Auslander systems

The authors generalize the dynamical system constructed by
J. Auslander in 1959, resulting in perhaps the simplest family of examples of minimal but not strictly ergodic systems. A characterization of unique ergodicity and mean-L-stability is given. The new systems are also shown to have zero topological entropy and fail to be weakly rigid. Some results on the set of idempotents in the enveloping semigroup are also achieved.

     

Suspended Particles Transport and Deposition in Saturated Granular Porous Medium: Particle Size Effects

An experimental study on the transport and deposition of suspended particles (SP) in a saturated porous medium (calibrated sand) was undertaken. The influence of the size distribution of the SP under different flow rates is explored. To achieve this objective, three populations with different particles size distributions were selected. The median diameter $d_{50}$ of these populations was 3.5, 9.5, and $18.3~\upmu \hbox {m}$ . To study the effect of polydispersivity, a fourth population noted “Mixture” ( $d_{50} = 17.4\; \upmu \hbox {m}$ ) obtained by mixing in equal proportion (volume) the populations 3.5 and $18.3\;\upmu \hbox {m}$ was also used. The SP transfer was compared to the dissolved tracer (DT) one. Short pulse was the technique used to perform the SP and the DT injection in a column filled with the porous medium. The breakthrough curves were competently described with the analytical solution of a convection–dispersion equation with first-order deposition kinetics. The results showed that the transport of the SP was less rapid than the transport of the DT whatever the flow velocity and the size distribution of the injected SP. The mean diameter of the recovered particles increases with flow rate. The longitudinal dispersion increases, respectively, with the increasing of the flow rates and the SP size distribution. The SP were more dispersive in the porous medium than the DT. The results further showed that the deposition kinetics depends strongly on the size of the particle transported and their distribution.     

On the Ni(x) integral function and its application to the Airy’s non-homogeneous equation

In this article, we discuss a recently introduced function, Ni(x), to which we will refer as the Nield-Kuznetsov function. This function is attractive in the solution of inhomogeneous Airy’s equation. We derive and document some elementary properties of this function and outline its application to Airy’s equation subject to initial conditions. We introduce another function, Ki(x), that arises in connection with Ni(x) when solving Airy’s equation with a variable forcing function. In Appendix A, we derive a number of properties of both Ni(x) and Ki(x), their integral representation, ascending and asymptotic series representations. We develop iterative formulae for computing all derivatives of these functions, and formulae for computing the values of the derivatives at x = 0. An interesting finding is the type of differential equations Ni(x) satisfies. In particular, it poses itself as a solution to Langer’s comparison equation.