Plasma Chemical Functionalisation of a Cameroonian Kaolinite Clay for a Greater Hydrophilicity

A Cameroonian kaolinite powder was treated with gliding arc plasma in order to increase the amount of hydroxyl functional groups present on its external surfaces. The functional changes that occurred were monitored by Fourier transform infrared spectroscopy. The crystalline changes were followed by the X-ray diffraction. The ionisation effect, acid effect, and water solubility of the treated samples were also evaluated. Results showed that there is breaking of the bonds in the Si–O–Si and Si–O–Al groups, followed by the formation of new aluminol (Al–OH) and silanol (Si–OH) groups at the external surface of kaolinite after exposing the clay to the gliding arc plasma. The increase in hydroxyl groups on the surface of kaolinite leads to the increase of its hydrophilicity. Moreover, new charges appear on its surfaces and no significant change in crystallinity has occurred. This study shows that clays in powder form being can effectively be functionalised by gliding arc plasma in spatial post discharge processing mode. Knowing that the treatment in spatial post discharge offers the possibility to process large amounts of clay, this work is of great interest to the industry.     

On a Regularized Family of Models for Homogeneous Incompressible Two-Phase Flows

We consider a general family of regularized models for incompressible two-phase flows based on the Allen–Cahn formulation in \(n\) -dimensional compact Riemannian manifolds for \(n=2,3\) . The system we consider consists of a regularized family of Navier–Stokes equations (including the Navier–Stokes- \(\alpha \) -like model, the Leray- \(\alpha \) model, the modified Leray- \(\alpha \) model, the simplified Bardina model, the Navier–Stokes–Voight model, and the Navier–Stokes model) for the fluid velocity \(u\) suitably coupled with a convective Allen–Cahn equation for the order (phase) parameter \(\phi \) . We give a unified analysis of the entire three-parameter family of two-phase models using only abstract mapping properties of the principal dissipation and smoothing operators and then use assumptions about the specific form of the parameterizations, leading to specific models, only when necessary to obtain the sharpest results. We establish existence, stability, and regularity results and some results for singular perturbations, which as special cases include the inviscid limit of viscous models and the \(\alpha \rightarrow 0\) limit in \(\alpha \) models. Then we show the existence of a global attractor and exponential attractor for our general model and establish precise conditions under which each trajectory \(\left( u,\phi \right) \) converges to a single equilibrium by means of a Lojasiewicz–Simon inequality. We also derive new results on the existence of global and exponential attractors for the regularized family of Navier–Stokes equations and magnetohydrodynamics models that improve and complement the results of Holst et al. (J Nonlinear Sci 20(5):523–567, 2010). Finally, our analysis is applied to certain regularized Ericksen–Leslie models for the hydrodynamics of liquid crystals in \(n\) -dimensional compact Riemannian manifolds.     

Robust control problems for the multilayer quasi-geostrophic system

In this article, we study some robust control problems associated with the multilayer quasi-geostrophic equations of the ocean and related to data assimilation in oceanography. We consider higher norms (compared to [T. Tachim Medjo, Robust control problems associated with the multilayer quasi-geostrophic equations of the ocean, Appl. Math. Optim. 51(3) (2005) 333–360]) in the definition of the cost functionals. We prove the existence and uniqueness of solutions. The result relies on better a priori estimates on the solutions to the multilayer quasi-geostrophic system obtained using a new formulation that we introduce for the multilayer quasi-geostrophic equation of the ocean. The new formulation replaces the non-homogenous boundary conditions (and the non-local constraint) on the stream-function by a simple homogenous Dirichlet boundary condition.     

Pullback attractors for closed cocycles

In this article, using a result of Pata and Zelik (2007) [45], we derive a general result on the existence of pullback attractors for closed cocycles acting on a Banach space, where the strong continuity is replaced by a much weaker requirement that the cocycle be a closed map. As application, we prove the existence of the pullback attractor of a cocycle associated with the z-weak solutions of a non-autonomous two-dimensional primitive equations of the ocean.     

On the Weak Solutions to a Stochastic 2D Simplified Ericksen-Leslie Model

Potential Analysis - We study in this article a stochastic version of a 2D Ericksen-Leslie systems. The system model the dynamic of nematic liquid crystals under the influence of stochastic...     

Averaging of the planetary 3D geostrophic equations with oscillating external forces

In this article, we consider a non-autonomous three-dimensional planetary geostrophic model of the ocean with a singularly oscillating external force depending on a small parameter ?. We prove the existence of the uniform global attractor A^?. Furthermore, using the method of [11] in the case of the two-dimensional Navier-Stokes systems, we study the convergence of A^? as ? goes to zero.     

New formulations of a Stokes type problem related to the primitive equations of the atmosphere and applications

Summary. The aim of this article is to propose new algorithms for a Stokes type system related to the primitive equations of atmosphere, which are the fundamental equations for the motion of the atmosphere [6]. We derive an equivalent formulation of these equations in which the natural constraint appearing in these equations is automatically satisfied without being explicitly imposed. Numerical algorithms based on the new formulation appeared to be very competitive compared to the Uzawa-Conjugate Gradient method. Received September 10, 1998 / Published online August 2, 2000     

Second-order Optimality Conditions for Optimal Control of the Primitive Equations of the Ocean with Periodic Inputs

We investigate in this article the Pontryagin’s maximum principle for control problem associated with the primitive equations (PEs) of the ocean with periodic inputs. We also derive a second-order sufficient condition for optimality. This work is closely related to Wang (SIAM J. Control Optim. 41(2):583–606, 2002) and He (Acta Math. Sci. Ser. B Engl. Ed. 26(4):729–734, 2006), in which the authors proved similar results for the three-dimensional Navier-Stokes (NS) systems.     

Attractors for the multilayer quasi-geostrophic equations of the ocean with delays

In this article, we study the multilayer quasi-geostrophic equations of the ocean with delays. We prove the existence of an attractor using the theory of pullback attractors.     

The exponential behavior of the stochastic three-dimensional primitive equations with multiplicative noise

In this article, we study the stability of weak solutions to the stochastic three-dimensional (3D) primitive equations (PEs) with multiplicative noise. In particular, we prove that under some conditions on the forcing terms, the weak solutions converge exponentially in the mean square and almost surely exponentially to the stationary solutions. We also prove a result related to the stabilization of these equations.