  This paper presents a numerical study of the Gay-Berne liquid crystal model
with parameters corresponding to calamitic (rod-shaped) molecules. The focus is
on the isotropic and nematic phases at temperatures above unity. There we find
strong correlations between the virial and potential-energy thermal
fluctuations, reflecting the hidden-scale invariance symmetry. This implies the
existence of isomorphs, which are curves in the thermodynamic phase diagram of
approximately invariant physics. We study numerically one isomorph in the
isotropic phase and one in the nematic phase. In both cases, good invariance of
the dynamics is demonstrated via data for the reduced-unit time-autocorrelation
functions of the mean-square displacement, angular velocity, force, torque, and
first- and second-order Legendre polynomial orientational order parameters.
Deviations from isomorph invariance are observed at short times for the
orientational time-autocorrelation functions, which reflects the fact that the
moment of inertia is assumed to be constant and thus not isomorph invariant in
reduced units. Structural isomorph invariance is demonstrated from data for the
radial distribution functions of the particles and their orientations. For
comparison, all quantities were also simulated along an isochore of similar
temperature variation in which case invariance is not observed. We conclude
that the thermodynamic phase diagram of the calamitic Gay-Berne model is
essentially one-dimensional in the studied regions as predicted by isomorph
theory, a fact that potentially allows for simplifications of future theories
and numerical studies.
