1
"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
3
:link(lws,http://lammps.sandia.gov)
5
:link(lc,Section_commands.html#comm)
13
fix ID group-ID gld Tstart Tstop N_k seed series c_1 tau_1 ... c_N_k tau_N_k keyword values ... :pre
15
ID, group-ID are documented in "fix"_fix.html command :ulb,l
16
gld = style name of this fix command :l
17
Tstart,Tstop = desired temperature at start/end of run (temperature units) :l
18
N_k = number of terms in the Prony series representation of the memory kernel :l
19
seed = random number seed to use for white noise (positive integer) :l
20
series = {pprony} is presently the only available option :l
21
c_k = the weight of the kth term in the Prony series (mass per time units) :l
22
tau_k = the time constant of the kth term in the Prony series (time units) :l
23
zero or more keyword/value pairs may be appended :l
24
keyword = {frozen} or {zero}
25
{frozen} value = {no} or {yes}
26
{no} = initialize extended variables using values drawn from equilibrium distribution at Tstart
27
{yes} = initialize extended variables to zero (i.e., from equilibrium distribution at zero temperature)
28
{zero} value = {no} or {yes}
29
{no} = do not set total random force to zero
30
{yes} = set total random force to zero :pre
35
fix 1 all gld 1.0 1.0 2 82885 pprony 0.5 1.0 1.0 2.0 frozen yes zero yes
36
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 :pre
40
Applies Generalized Langevin Dynamics to a group of atoms, as
41
described in "(Baczewski)"_#Baczewski. This is intended to model the
42
effect of an implicit solvent with a temporally non-local dissipative
43
force and a colored Gaussian random force, consistent with the
44
Fluctuation-Dissipation Theorem. The functional form of the memory
45
kernel associated with the temporally non-local force is constrained
48
IMPORTANT NOTE: While this fix bears many similarities to "fix
49
langevin"_fix_langevin.html, it has one significant
50
difference. Namely, "fix gld"_fix_gld.html performs time integration,
51
whereas "fix langevin"_fix_langevin.html does NOT. To this end, the
52
specification of another fix to perform time integration, such as "fix
53
nve"_fix_nve.html, is NOT necessary.
55
With this fix active, the force on the {j}th atom is given as
57
:c,image(Eqs/fix_gld1.jpg)
59
Here, the first term is representative of all conservative (pairwise,
60
bonded, etc) forces external to this fix, the second is the temporally
61
non-local dissipative force given as a Prony series, and the third is
62
the colored Gaussian random force.
64
The Prony series form of the memory kernel is chosen to enable an
65
extended variable formalism, with a number of exemplary mathematical
66
features discussed in "(Baczewski)"_#Baczewski. In particular, 3N_k
67
extended variables are added to each atom, which effect the action of
68
the memory kernel without having to explicitly evaluate the integral
69
over time in the second term of the force. This also has the benefit
70
of requiring the generation of uncorrelated random forces, rather than
71
correlated random forces as specified in the third term of the force.
73
Presently, the Prony series coefficients are limited to being greater
74
than or equal to zero, and the time constants are limited to being
75
greater than zero. To this end, the value of series MUST be set to
76
{pprony}, for now. Future updates will allow for negative coefficients
77
and other representations of the memory kernel. It is with these
78
updates in mind that the series option was included.
80
The units of the Prony series coefficients are chosen to be mass per
81
time to ensure that the numerical integration scheme stably approaches
82
the Newtonian and Langevin limits. Details of these limits, and the
83
associated numerical concerns are discussed in
84
"(Baczewski)"_#Baczewski.
86
The desired temperature at each timestep is ramped from {Tstart} to
87
{Tstop} over the course of the next run.
89
The random # {seed} must be a positive integer. A Marsaglia random
90
number generator is used. Each processor uses the input seed to
91
generate its own unique seed and its own stream of random
92
numbers. Thus the dynamics of the system will not be identical on two
93
runs on different numbers of processors.
97
The keyword/value option pairs are used in the following ways.
99
The keyword {frozen} can be used to specify how the extended variables
100
associated with the GLD memory kernel are initialized. Specifying no
101
(the default), the initial values are drawn at random from an
102
equilibrium distribution at {Tstart}, consistent with the
103
Fluctuation-Dissipation Theorem. Specifying yes, initializes the
104
extended variables to zero.
106
The keyword {zero} can be used to eliminate drift due to the
107
thermostat. Because the random forces on different atoms are
108
independent, they do not sum exactly to zero. As a result, this fix
109
applies a small random force to the entire system, and the
110
center-of-mass of the system undergoes a slow random walk. If the
111
keyword {zero} is set to {yes}, the total random force is set exactly
112
to zero by subtracting off an equal part of it from each atom in the
113
group. As a result, the center-of-mass of a system with zero initial
114
momentum will not drift over time.
118
[Restart, run start/stop, minimize info:]
120
The instantaneous values of the extended variables are written to
121
"binary restart files"_restart.html. Because the state of the random
122
number generator is not saved in restart files, this means you cannot
123
do "exact" restarts with this fix, where the simulation continues on
124
the same as if no restart had taken place. However, in a statistical
125
sense, a restarted simulation should produce the same behavior.
127
None of the "fix_modify"_fix_modify.html options are relevant to this
128
fix. No global or per-atom quantities are stored by this fix for
129
access by various "output commands"_Section_howto.html#howto_15.
131
This fix can ramp its target temperature over multiple runs, using the
132
{start} and {stop} keywords of the "run"_run.html command. See the
133
"run"_run.html command for details of how to do this.
135
This fix is not invoked during "energy minimization"_minimize.html.
139
This fix is part of the MISC package. It is only enabled if LAMMPS
140
was built with that package. See the "Making
141
LAMMPS"_Section_start.html#start_3 section for more info.
145
"fix langevin"_fix_langevin.html, "fix viscous"_fix_viscous.html,
146
"pair_style dpd/tstat"_pair_dpd.html
150
The option defaults are frozen = no, zero = no.
155
[(Baczewski)] A.D. Baczewski and S.D. Bond, J. Chem. Phys. 139, 044107 (2013).