174 lines
6.3 KiB
ReStructuredText
174 lines
6.3 KiB
ReStructuredText
.. index:: compute viscosity/cos
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compute viscosity/cos 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 viscosity/cos
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* ID, group-ID are documented in :doc:`compute <compute>` command
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* viscosity/cos = style name of this compute command
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Examples
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""""""""
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.. code-block:: LAMMPS
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units real
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compute cos all viscosity/cos
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variable V equal c_cos[7]
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variable A equal 0.02E-5 # A/fs^2
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variable density equal density
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variable lz equal lz
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variable reciprocalViscosity equal v_V/${A}/v_density*39.4784/v_lz/v_lz*100 # 1/(Pa*s)
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Description
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"""""""""""
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Define a computation that calculates the velocity amplitude of a group of atoms
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with an cosine-shaped velocity profile and the temperature of them
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after subtracting out the velocity profile before computing the kinetic energy.
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A compute of this style can be used by any command that computes a temperature
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(e.g., :doc:`thermo_modify <thermo_modify>`, :doc:`fix npt <fix_nh>`).
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This command together with :doc:`fix_accelerate/cos<fix_accelerate_cos>`
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enables viscosity calculation with periodic perturbation method,
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as described by :ref:`Hess<Hess1>`.
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An acceleration along the :math:`x`-direction is applied to the simulation
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system by using :doc:`fix_accelerate/cos<fix_accelerate_cos>` command.
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The acceleration is a periodic function along the :math:`z`-direction:
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.. math::
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a_{x}(z) = A \cos \left(\frac{2 \pi z}{l_{z}}\right)
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where :math:`A` is the acceleration amplitude, :math:`l_z` is the
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:math:`z`-length of the simulation box. At steady state, the acceleration
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generates a velocity profile:
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.. math::
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v_{x}(z) = V \cos \left(\frac{2 \pi z}{l_{z}}\right)
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The generated velocity amplitude :math:`V` is related to the
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shear viscosity :math:`\eta` by
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.. math::
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V = \frac{A \rho}{\eta}\left(\frac{l_{z}}{2 \pi}\right)^{2},
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and it can be obtained from ensemble average of the velocity profile via
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.. math::
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V = \frac{\sum\limits_i 2 m_{i} v_{i, x} \cos \left(\frac{2 \pi z_i}{l_{z}}\right)}{\sum\limits_i m_{i}}
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where :math:`m_i`, :math:`v_{i,x}` and :math:`z_i` are the mass,
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:math:`x`-component velocity, and :math:`z`-coordinate of a particle,
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respectively.
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After the cosine-shaped collective velocity in the :math:`x`-direction has been
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subtracted for each atom, the temperature is calculated by the formula
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.. math::
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\text{KE} = \frac{\text{dim}}{2} N k_B T,
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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` is the number of atoms in the group, :math:`k_B` is the Boltzmann
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constant, and :math:`T` is the absolute temperature.
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A symmetric tensor, stored as a six-element vector, is also calculated
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by this compute for use in the computation of a pressure tensor by the
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:doc:`compute pressue <compute_pressure>` command. The formula for
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the components of the tensor is the same as the above expression for
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:math:`E_\mathrm{kin}`, except that the 1/2 factor is NOT included and
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the :math:`v_i^2` is replaced by :math:`v_{i,x} v_{i,y}` for the
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:math:`xy` component, and so on. Note that because it lacks the 1/2
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factor, these tensor components are twice those of the traditional
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kinetic energy tensor. The six components of the vector are ordered
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:math:`xx`, :math:`yy`, :math:`zz`, :math:`xy`, :math:`xz`,
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:math:`yz`.
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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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However, in order to get meaningful results, the group ID of this compute should
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be all.
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The removal of the cosine-shaped velocity component by this command 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>`, and
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:doc:`fix langevin <fix_langevin>`.
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This compute subtracts out degrees of freedom due to fixes that
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constrain molecular motion, such as :doc:`fix shake <fix_shake>` and
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:doc:`fix rigid <fix_rigid>`. This means that the temperature of groups of
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atoms that include these constraints will be computed correctly. If
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needed, the subtracted degrees of freedom can be altered using the
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*extra* option of the :doc:`compute_modify <compute_modify>` command.
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See the :doc:`Howto thermostat <Howto_thermostat>` page for a discussion of
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different ways to compute temperature and perform thermostatting.
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----------
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Output info
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"""""""""""
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This compute calculates a global scalar (the temperature) and a global
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vector of length 7, which can be accessed by indices 1--7. The first
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six elements of the vector are those of the symmetric tensor discussed
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above. The seventh is the cosine-shaped velocity amplitude :math:`V`,
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which can be used to calculate the reciprocal viscosity, as shown in
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the example. These values can be used by any command that uses global
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scalar or vector values from a compute as input. See the :doc:`Howto
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output <Howto_output>` page for an overview of LAMMPS output options.
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The scalar value calculated by this compute is "intensive". The
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first six elements of vector values are "extensive",
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and the seventh element of vector values is "intensive".
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The scalar value is in temperature :doc:`units <units>`. The first
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six elements of vector values are in energy :doc:`units <units>`. The
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seventh element of vector value us in velocity :doc:`units <units>`.
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Restrictions
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""""""""""""
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This compute is part of the MISC package. It is only enabled if LAMMPS
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was built with that package. See the :doc:`Build package
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<Build_package>` page for more info.
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Since this compute depends on :doc:`fix accelerate/cos <fix_accelerate_cos>`
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which can only work for 3d systems, it cannot be used for 2d systems.
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Related commands
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""""""""""""""""
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:doc:`fix accelerate/cos <fix_accelerate_cos>`
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Default
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"""""""
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none
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----------
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.. _Hess1:
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**(Hess)** Hess, B. The Journal of Chemical Physics 2002, 116 (1), 209-217.
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