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@ -3,7 +3,7 @@
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\begin{document}
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$$
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P = \frac{N k_B T}{V} + \frac{\sum_{i}^{N} r_i \bullet f_i}{3V}
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P = \frac{N k_B T}{V} + \frac{\sum_{i}^{N} r_i \bullet f_i}{dV}
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$$
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\end{document}
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@ -36,10 +36,13 @@ in your system.
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<CENTER><IMG SRC = "Eqs/pressure.jpg">
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</CENTER>
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<P>where N is the number of atoms in the system (see discussion of DOF
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below), Kb is the Boltzmann constant, T is the temperature, V is the
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system volume, and the second term is the virial, computed within
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LAMMPS for all pairwise as well as 2-body, 3-body, 4-body bonded
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interactions.
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below), Kb is the Boltzmann constant, T is the temperature, d is the
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dimensionality of the system (2 or 3 for 2d/3d), V is the system
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volume (or area in 2d), and the second term is the virial, computed
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within LAMMPS for all pairwise as well as 2-body, 3-body, 4-body, and
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long-range interactions. <A HREF = "fix.html">Fixes</A> that impose constraints
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(e.g. the <A HREF = "fix_shake.html">fix shake</A> command) also contribute to the
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virial term.
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</P>
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<P>A 6-component pressure tensor is also calculated by this compute which
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can be output by the <A HREF = "thermo_style.html">thermo_style custom</A> command.
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@ -55,7 +58,7 @@ temperature of all atoms for consistency with the virial term, but any
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compute style that calculates temperature can be used, e.g. one that
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excludes frozen atoms or other degrees of freedom.
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</P>
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<P>Note that the N is the above formula is really degrees-of-freedom/3
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<P>Note that the N is the above formula is really degrees-of-freedom/d
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where the DOF is specified by the temperature compute. See the
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various <A HREF = "compute.html">compute temperature</A> styles for details.
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</P>
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@ -33,10 +33,13 @@ The pressure is computed by the standard formula
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:c,image(Eqs/pressure.jpg)
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where N is the number of atoms in the system (see discussion of DOF
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below), Kb is the Boltzmann constant, T is the temperature, V is the
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system volume, and the second term is the virial, computed within
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LAMMPS for all pairwise as well as 2-body, 3-body, 4-body bonded
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interactions.
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below), Kb is the Boltzmann constant, T is the temperature, d is the
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dimensionality of the system (2 or 3 for 2d/3d), V is the system
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volume (or area in 2d), and the second term is the virial, computed
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within LAMMPS for all pairwise as well as 2-body, 3-body, 4-body, and
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long-range interactions. "Fixes"_fix.html that impose constraints
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(e.g. the "fix shake"_fix_shake.html command) also contribute to the
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virial term.
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A 6-component pressure tensor is also calculated by this compute which
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can be output by the "thermo_style custom"_thermo_style.html command.
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@ -52,7 +55,7 @@ temperature of all atoms for consistency with the virial term, but any
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compute style that calculates temperature can be used, e.g. one that
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excludes frozen atoms or other degrees of freedom.
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Note that the N is the above formula is really degrees-of-freedom/3
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Note that the N is the above formula is really degrees-of-freedom/d
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where the DOF is specified by the temperature compute. See the
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various "compute temperature"_compute.html styles for details.
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@ -78,23 +78,26 @@ by the <I>p-style</I> argument. In each case, the desired pressure at each
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timestep is a ramped value during the run from the starting value to
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the end value.
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</P>
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<P>Style <I>xyz</I> means couple all 3 dimensions together when pressure is
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computed (isotropic pressure), and dilate/contract the 3 dimensions
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<P>Style <I>xyz</I> means couple all dimensions together when pressure is
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computed (isotropic pressure), and dilate/contract the dimensions
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together.
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</P>
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<P>Styles <I>xy</I> or <I>yz</I> or <I>xz</I> means that the 2 specified dimensions are
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coupled together, both for pressure computation and for
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dilation/contraction. The 3rd dimension dilates/contracts
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independently, using its pressure component as the driving force.
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These styles cannot be used for a 2d simulation.
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</P>
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<P>For style <I>aniso</I>, all 3 dimensions dilate/contract independently
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using their individual pressure components as the 3 driving forces.
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<P>For style <I>aniso</I>, all dimensions dilate/contract independently using
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their individual pressure components as the driving forces.
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</P>
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<P>For any of the styles except <I>xyz</I>, any of the independent pressure
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components (e.g. z in <I>xy</I>, or any dimension in <I>aniso</I>) can have
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their target pressures (both start and stop values) specified as NULL.
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This means that no pressure control is applied to that dimension so
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that the box dimension remains unchanged.
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that the box dimension remains unchanged. For a 2d simulation the z
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pressure components must be specified as NULL when using style
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<I>aniso</I>.
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</P>
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<P>In some cases (e.g. for solids) the pressure (volume) and/or
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temperature of the system can oscillate undesirably when a Nose/Hoover
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@ -69,23 +69,26 @@ by the {p-style} argument. In each case, the desired pressure at each
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timestep is a ramped value during the run from the starting value to
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the end value.
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Style {xyz} means couple all 3 dimensions together when pressure is
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computed (isotropic pressure), and dilate/contract the 3 dimensions
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Style {xyz} means couple all dimensions together when pressure is
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computed (isotropic pressure), and dilate/contract the dimensions
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together.
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Styles {xy} or {yz} or {xz} means that the 2 specified dimensions are
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coupled together, both for pressure computation and for
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dilation/contraction. The 3rd dimension dilates/contracts
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independently, using its pressure component as the driving force.
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These styles cannot be used for a 2d simulation.
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For style {aniso}, all 3 dimensions dilate/contract independently
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using their individual pressure components as the 3 driving forces.
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For style {aniso}, all dimensions dilate/contract independently using
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their individual pressure components as the driving forces.
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For any of the styles except {xyz}, any of the independent pressure
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components (e.g. z in {xy}, or any dimension in {aniso}) can have
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their target pressures (both start and stop values) specified as NULL.
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This means that no pressure control is applied to that dimension so
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that the box dimension remains unchanged.
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that the box dimension remains unchanged. For a 2d simulation the z
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pressure components must be specified as NULL when using style
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{aniso}.
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In some cases (e.g. for solids) the pressure (volume) and/or
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temperature of the system can oscillate undesirably when a Nose/Hoover
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|
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@ -82,23 +82,26 @@ by the <I>p-style</I> argument. In each case, the desired pressure at each
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timestep is a ramped value during the run from the starting value to
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the end value.
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</P>
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<P>Style <I>xyz</I> means couple all 3 dimensions together when pressure is
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computed (isotropic pressure), and dilate/contract the 3 dimensions
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<P>Style <I>xyz</I> means couple all dimensions together when pressure is
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computed (isotropic pressure), and dilate/contract the dimensions
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together.
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</P>
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<P>Styles <I>xy</I> or <I>yz</I> or <I>xz</I> means that the 2 specified dimensions are
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coupled together, both for pressure computation and for
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dilation/contraction. The 3rd dimension dilates/contracts
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independently, using its pressure component as the driving force.
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These styles cannot be used for a 2d simulation.
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</P>
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<P>For style <I>aniso</I>, all 3 dimensions dilate/contract independently
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using their individual pressure components as the 3 driving forces.
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<P>For style <I>aniso</I>, all dimensions dilate/contract independently using
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their individual pressure components as the driving forces.
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</P>
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<P>For any of the styles except <I>xyz</I>, any of the independent pressure
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components (e.g. z in <I>xy</I>, or any dimension in <I>aniso</I>) can have
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their target pressures (both start and stop values) specified as NULL.
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This means that no pressure control is applied to that dimension so
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that the box dimension remains unchanged.
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that the box dimension remains unchanged. For a 2d simulation the z
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pressure components must be specified as NULL when using style
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<I>aniso</I>.
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</P>
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<P>In some cases (e.g. for solids) the pressure (volume) and/or
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temperature of the system can oscillate undesirably when a Nose/Hoover
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|
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@ -71,23 +71,26 @@ by the {p-style} argument. In each case, the desired pressure at each
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timestep is a ramped value during the run from the starting value to
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the end value.
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Style {xyz} means couple all 3 dimensions together when pressure is
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computed (isotropic pressure), and dilate/contract the 3 dimensions
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Style {xyz} means couple all dimensions together when pressure is
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computed (isotropic pressure), and dilate/contract the dimensions
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together.
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Styles {xy} or {yz} or {xz} means that the 2 specified dimensions are
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coupled together, both for pressure computation and for
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dilation/contraction. The 3rd dimension dilates/contracts
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independently, using its pressure component as the driving force.
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These styles cannot be used for a 2d simulation.
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For style {aniso}, all 3 dimensions dilate/contract independently
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using their individual pressure components as the 3 driving forces.
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For style {aniso}, all dimensions dilate/contract independently using
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their individual pressure components as the driving forces.
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For any of the styles except {xyz}, any of the independent pressure
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components (e.g. z in {xy}, or any dimension in {aniso}) can have
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their target pressures (both start and stop values) specified as NULL.
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This means that no pressure control is applied to that dimension so
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that the box dimension remains unchanged.
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that the box dimension remains unchanged. For a 2d simulation the z
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pressure components must be specified as NULL when using style
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{aniso}.
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In some cases (e.g. for solids) the pressure (volume) and/or
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temperature of the system can oscillate undesirably when a Nose/Hoover
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