential]] and
[[Image:patchy_model.png|center]]
==References==
<references/>

[[category: models]]