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<HTML>
<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>
</CENTER>
<HR>
<H3>fix ti/rs command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID ti/rs lambda_initial lambda_final t_switch t_equil keyword value ...
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
<LI>ti/rs = style name of this fix command
<LI>lambda_initial/lambda_final = initial/final values of the coupling parameter
<LI>t_switch/t_equil = number of steps of the switching/equilibration procedure
<LI>keyword = <I>function</I>
<PRE> <I>function</I> value = function-ID
function-ID = ID of the switching function (1, 2 or 3)
</PRE>
</UL>
<P><B>Example:</B>
</P>
<PRE>fix ref all ti/rs 50.0 2000 1000
fix vf vacancy ti/rs 10.0 70000 50000 function 2
</PRE>
<P><B>Description:</B>
</P>
<P>This fix allows you to compute the free energy temperature dependence
by performing a thermodynamic integration procedure known as
Reversible Scaling <A HREF = "#deKoning99">(de Koning99,</A> <A HREF = "#deKoning00a"">de
Koning00a)</A>. The thermodynamic integration is performed
using the nonequilibrium method of Adiabatic Switching
<A HREF = "#Watanabe">(Watanabe,</A> <A HREF = "#deKoning96">de Koning96)</A>.
</P>
<P>The forces on the atoms are dynamically scaled during the simulation,
the rescaling is done in the following manner:
</P>
<CENTER><IMG SRC = "Eqs/fix_ti_rs_force.jpg">
</CENTER>
<P>where F_int is the total force on the atoms due to the interatomic
potential and lambda is the coupling parameter of the thermodynamic
integration.
</P>
<P>The fix acts as follows: during the first <I>t_equil</I> steps after the
fix is defined the value of lambda is <I>lambda_initial</I> , this is the
period to equilibrate the system in the lambda = <I>lambda_initial</I>
state. After this the value of lambda changes continuously from
<I>lambda_initial</I> to <I>lambda_final</I> according to the function defined
using the keyword <I>function</I> (described below), this is done in
<I>t_switch</I> steps. Then comes the second equilibration period of
<I>t_equil</I> to equilibrate the system in the lambda = <I>lambda_final</I>
state. After that the switching back to the lambda = <I>lambda_initial</I>
state is done using <I>t_switch</I> timesteps and following the same
switching function. After this period the value of lambda is kept
equal to <I>lambda_initial</I> indefinitely or until a <A HREF = "unfix.html">unfix</A>
erase the fix.
</P>
<P>The description of thermodynamic integration in both directions is
done in <A HREF = "#deKoning00b">de Koning00b</A>, the main reason is to try to
eliminate the dissipated heat due to the nonequilibrium process.
</P>
<P>The <I>function</I> keyword allows the use of three different switching
rates. The option <I>1</I> results in a constant rescaling where the lambda
parameter changes at a constant rate during the switching time
according to the switching function
</P>
<CENTER><IMG SRC = "Eqs/fix_ti_rs_function_1.jpg">
</CENTER>
<P>where tau is the scaled time variable t/t_switch. This switching
function has the characteristic that the temperature scaling is faster
at temperatures closer to the final temperature of the procedure. The
option number <I>2</I> performs the switching at a rate defined by the
following switching function
</P>
<CENTER><IMG SRC = "Eqs/fix_ti_rs_function_2.jpg">
</CENTER>
<P>This switching function has the characteristic that the temperature
scaling occurs at a constant rate during all the procedure. The option
number <I>3</I> performs the switching at a rate defined by the following
switching function
</P>
<CENTER><IMG SRC = "Eqs/fix_ti_rs_function_3.jpg">
</CENTER>
<P>This switching function has the characteristic that the temperature
scaling is faster at temperatures closer to the initial temperature of
the procedure.
</P>
<P>An example script using this command is provided in the
examples/USER/misc/ti directory.
</P>
<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
</P>
<P>No information about this fix is written to <A HREF = "restart.html">binary restart
files</A>.
</P>
<P>This fix computes a global vector quantitie which can be accessed by
various <A HREF = "Section_howto.html#howto_15">output commands</A>. The vector has
2 positions, the first one is the coupling parameter lambda and the
second one is the time derivative of lambda. The scalar and vector
values calculated by this fix are "extensive".
</P>
<P>No parameter of this fix can be used with the <I>start/stop</I> keywords of
the <A HREF = "run.html">run</A> command.
</P>
<P>The forces due to this fix are imposed during an energy minimization,
invoked by the <A HREF = "minimize.html">minimize</A> command.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "fix_ti_spring.html">fix ti/spring</A>
</P>
<P><B>Restrictions:</B>
</P>
<P>This command is part of the USER-MISC package. It is only enabled if
LAMMPS was built with those packages. See the <A HREF = "Section_start.html#start_3">Making
LAMMPS</A> section for more info.
</P>
<P><B>Default:</B>
</P>
<P>The keyword default is function = 1.
</P>
<HR>
<A NAME = "deKoning99"></A>
<P><B>(de Koning 99)</B> M. de Koning, A. Antonelli and S. Yip, Phys Rev Lett, 83, 3973 (1999).
</P>
<A NAME = "Watanabe"></A>
<P><B>(Watanabe)</B> M. Watanabe and W. P. Reinhardt, Phys Rev Lett, 65, 3301 (1990).
</P>
<A NAME = "deKoning96"></A>
<P><B>(de Koning 96)</B> M. de Koning and A. Antonelli, Phys Rev E, 53, 465 (1996).
</P>
<A NAME = "deKoning00a"></A>
<P><B>(de Koning 00a)</B> M. de Koning, A. Antonelli and S. Yip, J Chem Phys, 115, 11025 (2000).
</P>
<A NAME = "deKoning00b"></A>
<P><B>(de Koning 00b)</B> M. de Koning et al., Computing in Science & Engineering, 2, 88 (2000).
</P>
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