218 lines
9.7 KiB
ReStructuredText
218 lines
9.7 KiB
ReStructuredText
.. index:: compute temp/profile
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compute temp/profile command
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============================
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Syntax
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""""""
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.. code-block:: LAMMPS
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compute ID group-ID temp/profile xflag yflag zflag binstyle args
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* ID, group-ID are documented in :doc:`compute <compute>` command
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* temp/profile = style name of this compute command
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* xflag,yflag,zflag = 0/1 for whether to exclude/include this dimension
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* binstyle = *x* or *y* or *z* or *xy* or *yz* or *xz* or *xyz*
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.. parsed-literal::
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*x* arg = Nx
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*y* arg = Ny
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*z* arg = Nz
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*xy* args = Nx Ny
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*yz* args = Ny Nz
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*xz* args = Nx Nz
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*xyz* args = Nx Ny Nz
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Nx, Ny, Nz = number of velocity bins in *x*, *y*, *z* dimensions
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* zero or more keyword/value pairs may be appended
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* keyword = *out*
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.. parsed-literal::
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*out* value = *tensor* or *bin*
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Examples
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""""""""
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.. code-block:: LAMMPS
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compute myTemp flow temp/profile 1 1 1 x 10
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compute myTemp flow temp/profile 1 1 1 x 10 out bin
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compute myTemp flow temp/profile 0 1 1 xyz 20 20 20
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Description
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"""""""""""
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Define a computation that calculates the temperature of a group of
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atoms, after subtracting out a spatially-averaged center-of-mass
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velocity field, before computing the kinetic energy. This can be
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useful for thermostatting a collection of atoms undergoing a complex
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flow (e.g. via a profile-unbiased thermostat (PUT) as described in
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:ref:`(Evans) <Evans1>`). A compute of this style can be used by any command
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that computes a temperature (e.g. :doc:`thermo_modify <thermo_modify>`,
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:doc:`fix temp/rescale <fix_temp_rescale>`, :doc:`fix npt <fix_nh>`).
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The *xflag*, *yflag*, *zflag* settings determine which components of
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average velocity are subtracted out.
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The *binstyle* setting and its *Nx*, *Ny*, *Nz* arguments determine how bins
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are setup to perform spatial averaging. "Bins" can be 1d slabs, 2d pencils,
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or 3d bricks depending on which *binstyle* is used. The simulation box is
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partitioned conceptually into *Nx* :math:`\times` *Ny* :math:`\times` *Nz*
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bins. Depending on the *binstyle*, you may only specify one or two of these
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values; the others are effectively set to 1 (no binning in that dimension).
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For non-orthogonal (triclinic) simulation boxes, the bins are "tilted" slabs or
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pencils or bricks that are parallel to the tilted faces of the box. See the
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:doc:`region prism <region>` command for a discussion of the geometry of tilted
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boxes in LAMMPS.
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When a temperature is computed, the center-of-mass velocity for the
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set of atoms that are both in the compute group and in the same
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spatial bin is calculated. This bias velocity is then subtracted from
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the velocities of individual atoms in the bin to yield a thermal
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velocity for each atom. Note that if there is only one atom in the
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bin, its thermal velocity will thus be 0.0.
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After the spatially-averaged velocity field has been subtracted from
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each atom, the temperature is calculated by the formula
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.. math::
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\text{KE} = \left( \frac{\text{dim}}{N} - N_s N_x N_y N_z
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- \text{extra} \right) \frac{k_B T}{2},
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where KE is the total kinetic energy of the group of atoms (sum of
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:math:`\frac12 m v^2`; dim = 2 or 3 is the dimensionality of the simulation;
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:math:`N_s =` 0, 1, 2, or 3 for streaming velocity subtracted in 0, 1, 2, or 3
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dimensions, respectively; *extra* is the number of extra degrees of freedom;
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*N* is the number of atoms in the group; :math:`k_B` is the Boltzmann constant,
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and :math:`T` is the absolute temperature. The :math:`N_s N_x N_y N_z` term is
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the number of degrees of freedom subtracted to adjust for the removal of the
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center-of-mass velocity in each direction of the *Nx\*Ny\*Nz* bins, as
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discussed in the :ref:`(Evans) <Evans1>` paper. The extra term defaults to
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:math:`\text{dim} - N_s` and accounts for overall conservation of
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center-of-mass velocity across the group in directions where streaming velocity
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is *not* subtracted. This can be altered using the *extra* option of the
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:doc:`compute_modify <compute_modify>` command.
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If the *out* keyword is used with a *tensor* value, which is the default,
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a kinetic energy tensor, stored as a six-element vector, is also calculated by
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this compute for use in the computation of a pressure tensor. The formula for
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the components of the tensor is the same as the above formula, except that
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:math:`v^2` is replaced by :math:`v_x v_y` for the :math:`xy` component, and
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so on. The six components of the vector are ordered :math:`xx`, :math:`yy`,
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:math:`zz`, :math:`xy`, :math:`xz`, :math:`yz`.
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If the *out* keyword is used with a *bin* value, the count of atoms and
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computed temperature for each bin are stored for output, as an array of values,
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as described below. The temperature of each bin is calculated as described
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above, where the bias velocity is subtracted and only the remaining thermal
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velocity of atoms in the bin contributes to the temperature. See the note
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below for how the temperature is normalized by the degrees-of-freedom of atoms
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in the bin.
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The number of atoms contributing to the temperature is assumed to be
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constant for the duration of the run; use the *dynamic* option of the
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:doc:`compute_modify <compute_modify>` command if this is not the case.
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The removal of the spatially-averaged velocity field by this fix is
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essentially computing the temperature after a "bias" has been removed
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from the velocity of the atoms. If this compute is used with a fix
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command that performs thermostatting then this bias will be subtracted
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from each atom, thermostatting of the remaining thermal velocity will
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be performed, and the bias will be added back in. Thermostatting
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fixes that work in this way include :doc:`fix nvt <fix_nh>`,
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:doc:`fix temp/rescale <fix_temp_rescale>`,
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:doc:`fix temp/berendsen <fix_temp_berendsen>`,
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and :doc:`fix langevin <fix_langevin>`.
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This compute subtracts out degrees-of-freedom due to fixes that constrain
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molecular motion, such as :doc:`fix shake <fix_shake>` and
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:doc:`fix rigid <fix_rigid>`. This means the temperature of groups of atoms
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that include these constraints will be computed correctly. If needed, the
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subtracted degrees-of-freedom can be altered using the *extra* option of the
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:doc:`compute_modify <compute_modify>` command.
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.. note::
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When using the *out* keyword with a value of *bin*, the
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calculated temperature for each bin includes the degrees-of-freedom
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adjustment described in the preceding paragraph for fixes that
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constrain molecular motion, as well as the adjustment due to
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the *extra* option (which defaults to *dim* - *Ns* as described above),
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by fractionally applying them based on the fraction of atoms in each
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bin. As a result, the bin degrees-of-freedom summed over all bins exactly
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equals the degrees-of-freedom used in the scalar temperature calculation,
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:math:`\Sigma N_{\text{DOF}_i} = N_\text{DOF}` and the corresponding
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relation for temperature is also satisfied
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(:math:`\Sigma N_{\text{DOF}_i} T_i = N_\text{DOF} T`).
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These relations will break down in cases for which the adjustment
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exceeds the actual number of degrees of freedom in a bin. This could happen
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if a bin is empty or in situations in which rigid molecules
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are non-uniformly distributed, in which case the reported
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temperature within a bin may not be accurate.
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See the :doc:`Howto thermostat <Howto_thermostat>` page for a
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discussion of different ways to compute temperature and perform
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thermostatting. Using this compute in conjunction with a
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thermostatting fix, as explained there, will effectively implement a
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profile-unbiased thermostat (PUT), as described in :ref:`(Evans) <Evans1>`.
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Output info
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"""""""""""
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This compute calculates a global scalar (the temperature). Depending
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on the setting of the *out* keyword, it also calculates a global
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vector or array. For *out* = *tensor*, it calculates a vector of
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length 6 (KE tensor), which can be accessed by indices 1--6. For *out*
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= *bin* it calculates a global array which has 2 columns and :math:`N` rows,
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where :math:`N` is the number of bins. The first column contains the number
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of atoms in that bin. The second contains the temperature of that
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bin, calculated as described above. The ordering of rows in the array
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is as follows. Bins in :math:`x` vary fastest, then :math:`y`, then
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:math:`z`. Thus for a :math:`10\times 10\times 10` 3d array of bins, there
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will be 1000 rows. The bin with indices :math:`(i_x,i_y,i_z) = (2,3,4)` would
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map to row :math:`M = 10^2(i_z-1) + 10(i_y-1) + i_x = 322`, where the rows are
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numbered from 1 to 1000 and the bin indices are numbered from 1 to 10 in each
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dimension.
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These values can be used by any command that uses global scalar or
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vector or array values from a compute as input. See the
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:doc:`Howto output <Howto_output>` page for an overview of LAMMPS output
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options.
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The scalar value calculated by this compute is "intensive." The
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vector values are "extensive." The array values are "intensive."
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The scalar value will be in temperature :doc:`units <units>`. The
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vector values will be in energy :doc:`units <units>`. The first column
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of array values are counts; the values in the second column will be in
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temperature :doc:`units <units>`.
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Restrictions
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""""""""""""
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You should not use too large a velocity-binning grid, especially in
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3d. In the current implementation, the binned velocity averages are
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summed across all processors, so this will be inefficient if the grid
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is too large, and the operation is performed every timestep, as it
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will be for most thermostats.
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Related commands
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""""""""""""""""
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:doc:`compute temp <compute_temp>`, :doc:`compute temp/ramp <compute_temp_ramp>`, :doc:`compute temp/deform <compute_temp_deform>`, :doc:`compute pressure <compute_pressure>`
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Default
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"""""""
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The option default is out = tensor.
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----------
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.. _Evans1:
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**(Evans)** Evans and Morriss, Phys Rev Lett, 56, 2172-2175 (1986).
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