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We present a short overview of pressure calculation in molecular dynamics or Monte Carlo simulations. The emphasis is given to polarizable models in order to resolve the controversy caused by the paper of M. J. Louwerse and E. J. Baerends [Chem. Phys. Lett. 421, 138 (2006)] about pressure calculation in systems with periodic boundaries. We systematically derive expressions for the pressure and show that despite the lack of explicit pairwise additivity, the pressure formula for polarizable models is identical with that of nonpolarizable ones. However, a strict condition for using this formula is that the induced dipole should be in perfect mechanical equilibrium prior to pressure calculation. The perfect convergence of induced dipoles ensures conservation of energy as well. We demonstrate using more cumbersome but exact methods that the derived expressions for the polarizable model of water provide correct numerical results. We also show that the inaccuracy caused by imperfect convergence of the induced dipoles correlates with the inaccuracy of the calculated pressure. [ABSTRACT FROM AUTHOR]

This paper reviews basic results and recent developments in the field of small-scale gaseous hydrodynamics which has received significant attention in connection with small-scale science and technology. We focus on the modeling challenges arising from the breakdown of the Navier-Stokes description, observed when characteristic lengthscales become of the order of, or smaller than, the molecular mean free path. We discuss both theoretical results and numerical methods development. Examples of the former include the limit of applicability of the Navier-Stokes constitutive laws, the concept of second-order slip and the appropriate form of such a model, and how to reconcile experimental measurements of slipping flows with theory. We also review a number of recently developed theoretical descriptions of canonical nanoscale flows of engineering interest. On the simulation front, we review recent progress in characterizing the accuracy of the prevalent Boltzmann simulation method known as direct simulation Monte Carlo. We also present recent variance reduction ideas which address the prohibitive cost associated with the statistical sampling of macroscopic properties in low-speed flows. [ABSTRACT FROM AUTHOR]