Virtual Element Method for fourth order problems: L2−L^2-estimates

We analyse the family of $C^1$-Virtual Elements introduced in \cite{Brezzi:Marini:plates} for fourth-order problems and prove optimal estimates in $L^2$ and in $H^1$ via classical duality arguments

Refined shell elements for the analysis of functionally graded structures

The present paper considers the static analysis of plates and shells made of Functionally Graded Material (FGM), subjected to mechanical loads. Refined models based on the Carrera's Unified Formulation (CUF) are employed to account for grading material variation in the thickness direction. The governing equations are derived from the Principle of Virtual Displacement (PVD) in order to apply the Finite Element Method (FEM). A nine-nodes shell element with exact cylindrical geometry is considered. The shell can degenerate in the plate element by imposing an infinite radius of curvature. The Mixed Interpolation of Tensorial Components (MITC) technique is extended to the CUF in order to contrast the membrane and shear locking phenomenon. Different thickness ratios and orders of expansion for the displacement field are analyzed. The FEM results are compared with both benchmark solutions from literature and the results obtained using the Navier method that provides the analytical solution for simply-supported structures subjected to sinusoidal pressure loads. The shell element based on refined theories of the CUF turns out to be very efficient and its use is mandatory with respect to the classical models in the study of FGM structures

Rotating Electromagnetic Waves in Toroid-Shaped Regions

Electromagnetic waves, solving the full set of Maxwell equations in vacuum, are numerically computed. These waves occupy a fixed bounded region of the three dimensional space, topologically equivalent to a toroid. Thus, their fluid dynamics analogs are vortex rings. An analysis of the shape of the sections of the rings, depending on the angular speed of rotation and the major diameter, is carried out. Successively, spherical electromagnetic vortex rings of Hill's type are taken into consideration. For some interesting peculiar configurations, explicit numerical solutions are exhibited.Comment: 27 pages, 40 figure

Ecocontrastografia epatica nel cane: studi preliminari

The purpose of this study is to determine the normal perfusion dynamics in the canine liver using sulphur hexafluoride (Sonovue\uae) as contrast medium. Its effects have been investigated measuring the changes in liver grayscale enhancement in 11 dogs. Each dog received two separate bolus contrast injection (0.03 ml/kg and 0.06 ml/kg). Two different setup of the ultrasound machine were considered. Time/Mean Pixel Value curves were generated for selected regions of the liver, at 2 and at 4 cm of depth. The influence of cardiac output, heart rate and respiratory rate upon the arterial phase time, portal phase time, equilibrium phase, time to peak, time to 50% peak and maximum pixel value were investigate