Merge pull request #283 from akohlmey/grem-feature

\documentclass[12pt]{article}

\begin{document}

$$

  T_{eff} = \lambda + \eta (H - H_0)

$$

\end{document}

 No newline at end of file

"eos/table/rx"_fix_eos_table_rx.html,

"flow/gauss"_fix_flow_gauss.html,

"gle"_fix_gle.html,

"grem"_fix_grem.html,

"imd"_fix_imd.html,

"ipi"_fix_ipi.html,

"langevin/drude"_fix_langevin_drude.html,

"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c

:link(lws,http://lammps.sandia.gov)

:link(ld,Manual.html)

:link(lc,Section_commands.html#comm)

:line

fix grem command :h3

[Syntax:]

fix ID group-ID grem lambda eta H0 thermostat-ID :pre

ID, group-ID are documented in "fix"_fix.html command :ulb,l

grem = style name of this fix command :l

lambda = intercept parameter of linear effective temperature function :l

eta = slope parameter of linear effective temperature function :l

H0 = shift parameter of linear effective temperature function :l

thermostat-ID = ID of Nose-Hoover thermostat or barostat used in simulation :l,ule

[Examples:]

fix             fxgREM all grem 400 -0.01 -30000 fxnpt

thermo_modify   press fxgREM_press :pre

fix             fxgREM all grem 502 -0.15 -80000 fxnvt :pre

[Description:]

This fix implements the molecular dynamics version of the generalized

replica exchange method (gREM) originally developed by "(Kim)"_#Kim,

which uses non-Boltzmann ensembles to sample over first order phase

transitions. The is done by defining replicas with an enthalpy dependent

effective temperature

:c,image(Eqs/fix_grem.jpg)

with {eta} negative and steep enough to only intersect the characteristic

microcanonical temperature (Ts) of the system once, ensuring a unimodal

enthalpy distribution in that replica. {Lambda} is the intercept and

effects the generalized ensemble similar to how temperature effects a

Boltzmann ensemble. {H0} is a reference enthalpy, and is typically set

as the lowest desired sampled enthalpy.  Further explanation can be

found in our recent papers "(Malolepsza)"_#Malolepsza.

This fix requires a Nose-Hoover thermostat fix reference passed to the

grem as {thermostat-ID}. Two distinct temperatures exist in this generalized

ensemble, the effective temperature defined above, and a kinetic

temperature that controls the velocity distribution of particles as

usual. Either constant volume or constant pressure algorithms can be

used.

The fix enforces a generalized ensemble in a single replica

only. Typically, this ideaology is combined with replica 

exchange with replicas differing by {lambda} only

for simplicity, but this is not required. A multi-replica 

simulation can be run within the LAMMPS environment using the

"grem"_temper_grem.html command. This utilizes LAMMPS partition

mode and requires the number of available processors be 

on the order of the number of desired replicas. A 100-replica

simulation would require at least 100 processors (1 per world

at minimum). If a many replicas are needed on a small number of

processors, multi-replica runs can be run outside of LAMMPS.

An example of this can be found in examples/USER/misc/grem and 

has no limit on the number of replicas per processor. However, 

this is very inefficient and error prone and should be avoided

if possible. 

In general, defining the generalized ensembles is unique for every

system. When starting a many-replica simulation without any knowledge of

the underlying microcanonical temperature, there are several tricks we

have utilized to optimize the process.  Choosing a less-steep {eta}

yields broader distributions, requiring fewer replicas to map the

microcanonical temperature.  While this likely struggles from the same

sampling problems gREM was built to avoid, it provides quick insight to

Ts.  Initially using an evenly-spaced {lambda} distribution identifies

regions where small changes in enthalpy lead to large temperature

changes. Replicas are easily added where needed.

:line

[Restart, fix_modify, output, run start/stop, minimize info:]

No information about this fix is written to "binary restart

files"_restart.html.

The "thermo_modify"_thermo_modify.html {press} option is supported

by this fix to add the rescaled kinetic pressure as part of 

"thermodynamic output"_thermo_style.html.

[Restrictions:]

This fix is part of the USER-MISC package. It is only enabled if 

LAMMPS was built with that package. See the "Making 

LAMMPS"_Section_start.html#start_3 section for more info.

[Related commands:]

"grem"_temper_grem.html, "fix nvt"_fix_nh.html, "fix npt"_fix_nh.html, "thermo_modify"_thermo_modify.html

[Default:] none

:line

:link(Kim)

[(Kim)] Kim, Keyes, Straub, J. Chem. Phys., 132, 224107 (2010).

:link(Malolepsza)

[(Malolepsza)] Malolepsza, Secor, Keyes, J. Phys. Chem. B. 119 (42), 

13379-13384 (2015).

   fix_gld

   fix_gle

   fix_gravity

   fix_grem

   fix_halt

   fix_heat

   fix_imd