Merge pull request #560 from aershadinia/master

\documentclass[12pt]{article}

\begin{document}

$$ 

E = \epsilon \left[ \frac{2  \sigma_{LJ}^{12} \left(7 r^5+14 r^3 \sigma_{n}^2+3 r \sigma_{n}^4\right) }{945 \left(r^2-\sigma_{n}^2\right)^7} -\frac{ \sigma_{LJ}^6 \left(2 r \sigma_{n}^3+\sigma_{n}^2 \left(r^2-\sigma_{n}^2\right)\log{ \left[\frac{r-\sigma_{n}}{r+\sigma_{n}}\right]}\right) }{12 \sigma_{n}^5 \left(r^2-\sigma_{n}^2\right)} \right]\qquad \sigma_n < r < r_c

$$

\end{document}

"smd/wall/surface"_fix_smd_wall_surface.html,

"temp/rescale/eff"_fix_temp_rescale_eff.html,

"ti/spring"_fix_ti_spring.html,

"ttm/mod"_fix_ttm.html :tb(c=6,ea=c)

"ttm/mod"_fix_ttm.html

"wall/ees"_fix_wall_ees.html

"wall/region/ees"_fix_wall_ees.html :tb(c=6,ea=c)

:line

"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 wall/ees command :h3

fix wall/region/ees command :h3

[Syntax:]

fix ID group-ID style args :pre

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

style = {wall/ees} or {wall/region/ees} :l

  args for style {wall/ees}: one or more {face parameters} groups may be appended

  face = {xlo} or {xhi} or {ylo} or {yhi} or {zlo} or {zhi}

  parameters = coord epsilon sigma cutoff

    coord = position of wall = EDGE or constant or variable

      EDGE = current lo or hi edge of simulation box

      constant = number like 0.0 or -30.0 (distance units)

      variable = "equal-style variable"_variable.html like v_x or v_wiggle

    epsilon = strength factor for wall-particle interaction (energy or energy/distance^2 units)

      epsilon can be a variable (see below)

    sigma = size factor for wall-particle interaction (distance units)

      sigma can be a variable (see below)

    cutoff = distance from wall at which wall-particle interaction is cut off (distance units) :pre

  args for style {wall/region/ees}: {region-ID} {epsilon} {sigma} {cutoff}

    region-ID = region whose boundary will act as wall

    epsilon = strength factor for wall-particle interaction (energy or energy/distance^2 units)

    sigma = size factor for wall-particle interaction (distance units)

    cutoff = distance from wall at which wall-particle interaction is cut off (distance units) :pre

  :ule

[Examples:]

fix wallhi all wall/ees xlo -1.0 1.0 1.0 2.5 units box

fix wallhi all wall/ees xhi EDGE 1.0 1.0 2.5

fix wallhi all wall/ees v_wiggle 23.2 1.0 1.0 2.5

fix zwalls all wall/ees zlo 0.0 1.0 1.0 0.858 zhi 40.0 1.0 1.0 0.858 :pre

fix ees_cube all wall/region/ees myCube 1.0 1.0 2.5 :pre

[Description:]

Fix {wall/ees} bounds the simulation domain on one or more of its

faces with a flat wall that interacts with the ellipsoidal atoms in the

group by generating a force on the atom in a direction perpendicular to

the wall and a torque parallel with the wall.  The energy of

wall-particle interactions E is given by:

:c,image(Eqs/fix_wall_ees.jpg)

Introduced by Babadi and Ejtehadi in "(Babadi)"_#BabadiEjtehadi. Here,

{r} is the distance from the particle to the wall at position {coord},

and Rc is the {cutoff} distance at which the  particle and wall no

longer interact. Also,  sigma_n is the distance between center of

ellipsoid and the nearest point of its surface to the wall  The energy

of the wall (see the image below).

:c,image(JPG/fix_wall_ees_image.jpg)

Details of using this command and specifications are the same as

fix/wall command. You can also find an example in USER/ees/ under

examples/ directory.

The prefactor {epsilon} can be thought of as an

effective Hamaker constant with energy units for the strength of the

ellipsoid-wall interaction.  More specifically, the {epsilon} pre-factor

= 8 * pi^2 * rho_wall * rho_ellipsoid * epsilon

* sigma_a * sigma_b * sigma_c, where epsilon is the LJ parameters for

the constituent LJ particles and sigma_a, sigma_b, and sigma_c are radii

of ellipsoidal particles. Rho_wall and rho_ellipsoid are the number

density of the constituent particles, in the wall and ellipsoid

respectively, in units of 1/volume.

NOTE: You must insure that r is always bigger than sigma_n for

all particles in the group, or LAMMPS will generate an error.  This

means you cannot start your simulation with particles touching the wall

position {coord} (r = sigma_n) or with particles penetrating the wall (0 =< r < sigma_n) or with particles on the wrong side of the

wall (r < 0). 

Fix {wall/region/ees} treats the surface of the geometric region defined

by the {region-ID} as a bounding wall which interacts with nearby

ellipsoidal particles according to the EES potential introduced above.

Other details of this command are the same as for the "fix

wall/region"_fix_wall_region.html command.  One may also find an example

of using this fix in the examples/USER/misc/ees/ directory.

[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.

This fix requires that atoms be ellipsoids as defined by the

"atom_style ellipsoid"_atom_style.html command.

[Related commands:]

"fix wall"_fix_wall.html,

"pair resquared"_pair_resquared.html

[Default:]

none

:line

:link(BabadiEjtehadi)

[(Babadi)] Babadi and Ejtehadi, EPL, 77 (2007) 23002.