2013-07-26 06:03:32 +08:00
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<H3>fix gld command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>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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</PRE>
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<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
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<LI>gld = style name of this fix command
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<LI>Tstart,Tstop = desired temperature at start/end of run (temperature units)
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2013-07-26 06:21:01 +08:00
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<LI>N_k = number of terms in the Prony series representation of the memory kernel
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<LI>seed = random number seed to use for white noise (positive integer)
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2013-07-26 06:03:32 +08:00
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<LI>series = <I>pprony</I> is presently the only available option
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<LI>c_k = the weight of the kth term in the Prony series (mass per time units)
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<LI>tau_k = the time constant of the kth term in the Prony series (time units)
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<LI>zero or more keyword/value pairs may be appended
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<PRE>keyword = <I>frozen</I> or <I>zero</I>
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<I>frozen</I> value = <I>no</I> or <I>yes</I>
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<I>no</I> = initialize extended variables using values drawn from equilibrium distribution at Tstart
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<I>yes</I> = initialize extended variables to zero (i.e., from equilibrium distribution at zero temperature)
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<I>zero</I> value = <I>no</I> or <I>yes</I>
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2013-07-26 06:03:32 +08:00
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<I>no</I> = do not set total random force to zero
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<I>yes</I> = set total random force to zero
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</PRE>
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</UL>
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<P><B>Examples:</B>
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</P>
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<PRE>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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</PRE>
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<P><B>Description:</B>
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</P>
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<P>Applies Generalized Langevin Dynamics to a group of atoms, as
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described in <A HREF = "#Baczewski">(Baczewski)</A>. 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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</P>
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2013-07-26 06:21:01 +08:00
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<P>IMPORTANT NOTE: While this fix bears many similarities to <A HREF = "fix_langevin.html">fix
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langevin</A>, it has one significant
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difference. Namely, <A HREF = "fix_gld.html">fix gld</A> performs time integration,
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whereas <A HREF = "fix_langevin.html">fix langevin</A> does NOT. To this end, the
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specification of another fix to perform time integration, such as <A HREF = "fix_nve.html">fix
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nve</A>, is NOT necessary.
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</P>
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2013-07-26 06:03:32 +08:00
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<P>With this fix active, the force on the <I>j</I>th atom is given as
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</P>
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<CENTER><IMG SRC = "Eqs/fix_gld1.jpg">
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</CENTER>
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<P>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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</P>
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<P>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 <A HREF = "#Baczewski">(Baczewski)</A>. 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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</P>
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<P>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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<I>pprony</I>, 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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</P>
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<P>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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<A HREF = "#Baczewski">(Baczewski)</A>.
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</P>
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<P>The desired temperature at each timestep is ramped from <I>Tstart</I> to
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<I>Tstop</I> over the course of the next run.
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</P>
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<P>The random # <I>seed</I> 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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</P>
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<HR>
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<P>The keyword/value option pairs are used in the following ways.
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</P>
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<P>The keyword <I>frozen</I> 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 <I>Tstart</I>, 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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</P>
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<P>The keyword <I>zero</I> 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 <I>zero</I> is set to <I>yes</I>, 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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</P>
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2013-07-26 06:21:01 +08:00
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<HR>
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2013-07-26 06:03:32 +08:00
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<P><B>Restart, run start/stop, minimize info:</B>
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</P>
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<P>The instantaneous values of the extended variables are written to
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<A HREF = "restart.html">binary restart files</A>. 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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</P>
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2013-07-26 06:21:01 +08:00
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<P>None of the <A HREF = "fix_modify.html">fix_modify</A> 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 <A HREF = "Section_howto.html#howto_15">output commands</A>.
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</P>
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2013-07-26 06:03:32 +08:00
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<P>This fix can ramp its target temperature over multiple runs, using the
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<I>start</I> and <I>stop</I> keywords of the <A HREF = "run.html">run</A> command. See the
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<A HREF = "run.html">run</A> command for details of how to do this.
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</P>
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<P>This fix is not invoked during <A HREF = "minimize.html">energy minimization</A>.
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</P>
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2013-07-26 06:38:11 +08:00
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<P><B>Restrictions:</B>
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2013-07-26 06:03:32 +08:00
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</P>
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2013-07-26 06:21:01 +08:00
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<P>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 <A HREF = "Section_start.html#start_3">Making
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LAMMPS</A> section for more info.
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</P>
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2013-07-26 06:03:32 +08:00
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "fix_langevin.html">fix langevin</A>, <A HREF = "fix_viscous.html">fix viscous</A>,
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<A HREF = "pair_dpd.html">pair_style dpd/tstat</A>
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</P>
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<P><B>Default:</B>
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</P>
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<P>The option defaults are frozen = no, zero = no.
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</P>
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<HR>
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<A NAME = "Baczewski"></A>
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<P><B>(Baczewski)</B> A.D. Baczewski and S.D. Bond, J. Chem. Phys. 139, 044107 (2013).
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</P>
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</HTML>
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