**Shear modulus of simulated glass-forming model systems: Effects of
boundary condition, temperature, and sampling time**

JP Wittmer and H Xu and P Polinska and F Weysser and J Baschnagel, JOURNAL OF CHEMICAL PHYSICS, 138, 12A533 (2013).

DOI: 10.1063/1.4790137

The shear modulus G of two glass-forming colloidal model systems in d =
3 and d = 2 dimensions is investigated by means of, respectively,
molecular dynamics and Monte Carlo simulations. Comparing ensembles
where either the shear strain gamma or the conjugated (mean) shear
stress tau are imposed, we compute G from the respective stress and
strain fluctuations as a function of temperature T while keeping a
constant normal pressure P. The choice of the ensemble is seen to be
highly relevant for the shear stress fluctuations mu(F)(T) which at
constant tau decay monotonously with T following the affine shear
elasticity mu(A)(T), i.e., a simple two-point correlation function. At
variance, non-monotonous behavior with a maximum at the glass transition
temperature T-g is demonstrated for mu(F)(T) at constant gamma. The
increase of G below T-g is reasonably fitted for both models by a
continuous cusp singularity, G(T) proportional to (1 - T/T-g)(1/2), in
qualitative agreement with recent theoretical predictions. It is argued,
however, that longer sampling times may lead to a sharper transition.
(C) 2013 American Institute of Physics.
**http://dx.doi.org/10.1063/1.4790137**

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