documentation

doc/src/Commands_pair.txt

@@ -65,6 +65,7 @@ OPT.
 "colloid (go)"_pair_colloid.html,
 "comb (o)"_pair_comb.html,
 "comb3"_pair_comb.html,
+"cosine/squared"_pair_cosine_squared.html,
 "coul/cut (gko)"_pair_coul.html,
 "coul/cut/soft (o)"_pair_fep_soft.html,
 "coul/debye (gko)"_pair_coul.html,

doc/src/Eqs/pair_cosine_squared.tex

@@ -0,0 +1,16 @@
+\documentclass[12pt]{article}
+
+\usepackage{amsmath}
+
+\begin{document}
+
+\begin{align*}
+E = 
+\begin{cases}
+-\epsilon& \quad r < \sigma \\
+-\epsilon\cos\left(\frac{\pi\left(r - \sigma\right)}{2\left(r_c - \sigma\right)}\right)&\quad \sigma \leq r < r_c \\
+0& \quad r \geq r_c
+\end{cases}
+\end{align*}
+
+\end{document}

doc/src/Eqs/pair_cosine_squared_wca.tex

@@ -0,0 +1,11 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$
+ E = \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 
+                       2\left(\frac{\sigma}{r}\right)^6 + 1\right]
+                       , \quad r < \sigma
+$$
+
+\end{document}

doc/src/lammps.book

@@ -569,6 +569,7 @@ pair_charmm.html
 pair_class2.html
 pair_colloid.html
 pair_comb.html
+pair_cosine_squared.html
 pair_coul.html
 pair_coul_diel.html
 pair_coul_shield.html

doc/src/pair_cosine_squared.txt

@@ -0,0 +1,95 @@
+"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
+
+:link(lws,http://lammps.sandia.gov)
+:link(ld,Manual.html)
+:link(lc,Commands_all.html)
+
+:line
+
+pair_style cosine/squared command :h3
+
+[Syntax:]
+
+pair_style cosine/squared cutoff :pre
+
+cutoff = global cutoff for cosine-squared interactions (distance units) :ul
+
+pair_coeff i j eps sigma
+pair_coeff i j eps sigma cutoff
+pair_coeff i j eps sigma wca
+pair_coeff i j eps sigma cutoff wca :pre
+
+i,j = a particle type
+eps = interaction strength, i.e. the depth of the potential minimum (energy units)
+sigma = distance of the potential minimum from 0
+cutoff = the cutoff distance for this pair type, if different from global (distance units)
+wca = if specified a Weeks-Chandler-Andersen potential (with eps strength and minimum at sigma) is added, otherwise not :ul
+
+[Examples:]
+
+pair_style cosine/squared 3.0
+pair_coeff * * 1.0 1.3
+pair_coeff 1 3 1.0 1.3 2.0
+pair_coeff 1 3 1.0 1.3 wca
+pair_coeff 1 3 1.0 1.3 2.0 wca :pre
+
+[Description:]
+
+Style {cosine/squared} computes a potential of the form
+
+:c,image(Eqs/pair_cosine_squared.jpg)
+
+between two point particles, where (sigma, -epsilon) is the location of the (rightmost) minimum of the potential, as explained in the syntax section above.
+
+This potential was first used in \[1\] for a coarse-grained lipid membrane model.
+It is generally very useful as a non-specific interaction potential because it is fully adjustable in depth and width while joining the minimum at (sigma, -epsilon) and zero at (cutoff, 0) smoothly, requiring no shifting and causing no related artifacts, tail energy calculations etc. This evidently requires {cutoff} to be larger than {sigma}.
+
+If the {wca} option is used then a Weeks-Chandler-Andersen potential \[2\] is added to the above specified cosine-squared potential, specifically the following:
+
+:c,image(Eqs/pair_cosine_squared_wca.jpg)
+
+In this case, and this case only, the {sigma} parameter can be equal to {cutoff} (sigma = cutoff) which will result in ONLY the WCA potential being used (and print a warning), so the minimum will be attained at (sigma, 0). This is a convenience feature that enables a purely repulsive potential to be used without a need to define an additional pair style and use the hybrid styles.
+
+The energy and force of this pair style for parameters epsilon = 1.0, sigma = 1.0, cutoff = 2.5, with and without the WCA potential, are shown in the graphs below:
+
+:c,image(JPG/pair_cosine_squared_graphs.jpg)
+
+:line
+
+There are currently no accelerated versions of this potential, although this should be relatively easy to implement on the basis of the code for the accelerated versions of similar styles (e.g. lj/cut) and anyone needing them is encouraged to do so.
+
+:line
+
+[Mixing, shift, table, tail correction, restart, rRESPA info]:
+
+Mixing is not supported for this style.
+
+The {shift}, {table} and {tail} options are not relevant for this style.
+
+This pair style writes its information to "binary restart
+files"_restart.html, so pair_style and pair_coeff commands do not need
+to be specified in an input script that reads a restart file.
+
+These pair styles can only be used via the {pair} keyword of the
+"run_style respa"_run_style.html command.  They do not support the
+{inner}, {middle}, {outer} keywords.
+
+:line
+
+[Restrictions:]
+
+The {cosine/squared} style is part of the "USER-MISC" package. It is only
+enabled if LAMMPS is build with that package.  See the "Build
+package"_Build_package.html doc page for more info.
+
+[Related commands:]
+
+"pair_coeff"_pair_coeff.html,
+"pair_style lj/cut"_pair_lj.html
+
+[Default:] none
+
+:link(CKD,http://doi.org/10.1103/PhysRevE.72.011506)
+\[1\] "Cooke, Kremer and Deserno, Phys. Rev. E, 72, 011506 (2005)"_CKD
+:link(WCA,http://doi.org/10.1063/1.1674820)
+\[2\] "Weeks, Chandler and Andersen, J. Chem. Phys., 54, 5237 (1971)"_WCA

doc/src/pair_style.txt

@@ -129,6 +129,7 @@ accelerated styles exist.
 "colloid"_pair_colloid.html - integrated colloidal potential
 "comb"_pair_comb.html - charge-optimized many-body (COMB) potential
 "comb3"_pair_comb.html - charge-optimized many-body (COMB3) potential
+"cosine/squared"_pair_cosine_squared.html - Cooke-Kremer-Deserno membrane model potential
 "coul/cut"_pair_coul.html - cutoff Coulombic potential
 "coul/cut/soft"_pair_fep_soft.html - Coulombic potential with a soft core
 "coul/debye"_pair_coul.html - cutoff Coulombic potential with Debye screening

doc/src/pairs.txt

@@ -24,6 +24,7 @@ Pair Styles :h1
    pair_class2
    pair_colloid
    pair_comb
+   pair_cosine_squared
    pair_coul
    pair_coul_diel
    pair_coul_shield