The Lamination of Infinitely Renormalizable Dissipative Gap Maps: Analyticity, Holonomies and Conjugacies

Motivated by return maps near saddles for three-dimensional flows and also by return maps in the torus associated to Cherry flows, we study gap maps with derivative positive and smaller than one outside the discontinuity point. We prove that the lamination of infinitely renormalizable maps (or else maps with irrational rotation numbers) has analytic leaves in a natural subset of a Banach space of analytic maps of this kind. With maps having Hölder continuous derivative and derivative bounded away from zero, we also prove Hölder continuity of holonomies of the lamination and also of conjugacies between maps having the same combinatorics. © 2011 Springer Basel AG.

Stability of oxide films formed on mild steel in turbulent flow conditions of alkaline solutions at elevated temperatures

In the industries involving alkaline solutions in different process streams, the nature and stability of oxide films formed on the metallic surfaces determine the rates of erosion–corrosion of the equipment. In the present study the characteristics of the oxide films formed on AISI 1020 steel in a 2.75 M sodium hydroxide solution at temperatures up to 175°C, have been investigated by employing electrochemical techniques of cyclic voltammetry and chronoamperometry. The experiments were carried out in an autoclave system based upon a ‘rotating cylinder electrode’ geometry to determine the effects of turbulence on the stability of the films. The results suggest that little protection is afforded in the active region (at about −0.8 V_SHE). In the passive region at low potentials (−0.6 V to −0.4 V_SHE), it appears the films are compact and more stable, and therefore provide good protection. At higher potentials (>−0.4 V_SHE) in the passive region, the results suggest that film formation and dissolution occur simultaneously and the increase in temperature and turbulence causes a breakdown of the passive film resulting in a situation similar to nonprotective magnetite growth.

Micropolar flow in a porous channel with high mass transfer

Two dimensional flow of a micropolar fluid in a porous channel is investigated. The flow is driven by suction or injection at the channel walls, and the micropolar model due to Eringen is used to describe the working fluid. An extension of Berman's similarity transform is used to reduce the governing equations to a set of non-linear coupled ordinary differential equations. The latter are solved for large mass transfer via a perturbation analysis where the inverse of the cross-flow Reynolds number is used as the perturbing parameter. Complementary numerical solutions for strong injection are also obtained using a quasilinearisation scheme, and good agreement is observed between the solutions obtained from the perturbation analysis and the computations.

Effect of surface conditions on flow of a micropolar fluid driven by a porous stretching sheet

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