Florinda Capone

Onset of convection for ternary fluid mixtures saturating horizontal porous layers with large pores

— Ternary fluid mixtures saturating horizontal porous layers with large pores, uniformly rotating around the vertical axis, are investigated. The layers are heated from below, salted from above and from below by two salts. The stabilizing e¤ects of both the rotation and Brinkman terms on the conduction solution are analyzed. Sommario. — Vengono studiate miscele fluide ternarie saturanti uno strato poroso orizzontale uniformemente rotante attorno all’asse verticale, nell’ipotesi che i pori siano su‰cientemente grandi da tener conto della viscosità di Brinkman. Si ammette inoltre che lo strato sia riscaldato dal basso e salato dal basso e dall’alto da due diversi sali. Si studia la stabilità non lineare (globale) della soluzione di conduzione, mettendo in evidenza gli e¤etti stabilizzanti della rotazione e del termine di Brinkman, al variare dei numeri di Prandtl.

On the instability of double diffusive convection in porous media under boundary data periodic in space

The linear instability analysis of the motionless state for a binary fluid mixture in a porous layer, under horizontal periodic temperature and concentration gradients, is performed.

On the stability of non-autonomous perturbed Lotka-Volterra models

The paper is devoted to an extended Lotka-Volterra system of differential equations of predator-prey model. The extension is proposed with perturbation terms, which are null for the positive equilibrium state. In the original Lotka-Volterra system, the equilibrium state is not asymptotically stable due to the fact that perturbations are periodic in time. The aim of the paper is to characterize a form of perturbation terms guaranteeing the asymptotic stability or instability of equilibrium state. The reason of the proposed model is that for large time scale, the Lotka-Volterra model is too simple to be realistic. In the paper, the non-autonomous perturbations do not change the equilibrium state but introduce functions of time as well as for additional perturbed terms as for the main part of the equations modified from Lotka-Volterra model. Theorems are proposed in a renormalized form of the differential equations for time and the two variables. The key point of the paper comes from the use of a Liapunov function introduced in Section 2 which allows to obtain conditions for the asymptotic stability (Section 3) and instability (Section 4) by using a Cetaiev instability theorem following conditions on the renormalized coefficients in time of System (6). An appendix recalls the main results of the Liapunov Direct Method for non-autonomous binary systems of ordinary differential equations.

Erratum to: Influence of diffusion on the stability of equilibria in a reaction–diffusion system modeling cholera dynamic

A reaction–diffusion system modeling cholera epidemic in a non-homogeneously mixed population is introduced. The interaction between population and toxigenic Vibrio cholerae concentration in contaminated water has been taken into account. The existence of biologically meaningful equilibria is investigated together with their linear and nonlinear stability. Using the data collected during the Haiti cholera epidemic, a numerical simulation is performed.

Porous MHD Convection: Effect of Vadasz Inertia Term

The onset of porous convection in an electrically conducting fluid uniformly heated from below and embedded in an external transverse constant magnetic field is analysed. In particular the effect of Vadasz inertia term, measured through the Vadasz number

Double-diffusive penetrative convection simulated via internal heating in an anisotropic porous layer with throughflow

V_a

Penetrative convection via internal heating in anisotropic porous media

Va, on the instability threshold, is investigated. For the three-dimensional perturbations and full nonlinear problem it is shown that sub-critical instabilities do not exist and the global nonlinear stability is guaranteed by the linear stability. The long-time behaviour is characterized via the existence of