In this work, we propose a model for the orientation of inertialess spheroidal particles suspended in turbulent flows. This consists stochastic version Jeffery equation that can be included statistical Lagrangian description flow. It is compatible and coherent with turbulence models are widely used CFD codes simulation flow field practical large-scale applications. context, analyze numerical sc...

We investigate various kinds of bases in infinite dimensional Banach spaces. In particular, we consider the complexity of Hamel bases in separable and non-separable Banach spaces and show that in a separable Banach space a Hamel basis cannot be analytic, whereas there are non-separable Hilbert spaces which have a discrete and closed Hamel basis. Further we investigate the existence of certain c...

This paper seeks to provide clues as to why experimental evidence for the alignment of fibers in semi-dilute suspensions under shear flows does not match theoretical predictions. This paper posits that it is the coupling between Jeffery’s equation and Stokes’ equation that causes the deviation from theory. It is proposed that if the initial data is slightly non-uniform, then there is feedback v...