Differences

This shows you the differences between two versions of the page.

--- models:analytic [2019/02/23 09:41] – daniel
+++ models:analytic [2019/02/23 09:52] (current) – daniel
@@ Line 4: / Line 4: @@
 Analytic potentials use the parameters $\alpha_i$ as arguments to analytic function templates.
-A well-known example for this would be the Lennard-Jones potential, which uses two parameters $\epsilon$ and $\sigma$ to define a potential.
+A well-known example for this would be the Lennard-Jones potential, which uses two parameters $\epsilon$ and $\sigma$ to define a potential:
+$$V(r)=4\varepsilon\left[\left(\frac{\sigma}{r}\right)^{12}-\left(\frac{\sigma}{r}\right)^{6}\right]$$
 {{ :analytic.png?300 }}
-Using an analytic form for $V(r)$ allows to define the atomic interaction for all possible distances between atoms with very few parameters compared to tabulated potentials. The problem of local parameters (see [[#Tabulated potentials]]) is also not present, parameters are usually global parameters. In certain cases it is even possible to attribute some physical meaning to individual parameters.
+Using an analytic form for $V(r)$ allows to define the atomic interaction for all possible distances between atoms with very few parameters compared to tabulated potentials. The problem of local parameters (see [[tabulated|Tabulated potentials]]) is also not present, parameters are usually global parameters. In certain cases it is even possible to attribute some physical meaning to individual parameters.
 The analytic potential implementation in //potfit// has additional features which are only useful with this kind of interactions. They are described on the [[potfiles::format0|analytic format]] page.