Test volume method - Revision history

Nice and Tidy at 10:44, 7 February 2008

2008-02-07T10:44:58Z

← Older revision		Revision as of 12:44, 7 February 2008
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	The method is clearly inspired by the [[ Widom test-particle method]], which is used to obtain the [[chemical potential]].		The method is clearly inspired by the [[ Widom test-particle method]], which is used to obtain the [[chemical potential]].
	It has been argued that this method can be more useful than [[virial pressure]], since it avoids the calculation of forces (which are not needed in a [[Monte Carlo]] simulation). Moreover, there are interaction potentials that are [[Idealised models#Piecewise continuous models \|discontinuous]]. In such cases the forces are not well defined, and one would have to consider the limit of "almost-discontinuous" potentials instead, which can be cumbersome. However, it should be noted that it is not clear how to "blow up" a system containing molecules held by rigid constraints.		It has been argued that this method can be more useful than [[virial pressure]], since it avoids the calculation of forces (which are not needed in a [[Monte Carlo]] simulation). Moreover, there are interaction potentials that are [[Idealised models#Piecewise continuous models \|discontinuous]]. In such cases the forces are not well defined, and one would have to consider the limit of "almost-discontinuous" potentials instead, which can be cumbersome. However, it should be noted that it is not clear how to "blow up" a system containing molecules held by rigid constraints.
			==See also==
			*[[Test area method]]
	==References==		==References==
	#[http://dx.doi.org/10.1063/1.472721 V. I. Harismiadis, J. Vorholz, and A. Z. Panagiotopoulos "Efficient pressure estimation in molecular simulations without evaluating the virial", Journal of Chemical Physics '''105''' pp. 8469- (1996)]		#[http://dx.doi.org/10.1063/1.472721 V. I. Harismiadis, J. Vorholz, and A. Z. Panagiotopoulos "Efficient pressure estimation in molecular simulations without evaluating the virial", Journal of Chemical Physics '''105''' pp. 8469- (1996)]
	[[category: computer simulation techniques]]		[[category: computer simulation techniques]]

Nice and Tidy: Slight tidy up.

2008-02-07T10:44:01Z

Slight tidy up.

← Older revision		Revision as of 12:44, 7 February 2008
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	An alternative to the [[virial pressure]] route to calculating the pressure~~, there is~~ a method ~~which~~ consists on		The '''test volume method''' provides an alternative to the [[virial pressure]] route for calculating the [[pressure]] of a system. This method consists of
	evaluating the change in [[internal energy]], <math>\Delta U</math> produced by a small change in the volume of the system <math>\Delta V</math>.		evaluating the change in [[internal energy]], <math>\Delta U</math> produced by a small change in the volume of the system, <math>\Delta V</math>.

	This ~~should~~ be ~~tough~~ of as a "blow-up" (or "in") of the whole system, <math>x \rightarrow (1+\alpha) x</math> with a small <math>\alpha</math> (~~same~~ for <~~nowiki~~>y</~~nowiki~~> and <math>z</math>), exactly in the way as the [[virial pressure]] expression may be derived - not as leaving the particles in their places and changing the simulation cell (a procedure which does not make sense in general).		This can be thought of as a "blow-up" (or "in") of the whole system, <math>x \rightarrow (1+\alpha) x</math> with a small <math>\alpha</math> (similarly for <math>y</math> and <math>z</math>), exactly in the same way as the [[virial pressure]] expression may be derived, i.e. not as leaving the particles in their places and changing the simulation cell (a procedure which does not make sense in general).

	It can be shown that		It can be shown that
	:<math> p = \frac{ k_B T N}{V} + \frac{ k_B T }{ \Delta V } \log \langle \exp(-\Delta U/k_B T )\rangle,</math>		:<math> p = \frac{ k_B T N}{V} + \frac{ k_B T }{ \Delta V } \log \langle \exp(-\Delta U/k_B T )\rangle,</math>
	where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]].		where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]].
	The method is clearly inspired by the [[ Widom test-particle method]] to obtain the [[chemical potential]].		The method is clearly inspired by the [[ Widom test-particle method]], which is used to obtain the [[chemical potential]].
			It has been argued that this method can be more useful than [[virial pressure]], since it avoids the calculation of forces (which are not needed in a [[Monte Carlo]] simulation). Moreover, there are interaction potentials that are [[Idealised models#Piecewise continuous models \|discontinuous]]. In such cases the forces are not well defined, and one would have to consider the limit of "almost-discontinuous" potentials instead, which can be cumbersome. However, it should be noted that it is not clear how to "blow up" a system containing molecules held by rigid constraints.
	It has been argued that this method can be more useful than [[virial pressure]] since it avoids the calculation of forces (which are not needed in a [[Monte Carlo]] simulation). Moreover, there are interaction potentials that are discontinuous ~~- in this case,~~ the forces are not well defined, and one ~~should~~ consider the limit of "almost-discontinuous" potentials instead, which can be cumbersome. However, it is not clear how to "blow up" a system containing molecules held by rigid constraints.
	==References==		==References==
	#[http://dx.doi.org/10.1063/1.472721 V. I. Harismiadis, J. Vorholz, and A. Z. Panagiotopoulos "Efficient pressure estimation in molecular simulations without evaluating the virial", Journal of Chemical Physics '''105''' pp. 8469- (1996)]		#[http://dx.doi.org/10.1063/1.472721 V. I. Harismiadis, J. Vorholz, and A. Z. Panagiotopoulos "Efficient pressure estimation in molecular simulations without evaluating the virial", Journal of Chemical Physics '''105''' pp. 8469- (1996)]
			[[category: computer simulation techniques]]

Dduque: More info on advantages and limitations

2008-02-07T10:12:53Z

More info on advantages and limitations

← Older revision		Revision as of 12:12, 7 February 2008
Line 1:		Line 1:
	An alternative to the [[virial pressure]] route to calculating the pressure, there is a method which consists on		An alternative to the [[virial pressure]] route to calculating the pressure, there is a method which consists on
	evaluating the change in [[internal energy]], <math>\Delta U</math> produced by a small change in the volume of the system <math>\Delta V</math>. ~~It can be shown that~~		evaluating the change in [[internal energy]], <math>\Delta U</math> produced by a small change in the volume of the system <math>\Delta V</math>.

			This should be tough of as a "blow-up" (or "in") of the whole system, <math>x \rightarrow (1+\alpha) x</math> with a small <math>\alpha</math> (same for <nowiki>y</nowiki> and <math>z</math>), exactly in the way as the [[virial pressure]] expression may be derived - not as leaving the particles in their places and changing the simulation cell (a procedure which does not make sense in general).

			It can be shown that
	:<math> p = \frac{ k_B T N}{V} + \frac{ k_B T }{ \Delta V } \log \langle \exp(-\Delta U/k_B T )\rangle,</math>		:<math> p = \frac{ k_B T N}{V} + \frac{ k_B T }{ \Delta V } \log \langle \exp(-\Delta U/k_B T )\rangle,</math>
	where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]].		where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]].
	The method is clearly inspired by the [[ Widom test-particle method]] to obtain the [[chemical potential]].		The method is clearly inspired by the [[ Widom test-particle method]] to obtain the [[chemical potential]].

			It has been argued that this method can be more useful than [[virial pressure]] since it avoids the calculation of forces (which are not needed in a [[Monte Carlo]] simulation). Moreover, there are interaction potentials that are discontinuous - in this case, the forces are not well defined, and one should consider the limit of "almost-discontinuous" potentials instead, which can be cumbersome. However, it is not clear how to "blow up" a system containing molecules held by rigid constraints.
	==References==		==References==
	#[http://dx.doi.org/10.1063/1.472721 V. I. Harismiadis, J. Vorholz, and A. Z. Panagiotopoulos "Efficient pressure estimation in molecular simulations without evaluating the virial", Journal of Chemical Physics '''105''' pp. 8469- (1996)]		#[http://dx.doi.org/10.1063/1.472721 V. I. Harismiadis, J. Vorholz, and A. Z. Panagiotopoulos "Efficient pressure estimation in molecular simulations without evaluating the virial", Journal of Chemical Physics '''105''' pp. 8469- (1996)]

Nice and Tidy: Added year to Ref.

2008-02-07T09:56:26Z

Added year to Ref.

← Older revision		Revision as of 11:56, 7 February 2008
Line 4:		Line 4:
	:<math> p = \frac{ k_B T N}{V} + \frac{ k_B T }{ \Delta V } \log \langle \exp(-\Delta U/k_B T )\rangle,</math>		:<math> p = \frac{ k_B T N}{V} + \frac{ k_B T }{ \Delta V } \log \langle \exp(-\Delta U/k_B T )\rangle,</math>
	where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]].		where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]].

	The method is clearly inspired by the [[ Widom test-particle method]] to obtain the [[chemical potential]].		The method is clearly inspired by the [[ Widom test-particle method]] to obtain the [[chemical potential]].

	==References==		==References==
	#[http://dx.doi.org/10.1063/1.472721 V. I. Harismiadis, J. Vorholz, and A. Z. Panagiotopoulos "Efficient pressure estimation in molecular simulations without evaluating the virial", Journal of Chemical Physics '''105''' p. 8469 ]		#[http://dx.doi.org/10.1063/1.472721 V. I. Harismiadis, J. Vorholz, and A. Z. Panagiotopoulos "Efficient pressure estimation in molecular simulations without evaluating the virial", Journal of Chemical Physics '''105''' pp. 8469- (1996)]

Dduque: New page: An alternative to the virial pressure route to calculating the pressure, there is a method which consists on evaluating the change in internal energy, $\Delta U$ produce...

2008-02-07T09:53:22Z

New page: An alternative to the virial pressure route to calculating the pressure, there is a method which consists on evaluating the change in internal energy, <math>\Delta U</math> produce...

New page

An alternative to the [[virial pressure]] route to calculating the pressure, there is a method which consists on
evaluating the change in [[internal energy]], <math>\Delta U</math> produced by a small change in the volume of the system <math>\Delta V</math>. It can be shown that

:<math> p = \frac{ k_B T N}{V} + \frac{ k_B T }{ \Delta V } \log \langle \exp(-\Delta U/k_B T )\rangle,</math>
where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the [[temperature]].

The method is clearly inspired by the [[ Widom test-particle method]] to obtain the [[chemical potential]].

==References==
#[http://dx.doi.org/10.1063/1.472721 V. I. Harismiadis, J. Vorholz, and A. Z. Panagiotopoulos "Efficient pressure estimation in molecular simulations without evaluating the virial", Journal of Chemical Physics '''105''' p. 8469 ]

Test volume method - Revision history

Nice and Tidy at 10:44, 7 February 2008

Nice and Tidy: Slight tidy up.

Dduque: More info on advantages and limitations

Nice and Tidy: Added year to Ref.

Dduque: New page: An alternative to the virial pressure route to calculating the pressure, there is a method which consists on evaluating the change in internal energy, \Delta U produce...

Dduque: New page: An alternative to the virial pressure route to calculating the pressure, there is a method which consists on evaluating the change in internal energy, $\Delta U$ produce...