banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Hard ellipsoids: Analytically approaching the exact overlap distance
Rent this article for
View: Figures


Image of FIG. 1.
FIG. 1.

Two ellipsoids at different contact configurations. The exact center-center distance at contact, σ, is given as a function of σ and σ. The relations among the normal versors , and the center-center vector are also shown. The BP approximation produces the exact solution for all cases but e. MBP yields the exact solution for all shown cases.

Image of FIG. 2.
FIG. 2.

(a) Appearance frequency, F, against the percentage of deviation of the analytical overlap distance with the corresponding exact distance, , for the 1:5 oblate case. The histogram is built by considering N c = 1 × 108 random positions and orientations. (b) Average deviation, (bullets), and the optimized γ parameter, γ min (open symbols), for several aspect-ratios. The vertical dark line at 1:5 points out the case shown in panel (a). Dark (black) solid lines, light (cyan) solid lines, and (red) dashed lines correspond to the BP, MBP with γ = 1, and MBP with γ min analytical expressions, respectively.

Image of FIG. 3.
FIG. 3.

(a) Equations of state of the exact and analytical hard 1:5 oblate ellipsoidal models, Z(φ) (φ is the volume fraction). (b) Isothermal compressibility obtained from density fluctuations, χ(φ). (c) Order parameter, Q 6(φ). For all panels, black circles, cyan squares, red crosses, and blue plus symbols correspond to the exact PW overlap distance, and the analytical solutions given by BP, MBP with γ = 1, and MBP with γ = γ min , respectively. All data correspond to N = 100.

Image of FIG. 4.
FIG. 4.

(a) Probability distribution functions (PDFs) of volume fraction fluctuations for each of the n r = 64 pressure values and for N = 200. (b) Equations of state, Z(φ). (c) Isothermal compressibilities, χ(φ), obtained from density fluctuations. (d) Order parameters, Q 6(φ). For panels (b)–(d), dark circles and light squares correspond to N = 200 and N = 100, respectively. Vertical dotted lines highlight the N = 200 transitions. All data correspond to the analytical MBP case with γ = γ min .

Image of FIG. 5.
FIG. 5.

Radial distribution functions (black lines), g(r), and their corresponding order parameter (cyan lines), p(r), for different pressures (increasing from left to right). Panels (a)–(d) correspond to the isotropic, nematic, crystal A, and crystal B structures. The insets show the corresponding snapshots.

Image of FIG. 6.
FIG. 6.

Detail of the different crystal structures found in the N = 200 system (cases (d) and (e) of Fig. 4). The shown α angles, defined as where is the versor pointing along the stack axis, are close to 62° and 44° for crystal A and B, respectively.


Article metrics loading...


Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Hard ellipsoids: Analytically approaching the exact overlap distance