the mode coupling form $\tau_s(T)\sim (T-T_{C})^{-\gamma}$ to find $T_C$. For the self part of the intermediate scattering function, the actual value of $\tau_{s}$ increases as the magnitude of the wave vector decreases [@Kob95b]. However, the value of $T_C$ is independent of $k$. $\tau_s(T)$ versus temperature and the mode coupling fit are shown in Figure \[fig:mct\_tau\]. We find the best fit with the mode coupling temperature $T_C = 0.303$ which corresponds to $\Gamma=1.46$. Note that $T_C$ is determined from measurements made at temperatures where the system is equilibrated. Also shown in Figure \[fig:mct\_tau\] is the fit to the Vogel–Fulcher form $\tau_s(T)=A\exp[B/(T-T_{VF})]$ with $T_{VF}=0.21$ which corresponds to $\Gamma=1.60$. In doing the Vogel–Fulcher fit, we were able to use a much broader range of temperatures since $T_{VF}$ is much lower than the mode coupling $T_{C}$.

[Fig2.eps]{}

The full intermediate scattering function $F(\vec{k},t)$ is given by [@Hansen] $$F_{\alpha}(\vec{k},t)=\frac{1}{N_{\alpha}}\left\langle
\rho_{\vec{k},\alpha}(t)\rho_{-\vec{k},\alpha}(0)\right\rangle
\label{eq:fullFkt}$$ where the Fourier transform of the density $\rho_{\vec{k}}(t)=\sum_{i=1}^{N}e^{-i\vec{k}\cdot\vec{r}_{i}(t)}$. The subscript $\alpha$ refers to the particle type, A or B. The longest $\alpha$ relaxation time can be determined from the full intermediate scattering function evaluated at $k=k_{max}$ [@Rinaldi01]. We set $k_{max}=2\pi \cdot 8.3666/L$ ($L=8$) which is the location of the first peak in the structure 