@@ -157,8 +157,10 @@ interacting through a Lennard-Jones (LJ) potential with a cut-off equal
157157to :math: `r_c = 4.0 ` length units :cite: `wang2020lennard,fischer2023history `:
158158
159159.. math ::
160- E_{ij}(r) = 4 \epsilon _{ij} \left [ \left ( \dfrac {\sigma _{ij}}{r} \right )^{12 }
161- - \left ( \dfrac {\sigma _{ij}}{r} \right )^{6 } \right ], \quad \text {for} \quad r < r_c,
160+ :label: eq_LJ
161+
162+ E_{ij}(r) = 4 \epsilon _{ij} \left [ \left ( \dfrac {\sigma _{ij}}{r} \right )^{12 }
163+ - \left ( \dfrac {\sigma _{ij}}{r} \right )^{6 } \right ], \quad \text {for} \quad r < r_c,
162164
163165 where :math: `r` is the inter-particle distance, :math: `\epsilon _{ij}` is
164166the depth of the potential well that determines the interaction strength, and
@@ -264,7 +266,7 @@ created at random positions within the simulation box, with some in very
264266close proximity to each other. This proximity results in a large
265267initial potential energy due to the repulsive branch of the
266268Lennard-Jones potential [i.e.,~the term in :math: `1 /r^{12 }` in
267- Eq. INSERT EQUATION ]. As the energy minimization progresses, the energy
269+ Eq. :eq: ` eq_LJ ` ]. As the energy minimization progresses, the energy
268270decreases - first rapidly - then more gradually, before plateauing at a
269271negative value. This indicates that the atoms have moved to reasonable
270272distances from one another.
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