diff --git a/doc/Eqs/pair_lj_cubic.jpg b/doc/Eqs/pair_lj_cubic.jpg new file mode 100644 index 0000000000..e52392b87e Binary files /dev/null and b/doc/Eqs/pair_lj_cubic.jpg differ diff --git a/doc/Eqs/pair_lj_cubic.tex b/doc/Eqs/pair_lj_cubic.tex new file mode 100644 index 0000000000..bb4ea9c589 --- /dev/null +++ b/doc/Eqs/pair_lj_cubic.tex @@ -0,0 +1,12 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + E &=& u_{LJ}(r) \qquad r \leq r_s \\ + &=& u_{LJ}(r_s) + (r-r_s) u'_{LJ}(r) - \frac{1}{6} A_3 (r-r_s)^3 \qquad r_s < r \leq r_c \\ + &=& 0 \qquad r > r_c +\end{eqnarray*} + + +\end{document} diff --git a/doc/pair_lj_cubic.html b/doc/pair_lj_cubic.html index 2fb0464c19..3df6c4f972 100644 --- a/doc/pair_lj_cubic.html +++ b/doc/pair_lj_cubic.html @@ -23,19 +23,29 @@ pair_coeff * * 1.0 0.8908987

Description:

The lj/cubic style computes a truncated LJ interaction potential whose -energy and force are continuous everywhere. This is -achieved by replacing the LJ function outside the inflection point with -a cubic function of distance, so that both the energy and force are -continuous at the inflection point, and go to zero at the -cutoff distance. The LJ potential inside the inflection point is -unchanged. The location of the inflection point rs is defined -by the LJ diameter, rs/sigma = (26/7)^1/6. The cutoff distance -is defined by rcut/rs = 67/48. +energy and force are continuous everywhere. +Inside the inflection point the interaction is identical to the +standard 12/6 Lennard-Jones potential. +The LJ function outside the inflection point is replaced +with a cubic function of distance. The energy, force and second +derivative are continuous at the inflection point. +The cubic coefficient A3 is chosen so +that both energy and force go to zero at the cutoff distance. +Outside the cutoff distance the energy and force are zero.

-

This potential is commonly used to study the shock compression +

+
+

The location of the inflection point rs is defined +by the LJ diameter, rs/sigma = (26/7)^1/6. The cutoff distance +is defined by rc/rs = 67/48. The analytic expression for the +the cubic coefficient +A3*rmin^3/epsilon = 27.93357 is given in the paper +Holian and Ravelo (Holian). +

+

This potential is commonly used to study the mechanical behavior of FCC solids, as in the paper by Holian and Ravelo (Holian).

-

The following coefficients must be defined for each pair of atoms +

The following coefficients must be defined for each pair of atom types via the pair_coeff command as in the example above, or in the data file or restart files read by the read_data or read_restart @@ -46,8 +56,8 @@ commands, or by mixing as described below:

Note that sigma is defined in the LJ formula as the zero-crossing distance for the potential, not as the energy minimum, which -is located at 2^(1/6)*sigma. In the above example, sigma = 0.8908987, -so the energy minimum is located at r = 1. +is located at rmin = 2^(1/6)*sigma. In the above example, sigma = 0.8908987, +so rmin = 1.

diff --git a/doc/pair_lj_cubic.txt b/doc/pair_lj_cubic.txt index f0a864c609..f1dcac30be 100644 --- a/doc/pair_lj_cubic.txt +++ b/doc/pair_lj_cubic.txt @@ -20,19 +20,29 @@ pair_coeff * * 1.0 0.8908987 :pre [Description:] The {lj/cubic} style computes a truncated LJ interaction potential whose -energy and force are continuous everywhere. This is -achieved by replacing the LJ function outside the inflection point with -a cubic function of distance, so that both the energy and force are -continuous at the inflection point, and go to zero at the -cutoff distance. The LJ potential inside the inflection point is -unchanged. The location of the inflection point rs is defined -by the LJ diameter, rs/sigma = (26/7)^1/6. The cutoff distance -is defined by rcut/rs = 67/48. +energy and force are continuous everywhere. +Inside the inflection point the interaction is identical to the +standard 12/6 "Lennard-Jones"_pair_lj.html potential. +The LJ function outside the inflection point is replaced +with a cubic function of distance. The energy, force and second +derivative are continuous at the inflection point. +The cubic coefficient A3 is chosen so +that both energy and force go to zero at the cutoff distance. +Outside the cutoff distance the energy and force are zero. -This potential is commonly used to study the shock compression +:c,image(Eqs/pair_lj_cubic.jpg) + +The location of the inflection point rs is defined +by the LJ diameter, rs/sigma = (26/7)^1/6. The cutoff distance +is defined by rc/rs = 67/48. The analytic expression for the +the cubic coefficient +A3*rmin^3/epsilon = 27.93357 is given in the paper +Holian and Ravelo "(Holian)"_#Holian. + +This potential is commonly used to study the mechanical behavior of FCC solids, as in the paper by Holian and Ravelo "(Holian)"_#Holian. -The following coefficients must be defined for each pair of atoms +The following coefficients must be defined for each pair of atom types via the "pair_coeff"_pair_coeff.html command as in the example above, or in the data file or restart files read by the "read_data"_read_data.html or "read_restart"_read_restart.html @@ -43,8 +53,8 @@ sigma (distance units) :ul Note that sigma is defined in the LJ formula as the zero-crossing distance for the potential, not as the energy minimum, which -is located at 2^(1/6)*sigma. In the above example, sigma = 0.8908987, -so the energy minimum is located at r = 1. +is located at rmin = 2^(1/6)*sigma. In the above example, sigma = 0.8908987, +so rmin = 1. :line