Generalized bond order parameters to characterize transient crystals.

Higher order parameters in the hard disk fluid are computed to investigate the number, the lifetime, and size of transient crystal nuclei in the pre-freezing phase. The methodology introduces further neighbor shells bond orientational order parameters and coarse-grains the correlation functions needed for the evaluation of the stress autocorrelation function for the viscosity. We successfully reproduce results by the previous collision method for the pair orientational correlation function, but some two orders of magnitude faster. This speed-up allows calculating the time dependent four body orientational correlation between two different pairs of particles as a function of their separation, needed to characterize the size of the transient crystals. The result is that the slow decay of the stress autocorrelation function near freezing is due to a large number of rather small crystal nuclei lasting long enough to lead to the molasses tail.

Instability in pipe flow.

The long-puzzling, unphysical result that linear stability analyses lead to no transition in pipe flow, even at infinite Reynolds number, is ascribed to the use of stick boundary conditions, because they ignore the amplitude variations associated with the roughness of the wall. Once that length scale is introduced (here, crudely, through a corrugated pipe), linear stability analyses lead to stable vortex formation at low Reynolds number above a finite amplitude of the corrugation and unsteady flow at a higher Reynolds number, where indications are that the vortex dislodges. Remarkably, extrapolation to infinite Reynolds number of both of these transitions leads to a finite and nearly identical value of the amplitude, implying that below this amplitude, the vortex cannot form because the wall is too smooth and, hence, stick boundary results prevail.

Phase separation in mixtures of ionized iron in a hydrogen plasma.

The accuracy of the hypernetted chain theory for mixtures of iron nuclei and protons in a charge-neutralizing background is demonstrated by comparison with molecular dynamics calculations. Near critical conditions the Debye-Hückel approximation fails to converge, even with second-order concentration corrections. The critical conditions, determined by assuming a uniform electron gas background, have a critical temperature more than a factor of 2 lower than present estimates of interior solar conditions. Qualitative arguments are made that including the polarization of the electron gas background would not change this result significantly and thus phase separation of iron in the interior of the sun is unlikely.

Dielectric constant of atomic fluids with variable polarizability.

The Clausius-Mossotti function for the dielectric constant is expanded in terms of single atom and pair polarizabilities, leading to contributions that depend on both the trace and the anisotropy of the pair-polarizability tensor. The short-range contribution of the anisotropic part to the pair polarizabilities has previously been obtained empirically from light scattering experiments, whereas the trace contribution is now empirically determined by comparison to dielectric experiments. For helium, the short-range trace part agrees well with electronic structure calculations, whereas for argon qualitative agreement is achieved.

Relation between the local field at large distances from a charge or dipole and the dielectric constant.

The local field at large distances from a charged or dipolar impurity in a nonpolar polarizable fluid is related to the dielectric constant of the medium. The predicted local field agrees accurately with molecular dynamics results. In contrast, the usual continuum theory prediction is only accurate to first order in the polarizability and leads to serious error for realistic values of the polarizability. At smaller distances these relations cannot be used to define a physically reasonable local dielectric constant and consequently the local field is more satisfactorily described in terms of a screening function.