On the global well-posedness of the critical quasi-geostrophic equation

We prove the global well-posedness of the critical dissipative quasi-geostrophic equation for large initial data belonging to the critical Besov space $\dot B^0_{\infty,1}(\RR^2).

Effect of adsorbed water on the specific surface area of some standards cotton

It is well known that cotton fibers are sensitive to moisture. The interactions of cellulose chains and water molecules could therefore have an influence on the fiber properties. In this presentation, we will investigate the effect of adsorbed water on the specific surface area of standards cotton fibers. The amount of adsorbed water was determined by Thermogravimetric analysis. Adsorption of methylene blue in aqueous phase was used to measure the surface specific area. A numerical relationship of the form SBM =a +b X has been obtained, where SBM represents the specific surface area, X the percentage of adsorbed water, a and b are experimental constants. (Résumé d'auteur

Sliding mode control for high-precision motion of a piezostage

In this paper, control of piezostage using sliding mode control (SMC) method is presented. Due to the fast dynamics of piezostage and since high accuracy is required the special attention is paid to avoid chattering. The presence of hysteresis characteristics represents main nonlinearity in the system. Structure of proposed SMC controller is proven to offer chattering-free motion and rejection of the disturbances represented by hysteresis and the time variation of the piezostack parameters. In order to enhance the accuracy of the closed loop system, a combination of disturbance rejection method and the SMC controller is explored and its effectiveness is experimentally demonstrated. The disturbance observer is constructed using a second-order lumped parameter model of the piezostage and is based on SMC framework. Closed-loop experiments are presented using proportional-integral-derivative controller and sliding mode controller with disturbance compensation for the purpose of comparison

Experimental investigation of a SMC high precision control

In this paper a discrete-time Sliding-Mode (SM) based controller for high accuracy position control is investigated. The controller is designed for a general SISO system with nonlinearity and external disturbance. It will be shown that application of the proposed controller forces the state trajectory to be within an O(Ts 2). The proposed controller is applied to a stage driven by a piezo drive that is known to suffer from nonlinearity. As a separate idea to enhance the accuracy of the closed loop system a combination of disturbance rejection method and the SMC controller is explored and its effectiveness is experimentally demonstrated. Closed-loop experiments are presented using PID controller with and without disturbance compensation and Sliding-Mode Controller with and without disturbance compensation for the purpose of comparison

Global well-posedness for the Navier-Stokes-Boussinesq system with axisymmetric data

In this paper we prove the global well-posedness for a three-dimensional Boussinesq system with axisymmetric initial data. This system couples the Navier-Stokes equation with a transport-diffusion equation governing the temperature. Our result holds uniformly with respect to the heat conductivity coefficient $\kappa \geq 0$ which may vanish.Comment: 22 page

Global large solutions to 3-D inhomogeneous Navier-Stokes system with one slow variable

In this paper, we are concerned with the global wellposedness of 3-D inhomogeneous incompressible Navier-Stokes equations \eqref{1.3} in the critical Besov spaces with the norm of which are invariant by the scaling of the equations and under a nonlinear smallness condition on the isentropic critical Besov norm to the fluctuation of the initial density and the critical anisotropic Besov norm of the horizontal components of the initial velocity which have to be exponentially small compared with the critical anisotropic Besov norm to the third component of the initial velocity. The novelty of this results is that the isentropic space structure to the homogeneity of the initial density function is consistent with the propagation of anisotropic regularity for the velocity field. In the second part, we apply the same idea to prove the global wellposedness of \eqref{1.3} with some large data which are slowly varying in one direction