Structure of saturated RSA ellipse packings

Motivated by the recent observation of liquid glass in suspensions of ellipsoidal colloids, we examine the structure of (asymptotically) saturated RSA ellipse packings. We determine the packing fractions $\phi_{\rm s}(\alpha)$ to high precision, finding an empirical analytic formula that predicts $\phi_{\rm s}(\alpha)$ to within less than $0.1\%$ for all $\alpha \leq 10$. Then we explore how these packings' positional-orientational order varies with $\alpha$. We find a transition from tip/side- to side/side-contact-dominated structure at $\alpha = \alpha_{\rm TS} \simeq 2.4$. At this aspect ratio, the peak value $g_{\rm max}$ of packings' positional-orientational paircorrelation functions is minimal, and systems can be considered maximally locally disordered. For smaller (larger) $\alpha$, $g_{\rm max}$ increases exponentially with deceasing (increasing) $\alpha$. Local nematic order and structures comparable to the precursor domains observed in experiments gradually emerge as $\alpha$ increases beyond $3$. For $\alpha \gtrsim 5$, single-layer lamellae become more prominent, and long-wavelength density fluctuations increase with $\alpha$ as packings gradually approach the rod-like limit.