A modification of the classical Navier–Stokes equations has recently been proposed by Brenner [Is the tracer velocity of a fluid continuum equal to its mass velocity? Phys. Rev. E 70 (2004) Art. No. 061201; Kinematics of volume transport, Physica A 349 (2005) 11–59; Navier–Stokes revisited,...

Jeans instability is derived for the case of a low-density self-gravitating gas beyond the Navier–Stokes equations. The Jeans instability criterium is shown to depend on a Burnett coefficient if the formalism is taken up to fourth order in the wave number. It is also shown that previously...

Using a self-consistent 4D spectral analysis of fully developed Navier–Stokes–Boussinesq turbulence (involving the dynamical response on small scale isotropic configurations) leads to a manyfold ℘(k) for the second-order scaling exponent. Plots of both energy and Reynolds stress spectra...

We study, via hydrodynamic equations, the granular temperature profile of a granular fluid under gravity and subjected to energy injection from a base. It is found that there exists a turn-up in the granular temperature and that, far from the base, it increases linearly with height. We show that...

Microscopic simulations of plane Poiseuille flow for a dilute gas are presented. Although the flow is laminar (Reynolds number ≈10) and sub-sonic, the temperature and pressure profiles measured in the simulations differ qualitatively from the hydrodynamic predictions. The results are in...

Three problems in the statistical mechanics of models for an assembly of molecular motors interacting with cytoskeletal filaments are reviewed. First, a description of the hydrodynamical behaviour of density–density correlations in fluctuating ratchet models for interacting molecular motors is...

This paper explores the rather controversial proposal by Howard Brenner that the velocities that follow from the mass flux and from the translational momentum in a fluid, are not equal. We show that standard non-equilibrium thermodynamics can be formulated such that it is in full agreement with...

It was proved that balance equations for systems with corpuscular structure can be derived if a kinematic description by piece-wise analytic functions is available (Vamoş et al., Physica A 227 (1996) 81). This article presents a rigorous derivation of an one-dimensional hydrodynamic model for...

The high cost of microalgae cultivation is one of the major hurdles in large scale production of microalgal biofuels. Cultivation in closed photobioreactors (PBR) to achieve high culture concentrations is a potential solution. However, existing PBR designs do not have the desired efficiencies,...