Our recent results on stability and multiplicity of ̄ow states for con®ned ̄ows of an incompressible Newtonian ̄uid are surveyed. The considered laminar ̄ows are caused by either thermal, mechanical, or electromagnetic effects and beyond the stability limit exhibit multiplicity of stable, steady or oscillatory, asymptotic states. Stability diagrams as well as examples of multiple ̄ow states are ...

The aim of this study is to investigate the effects of non-Newtonian blood rheology models on the wall shear stress (WSS) distribution in a cohort of patients-specific coronary arteries. Twenty patients with diseased left anterior descending (LAD) coronary arteries (with varying degrees of stenosis severity from mild to severe) who underwent angiography and in-vivo pressure measurements were se...

This paper treats transience for queueing network models by considering an asso ciated uid model If starting from any initial condition the uid model explodes at a linear rate then the associated queueing network with i i d service times and a renewal arrival process explodes faster than any fractional power

This essay investigates the magnetoviscous properties of ferro uid ow in both an external magnetic eld and in zero eld. Zeroeld properties of ferro uids are examined. Phenomena such as the dramatic increase in ferro uid viscosity in the presensce of a static eld as well as negative viscosity for an alternating magnetic eld are described.

A nonlinear feedback control law that achieves global asymptotic stabilization of a 2D thermal convection loop (widely known for its `Lorenz systema approximation) is presented. The loop consists of viscous Newtonian #uid contained in between two concentric cylinders standing in a vertical plane. The lower half of the loop is heated while the upper half is cooled, which makes the no-motion stea...

General e ective-stress rules are derived for various physical properties of inhomogeneous porous rocks. Some rigorous relations arising in the analysis show that the uid (pore) pressure pf is least e ective at counteracting the changes caused by con ning pressure for the solid (grain) volume; pf is more e ective for the total (solid plus pore) volume; pf is still more e ective for the pore vol...

Ideal incompressible ‡uid is a Hamiltonian system which possesses an in…nite number of inte-grals, the circulations of velocity over closed ‡uid contours. This allows one to split all the degrees of freedom into the driving ones and the "slave" ones, the latter to be determined by the integrals of motions. The "slave" degrees of freedom correspond to "potential part" of motion, which is driven ...

Although there are many excellent ways presenting the principle of the classical calculus, the novel presentations probably leads most naturally to the development of the non-Newtonian calculus. The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Since this self-contained work is intended for a wide audience, inc...