forked from lijiext/lammps
179 lines
6.6 KiB
Plaintext
179 lines
6.6 KiB
Plaintext
.. index:: fix gld
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fix gld command
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===============
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Syntax
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""""""
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.. parsed-literal::
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fix ID group-ID gld Tstart Tstop N_k seed series c_1 tau_1 ... c_N_k tau_N_k keyword values ...
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* ID, group-ID are documented in :doc:`fix <fix>` command
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* gld = style name of this fix command
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* Tstart,Tstop = desired temperature at start/end of run (temperature units)
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* N_k = number of terms in the Prony series representation of the memory kernel
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* seed = random number seed to use for white noise (positive integer)
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* series = *pprony* is presently the only available option
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* c_k = the weight of the kth term in the Prony series (mass per time units)
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* tau_k = the time constant of the kth term in the Prony series (time units)
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* zero or more keyword/value pairs may be appended
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.. parsed-literal::
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keyword = *frozen* or *zero*
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*frozen* value = *no* or *yes*
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*no* = initialize extended variables using values drawn from equilibrium distribution at Tstart
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*yes* = initialize extended variables to zero (i.e., from equilibrium distribution at zero temperature)
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*zero* value = *no* or *yes*
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*no* = do not set total random force to zero
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*yes* = set total random force to zero
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Examples
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""""""""
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.. parsed-literal::
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fix 1 all gld 1.0 1.0 2 82885 pprony 0.5 1.0 1.0 2.0 frozen yes zero yes
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fix 3 rouse gld 7.355 7.355 4 48823 pprony 107.1 0.02415 186.0 0.04294 428.6 0.09661 1714 0.38643
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Description
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"""""""""""
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Applies Generalized Langevin Dynamics to a group of atoms, as
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described in :ref:`(Baczewski) <Baczewski>`. This is intended to model the
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effect of an implicit solvent with a temporally non-local dissipative
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force and a colored Gaussian random force, consistent with the
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Fluctuation-Dissipation Theorem. The functional form of the memory
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kernel associated with the temporally non-local force is constrained
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to be a Prony series.
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.. note::
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While this fix bears many similarities to :doc:`fix langevin <fix_langevin>`, it has one significant
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difference. Namely, :doc:`fix gld <fix_gld>` performs time integration,
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whereas :doc:`fix langevin <fix_langevin>` does NOT. To this end, the
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specification of another fix to perform time integration, such as :doc:`fix nve <fix_nve>`, is NOT necessary.
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With this fix active, the force on the *j*\ th atom is given as
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.. image:: Eqs/fix_gld1.jpg
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:align: center
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Here, the first term is representative of all conservative (pairwise,
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bonded, etc) forces external to this fix, the second is the temporally
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non-local dissipative force given as a Prony series, and the third is
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the colored Gaussian random force.
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The Prony series form of the memory kernel is chosen to enable an
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extended variable formalism, with a number of exemplary mathematical
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features discussed in :ref:`(Baczewski) <Baczewski>`. In particular, 3N_k
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extended variables are added to each atom, which effect the action of
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the memory kernel without having to explicitly evaluate the integral
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over time in the second term of the force. This also has the benefit
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of requiring the generation of uncorrelated random forces, rather than
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correlated random forces as specified in the third term of the force.
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Presently, the Prony series coefficients are limited to being greater
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than or equal to zero, and the time constants are limited to being
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greater than zero. To this end, the value of series MUST be set to
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*pprony*\ , for now. Future updates will allow for negative coefficients
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and other representations of the memory kernel. It is with these
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updates in mind that the series option was included.
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The units of the Prony series coefficients are chosen to be mass per
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time to ensure that the numerical integration scheme stably approaches
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the Newtonian and Langevin limits. Details of these limits, and the
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associated numerical concerns are discussed in
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:ref:`(Baczewski) <Baczewski>`.
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The desired temperature at each timestep is ramped from *Tstart* to
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*Tstop* over the course of the next run.
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The random # *seed* must be a positive integer. A Marsaglia random
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number generator is used. Each processor uses the input seed to
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generate its own unique seed and its own stream of random
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numbers. Thus the dynamics of the system will not be identical on two
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runs on different numbers of processors.
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----------
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The keyword/value option pairs are used in the following ways.
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The keyword *frozen* can be used to specify how the extended variables
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associated with the GLD memory kernel are initialized. Specifying no
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(the default), the initial values are drawn at random from an
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equilibrium distribution at *Tstart*\ , consistent with the
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Fluctuation-Dissipation Theorem. Specifying yes, initializes the
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extended variables to zero.
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The keyword *zero* can be used to eliminate drift due to the
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thermostat. Because the random forces on different atoms are
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independent, they do not sum exactly to zero. As a result, this fix
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applies a small random force to the entire system, and the
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center-of-mass of the system undergoes a slow random walk. If the
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keyword *zero* is set to *yes*\ , the total random force is set exactly
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to zero by subtracting off an equal part of it from each atom in the
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group. As a result, the center-of-mass of a system with zero initial
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momentum will not drift over time.
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----------
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**Restart, run start/stop, minimize info:**
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The instantaneous values of the extended variables are written to
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:doc:`binary restart files <restart>`. Because the state of the random
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number generator is not saved in restart files, this means you cannot
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do "exact" restarts with this fix, where the simulation continues on
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the same as if no restart had taken place. However, in a statistical
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sense, a restarted simulation should produce the same behavior.
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None of the :doc:`fix_modify <fix_modify>` options are relevant to this
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fix. No global or per-atom quantities are stored by this fix for
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access by various :ref:`output commands <howto_15>`.
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This fix can ramp its target temperature over multiple runs, using the
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*start* and *stop* keywords of the :doc:`run <run>` command. See the
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:doc:`run <run>` command for details of how to do this.
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This fix is not invoked during :doc:`energy minimization <minimize>`.
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Restrictions
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""""""""""""
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This fix is part of the MISC package. It is only enabled if LAMMPS
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was built with that package. See the :ref:`Making LAMMPS <start_3>` section for more info.
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Related commands
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""""""""""""""""
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:doc:`fix langevin <fix_langevin>`, :doc:`fix viscous <fix_viscous>`,
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:doc:`pair_style dpd/tstat <pair_dpd>`
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Default
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"""""""
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The option defaults are frozen = no, zero = no.
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----------
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.. _Baczewski:
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**(Baczewski)** A.D. Baczewski and S.D. Bond, J. Chem. Phys. 139, 044107 (2013).
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.. _lws: http://lammps.sandia.gov
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.. _ld: Manual.html
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.. _lc: Section_commands.html#comm
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