Pressure - Revision history

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

2018-03-02T11:22:04Z

References: Added a recent publication

← Older revision		Revision as of 13:22, 2 March 2018
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	*[http://dx.doi.org/10.1063/1.4948711 Ronald E. Miller, Ellad B. Tadmor, Joshua S. Gibson, Noam Bernstein and Fabio Pavia "Molecular dynamics at constant Cauchy stress", Journal of Chemical Physics '''144''' 184107 (2016)]		*[http://dx.doi.org/10.1063/1.4948711 Ronald E. Miller, Ellad B. Tadmor, Joshua S. Gibson, Noam Bernstein and Fabio Pavia "Molecular dynamics at constant Cauchy stress", Journal of Chemical Physics '''144''' 184107 (2016)]
	*[http://dx.doi.org/10.1063/1.4984834 E. R. Smith, D. M. Heyes, and D. Dini "Towards the Irving-Kirkwood limit of the mechanical stress tensor", Journal of Chemical Physics '''146''' 224109 (2017)]		*[http://dx.doi.org/10.1063/1.4984834 E. R. Smith, D. M. Heyes, and D. Dini "Towards the Irving-Kirkwood limit of the mechanical stress tensor", Journal of Chemical Physics '''146''' 224109 (2017)]
			*[https://doi.org/10.1063/1.5019424 Matthias Krüger, Alexandre Solon, Vincent Démery, Christian M. Rohwer, and David S. Dean "Stresses in non-equilibrium fluids: Exact formulation and coarse-grained theory", Journal of Chemical Physics '''148''' 084503 (2018)]

134.58.253.57 at 12:45, 2 January 2018

2018-01-02T12:45:12Z

← Older revision		Revision as of 14:45, 2 January 2018
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	'''Pressure''' (<math>p</math>) is the force per unit area applied on a surface, in a direction perpendicular to that surface, i.e. the scalar part of the [[stress]] tensor under equilibrium/~~hydrosatic~~ conditions.		'''Pressure''' (<math>p</math>) is the force per unit area applied on a surface, in a direction perpendicular to that surface, i.e. the scalar part of the [[stress]] tensor under equilibrium/hydrostatic conditions.
	==Thermodynamics==		==Thermodynamics==
	In thermodynamics the pressure is given by		In thermodynamics the pressure is given by

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

2017-06-19T15:57:07Z

References: Added a recent publication

← Older revision		Revision as of 17:57, 19 June 2017
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	*[http://dx.doi.org/10.1063/1.4944620 Sadrul Chowdhury, Sneha Abraham, Toby Hudson and Peter Harrowell "Long range stress correlations in the inherent structures of liquids at rest", Journal of Chemical Physics '''144''' 124508 (2016)]		*[http://dx.doi.org/10.1063/1.4944620 Sadrul Chowdhury, Sneha Abraham, Toby Hudson and Peter Harrowell "Long range stress correlations in the inherent structures of liquids at rest", Journal of Chemical Physics '''144''' 124508 (2016)]
	*[http://dx.doi.org/10.1063/1.4948711 Ronald E. Miller, Ellad B. Tadmor, Joshua S. Gibson, Noam Bernstein and Fabio Pavia "Molecular dynamics at constant Cauchy stress", Journal of Chemical Physics '''144''' 184107 (2016)]		*[http://dx.doi.org/10.1063/1.4948711 Ronald E. Miller, Ellad B. Tadmor, Joshua S. Gibson, Noam Bernstein and Fabio Pavia "Molecular dynamics at constant Cauchy stress", Journal of Chemical Physics '''144''' 184107 (2016)]
			*[http://dx.doi.org/10.1063/1.4984834 E. R. Smith, D. M. Heyes, and D. Dini "Towards the Irving-Kirkwood limit of the mechanical stress tensor", Journal of Chemical Physics '''146''' 224109 (2017)]

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

2016-05-17T11:19:11Z

References: Added a recent publication

← Older revision		Revision as of 13:19, 17 May 2016
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	*[http://dx.doi.org/10.1063/1.4900773 F. J. Martínez-Ruiz, F. J. Blas, B. Mendiboure and A. I. Moreno-Ventas Bravo "Effect of dispersive long-range corrections to the pressure tensor: The vapour-liquid interfacial properties of the Lennard-Jones system revisited", Journal of Chemical Physics '''141''' 184701 (2014)]		*[http://dx.doi.org/10.1063/1.4900773 F. J. Martínez-Ruiz, F. J. Blas, B. Mendiboure and A. I. Moreno-Ventas Bravo "Effect of dispersive long-range corrections to the pressure tensor: The vapour-liquid interfacial properties of the Lennard-Jones system revisited", Journal of Chemical Physics '''141''' 184701 (2014)]
	*[http://dx.doi.org/10.1063/1.4944620 Sadrul Chowdhury, Sneha Abraham, Toby Hudson and Peter Harrowell "Long range stress correlations in the inherent structures of liquids at rest", Journal of Chemical Physics '''144''' 124508 (2016)]		*[http://dx.doi.org/10.1063/1.4944620 Sadrul Chowdhury, Sneha Abraham, Toby Hudson and Peter Harrowell "Long range stress correlations in the inherent structures of liquids at rest", Journal of Chemical Physics '''144''' 124508 (2016)]
			*[http://dx.doi.org/10.1063/1.4948711 Ronald E. Miller, Ellad B. Tadmor, Joshua S. Gibson, Noam Bernstein and Fabio Pavia "Molecular dynamics at constant Cauchy stress", Journal of Chemical Physics '''144''' 184107 (2016)]

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

2016-04-05T12:14:18Z

References: Added a recent publication

← Older revision		Revision as of 14:14, 5 April 2016
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	*[http://dx.doi.org/10.1063/1.4807305 J. P. Wittmer, H. Xu, P. Polińska, F. Weysser, and J. Baschnagel "Communication: Pressure fluctuations in isotropic solids and fluids", Journal of Chemical Physics '''138''' 191101 (2013)]		*[http://dx.doi.org/10.1063/1.4807305 J. P. Wittmer, H. Xu, P. Polińska, F. Weysser, and J. Baschnagel "Communication: Pressure fluctuations in isotropic solids and fluids", Journal of Chemical Physics '''138''' 191101 (2013)]
	*[http://dx.doi.org/10.1063/1.4900773 F. J. Martínez-Ruiz, F. J. Blas, B. Mendiboure and A. I. Moreno-Ventas Bravo "Effect of dispersive long-range corrections to the pressure tensor: The vapour-liquid interfacial properties of the Lennard-Jones system revisited", Journal of Chemical Physics '''141''' 184701 (2014)]		*[http://dx.doi.org/10.1063/1.4900773 F. J. Martínez-Ruiz, F. J. Blas, B. Mendiboure and A. I. Moreno-Ventas Bravo "Effect of dispersive long-range corrections to the pressure tensor: The vapour-liquid interfacial properties of the Lennard-Jones system revisited", Journal of Chemical Physics '''141''' 184701 (2014)]
			*[http://dx.doi.org/10.1063/1.4944620 Sadrul Chowdhury, Sneha Abraham, Toby Hudson and Peter Harrowell "Long range stress correlations in the inherent structures of liquids at rest", Journal of Chemical Physics '''144''' 124508 (2016)]

141.212.161.179: /* Virial pressure */

2015-04-10T18:03:17Z

Virial pressure

← Older revision		Revision as of 20:03, 10 April 2015
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	The '''virial pressure''' is commonly used to obtain the [[pressure]] from a general simulation. It is particularly well suited to [[molecular dynamics]], since [[Newtons laws#Newton's second law of motion \|forces]] are evaluated and readily available. For pair interactions, one has (Eq. 2 in <ref>[http://dx.doi.org/10.1063/1.2363381 Enrique de Miguel and George Jackson "The nature of the calculation of the pressure in molecular simulations of continuous models from volume perturbations", Journal of Chemical Physics '''125''' 164109 (2006)]</ref>):		The '''virial pressure''' is commonly used to obtain the [[pressure]] from a general simulation. It is particularly well suited to [[molecular dynamics]], since [[Newtons laws#Newton's second law of motion \|forces]] are evaluated and readily available. For pair interactions, one has (Eq. 2 in <ref>[http://dx.doi.org/10.1063/1.2363381 Enrique de Miguel and George Jackson "The nature of the calculation of the pressure in molecular simulations of continuous models from volume perturbations", Journal of Chemical Physics '''125''' 164109 (2006)]</ref>):

	:<math> p = \frac{ k_B T N}{V} + \frac{ 1 }{ d V } \overline{ \sum_{i<j} {\mathbf f}_{ij} {\mathbf r}_{ij} }, </math>		:<math> p = \frac{ k_B T N}{V} + \frac{ 1 }{ V d } \overline{ \sum_{i<j} {\mathbf f}_{ij} {\mathbf r}_{ij} }, </math>

	where <math>p</math> is the pressure, <math>T</math> is the [[temperature]], <math>V</math> is the volume and <math>k_B</math> is the [[Boltzmann constant]].		where <math>p</math> is the pressure, <math>T</math> is the [[temperature]], <math>V</math> is the volume and <math>k_B</math> is the [[Boltzmann constant]].
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	For example, for the [[Lennard-Jones model \| Lennard-Jones potential]], <math>f(r)=24\epsilon(2(\sigma/r)^{12}- (\sigma/r)^6 )/r</math>. Hence, the expression reduces to		For example, for the [[Lennard-Jones model \| Lennard-Jones potential]], <math>f(r)=24\epsilon(2(\sigma/r)^{12}- (\sigma/r)^6 )/r</math>. Hence, the expression reduces to
	:<math> p = \frac{ k_B T N}{V} + \frac{ 1 }{ d V } \overline{ \sum_{i<j} f(r_{ij}) r_{ij} }. </math>		:<math> p = \frac{ k_B T N}{V} + \frac{ 1 }{ V d } \overline{ \sum_{i<j} f(r_{ij}) r_{ij} }. </math>

	Notice that most [[Realistic models \|realistic potentials]] are attractive at long ranges; hence the first correction to the ideal pressure will be a negative contribution: the [[second virial coefficient]]. On the other hand, contributions from purely repulsive potentials, such as [[hard sphere model \| hard spheres]], are always positive.		Notice that most [[Realistic models \|realistic potentials]] are attractive at long ranges; hence the first correction to the ideal pressure will be a negative contribution: the [[second virial coefficient]]. On the other hand, contributions from purely repulsive potentials, such as [[hard sphere model \| hard spheres]], are always positive.

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

2014-11-17T12:29:54Z

References: Added a recent publication

← Older revision		Revision as of 14:29, 17 November 2014
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	*[http://dx.doi.org/10.1063/1.4755946 Jerry Zhijian Yang, Xiaojie Wu, and Xiantao Li "A generalized Irving–Kirkwood formula for the calculation of stress in molecular dynamics models", Journal of Chemical Physics '''137''' 134104 (2012)]		*[http://dx.doi.org/10.1063/1.4755946 Jerry Zhijian Yang, Xiaojie Wu, and Xiantao Li "A generalized Irving–Kirkwood formula for the calculation of stress in molecular dynamics models", Journal of Chemical Physics '''137''' 134104 (2012)]
	*[http://dx.doi.org/10.1063/1.4807305 J. P. Wittmer, H. Xu, P. Polińska, F. Weysser, and J. Baschnagel "Communication: Pressure fluctuations in isotropic solids and fluids", Journal of Chemical Physics '''138''' 191101 (2013)]		*[http://dx.doi.org/10.1063/1.4807305 J. P. Wittmer, H. Xu, P. Polińska, F. Weysser, and J. Baschnagel "Communication: Pressure fluctuations in isotropic solids and fluids", Journal of Chemical Physics '''138''' 191101 (2013)]
			*[http://dx.doi.org/10.1063/1.4900773 F. J. Martínez-Ruiz, F. J. Blas, B. Mendiboure and A. I. Moreno-Ventas Bravo "Effect of dispersive long-range corrections to the pressure tensor: The vapour-liquid interfacial properties of the Lennard-Jones system revisited", Journal of Chemical Physics '''141''' 184701 (2014)]

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

2013-05-21T14:58:11Z

References: Added a recent publication

← Older revision		Revision as of 16:58, 21 May 2013
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	*[http://dx.doi.org/10.1063/1.3692733 Péter T. Kiss and András Baranyai "On the pressure calculation for polarizable models in computer simulation", Journal of Chemical Physics '''136''' 104109 (2012)]		*[http://dx.doi.org/10.1063/1.3692733 Péter T. Kiss and András Baranyai "On the pressure calculation for polarizable models in computer simulation", Journal of Chemical Physics '''136''' 104109 (2012)]
	*[http://dx.doi.org/10.1063/1.4755946 Jerry Zhijian Yang, Xiaojie Wu, and Xiantao Li "A generalized Irving–Kirkwood formula for the calculation of stress in molecular dynamics models", Journal of Chemical Physics '''137''' 134104 (2012)]		*[http://dx.doi.org/10.1063/1.4755946 Jerry Zhijian Yang, Xiaojie Wu, and Xiantao Li "A generalized Irving–Kirkwood formula for the calculation of stress in molecular dynamics models", Journal of Chemical Physics '''137''' 134104 (2012)]
			*[http://dx.doi.org/10.1063/1.4807305 J. P. Wittmer, H. Xu, P. Polińska, F. Weysser, and J. Baschnagel "Communication: Pressure fluctuations in isotropic solids and fluids", Journal of Chemical Physics '''138''' 191101 (2013)]

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

2012-10-08T10:30:40Z

References: Added a recent publication

← Older revision		Revision as of 12:30, 8 October 2012
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	*[http://dx.doi.org/10.1063/1.3626410 Takenobu Nakamura, Wataru Shinoda, and Tamio Ikeshoji "Novel numerical method for calculating the pressure tensor in spherical coordinates for molecular systems", Journal of Chemical Physics '''135''' 094106 (2011)]		*[http://dx.doi.org/10.1063/1.3626410 Takenobu Nakamura, Wataru Shinoda, and Tamio Ikeshoji "Novel numerical method for calculating the pressure tensor in spherical coordinates for molecular systems", Journal of Chemical Physics '''135''' 094106 (2011)]
	*[http://dx.doi.org/10.1063/1.3692733 Péter T. Kiss and András Baranyai "On the pressure calculation for polarizable models in computer simulation", Journal of Chemical Physics '''136''' 104109 (2012)]		*[http://dx.doi.org/10.1063/1.3692733 Péter T. Kiss and András Baranyai "On the pressure calculation for polarizable models in computer simulation", Journal of Chemical Physics '''136''' 104109 (2012)]
			*[http://dx.doi.org/10.1063/1.4755946 Jerry Zhijian Yang, Xiaojie Wu, and Xiantao Li "A generalized Irving–Kirkwood formula for the calculation of stress in molecular dynamics models", Journal of Chemical Physics '''137''' 134104 (2012)]

Carl McBride: /* Virial pressure */ Added a reference

2012-06-05T12:15:01Z

Virial pressure: Added a reference

← Older revision		Revision as of 14:15, 5 June 2012
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	where where <math>\ \sigma_{x}</math>, <math>\ \sigma_{y}</math>, and <math>\ \sigma_{z}</math> are normal stresses, and <math>\ \tau_{xy}</math>, <math>\ \tau_{xz}</math>, <math>\ \tau_{yx}</math>, <math>\ \tau_{yz}</math>, <math>\ \tau_{zx}</math>, and <math>\ \tau_{zy}</math> are shear stresess.		where where <math>\ \sigma_{x}</math>, <math>\ \sigma_{y}</math>, and <math>\ \sigma_{z}</math> are normal stresses, and <math>\ \tau_{xy}</math>, <math>\ \tau_{xz}</math>, <math>\ \tau_{yx}</math>, <math>\ \tau_{yz}</math>, <math>\ \tau_{zx}</math>, and <math>\ \tau_{zy}</math> are shear stresess.
	==Virial pressure==		==Virial pressure==
	The '''virial pressure''' is commonly used to obtain the [[pressure]] from a general simulation. It is particularly well suited to [[molecular dynamics]], since [[Newtons laws#Newton's second law of motion \|forces]] are evaluated and readily available. For pair interactions, one has:		The '''virial pressure''' is commonly used to obtain the [[pressure]] from a general simulation. It is particularly well suited to [[molecular dynamics]], since [[Newtons laws#Newton's second law of motion \|forces]] are evaluated and readily available. For pair interactions, one has (Eq. 2 in <ref>[http://dx.doi.org/10.1063/1.2363381 Enrique de Miguel and George Jackson "The nature of the calculation of the pressure in molecular simulations of continuous models from volume perturbations", Journal of Chemical Physics '''125''' 164109 (2006)]</ref>):

	:<math> p = \frac{ k_B T N}{V} + \frac{ 1 }{ d V } \overline{ \sum_{i<j} {\mathbf f}_{ij} {\mathbf r}_{ij} }, </math>		:<math> p = \frac{ k_B T N}{V} + \frac{ 1 }{ d V } \overline{ \sum_{i<j} {\mathbf f}_{ij} {\mathbf r}_{ij} }, </math>